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Illustration showing snapshots from a simulation by astrophysicist Volker Springel of the Max Planck Institute in Germany. It represents the growth of cosmic structure (galaxies and voids) when the universe was 0.9 billion, 3.2 billion and 13.7 billion years old (now). Image via Volker Springel/ MPE/Kavli Foundation.

What Is Dark Energy?

During the 20th century, the idea that the Universe existed in a steady state was seriously challenged and eventually dismissed by the discovery that the Universe is not only expanding but is also doing so at an accelerating rate. The reason for this accelerating expansion is thus far unknown, but scientists have given this force a name–albeit one that is a placeholder–dark energy.

Explaining this accelerating rate of expansion has become one of the most challenging problems in cosmology. The fact that the value for this acceleration varies wildly between theory and practical observations has created a raft of problems in itself. This means that the net result arising from any attempt to explain dark energy creates more questions than it answers.

Dark Energy: The Basics

Illustration showing snapshots from a simulation showing the growth of cosmic structure (galaxies and voids) when the universe was 0.9 billion, 3.2 billion and 13.7 billion years old (now). (Volker Springel/ MPE/Kavli Foundation)

Dark energy is whatever is causing the expansion of the Universe to accelerate. One of the most striking things about this mysterious energy is just how much ‘stuff’ in the Universe it accounts for. If you consider the contents of the cosmos to be matter and energy –more formally known as the Universe’s mass-energy density–then dark energy accounts for between 68% to 72% of all cosmic ‘stuff.’

Dark matter is the second-largest contributor, with just a tiny proportion of the Universe’s ‘stuff’ made up of the baryonic matter consisting of atoms that we see around us on a day-to-day basis.

This is even more staggering when you consider that all the stars, planets, dust, gas and cosmic bodies that make up the visible Universe are contained in this tiny fraction of cosmic stuff that doesn’t even amount to 5% of the Universe’s contents.

Dark energy could very roughly be described as a force acting in opposition to gravity. Whereas the more familiar everyday force of gravity holds objects like planets and stars together in orbits, dark energy acts as a repulsive force, driving galaxies themselves apart. But, whereas gravity acts upon objects themselves, dark energy acts on the very fabric of spacetime between objects. Because dark matter is the largest contributor to gravity, this means this mysterious substance is locked in what has been termed a ‘cosmic tug of war.’ And it’s clear during our current epoch, dark energy is winning!

A popular analogy for this is the description of the Universe as the surface of a balloon. Galaxies are represented by two marker ink dots on this surface. As the balloon is inflated the points move apart with the very space between them expanding.

Repeat the experiment with three unevenly placed dots and it is clear that the dots that are initially further apart recede away from each other more rapidly. This extremely rough analogy carries over to galaxies. The further apart the galaxies are, the more quickly they recede.

The expanding universe as the surface of a balloon (Bianchi, E., Rovelli, C. & Kolb, R. Is dark energy really a mystery?. Nature 466, 321–322 (2010). https://doi.org/10.1038/466321a)

An Expanding Surprise

The discovery that the Universe is expanding came as a considerable shock to the scientific community when it was confirmed by Edwin Hubble in 1929. Hubble had built upon theory provided by George Lemaitre and Alexander Friedman who had used the equations of general relativity to predict that the Universe was non-static, something that very much contradicted the scientific consensus of the time.

Ann Field STScl

Albert Einstein who devised general relativity had also found that his geometric theory of gravity predicted a non-static Universe, something he wasn’t exactly comfortable with. Despite having already killed many of the sacred cows of physics, Einstein was unwilling to do away with the concept of a static Universe. To recover a static Universe that was neither expanding nor contracting, the world’s most famous scientist introduced to his equations a ‘fudge factor’ called the cosmological constant–commonly represented with the Greek letter lambda.

The cosmological constant was in danger from the start. Once Hubble managed to persuade Einstein that the Universe was indeed expanding, the physicist abandoned the cosmological constant, allegedly describing it as his ‘greatest blunder’ in his later years. The cosmological constant wouldn’t stay in the cosmological dustbin for very long, however.

If physicists had been surprised by the discovery at the beginning of the 20th Century that the Universe is expanding, they would be blown away when at the end of that same century when the observations of distant supernovae made by two separate teams of astronomers revealed that not only is the Universe expanding, it is doing so at an accelerating rate.

To understand why this is shocking and how it leads to the conclusion that some repulsive force is driving this expansion, it is necessary to journey to the very beginning of time… Let’s take some balloons too…

Escaping the Big Crunch

A diagram of the expansion of the Universe. This accelerating expansion of the Universe could be explained by an early dark energy model. (NASA/ WMAP Team). Credit: NASA

When thinking about the initial expansion of the Universe it makes sense to conclude that the introduction of an attractive force within that Universe would slow and eventually halt this expansion. That is exactly what gravity should do, and it seems did do during the early stages of expansion that had nothing to do with dark energy (we think).

Some cosmologists are willing to go a step further. If there is no outward pressure but an inward attractive force, shouldn’t the Universe actually start to contract?

This leads to the theory that the Universe will end in what physicists term the ‘Big Crunch’–an idea that dark energy could make obsolete. Think about how counter-intuitive this was to scientists when the idea was first suggested and evidenced. Let’s return to the balloon analogy; imagine you stop blowing into the balloon, and instead start sucking the air out of it.

How shocked would you be to find that the balloon isn’t contracting, it’s continuing to expand? And not just that, it’s actually expanding faster than it was when you were blowing into it!

With that in mind, consider the initial moments of the Universe. Beginning in an indescribably dense and hot state, squeezed into a quantum speck, the Universe undergoes a period of rapid expansion. This period of expansion wasn’t driven by dark energy. As it expands, the Universe cools allowing electrons to form atoms with protons and neutrons, which in turn frees photons to travel the cosmos.

Soon there is enough matter in the Universe to allow the attractive force of gravity to slow its expansion. And this does seem to be what happened in the early cosmos. The rapid inflation of the infant Universe is believed to have halted at around 10 -32 seconds after the Big Bang, with the Universe still expanding, albeit at a much slower rate.

Euclid Assessment Study Report

This period of expansion continued to slow as a result of the growing dominance of matter during what cosmologists call the ‘matter-dominated epoch.’ But, at around 9.8 billion years into the Universe’s 13.8 billion year history, something strange begins to happen. The Universe begins to expand again, this time at an accelerating rate.

This is the dawn of the dark energy dominated epoch.

The Cosmological Constant is Back and Still Causing Trouble

Observations of the redshift of distant supernovae in the later 1990s showed cosmologists that not only was the Universe expanding, but it was doing so at an accelerating rate. (ESO)

That explains why the accelerating expansion of the Universe is so troubling and the need to introduce the placeholder concept of dark energy to explain it. Yet this accelerating expansion would still need a mathematical representation in equations used to describe the Universe. To do this cosmologists would return to the cosmological constant and its symbol, lambda.

This new iteration of the cosmological constant would be used in a different way to Einstein’s version. Whereas the earlier cosmological constant was used to balance gravity and hold the Universe steady and static, this new version would be used to overwhelm gravity and account for the acceleration of its expansion. But, this revised use of the cosmological constant does not mean it is any less troublesome than Einstein had found its predecessor.

In fact, the difference between the cosmological constant’s measured value, found by measuring the redshift of distant Type Ia supernovae, diverges from the value predicted by quantum field theory and particle physics by a value as large as 10121 (that’s 1 followed by 121 zeroes). Thus, it should come as no surprise that this value has been described as the worst prediction in the history of physics.

And as it represents the action of dark energy, that makes dark energy itself cosmology’s biggest conundrum.

OK… But What is Dark Energy?

So by now, you might well be thinking all of this is all fine and good, but this article specifically asks ‘what is dark energy?’ Isn’t it time to get to answering this question? It should come as no surprise that the answer is no one knows. But, that doesn’t mean that cosmologists don’t have some very good ideas.

One of the explanations for dark energy says that it could be vacuum energy, an underlying background energy that permeates that Universe and is represented by the cosmological constant. The most commonly cited evidence for vacuum energy–the energy of ’empty’ space which manifests as the Casimir effect.

Without delving too deeply into this, as relativity states that energy and mass are equivalent and mass has gravitational effects, then it stands to reason if empty space has vacuum energy, this too should contribute to the effect of gravity across the cosmos. That contribution has been factored in as a negative repulsive influence acting against the attractive influence of gravity.

Many explanations for dark energy exist, including the possibility that general relativity is incorrect and dark energy doesn’t exist at all.

The big problem with this is that quantum field theory suggests that this negative pressure contribution from vacuum energy should arise from all particles and thus, should give lambda a value that is tremendously larger than that obtain when our astronomers measure the redshift of Type Ia supernovae in distant galaxies.

This problem could be solved by dark energy’s effects being the result of something other than vacuum energy, of course. The Universe’s accelerating expansion could be due to some, as of yet undiscovered fundamental force of nature. Alternatively, it could indicate that our best current theory of gravity–general relativity– is incorrect.

A new generation of cosmologists is currently actively tackling the dark energy puzzle with new and revolutionary ideas. These include the idea that dark energy could have started work in the early Universe, an idea proposed by Early Dark Energy (EDE) models of the Universe. Another alternative is that dark energy does not influence the curvature of the Universe, or perhaps does so weakly–a theory referred to as the ‘well-behaved cosmological constant.’

As unsatisfying an answer as it is, the only honest way of addressing the question ‘what is dark energy?’ right now is by saying; we just don’t know. But, science wouldn’t be anywhere near as fascinating without mysteries to solve, and revolutionary ideas to be uncovered.

Computer simulation of gravitational wave emissions S. Ossokine, A. Buonanno (Max Planck Institute for Gravitational Physics), Simulating eXtreme Spacetimes project, W. Benger (Airborne Hydro Mapping GmbH)

What are Gravitational Waves?

Whilst it may not have the snappiest name, the event GW150914 is pretty significant in terms of our understanding of the Universe. This event, with a name that includes ‘GW’ as a prefix which is an abbreviation of ‘Gravitational Wave’ and the date of observation–15/09/14– marked humanity’s first direct detection of gravitational waves.

This was groundbreaking on two fronts; firstly it successfully confirmed a prediction made by Albert Einstein’s theory of general relativity almost a century before. A prediction that stated events occurring in the Universe do not just warp spacetime, but in certain cases, can actually send ripples through this cosmic fabric.

Numerical simulation of two inspiralling black holes that merge to form a new black hole. Shown are the black hole horizons, the strong gravitational field surrounding the black holes, and the gravitational waves produced ( S. Ossokine, A. Buonanno (Max Planck Institute for Gravitational Physics), Simulating eXtreme Spacetimes project, W. Benger (Airborne Hydro Mapping GmbH)).

The second significant aspect of this observation was the fact that it represented an entirely new way to ‘see’ the Universe, its events and objects. This new method of investigating the cosmos has given rise to an entirely new form of astronomy; multimessenger astronomy. This combines ‘traditional’ observations of the Universe in the electromagnetic spectrum with the detection of gravitational waves, thus allowing us to observe objects that were previously invisible to us.

Thus, the discovery of gravitational waves truly opened up an entirely new window on the cosmos, but what are gravitational waves, what do they reveal about the objects that create them, and how do we detect such tiny tremblings in reality itself?

Gravitational Waves: The Basics

  • Gravitational waves are ripples in the fabric of spacetime.
  • These ripples travel from their source at the speed of light.
  • The passage of gravitational waves squash and stretch space itself.
  • Gravitational waves can be detected by measuring these infinitesimally small changes in the distance between objects.
  • They are created when an object or an event that curves spacetime causes that curvature to change shape.
  • Amongst the causes of gravitational waves are colliding black holes and neutron stars, supernovae, and stars that are undergoing gravitational collapse.

Theoretical Underpinnings

Imagine sitting at the side of a lake, quietly observing the tranquil surface of the water undisturbed by nature, the wind, or even by the slightest breeze. Suddenly a small child runs past hurling a pebble into the lake. The tranquillity is momentarily shattered. But, even as peace returns, you watch ripples spread from the centre of the lake diminishing as they reach the banks, often splitting or reflecting back when they encounter an obstacle.

The surface of the lake is a loose 2D analogy for the fabric of spacetime, the pebble represents an event like the collision of two black holes, and our position on Earth is equivalent to a blade of grass on the bank barely feeling the ripple which has diminished tremendously in its journey to us.

Poincaré and Einstein both saw the possibility of gravitational waves propagating through space-time at the speed of light

Gravitational waves were first predicted by Henri Poincare in 1905 as disturbances in the fabric of spacetime that propagate at the speed of light, but it would take another ten years for the concept to really be seized upon by physicists. This happened when Albert Einstein predicted the same phenomenon as part of his revolutionary 1916 geometric theory of gravity, better known as general relativity.

Whilst this theory is most well-known for suggesting that objects with mass would cause warping of spacetime, it also went a step further positing that an accelerating object should change this curvature and cause a ripple to echo through spacetime. Such disturbances in spacetime would not have been permissible in the Newtonian view of gravity which saw the fabric of space and time as separate entities upon which the events of the Universe simply play out.

But upon Einstein’s dynamic and changing stage of united spacetime, such ripples were permissible.

Gravitational waves arose from the possibility of finding a wave-like solution to the tensor equations at the heart of general relativity. Einstein believed that gravitational waves should be generated en masse by the interaction of massive bodies such as binary systems of super-dense neutron stars and merging black holes.

The truth is that such ripples in spacetime should be generated by any accelerating objects but Earth-bound accelerating objects cause perturbations that are far too small to detect. Hence why our investigations must turn to areas of space where nature provides us with objects that are far more massive.

As these ripples radiate outwards from their source in all directions and at the speed of light, they carry information about the event or object that created them. Not only this, but gravitational waves can tell us a great deal about the nature of spacetime itself.

Where do Gravitational Waves Come From?

There are a number of events that can launch gravitational waves powerful enough for us to detect with incredibly precise equipment here on Earth. These events are some of the most powerful and violent occurrences that the Universe has to offer. For instance, the strongest undulations in spacetime are probably caused by the collision of black holes.

Other collision events are associated with the production of strong gravitational waves; for example the merger between a black hole and a neutron star, or two neutron stars colliding with each other.

But, a cosmic body doesn’t always need a partner to make waves. Stellar collapse through supernova explosion–the process that leaves behind stellar remnants like black holes and neutron stars– also causes the production of gravitational waves.

A simulation of gravitational waves emitted by a binary pulsar consisting of two neutron stars

To understand how gravitational waves are produced, it is useful to look to pulsars–binary systems of two neutron stars that emit regular pulses of electromagnetic radiation in the radio region of the spectrum.

Einstein’s theory suggests that a system such as this should be losing energy by the emission of gravitational waves. This would mean that the system’s orbital period should be decreasing in a very predictable way.

The stars draw together as there is less energy in the system to resist their mutual gravitational attraction, and as a result, their orbit increases in speed, and thus the pulses of radio waves are emitted at shorter intervals. This would mean that the time it takes for the radio wave to be directly facing our line of sight would be reduced; something we can measure.

This is exactly what was observed in the Hulse-Taylor system (PSR B1913±16), discovered in 1974, which is comprised of two rapidly rotating neutron stars. This observation earned Russell A. Hulse and Joseph H. Taylor, Jr, both of Princeton University, the 1993 Nobel Prize in Physics. The reason given by the Nobel Committee was: “for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation.”

An animation illustrating how gravitational waves are emitted by two neutron stars as they orbit each other eventually colliding (credit: NASA/Goddard Space Flight Center).

Though inarguably an impressive and important scientific achievement, this was still only indirect evidence of gravitational waves. Whilst the effect Einstein predicted of shortening of the pulsar’s spin was definitely present, this wasn’t an actual direct detection.

In fact, though not alive to witness this momentous achievement, Einstein had predicted that this would be the only way we could ever garner any hint of gravitational waves. The great physicist believed those spacetime ripples would be so faint that they would remain impossible to detect by any technological means imaginable at that time.

Fortunately, Einstein was wrong.

How do we Detect Gravitational Waves?

It should come as no surprise that actually detecting a gravitational wave requires a piece of equipment of tremendous sensitivity. Whilst the effect of gravitational waves–the squashing and stretching space itself–sounds like something that should pre-eminently visible, the degree by which this disturbance occurs is so tiny it is totally imperceptible.

Fortunately, there is a branch of physics that is pretty adept at deal with the tiny. To spot gravitational waves, researchers would use an effect called interference, something demonstrated in the most famous quantum physics experiment of all time; the double-slit experiment.

Physicists realised that a laser interferometer could be used to measure the tiny squashing and stretching of space as it would cause the arms of the equipment to shrink by a minute amount. This means when splitting a laser and sending it through the arms of an interferometer the squeezing of space caused by the passage of a gravitational wave would cause one laser to arrive slightly ahead of the other–meaning they are out of phase and causing destructive interference. Thus, this difference in arrival times causes interference that gives an indication that gravitational waves have rippled across one of the arms.

But, not just any laser interferometer would do. Physicists would need an interferometer so large that it constituents a legitimate feat in engineering. Enter the Laser Interferometer Gravitational-wave Observatory (LIGO).

Schematic showing how LIGO works. (Johan Jarnestad/The Royal Swedish Academy of Sciences)

The LIGO detector uses two laser emitters based at the Hanford and Livingstone observatories, separated by thousands of kilometres apart to form an incredibly sensitive interferometer. From these emitters, lasers are sent down the ‘arms’ of the interferometer which are actually 4km long vacuum chambers.

This results in a system that is so sensitive it can measure a deviation in spacetime that is as small as 1/10,000 the size of an atomic nucleus. To put this into an astronomical context; it is equivalent to spotting a star at a distance of 4.2 light-years and pinpointing its location to within the width of a human hair! This constitutes the smallest measurement ever practically attempted in any science experiment.

And in 2015, this painstaking operation paid off.

On 14th September 2015, the LIGO and Virgo collaboration spotted a gravitational wave signal emanating from the spiralling in and eventual merger of two black holes, one 29 times the mass of the Sun, the other 36 times our star’s mass. From changes in the signal received the scientists were also able to observe the resultant single black hole.

The signal, named GW150914, represented not just the first observation of gravitational waves, but also the first time humanity had ‘seen’ a binary stellar-mass black hole system, proving that such mergers could exist in the Universe’s current epoch.

Different Kinds of Gravitational Waves

Since the initial detection of gravitational waves, researchers have made a series of important and revelatory detections. These have allowed scientists to classify different types of gravitational waves and the objects that may produce them.

Continuous Gravitational Waves

A single spinning massive object like a neutron star is believed to cause a continuous gravitational wave signal as a result of imperfections in the spherical shape of this star. if the rate of spin remains constant, so too are the gravitational waves it emits–it is continuously the same frequency and amplitude much like a singer holding a single note. Researchers have created simulations of what an arriving continuous gravitational wave would sound like if the signal LIGO detected was converted into a sound.

The sound of a continuous gravitational wave of the kind produced by a neutron star can be heard below.

(SXS Collaboration)

Compact Binary Inspiral Gravitational Waves

All of the signals detected by LIGO thus far fit into this category as gravitational waves created by pairs of massive orbiting objects like black holes or neutron stars.

The sources fit into three distinct sub-categories:

  • Binary Black Hole (BBH)
  • Binary Neutron Star (BNS)
  • Neutron Star-Black Hole Binary (NSBH)

Each of these types of binary pairing creates its own unique pattern of gravitational waves but shares the same overall mechanism of wave-generation–inspiral generation. This process occurs over millions of years with gravitational waves carrying away energy from the system and causing the objects to spiral closer and closer until they meet. This also results in the objects moving more quickly and thus creating gravitational waves of increasing strength.

The ‘chirp’ of an eventual merger between neutron stars has been translated to sound waves and can be heard below.

Max Planck Institute for Gravitational Physics

Stochastic Gravitational Waves

Small gravitational waves that even LIGO is unable to precisely pinpoint could be passing over Earth from all directions at all times. These are known as stochastic gravitational waves due to their random nature. At least part of this stochastic signal is likely to have originated in the Big Bang.

Should we eventually be able to detect this signal it would allow us to ‘see’ further back into the history of the Universe than any electromagnetic signal could, back to the epoch before photons could freely travel through space.

The simulated sound of this stochastic signal can be heard below.

(R. Williams (STScI), the Hubble Deep Field Team, NASA)

It is extremely likely given the variety of objects and events in the Universe that other types of gravitational wave signals exist. This means that the quest to detect such signals is really an exploration of the unknown. Fortunately, our capacity to explore the cosmos has been boosted tremendously by our ability to detect gravitational waves.

A New Age of Astronomy

GW150914 conformed precisely to the predictions of general relativity, confirming Einstein’s most revolutionary theory almost exactly six decades after his death in 1955. That doesn’t mean that gravitational waves are done teaching us about the Universe. In fact, these ripples in spacetime have given us a whole new way to view the cosmos.

Before the discovery of gravitational waves, astronomers were restricted to a view of the Universe painted in electromagnetic radiation and therefore our observations have been confined to that particular spectrum.

Using the electromagnetic spectrum alone, astronomers have been able to discover astronomical bodies and even the cosmic microwave background (CMB) radiation, a ‘relic’ of one of the very first events in the early universe, the recombination epoch when electrons joined with protons thus allowing photons to begin travelling rather than endlessly scattering. Therefore, the CMB is a marker of the point the universe began to be transparent to light.

Yet despite the strides traditional astronomy has allowed us to make in our understanding of the cosmos, the use of electromagnetic radiation is severely limited. It does not allow us to directly ‘see’ black holes, from which light cannot escape. Nor does it allow us to see non-baryonic, non-luminous dark matter, the predominant form of matter in galaxies–accounting for around 85% of the universe’s total mass. As the term ‘non-luminous’ suggests dark matter does not interact with the electromagnetic spectrum, it neither absorbs nor emits light. This means that observations in the electromagnetic spectrum alone will never allow us to see the majority of the matter in the universe.

Clearly, this is a problem. But one that can be avoided by using the gravitational wave spectrum as both black holes and dark matter do have considerable gravitational effects.

Gravitational waves also have another significant advantage over electromagnetic radiation.

This new form of astronomy measures the amplitude of the travelling wave, whilst electromagnetic wave astronomy measures the energy of the wave, which is proportional to the amplitude of the wave squared.

Therefore the brightness of an object in traditional astronomy is given by 1/distance² whilst ‘gravitational brightness’ falls off by just 1/distance. This means that the visibility of stars persists in gravitational waves for a much greater distance than the same factor persists in the electromagnetic spectrum.

Of course, none of this is to suggest that gravitational wave astronomy will ‘replace’ traditional electromagnetic spectrum astronomy. In fact the two are most powerful when they are unified in an exciting new discipline–multimessenger astronomy

Sources and Further Reading

Maggiore. M., Gravitational Waves: Theory and Experiments, Oxford University Press, [2019]

Maggiore. M., Gravitational Waves: Astrophysics and Cosmology, Oxford University Press, [2019]

Collins. H., Gravity’s Kiss:  The Detection of Gravitational Waves, MIT Press, [2017]

Look Deeper, LIGO, [https://www.ligo.caltech.edu/page/look-deeper]

What are Black Holes: The Journey From Theory to Reality

Black holes are cosmic bodies that pack an immense amount of mass into a surprisingly small space. Due to their extremely intense gravity, nothing can escape their grasp — not even light which defines the universe’s speed limit.

April 10th, 2019 marked a milestone in science history when the team at the Event Horizon Telescope revealed the first image of a supermassive black hole. As a result, these areas of space created when stars reach the end of their nuclear fuel burning and collapse creating massive gravitational wells, completed their transition from theory to reality.

This transition has been further solidified since with the revelation of a second, much clearer image of the supermassive black hole (SMBH) at the centre of the galaxy Messier 87 (M87). This second image revealing details such as the orientation of the magnetic fields that surround it and drive its powerful jets that extend for light-years.

(EHT Collaboration)

The study of black holes could teach us much more than about these spacetime events and the environments that home them, however. Because cosmologists believe that most galaxies have an SMBH sat at their centre, greedily consuming material like a fat spider lurking at the centre of a cosmic web, learning more about these spacetime events can also teach us how galaxies themselves evolve.

The origin of black holes is one that runs in reverse to that of most astronomical objects. We didn’t discover some mysterious object in the distant cosmos and then began to theorise about it whilst making further observations.

Rather, black holes entered the scientific lexicon in a way that is more reminiscent of newly theorised particles in particle physics; emerging first from the solutions to complex mathematics. In the case of black holes, the solutions to the field equations employed by Einstein in his most important and revolutionary theory.

Just as a physical black hole forms from the collapse of a star, the theory of black holes emerged from the metaphorical collapse of the field equations that govern the geometrical theory of gravity; better known as general relativity.

One of the most common misconceptions about black holes arises from their intrinsic uniqueness and the fact that there really isn’t anything else like them in the Universe.

That’s Warped: Black Holes and Their Effect on Spacetime

General relativity introduced the idea that mass has an effect on spacetime, a concept fundamental to the idea that space and time are not passive stages upon which the events of the universe play out. Instead, those events shape that stage. As John Wheeler brilliantly and simply told us; when it comes to general relativity:

“Matter tells space how to curve. Space tells matter how to move.”

John Wheeler

The most common analogy is for this warping of space is that of placing objects on a stretched rubber sheet. The larger the object the deeper the ‘dent’ and the more extreme the curvature it creates. In our analogy, a planet is a marble, a star an apple, and a black hole a cannonball.

Thus, considering this a black hole isn’t really ‘an object’ at all but, is actually better described as a spacetime event. When we say ‘black hole’ what we really mean is an area of space that is so ‘warped’ by a huge amount of mass condensed into a finite point that even light itself doesn’t have the necessary velocity to escape it.

This point at which light can no longer escape marks the first of two singularities that define black holes–points at which solutions of the equations of general relativity go to infinity.

The Event Horizon and the Central Singularity

The event horizon of a black hole is the point at which its escape velocity exceeds the speed of light in vacuum (c). This occurs at a radius called the Schwarzchild radius–named for astrophysicist Karl Schwarzschild, who developed a solution for Einstien’s field equations whilst serving on the Eastern Front in the First World War.

His solution to Einstein’s field equations–which would unsurprisingly become known as the Schwarzschild solution– described the spacetime geometry of an empty region of space. It had two interesting features — two singularities — one a coordinate singularity the other, a gravitational singularity. Both take on significance in the study of black holes.

Dealing with the coordinate singularity, or the Schwarzchild radius first.

The Schwarzchild radius (Rs) also takes on special meaning in cases where the radius of a body shrinks within this Schwarzschild radius (ie. Rs >r). When a body’s radius shrinks within this limit, it becomes a black hole.

All bodies have a Schwarzschild radius, but as you can see from the calculation below for a body like Earth, Rs falls well-within its radius.

That’s part of what makes black holes unique; their Schwartzchild radius is outside their physical radius because their mass is compressed into such a tiny space.

Because the outer edge of the event horizon is the last point at which light can escape it also marks the last point at which events can be seen by distant observers. Anything past this point can never be observed.

The reason the Schwarzschild radius is called a ‘coordinate singularity’ is that it can be removed with a clever choice of coordinate system. The second singularity can’t be dealt with in this way. This makes it the ‘true’ physical singularity of the black hole itself.

This is known as the gravitational singularity and is found at the centre of the black hole (r=0). This is the end-point for every particle that falls into a black hole. It’s also the point the Einstein field equations break down… maybe even all the laws of physics themselves.

The fact that the escape velocity of the event horizon exceeds the speed of light means that no physical signal could ever carry information from the central singularity to distant observers. We are forever sealed off from this aspect of black holes, which will therefore forever remain in the domain of theory.

How to Make a Black Hole

We’ve already seen that for a body with the mass of Earth to become a black hole, its diameter would have to shrink to less than 2cm. This is obviously something that just isn’t possible. In fact, not even our Sun has enough mass to end its life as a black hole. Only stars with around three times the mass of the Sun are massive enough to end their lives in this way.

But why is that the case?

It won’t surprise you to learn that for an astronomical body to become a black hole it must meet and exceed a series of limits. These limits are created by outward forces that are resisting against the inward force that leads to gravitational collapse.

For planets and other bodies with relatively small masses, the electromagnetic repulsion between atoms is strong enough to grant them stability against total gravitational collapse. For large stars the situation is different.

During the main life cycle of stars–the period of the fusion of hydrogen atoms to helium atoms–the primary protection against gravitational collapse is the outward thermal and radiation pressures that are generated by these nuclear processes. That means that the first wave of gravitational collapse occurs when a star’s hydrogen fuel is exhausted and inward pressure can no longer be resisted.

Should a star have enough mass, this collapse forces together atoms in the nucleus enough to reignite nuclear fusion— with helium atoms now fusing to create heavier elements. When this helium is exhausted, the process happens again, with the collapse again stalling if there is enough pressure to trigger the fusion of heavier elements still.

Stars like the Sun will eventually reach the point where their mass is no longer sufficient to kick start the nuclear burning of increasingly heavier elements. But if it isn’t nuclear fusion that is generating the outward forces that prevent complete collapse, what is preventing these lower-mass stars from becoming black holes?

Placing Limits on Gravitational Collapse

Lower-mass stars like the Sun will end their lives as white dwarf stars with a black hole form out of reach. The mechanism protecting these white dwarfs against complete collapse is a quantum mechanical phenomenon called degeneracy.

This ‘degeneracy pressure is a factor of the Pauli exclusion principle, which states that certain particles– known as fermions, which include electrons, protons, and neutrons– are forbidden from occupying the same ‘quantum states.’ This means that they resist being tightly crammed together.

This theory and the limitation it introduced led Indian-American astrophysicist Subrahmanyan Chandrasekhar to question if there was an upper cap at which this protection against gravitational collapse would fail.

Chandrasekhar –awarded the 1983 Nobel Prize in physics for his work concerning stellar evolution– proposed in 1931 that above 1.4 solar masses, a white dwarf would no longer be protected from gravitational collapse by degeneracy pressure. Past this limit — termed the Chandrasekhar limit — gravity overwhelms the Pauli exclusion principle and gravitational collapse can continue.

But there is another limit that prevents stars of even this greater mass from creating black holes.

Thanks to the 1932 discovery of neutrons— the neutral partner of protons in atomic nuclei — Russian theoretical physicist Lev Landau began to ponder the possible existence of neutron stars. The outer part of these stars would contain neutron-rich nuclei, whilst the inner sections would be formed from a ‘quantum fluid’ comprised of mostly neutrons

These neutron stars would also be protected against gravitational collapse by degeneracy pressure — this time provided by this neutron fluid. In addition to this, the greater mass of the neutron in comparison to the electron would allow neutron stars to reach a greater density before undergoing collapse.

By 1939, Robert Oppenheimer had calculated that the mass-limit for neutron stars would be roughly 3 times the mass of the Sun.

To put this into perspective, a white dwarf with the mass of the Sun would be expected to have a millionth of our star’s volume — giving it a radius of 5000km, roughly that of the Earth. A neutron star of a similar mass though would have a radius of about 20km — roughly the size of a city.

Above the Oppenheimer-Volkoff limit, gravitational collapse begins again. This time no limits exist between this collapse and the creation of the densest possible state in which matter can exist. The state found at the central singularity of a black hole.

We’ve covered the creation of black holes and the hurdles that stand in the way of the formation of such areas of spacetime, but theory isn’t quite ready to hand black holes over to practical observations just yet. The field equations of general relativity can also be useful in the categorisation of black holes.

The four types of black holes

Categorising black holes is actually fairly straight-forward thanks to the fact that they possess very few independent qualities. John Wheeler had a colourful way of describing this lack of characteristics. The physicist once commented that black holes ‘have no hair,’ meaning that outside a few characteristics they are essentially indistinguishable. This comment became immortalised as the no-hair theorem of black holes.

Black holes have only three independent measurable properties — mass, angular momentum and electric charge. All black holes must have mass, so this means there are only four different types of a black hole based on these qualities. Each is defined by the metric or the function used to describe it.

This means that black holes can be quite easily catagorised by the properties they possess as seen below.

This isn’t the most common or most suitable method of categorising black holes, however. As mass is the only property that is common to all black holes, the most straight-forward and natural way of listing them is by their mass. These mass categories are imperfectly defined and so far black holes in some of the categories–most notably intermediate black holes– remain undetected.

Cosmologists believe that the majority of black holes are rotating and non-charged Kerr black holes. And the study of these spacetime events reveals a phenomenon that perfectly exemplifies their power and influence on spacetime.

The Anatomy of a Kerr Black Hole

The mathematics of the Kerr metric used to describe non-charged rotating black holes reveals that as they rotate, the very fabric of spacetime that surrounds them is dragged along in the direction of the rotation.

The powerful phenomenon is known as ‘frame-dragging’ or the Lense-Thirring effect and leads to the violent churning environments that surround Kerr black holes. Recent research has revealed that this frame-dragging could be responsible for the breaking and reconnecting of magnetic field lines that in-turn, launch powerful astrophysical jets into the cosmos.

The static limit of a Kerr black hole also has an interesting physical significance. This is the point at which light–or any particle for that matter– is no-longer free to travel in any direction. Though not a light-trapping surface like the event horizon, the static limit pulls light in the direction of rotation of the black hole. Thus, light can still escape the static limit but only in a specific direction.

British theoretical physicist and 2020 Nobel Laureate Sir Roger Penrose also suggested that the static limit could be responsible for a process that could cause black holes to ‘leak’ energy into the surrounding Universe. Should a particle decay into a particle and its corresponding anti-particle at the edge of the static limit it would be possible for the latter to fall into the black hole, whilst its counterpart is launched into the surrounding Universe.

This has the net effect of reducing the black hole’s mass whilst increasing the mass content of the wider Universe.

We’ve seen what happens to light at the edge of a black hole and explored the fate of particles that fall within a Kerr black hole’s static limit, but what would happen to an astronaut that strayed too close to the edge of such a spacetime event?

Death by Spaghettification

Of course, any astronaut falling into a black hole would be completely crushed upon reaching its central gravitational singularity, but the journey may spell doom even before this point has been reached. This is thanks to the tidal forces generated by the black hole’s immense gravitational influence.

As the astronaut’s centre of mass falls towards the black hole, the object’s effect on spacetime around it causes their head and feet to arrive at significantly different times. The difference in the gravitational force at the astronaut’s head and feet gives rise to such a huge tidal force that means their body would be simultaneously compressed at the sides and stretched out.

Physicists refer to this process as spaghettification. A witty name for a pretty horrible way to die. Fortunately, we haven’t yet lost any astronauts to this bizarre demise, but astronomers have been able to watch stars meet the same fate.

For a stellar-mass black hole, spaghettification would occur not just before our astronaut reaches the central singularity, but also well before they even hit the event horizon. For a black hole 40 times the mass of our Sun — spaghettification would occur at about 1,000 km out from the event horizon, which is, itself, 120 km from the central gravitational singularity.

As well as developing the Oppenheimer-Volkoff limit, Oppenheimer also used general relativity to describe how a total gravitational collapse should appear to a distant observer. They would consider the collapse to take an infinitely long time, the process appearing to slow and freeze as the star’s surface shrinks towards the Schwarzschild radius.

An astronaut falling into a black hole would be immortalized in a similar way to a distant observer, though they themselves–could they have survived spaghettification– they would notice nothing. The passing of Rs would just seem a natural part of the fall to them despite it marking the point of no return.

Much More to Learn…

After emerging from the mathematics of general relativity at the earlier stages of the 20th Century, black holes have developed from a theoretical curiosity to the status of scientific reality. In the process, they have indelibly worked their way into our culture and lexicon.

The Event Horizon Telescope (EHT) collaboration, who produced the first ever image of a black hole released in 2019, has today a new view of the massive object at the centre of the Messier 87 (M87) galaxy: how it looks in polarised light. This is the first time astronomers have been able to measure polarisation, a signature of magnetic fields, this close to the edge of a black hole. (EHT Collaboration)
The Event Horizon Telescope (EHT) collaboration, which produced the first-ever image of a black hole released in 2019, has today a new view of the massive object at the centre of the Messier 87 (M87) galaxy: how it looks in polarised light. This is the first time astronomers have been able to measure polarisation, a signature of magnetic fields, this close to the edge of a black hole. (EHT Collaboration)

Perhaps the most exciting thing about black holes is that there is so much we don’t yet know about them. As a striking example of that, almost all the information listed above resulted just from theory and the interrogation of the maths of Einstein’s field equations.

Unlocking the secrets held by black holes could, in turn, reveal how galaxies evolve and how the Universe itself has changed since its early epochs.

Sources and Further Reading

Relativity, Gravitation and Cosmology, Robert J. Lambourne, Cambridge Press, [2010].

Relativity, Gravitation and Cosmology: A basic introduction, Ta-Pei Cheng, Oxford University Press, [2005].

Extreme Environment Astrophysics, Ulrich Kolb, Cambridge Press, [2010].

Stellar Evolution and Nucleosynthesis, Sean G. Ryan, Andrew J. Norton, Cambridge Press, [2010].

Cosmology, Matts Roos, Wiley Publishing, [2003].

What is Mass-Energy Equivalence (E=mc^2): the most famous formula in science

In a series of papers beginning in 1905 Einstein’s theory of special relativity revolutionized the concepts of space and time, uniting them into a single entity–spacetime. But, the most famous element of special relativity–as famous as the man himself–was absent from the first paper.

Mass-energy equivalence, represented by E=mc2, would be introduced in a later paper published in November 1905. And just as Einstein had already unified space and time–this paper would unite energy and mass.

So what does the mass-energy equivalence tell us and what is the equation E=mc2 saying about the Universe?

The Basics

If you wanted to walk away from this article with one piece of information about the equation E=mc2 (and I hope you won’t) what would that be?

Essentially the simplified version of the equation of special relativity tells us that mass and energy are different forms of the same thing– mass is a form of energy. Probably the second most important piece of information to take away is the fact that these two aspects of the Universe are interchangeable, and the mitigating factor is the speed of light squared.

Still with us? Good!

Perhaps the most surprising thing about the equation E=mc2 is how deceptively simple it is for something so profound. Especially when considering that as the equation that describes how stars release energy and thus make all life possible. Mathematical formulae don’t get much more foundational.

Gathering Momentum: Where Does the Mass-Energy Equivalence Come From?

There are actually a few ways of considering the origin of E=mc2. One way is by considering how the relationship it describes can emerge when comparing the relativistic equation for momentum and its Newtonian counterpart. The major difference between the two, as you’ll see below, is multiplication by the Lorentz factor — you might remember in the last part of this guide to special relativity —concerning space and time— I told you it gets everywhere in special relativity!

Whilst you could argue that the only difference between the two is that velocity (v) has been replaced with a more complex counterpart that approaches v when speeds are far less than light–everyday speeds that we see everyday objects around us move at–but some physicists find this more significant than a mere substitution.

These scientists would argue that this new factor ‘belongs’ to the mass of the system in question. This view means that mass increases as velocity increases, and this means there is a discernable difference between an object’s ‘moving mass’ and its ‘rest mass.’

So, let’s look at that equation for momentum again with the idea of rest mass included.

So, if mass is increasing as velocity increases, what is responsible for this rise?

Let’s conduct an experiment to find out. Our lab bench is the 2-mile long linear particle accelerator at SLAC National Laboratory, California. Using powerful electromagnetic forces, we take electrons and accelerate them to near the speed of light. When the electrons emerge at the other end of the accelerator we find that their relativistic mass has increased by a staggering factor of 40,000.

As the electrons slow, they lose this mass again. Thus, we can see it’s the addition of kinetic energy to the object that is increasing its mass. That gives us a good hint that energy and mass are interconnected.

But, this conclusion leads to an interesting question; if the energy of motion is associated with an object’s mass when it is moving, is there energy associated with the object’s mass when it is at rest, and what kind of energy could this be?

Locked-Up Energy

An object at rest without kinetic energy can, with the transformation of an infinitesimally small amount of mass, provide energy enough to power the stars.

As the equation E=mc2 and the fact that the speed of light squared is an extremely large number implies, in terms of energy just a little mass goes a very long way. To demonstrate this, let’s see how much energy would be released if you could completely transform the rest mass of a single grain of sugar.

That’s a lot of energy!

In fact, it is roughly equivalent to the amount of energy released by ‘little boy’– the nuclear fission bomb that devastated Hiroshima on the 6th August 1945.

That means that even when an object is at standstill it has energy associated with it. A lot of energy.

As you might have guessed by this point, as energy and mass are closely associated and there are many forms of energy there are also many ways to give an object increased mass. Heating a metal rod, for example, increases the rod’s mass, but by such a small amount that it goes unnoticed. Just as liberating a tiny bit of mass releases a tremendous amount of energy, adding a relatively small amount of heat energy results in an insignificant mass increase.

We’ve already seeen that we can accelerate a particle and increase its relativistic mass, but is there anything we can do to increase a system’s rest mass?

E=mc2: Breaking the Law (and Billiard Balls)!

Until the advent of special relativity two laws, in particular, had governed the field of physics when it comes to collisions, explosions, and all that cool violent stuff: the conservation of mass and the conservation of energy. Special relativity challenged this, suggesting instead that it is not mass or energy that is conserved, but the total relativistic energy of the system.

Let’s do another experiment to test these ideas… The first location we’ll travel to in order to do this… a billiard table at the Dog & Duck pub, London.

At the billiard table, we strike a billiard ball 0.17 kg toward a stationary billiard ball of the same mass at around 2 metres per second. We hit the ball perfectly straight on so that all of the kinetic energy of the first ball is transferred to the second ball.

If we could measure the kinetic energy of the initial ball, then measure the kinetic energy of both balls after the collision, we would find that–accounting for the small losses of energy to heat and sound–the total energy of the system after the collision is the same as the energy before the collision.

That’s the conservation of energy.

Let’s rerun that experiment again, but this time we launch the billard ball so hard that instead of knocking the target ball across the table, it shatters it. Collecting together the fragments of the shattered ball and remeasuring the mass of the system, we would find the final mass is exactly the same as the initial mass.

And that’s the conservation of mass.

We’re starting to get funny looks from the Dog & Duck regulars now, and the landlord looks angry about the destruction of one of his billiard balls. Luckily, the third part of our test requires we relocate to CERN, Geneva. So we down our drinks, grab our coats and hurry out the door.

Trying the experiment a third time, we are going to replace the billiard table with the Large Hadron Collider (LHC)–that’s some upgrade– and the billiard balls with electrons and their equal rest mass anti-particles– positrons.

Using powerful magnets to feed these fundamental particles with kinetic energy we accelerate them to near light speed, directing them towards each other and colliding them. The result is a shower of particles that previously weren’t present. But, unlike in our billiard ball example, when we measure the rest mass of the system it has not remained the same.

Just one of the particles we observe after the collision event is a neutral pion–a particle with a rest mass 264 times the rest mass of an electron and thus 132 times the initial rest mass we began with.

Clearly, the creation of this pion has taken some of the kinetic energy we poured into the electrons and converted it to rest mass. We watch as the pion decays into a muon with a rest mass 204 times that of an electron, and this decays into particles that are lighter still. Each time the decay releases energy in the form of pulses of light.

Relativistic Energy .vs Rest Energy

By now it is probably clear that in special relativity rest mass and relativistic mass are very different concepts, which means that it shouldn’t come as too much of a surprise that rest energy and relativistic energy are also separate things.

Let’s alter that initial infographic to reflect the fact that the equation E=mc2 actually describes rest energy.

This raises the questions (if I’m doing this right that is) what is the equation for relativistic energy?

It’s time for another non-surprise. The equation for relativistic energy is just the equation for rest energy with that Lorentz factor playing a role.

Ultimately, it is this relativistic energy that is conserved, thus whilst we’ve sacrificed earlier ideas of the conservation of mass and the conservation of energy, we’ve recovered a relativistic version of those laws.

Of course, the presence of that Lorentz factor tells us that when speeds are nowhere near that of light — everyday speeds like that of the billiard balls in the Dog & Duck–the laws of conservation of mass and energy are sufficeint to describe these low-energy systems.

The Consequences of E=mc2

It’s hard to talk about the energy-mass equivalence or E=mc2 without touching upon the nuclear weapons that devasted Hiroshima and Nagasaki at the close of the Second World War.

It’s an unfortunate and cruel irony that Einstein–a man who was a staunch pacifist during his lifetime–has his name eternally connected to the ultimate embodiment of the most destructive elements of human nature.

The Sun photographed at 304 angstroms by the Atmospheric Imaging Assembly (AIA 304) of NASA's Solar Dynamics Observatory (SDO). This is a false-color image of the Sun observed in the extreme ultraviolet region of the spectrum. (NASA)
The Sun photographed at 304 angstroms by the Atmospheric Imaging Assembly (AIA 304) of NASA’s Solar Dynamics Observatory (SDO). This is a false-colour image of the Sun observed in the extreme ultraviolet region of the spectrum. (NASA)

Nuclear radiation had been discovered at least a decade before Einstein unveiled special relativity, but scientists had struggled to explain exactly where that energy was coming from.

That is because as rearranging E=mc2 implies, a small release of energy would be the result of the loss of an almost infinitesimally small amount of rest mass –certainly immeasurable at the time of discovery.

Of course, as we mention above, we now understand that small conversion of rest mass into energy to be the phenomena that power the stars. Every second, our own star–the Sun– takes roughly 600 tonnes of hydrogen and converts it to 596 tonnes of helium, releasing the difference in rest mass between the two as around 4 x 1026 Joules of energy.

We’ve also harnessed the mass-energy equivalence to power our homes via nuclear power plants, as well as using it to unleash a terrifying embodiment of death and destruction into our collective imaginations.

We could probably ruminate more about special relativity and its elements, as its importance to modern physics simply cannot be overstated. But, Einstein wasn’t done.

Thinking about spacetime, energy and mass had open a door and started Einstein on an intellectual journey that would take a decade to complete.

The great physicist saw special relativity as a great theory to explain physics in an empty region of space, but what if that region is occupied by a planet or a star? In those ‘general’ circumstances, a new theory would be needed. And in 1915, this need would lead Einstein to his greatest and most inspirational theory–the geometric theory of gravity, better known as general relativity.

Sources and Further Reading

Stannard. R., ‘Relativity: A Short Introduction,’ Oxford University Press, [2008].

Lambourne. R. J., ‘Relativity, Gravitation and Cosmology,’ Cambridge University Press, [2010].

Cheng. T-P., ‘Relativity, Gravitation and Cosmology,’ Oxford University Press, [2005].

Fischer. K., ‘Relativity for Everyone,’ Springer, [2015].

Takeuchi. T., ‘An Illustrated Guide to Relativity,’ Cambridge University Press, [2010].

What is Special Relativity: A Guide to Spacetime, Time Dilation and Length Contraction

Imagine a passenger sat aboard a train. They awake from sleep and see another train moving past at a constant velocity. The passenger is momentarily confused. Which train is moving? Theirs or the one opposite?

In 1905 this idle thought and the concept of relative motion would inspire one of science’s most important theories. Over a series of four papers, Albert Einstein, a patent clerk in Bern, Switzerland, would change physics forever. The theory encapsulated by those papers–special relativity– would reformulate not just the laws of motion, but the relationship between matter and energy, and the very nature of time and space themselves.

Thanks to special relativity what was once immutable and unchanging became an active player in the events of the Universe. Something that Albert Einstein, the theory’s father would only expand upon in the future. But, before that, uniting space and time as one entity–spacetime–would have some remarkable consequences for these previously separate aspects of the Universe and for the mechanics that govern its events.

Spacetime, Inertial Reference Frames, and Relative Motion

Spacetime is filled with events–it would be rather boring if it wasn’t. These events can be as mundane as egg crack on the kitchen floor, to events as powerful and violent as the eruptions of supernovea.

Robert Lea

Within spacetime are inertial reference frames–areas filled with synchronised clocks that allow events to be given coordinates. If one inertial frame exists then an infinite amount exist in relative motion.

In each inertial reference frame is an observer. For the sake of our thought experiments, these will be twin sisters Astra and Terra. One important thing to note, just like in the train analogy which opened our explorations, these observers believe that they are stationary in their frame.

Twin sisters Terra and Astra borrow their father’s sports car to demonstrate this. Terra stands on a bridge as Astra races towards her in her father’s car at a steady velocity of 100mph. Terra will see Astra’s reference frame approaching at this speed and she and the bridge are at rest As far as Astra is concerned, she considers herself and the car at rest, and that it is the bridge that races towards her at 100mph.

This only holds if these frames are inertial–not accelerating or turning which is counted as acceleration in physics. Think about it like this; in the train analogy, the passenger doesn’t know if their train is moving or if it’s the train opposite. If the train was accelerating–the passenger would ‘feel’ this acceleration and thus know which train is moving.

The exclusion of accelerating frames will become important later.

Let’s now explore the consequences of relative motion on how observers measure the events that occur around them.


Years later, Terra and Astra’s father finally ungrounds them both for the destruction of both his car and a local bridge, meaning Terra can escort Astra to the local train station as she embarks on a journey to astronaut training camp. As the train pulls away from the platform and achieves a constant velocity, lightning strikes it at the front and the back, getting Terra–a theoretical physicist–thinking about how she and her twin sister would have experienced the event.

This encapsulates a revolutionary aspect of Einstein’s 1905 theory, the idea that observers in different reference frames experience time and space differently. So much so that observers in different reference frames can disagree on the order in which events occur.

Terra sees event 1-the front of the train struck by lightning, occur at the same time as event 2-the back of the train struck by lightning. Astra, however, sees event 1 occur before event 2.

But what about the law of causality? What is to prevent event A that causes event B being seen after that effect in a particular frame and thus in that reference frame having the consequence of putting effect before cause?

This might not sound like a problem, but say Astra sees B before A, she could potentially send a signal to Terra about B that is received before A has even happened. Maybe quick enough that Terra could actually stop A from occurring?

Terra ponders this as she screams at her more adventurous sister to sit inside the train rather than stand on its roof.

Transformations in Special Relativity

When examining the rules that Einstein would need to transform coordinates from one inertial reference frame to another, the physicist discovered that they were identical to the transformations developed by Dutch physicist Hendrik Lorentz.

Lorentz had arrived at these transformations whilst considering James Clerk Maxwell’s laws of electromagnetism. This finding excited Einstein, as a major reason he began speculating about the nature of light and the speed at which it travels was a result of Maxwell’s laws of electromagnetism. 

These laws didn’t just unite the phenomenon of electricity with magnetism — creating electromagnetism (over the coming decades, physicists will get much more adventurous with nomenclature) — Maxwell found that electromagnetic waves travelled at 3.0 x10 ⁸ m/s — exactly the speed of light.

Thus, Einstein’s predecessor had found that light is an electromagnetic wave.

The use of the Lorentz factor in the transformations of special relativity leads to a stunning consequence. The fact that nothing with mass can travel at the speed of light. But the use of Maxwell’s equations will deliver another, equally impressive aspect to the nature of light and its speed in a vacuum.

The fact that it is absolute.

Absolute C

As well as proving the universe with a speed limit, the speed of light in a vacuum also proves counter-intuitive by taking the same value in all reference frames. Astra and Terra will use a gun and laser pen to demonstrate this phenomenon.

Clearly, if light behaved like any other projectile Astra who is in a reference frame travelling at c/2 would measure the speed of light racing away from her at c, whilst Terra should register it travelling at c + c/2. But, she doesn’t she also registers it as travelling at c.

The reason this should be the case is, Einstein reasoned, that if it were different then if he raced a beam of light at c, he could turn and see that light as a stationary electromagnetic wave, something that is forbidden by Maxwell’s laws of electromagnetism.

It’s the invariance of c and the fact nothing can accelerate beyond it that saves causality and ensures that an effect cannot precede a cause.

(Robert Lea)

Thus, in special relativity, not everything is mutable between reference frames. In fact, the first of two postulates Einstein adopted when thinking about relativity is the fact that the laws of physics should be the same in all inertial reference frames. 

Terra jots down her ideas about how what she has learned from here experiments thus far whilst mulling over the fact her sister runs much faster since being on a train that was struck by lightning.

The Two Postulates of Special Relativity

The idea that light travels at c in a vacuum in all frames to all observers gives Einstein his second postulate for special relativity. The speed of light in a vacuum has the same constant value (3.0 x 108 m/s) in all internal reference frames.

Exploring this second postulate, Terra wonders how is it possible that both she and Astra could register the same value for the speed of light in a vacuum?

Something must be different between the two frames. It turns out that there is a difference and Einstein realised that it has stunning consequences for our concepts of space and time. Or more precisely for Einstien’s united entity, spacetime.

Time Dilation: Physics on Flexitime

In special relativity, it is accepted that ‘moving clocks run slow.’ To put this in a more understandable way, an observer in an inertial reference frame will observe the clock in another inertial reference frame that is in relative motion moving slowly.

The idea that ‘moving clocks run slow’ gave rise to one of science’s most famous thought experiments. The so-called ‘Twin Paradox’. The paradox element of the example arises from the idea that if Terra sees Astra’s clock run slow, and Astra sees Terra’s clock run slow, what happens when the twin sisters meet back up?

Surely Astra will expect Terra to be younger upon her return, whilst Terra will expect Astra to be younger?

To demonstrate this idea Astra will once again embark on a journey in her ship, but this time rather than a short jaunt she will leave for a distant star system, a journey that will separate the twins for many years.

The answer to this paradox lies in the fact that special relativity works only in non-inertial frames–that is frames that aren’t accelerating. Whilst Terra’s frame remains in constant motion, it’s clear that Astra’s frame MUST accelerate at points. For example, Astra has to turn her ship around to return to earth, that means that even if she manages to do so with slowing down (deceleration also counts as acceleration in physics) circular motion is acceleration too!

A practical demonstration of the effect described in the twin paradox thought experiment can be seen in particle accelerators. As particles that decay in incredibly short lengths of time are accelerated to speeds approaching that of light researchers can measure them lasting for longer than they should. Of course, if a scientist could race alongside the hurtling particle this scientist would measure it decaying in the usual amount of time.

There’s another factor to special relativity that affects that can be seen with short-lived particles.

Muons are short-lived particles that are created in Earth’s upper atmosphere when it is struck with cosmic rays, that exist for 2.2 microseconds. Even when factoring in time dilation and the incredible velocity of muons–0.98c or 98% the speed of light–very few of these particles should survive long enough to strike the surface of our planet. And yet far too many do just this.

Something else must be working to enable the muons to reach the ground. What if, as well as granting them extended time special relativity could also shorten the distance that the electron-like particles have to cover?

Length Contraction: Short on Space

Possibly an even more counterintuitive idea than time dilation is length contraction–or Lorentz contraction. Whilst time can sometimes seem to us like an abstract concept (who hasn’t experienced the seemingly stretched time of a workday or a school day?) length–distance–is something we can see and measure quite easily. The idea that you could take a solid iron rod and measure it to have different lengths depending on the speed at which it moves and whether you are moving with it or not sounds absurd.

But it’s correct.

Of course, like time dilation we don’t see these effects in everyday life as the velocities required to cause length contraction are close to the speed of light in a vacuum. Fortunately, Astra and Terra are on hand to demonstrate again as its time to put the rocket ship away. In their attempt to park Astra’s ship in Terra’s barn they discover another paradox.

Clearly that from the perspective of Terram, the ship will fit in the barn, albeit briefly. Astra disagrees.

So what is the solution?

Obviously, the ship isn’t going to fit when it is stationary, but the sisters want to know if there is a point when the whole ship will be inside the barn. Fortunately, the barn also has back gates so they can run the experiment without too much damage.

The key to solving this paradox is simultaneity. Because events can occur in different orders for observers in different reference frames, it’s quite possible for Terra and Astra to disagree whether the rocket was ever fully inside that barn.

This is the spatial equivalent of the twin paradox and the answer to the question ‘which sister is correct’ in both cases is the same: both.

What both of these effects tell us is that in special relativity there is no reference frame that has ‘privilege’ over another.

But There’s More…

Thus far we’ve focused our discussion on how Einstein’s theory of special relativity affected how we think about the world, but in terms of changing the world, no element of this theory had as much impact as the matter/energy equivalence. It was this concept and E=mc2 the equation that embodies it, that would give rise to the atom bomb and the mushroom cloud that is etched in our minds as the ultimate symbol of destruction.

It is cruelly ironic that a lifelong pacifist like Einstein will forever be linked with man’s most destructive impulses.

But, as the sun sets over the shattered doors of Terra’s barn, Astra suggests to her now elderly twin that this is a discussion for another day.

Sources and Further Reading

Lambourne. R. J., ‘Relativity, Gravitation and Cosmology,’ Cambridge University Press, [2010].

Cheng. T-P., ‘Relativity, Gravitation and Cosmology,’ Oxford University Press, [2005].

Fischer. K., ‘Relativity for Everyone,’ Springer, [2015].

Takeuchi. T., ‘An Illustrated Guide to Relativity,’ Cambridge University Press, [2010].

Time Travel Without the Paradoxes

Time Travel Without the Paradoxes

It’s one of the most popular ideas in fiction — travelling back through time to alter the course of history. The idea of travelling through time — more than we do every day that is — isn’t just the remit of science fiction writers though. Many physicists have also considered the plausibility of time travel, especially since Einstein’s theory of special relativity changed our concept of what time actually is. 

Yet, as many science fiction epics warn, such a journey through time could carry with it some heavy consequences. 

Ray Bradbury’s short story ‘A Sound of Thunder’ centres around a group of time travellers who blunder into prehistory, making changes that have horrendous repercussions for their world. In an even more horrific example of a paradox, during an award-winning episode of the animated sci-fi sitcom Futurama, the series’ hapless hero Fry travels back in the past and in the ultimate grandfather paradox, kills his supposed gramps. Then, after ‘encounter’ with his grandmother, Fry realises why he hasn’t faded from reality, he is his own grandfather. 

Many theorists have also considered methods of time travel without the risk of paradox. Techniques that don’t require the rather extreme measure of getting overly friendly with one’s own grandmother Fry. These paradox-escape mechanisms range from aspects of mathematics to interpretations of quantum weirdness. 

ZME’s non-copyright infringing time machine. Any resemblance to existing time travel devices is purely coincidental *cough* (Christopher Braun CC by SA 1.0/ Robert Lea)

Before looking at those paradox escape plans it’s worth examining just how special relativity changed our thinking about time, and why it started theoretical physicists really thinking about time travel. 

Luckily at ZME Science, we have a pleasingly non-copyright infringing time machine to travel back to the past. Let’s step into this strange old phone booth, take a trip to the 80s to pick up Marty and then journey back to 1905, the year Albert Einstein published ‘Zur Elektrodynamik bewegter Körper’ or ‘On the Electrodynamics of Moving Bodies.’ The paper that gave birth to special relativity. 

Don’t worry Marty… You’ll be home before you know it… Probably.

A Trip to 1905: Einstein’s Spacetime is Born

As Marty reads the chronometer and discovers that we have arrived in 1905, he questions why this year is so important? At this point, physics is undergoing a revolution that will give rise to not just a new theory of gravity, but also will reveal the counter-intuitive and somewhat worrisome world of the very small. And a patent clerk in Bern, Switzerland , who will be at the centre of this revolution,  is about to have a very good year. 

The fifth year of the 20th Century will come to be referred to as Albert Einstein’s ‘Annus mirabilis’ — or miracle year — and for good reason. The physicist will publish four papers in 1905, the first describing the photoelectric effect, the second detailing Brownian motion. But, as impressive those achievements are–one will see him awarded the Nobel after all–it’s the third and fourth papers we are interested in. 

1905: young Albert Einstein contenplates the future, unaware he is about to change the way we think about time and space forever. (Original Author Unknown)
1905: young Albert Einstein contemplates the future, unaware he is about to change the way we think about time and space forever. (Original Author Unknown)

In these papers, Einstein will first introduce special relativity and then will describe mass-energy equivalence most famously represented by the reduced equation E=mc². It’s no exaggeration to say that these works will change how we think of reality entirely — especially from a physics standpoint. 

Special relativity takes time — and whereas it had previously been believed to be its own separate entity — unites it with the four known dimensions of space. This creates a single fabric— spacetime. But the changes to the concept of time didn’t end there. Special relativity suggests that time is different depending on how one journeys through it. The faster an object moves the more time ‘dilates’ for that object. 

This idea of time running differently in different reference frames is how relativity gets its name. The most famous example for the time difference is the ‘twin paradox.’

Meet twin sisters Stella and Terra. Stella is about to undertake a mission to a distant star in a craft that is capable of travelling at near the speed of light, leaving her sister, Terra, behind on Earth. 

A spacetime diagram of Terra’s journey through spacetime, against her twin Stella’s. Less ‘proper time’ passes for Stella than Terra meaning when she returnes to Earth Terra has aged more than she has. (Robert Lea)

After travelling away from Earth at near the speed of light, then undertaking a return journey at a similar speed, Stella touches down and exits her craft to be greeter by Terra who has aged more in relation to herself. More time has passed for the ‘static’ Earthbound twin than for her sister who underwent the journey into space.

Thus, one could consider Stella to have travelled forward in time. How else could a pair of twins come to be of considerably different ages? That’s great, but what about moving backwards through time? 

Well, if the faster a particle in a reference frame moves, the ‘slower’ time progresses in that frame, it raises the question, is there a speed at which time stands still? And if so, is there a speed beyond this at which time would move backwards? 

A visualisation of a tachyon. Because a tachyon would always travel faster than light, it would not be possible to see it approaching. After a tachyon has passed nearby, an observer would be able to see two images of it, appearing and departing in opposite directions.
(Wiki CC by SA 3.0)

Tachyons are hypothetical particles that travel faster than the speed of light — roughly considered as the speed at which time would stand still — and thus, would move backwards rather than forwards in time. The existence of tachyons would open up the possibility that our space-bound sister could receive a signal from Terra and send her back a tachyon response. Due to the nature of tachyons, this response could be received by Terra before she sent the initial signal.

Here’s where that becomes dangerous; what if Stella sends a tachyon signal back that says ‘Don’t signal me’? Then the original signal isn’t sent, leading to the question; what is Stella responding to?

Or in an even more extreme example; what if Stella sends a tachyon signal back that is intercepted by herself before she embarks on her journey, and that signal makes her decide not to embark on that journey in the first place? Then she’ll never be in space to send the tachyon signal… but, if that signal isn’t sent then she would have embarked on the journey…

And that’s the nature of the causality violating paradoxes that could arise from even the ability to send a signal back through time. Is there a way out of this paradox?


Interlude. From the Journal of Albert Einstein

27th September 1905

A most astounding thing happened today. A young man in extraordinary attire visited me at the patent office. Introducing himself as ‘Marty’ the youngster proceeded to question me about my paper ‘On the Electrodynamics of Moving Bodies‘– a surprise especially as it was only published yesterday.

In particular, the boy wanted to know about my theory’s implications on time travel! A pure flight of fancy of course… Unless… For another time perhaps.

If this wasn’t already unusual to the extreme, after our talk, I walked Marty to the banks of the Aare river where he told me that his transportation awaited him. I was, of course expecting a boat. I was therefore stunned when the boy stepped into a battered red box, which then simply disappeared.

I would say this was a figment of my overworked imagination, a result of tiredness arising from working the patent office during the day and writing papers at night. That is, were I the only witness!

A young man also saw the box vanish, and his shock must have been more extreme than mine for he stumbled into the river disappearing beneath its surface.

His body has not yet been recovered… I fear the worst.

Present Day: The Self Correcting Universe

As the battered old phone box rematerializes in the present day, Marty is determined to seek out an academic answer to the time travel paradox recounted to him in 1905. 

He pays a visit to the University of Queensland where Bachelor of Advanced Science student Germain Tobar has been investigating the possibility of time travel. Under the supervision of physicist Dr Fabio Costa, Tobar believes that a mathematical ‘out’ from time travel paradoxes may be possible.

“Classical dynamics says if you know the state of a system at a particular time, this can tell us the entire history of the system,” Tobar explains. “For example, if I know the current position and velocity of an object falling under the force of gravity, I can calculate where it will be at any time.

“However, Einstein’s theory of general relativity predicts the existence of time loops or time travel — where an event can be both in the past and future of itself — theoretically turning the study of dynamics on its head.”

Tobar believes that the solution to time travel paradoxes is the fact that the Universe ‘corrects itself’ to remove the causality violation. Events will occur in such a way that paradoxes will be removed.

So, take our twin dilemma. As you recall Stella has sent herself a tachyon message that has persuaded her younger self not to head into space. Tobar’s theory — which he and his supervisor Costa say they arrived at mathematically by squaring the numbers involved in time travel calculations — suggests that one of two things could happen.

Some event would force Stella to head into space, she could accidentally stumble into the capsule perhaps, or receive a better incentive to head out on her journey. Or another event could send out the tachyon signal, perhaps Stella could accidentally receive the signal from her replacement astronomer. 

“No matter what you did, the salient events would just recalibrate around you,” says Tobar. “Try as you might, to create a paradox, the events will always adjust themselves, to avoid any inconsistency.

“The range of mathematical processes we discovered show that time travel with free will is logically possible in our universe without any paradox.”

The Novikov self-consistency principle
The Novikov self-consistency principle (Brightroundircle/ Robert Lea)

Tobar’s solution is similar in many ways to he Novikov self-consistency principle — also known as Niven’s Law of the conservation of history — developed by Russian physicist Igor Dmitriyevich Novikov in the late 1970s. This theory suggested the use of geodesics similar to those used to describe the curvature of space in Einstein’s theory of general relativity to describe the curvature of time. 

These closed time-like curves (CTCs) would prevent the violation of any causally linked events that lie on the same curve. It also suggests that time-travel would only be possible in areas where these CTCs exist, such as in the presence of wormholes as speculated by Kip Thorne and colleagues in the 1988 paper “Wormholes, Time Machines, and the Weak Energy Condition”. The events would cyclical and self-consistent. 

The difference is, whereas Tobar suggests a self-correcting Universe, this idea strongly implies that time-travellers would not be able to change the past, whether this means they are physically prevented or whether they actually lack the ability to chose to do so. In our twin analogy, Stella’s replacement sends out a tachyon signal and travelling along a CTC, it knocks itself off course, meaning Stella receives rather than its intended target.

After listening to Tobar, strolling back to his time machine Marty takes a short cut through the local graveyard. Amongst the gravestones baring unfamiliar dates and names, he notices something worrying–chilling, in fact. There chiselled in ageing stone, his grandfather’s name.

The date of his death reads 27th September 1905. 

Interlude: From the Journal of Albert Einstein

29th September 1905

This morning the Emmenthaler Nachrichten reports that the body of the unfortunate young man who I witnessed fall into the Aare has been recovered. The paper even printed a picture of the young man. 

I had not realised at the time, but the boy bares the most remarkable resemblance to Marty — the unusually dressed youngster who visited with me the very day the boy fell…

Strange I such think of Marty’s attire so frequently, the young man told me his garish armless jacket, flannel shirt and ‘jeans’ were ‘all the rage in the ‘86.’ 

Yet, though I was seven in 1886 and have many vague memories from that year, I certainly do not remember such colourful clothes…

Lost in Time: How Quantum Physics provides an Escape Route From Time Travel Paradoxes

Marty folds the copy of the Emmenthaler Nachrichten up and places it on the floor of the cursed time machine that seems to have condemned him. The local paper has confirmed his worst fears; his trip to the past to visit Einstein doomed his grandfather. 

After confirming his ancestry, he knows he is caught in a paradox. He waits to be wiped from time…

After some time, Marty wonders how it could possibly be that he still lives? Quantum physics, or more specifically one interpretation of it has the answer. A way to escape the (literal) grandfather paradox. 

The double slit experiment (Robert Lea)

The ‘many worlds’ interpretation of quantum mechanics was first suggested by Hugh Everett III in the 1950s as a solution to the problem of wave-function collapse demonstrated in Young’s infamous double-slit experiment.

As the electron is travelling it can be described as a wavefunction with a finite probability of passing through either slit S1 or slit S2. When the electron appears on the screen it isn’t smeared across it as a wave would be. It’s resolved as a particle-like point. We call this the collapse of the wavefunction as wave-like behaviour has disappeared, and it’s a key factor of the so-called Copenhagen interpretation of quantum mechanics.

The question remained, why does the wavefunction collapse? Hugh Everett asked a different question; does the wavefunction collapse at all?

The Many Worlds Interpretation of Quantum Physics (Robert Lea)

Everett imagined a situation in which instead of the wavefunction collapsing it continues to grow exponentially. So much so that eventually the entire universe is encompassed as just one of two possible states. A ‘world’ in which the particle passed through S1, and a world where the particle passed through S2.

Everett also stated the same ‘splitting’ of states would occur for all quantum events, with different outcomes existing in different worlds in a superposition of states. The wavefunction simply looks like it has collapsed to us because we occupy one of these worlds. We are in a superposition of states and are forbidden from seeing the other outcome of the experiment.

Marty realises that when he arrived back in 1905, a worldline split occurred. He is no longer in the world he came from– which he labels World 1. Instead, he has created and occupies a new world. When he travels forward in time to speak to Tobar he travels along the timeline of this world–World 2.

This makes total sense. In the world Marty left, a phone box never appeared on the banks of the Aera on September 27th 1905. This world is intrinsically different than the one he left.

What happens as a result of Marty’s first journey to 1905 according to the Many World’s Interpretation (Robert Lea)

He never existed in this world and in truth he hasn’t actually killed his grandfather. His grandfather exists safe and sound back in 1905 of World 1. If the Many World’s Interpretation of quantum physics is the correct solution to the grandfather paradox, however, then Marty can never return to World 1. It’s intrinsic to this interpretation that superpositioned worlds cannot interact with each other.

With reference to the diagrams above, Marty can only move ‘left and down’ or ‘right’–up is a forbidden direction because it’s his presence at a particular moment that creates the new world. This makes total sense, he has changed history and is in a world in which he appeared in 1905. He can’t change that fact.

The non-interaction rule means no matter what measures he takes, every time he travels back into the past he creates a new state and hops ‘down’ to that state and can then only move forward in time (right) on that line.

Marty’s multiple journey’s to the past create further ‘worlds’ (Robert Lea)

So what happens when Marty travels back to the past in an attempt to rescue his world? He inadvertently creates another state–World 3. This world may resemble World 1 & 2 in almost every conceivable way, but according to the application of the interpretation, it is not the same due to one event–one extra phone box on the banks of the River Aare for each journey back.

As Marty continues to attempt to get back to World 1 — his home — he realises he now lives in a world in which one day in September 1905 on the streets of Bern, hundreds of phone box suddenly appeared on the banks of the Aare, and then simply disappeared.

The sudden appearance of hundreds of red telephone boxes around the banks of the River Aare really started to affect property prices. (Britannica)

He also realises that his predicament answers the question ‘if time travellers exist why do they never appear in our time?’ The truth being, that if a person exists in the world from which these travellers departed they can never ‘get back’ to this primary timeline. 

To someone in World 1, the advent of time travel will just result in the gradual disappearance of daring physicists. That’s the moment it dawns on Marty that as far as World 1 — his world — is concerned, he stepped in a phone box one day and vanished, never to return.

Marty escaped the time travel paradox but doomed himself to wander alternate worlds.

Hey… how do we get our time machine back?


AI uses Einstein’s special relativity to predict future events

Credit: Pixabay.

If you kick a football forward, you will have a fairly good idea about its trajectory. For instance, you will be able to anticipate that the football will roll forward in the direction it was pushed and even where it might end up after it bounces off an obstacle.

Owing to a lifetime of experience with the planet’s gravity and laws of physics, as well as millions of years of evolution hardwired into our brains, humans are pretty good at inferring causal relationships. You kick a ball, it will start moving forward. And if you were to freeze the movement of the ball in space and time, you would be good at predicting where the ball ends up, frame by frame, with each passing second.

But believe it or not, even supposedly ‘smart’ machine learning algorithms would find this task challenging. While AIs are good at spotting patterns of correlation, they can be very poor at predicting an event triggered by a subsequent event a number of steps into the future. For an AI, predicting that a ball moves in reverse rather than forward once you kick wouldn’t be nonsense.

In order to improve causal reasoning in AIs, researchers at Imperial College London thought outside the box and took inspiration from Einstein‘s theory of special relativity. What’s the connection, you might ask?

One of the consequences of Einstein’s theory of special relativity is that nothing can travel faster than the speed of light. But this also means that there are boundaries of cause and effect in spacetime, which can be mathematically described. The resulting mathematical structures are known as light cones.

Spacetime is constructed by taking instantaneous snapshots of space at successive instants of time and stacking them up — think of a movie where each frame represents such an instance of time.

To get an idea of how light cones work, imagine an explosion of TNT. Light will propagate out from the TNT in an expanding spherical shell. In a two dimensional space, it will look like an expanding circle, whose radius can never expand more than the distance traveled by light for a given timeline.

If we stack up these spatial snapshots, you end up with a spacetime diagram that corresponds to a cone, where the pointy end corresponds to the origin of an event and the subsequent ever-expanding circles represent causal events. Light cones are usually represented as an hourglass figure, with the bottom cone representing spacetime in reverse: if you follow the circles you can gain information about possible pasts that could have led to the original event.

Light cones. Credit: University of Pittsburgh.

In order to predict events, such as the next frame in a movie, AIs are typically fed millions of clips that allow the algorithm to generate new frames that are similar to the preceding ones, ultimately picking the one that best suits the context. That works well enough for some applications such as bionic limbs developed by the likes of Tej Kohli or Open Bionics, but there’s always room for improvmeent.

Taking inspiration from light cones, researchers led by Athanasios Vlontzos at Imperial College London used two datasets, one consisting of handwritten digits, the other showing people walking and waving their arms in a time series, to generate frames similar to the ones in the dataset.

What sets this approach apart from other algorithms is that frames from the datasets were not shown in sequence. Instead, the AI grouped frames by similarity and then used the light-cone algorithm to draw a boundary.

Although this algorithm was not trained to fill in the blanks in the sequence, it did a good job of predicting which frames came next.

“We utilize the concept of a light cone from special relativity to restrict and traverse the latent space of an arbitrary model. We demonstrate successful applications in causal image synthesis and future video frame prediction on a dataset of images. Our framework is architecture- and task-independent and comes with strong theoretical guarantees of causal capabilities,” the researchers wrote.

AIs that can predict causal events like humans would be highly desirable for a number of applications. Self-driving cars would be more accurate at predicting the motion of a cyclist or other vehicles on the road, thereby reducing traffic-related accidents, same goes for industrial robots that interact with human workers on the assembly line. In medicine, causal algorithms would be more sensible at recommending treatments that need to run their course step by step.

The light cone algorithm was described in a study published in the preprint server arXiv.

Article updated on September 7 for clarity. A paragraph describing how light cones are represented incorrently stated that a reverse cone indicates possible pasts ‘triggered by the original event’ rather than ‘possible pasts that could have led to the original event’.

The Cosmological Constant. Einstein's 'greatest blunder' is an expanding problem

The Cosmological Constant: How Einstein’s ‘greatest blunder’ became an expanding problem

The Cosmological Constant. Einstein's 'greatest blunder' is an expanding problem
The Cosmological Constant–represented by the Greek letter lambda–Einstein’s ‘greatest blunder’ is an expanding problem

The cosmological constant is a problem. Actually, that is an understatement, the cosmological constant was a problem, is a problem, and may always be a problem. To understand why this little constant has caused so stress for cosmologists, it is necessary to divide its history into two very distinct eras, and perhaps then, consider its future. Thus this introduction is to the cosmological constant what Marley’s ghost was to Scrooge. A warning of a trip through its history, its future, and perhaps, offering it a hint of redemption. 

The current theoretical estimations of the cosmological constant differ from the experimental measurements by such a shocking and huge magnitude, that it has often been referred to as ‘the worst prediction in the history of science.’ And as these values are provided by the non-unitable fields of physics quantum field theory and general relativity, respectively, finding an agreeable value for the constant, or even the reason why the values diverge so greatly could be the key to finding a quantum theory of gravity. 

Before embarking on that trip, let’s first meet our Scrooge — the central character of this potential redemption arc. The cosmological constant represents now, something different than it did when it was first introduced.

The easiest way to understand what it means now is by considering dark energy — the hypothetical force driving the Universe apart — to be the physical manifestation of the cosmological constant. As such, again solving the mystery of the cosmological constant could be the key to discovering exactly what dark energy is, and, in turn, discovering what the final fate of the Universe will look like. 

In many ways, the cosmological constant can be considered as a ‘counterpoint’ to gravity, a value for a force that repels as gravity attracts. This is something that links its present with its past. 

Einstein’s biggest blunder?

It’s sometimes mind-boggling to consider that the biggest problem in modern physics is a hangover from 1917. With all the advancements we have made in terms of understanding our Universe, how can this one little element, provide such a challenge?

The key to understanding why the cosmological constant has been such a thorn in the side of physics is understanding how it confounded the greatest physicist who ever lived — Albert Einstein. 

The cosmological constant, often represented by the Greek letter Lambda (λ), was added to Einstein’s field equations to balance the force of gravity. This is explainable by the fact that if only gravity acts in the Universe — an attractive force — then how can it not be shrinking? How did it form at all, if all matter is naturally drawn together?

Einstein felt that his field equations needed a repulsive factor to counter-balance the attractive force of gravity, and if this sounds like an ad-hoc solution — a fudge factor — that is because it was. Not only was the cosmological constant something of an arbitrary ‘fix’ it also made the field equations unstable. A slight variation should, according to these revised equations, cause the Universe to fall out of its static state. For example, if separation increases, gravitational attraction decreases and repulsion increases — resulting in further deviation from the initial state.  

Einstein was influenced to introduce the cosmological constant by the fact that the scientific consensus in 1917 was that the Universe was static — neither expanding nor contracting — and Einstein agreed with the consensus. Unfortunately, his field equations disagreed.

The field equations of general relativity did not allow for a static universe, predicting that the Universe should either be contracting or expanding. Thus, the first role that the cosmological constant was to provide negative pressure to counterbalance gravity. The argument underpinning this addition was that even empty space-time has a gravitational influence, a so-called vacuum energy. 

For twelve years, the cosmological constant remained in the field equations, fulfilling this role. But, trouble was brewing on the horizon, and by ‘the horizon,’ we mean the most distant horizon imaginable — the very edge of the Universe. 

Our understanding of the cosmos was about to change forever…

Hubble trouble — an expanding problem

It may be slightly difficult to believe today, but just 90 years ago we understood far less about the cosmos and the Universe around us. The idea of billions of galaxies outside of our Milky Way was almost undreamt of, as was the idea that these galaxies could be receding from each other as space expands. Likewise, the idea that the Universe could have inflated from an infinitely small point — the concept of the ‘Big Bang’ was pure fantasy. 

In 1929, Edwin Hubble’s seminal paper “A relation between distance and radial velocity among extra-galactic nebulae” would change this thinking forever. Hubble showed that the Universe was not infinite in either its reach or its age. In this relatively short paper, the astronomer presented the first observational evidence that distant galaxies are moving away from us, and further to this, the more distant they are, the more rapidly they recede. 

A simple sketch of a graph showing velocity against distance for distant galaxies revealed a profound insight about the Universe around us (Hubble, 1929) 

What Hubble was unaware about when he published his 1929 paper, was that other physicists had already provided solutions to Einstein’s field equations that his results confirmed. Both Alexander Friedmann, a Russian cosmologist, and Georges Lemaitre, a Catholic priest, mathematician, astronomer, and professor of physics, had provided solutions to the field equations that showed an expanding Universe. Even with this theoretical basis, Einstein wanted to see this evidence for himself, not being quite ready to scrap his cosmological constant and accept a non-static universe.

I need to see this for myself. Einstein visits the Mount Wilson observatory and meets Hubble. (CalTech)

On January 29th 1931, Edwin Hubble met Einstein at Mount Wilson, taking him to see the famous 100-inch telescope where the astronomer had made the observation that doomed the first iteration of the cosmological constant. Shortly after Einstein published his first paper with revised field equations omitting lambda. He deemed the constant ‘redundant’ as relativity could explain the expansion of the Universe without it.

George Gamow, physicist and cosmologist, remarked in a 1956 Scientific American article and then later in his autobiography, that Einstein had confided in him that the introduction of the cosmological constant was his ‘biggest blunder.’ The remark has now passed into the lore surrounding the great scientist, and even though we can’t be certain that he actually said it, he very likely believed it. 

Yet, despite Einstein’s dismissal of the cosmological constant, many physicists were not quite ready to give up on this element of general relativity just yet. They argued without a cosmological constant term, models of the evolution of the cosmos would predict a universe with an age younger than the oldest stars within it. 

And though Einstein was unmoved by this argument, in 1998, 43 years after his death, the cosmological constant and the symbol that represents it would be rescued from obscurity and drafted to explain a new, but related conundrum.

The modern cosmological constant and dark energy

There is something of a pleasing irony about the fact that it was the discovery of the Universe expanding that consigned the cosmological constant to the dustbin and it was the equally important discovery that this same expansion is accelerating that saved it. 

During the cosmological constant’s ‘downtime’ our understanding of the origins of the Universe underwent a revolution. Cosmologists were able to deduce that regions of the Universe now separated by unimaginable distances were once in close proximity. The idea that the Universe expanded in a period of rapid inflation from an infinitely small point — though this point would become progressively smaller — to the vast entity we see today was accepted and termed the ‘Big Bang.’ 

Yet the commonly held idea that this period of rapid inflation had given way to a more steady rate was challenged in 1998.

Three distant Type Ia supernovas, as observed by the Hubble Space Telescope in 1997. Since Type Ia supernovas have the same luminosity, they are used in measuring dark energy and its effects on the expansion of the universe. The bottom images are details of the upper wide views. The supernovas at left and centre occurred about five billion years ago; the right, seven billion years ago. (Photo AURA/STScI/NASA/JPL (NASA photo # STScI-PRC98–02a-js))

In the mid-nineties, cosmologists had used solutions to the field equations of general relativity to assess the geometry of the Universe, determining that it is flat. This left some problems to be addressed. In a flat universe, we should have a matter/energy density which matches a value known as the critical density. Yet all the matter and energy that we can observe accounts for only a third of this value. Further to this missing energy problem, the flat universe suffers from a cosmic age problem, why do the oldest stars appear older than the predicted age of a flat universe?

The expansion of the Universe as depicted in this image may have forced the cosmological constant into a hiatus, but it was out for good. C. FAUCHER-GIGUÈRE, A. LIDZ, AND L. HERNQUIST, SCIENCE 319, 5859 (47)

One solution to these problems could arise if the Universe is filled with a fluid of negative pressure, a ‘dark energy’ that accounts for the energy deficit and provides accelerated expansion that would neatly explain the Universe taking a longer time to reach its current state. To measure this changing rate of expansion researchers would need a tool that could measure extraordinarily large cosmic distances — as large as 5 billion light-years, in fact. 

In 1998, astronomers found evidence of such a theoretical fluid from observations of the redshifts of distant yet incredibly, bright Type Ia supernovae — often referred to as ‘standard candles’ due to their reliability in measuring cosmic distances. And of course, scientists would need a symbol to represent dark energy within their equations. As cosmology already had such a representation of negative pressure, why not simply resurrect it and place it back in the equations of general relativity?

But, they should not have been surprised, given its history, that re-employing the cosmological constant would bring new problems.

Still crazy after all these years…

The new issues with the cosmological constant very much reflect the major hurdles within physics as it currently stands. Whilst revolutions were being made on incredibly large scales thanks to cosmology, our understanding of the incredibly small was burgeoning thanks to the success of quantum physics. 

The problem arises from the fact that quantum physics — and in particular quantum field theory — and general relativity can not be reconciled, there is no theory of quantum gravity. 

If we are creative and slightly whimsical, we could perhaps give this struggle to unify these disciplines a value — 10¹²¹ — the magnitude between which the quantum field theory’s theoretical prediction of the cosmological constant and the observed value provided by cosmology. This massive disparity–often described as ‘the worst theoretical prediction in the history of science’– arises from the fact that quantum field theory predicts that virtual particles are popping in and out of existence at all times — an idea that may sound ridiculous but has been experimentally verified — even in the vacuum of space. Thus particles should have a measurable effect on the vacuum energy driving the expansion of the Universe but such an effect isn’t measured by cosmologists observing the redshifts of Type Ia supernovae.

Virtually impossible: A pair of virtual particles, one with a positive charge and one with a negative charge briefly come into existence and disappear. Such particles should have an effect on the expansion of the Universe according to quantum field theory.

There are, of course, solutions. Dark energy could be associated with some, as yet undiscovered field, which fills space in a way similar to that of the Higgs field from which the recently discovered Higgs boson emerges. Or perhaps other constants that occupy an unchallenged place in our equations of gravity aren’t constants at all but vary with time, as University of Geneva cosmologists Lucas Lombriser suggests. More extreme solutions lie in the suggestion that Einstein’s theory of gravity must be modified to account for dark energy — all though this family of theories, MONDS, are steadily moving out of favour within the physics community.

Whatever the solution to this problem is, it has a remarkable impact on the future of the Universe. Determining the true value of the cosmological constant and the strength of dark energy driving this accelerating expansion will ultimately tell us if the Universe’s final fate is to rip apart or violently crush together. 

Whether by ‘Big Rip’ or ‘Big Crunch’ the Universe’s end will be determined by the value of the cosmological constant. A value that still continues to evade us and confuse us as much as it did Einstein.


Ta-Pei Cheng, Relativity, Gravitation and Cosmology, Oxford Press, (2010).

Robert Lambourne, Stephen Serjeant, Mark Jones, An Introduction to Galaxies and Cosmology, Cambridge Press, (2015).

Frank Close, The New Cosmic Onion, Taylor &Francis, (2007).

Cormac O’Raifeartaigh, Investigating the legend of Einstein’s “biggest blunder”, Physics Today, (2018)

Matts Roos, Introduction to Cosmology, Wiley, (2003). 

Hard work, not genius, is what should inspire the next generation of scientists

Like in any line of work, good role models and mentors are essential motivators that predict career success. However, it’s often easy to lose track of the bigger picture and think that you’ll never be good enough for a career in science. After all, that’s for geniuses and nerds, some might say — except that’s not true at all.

Yes, working in science is demanding, but it just means that you have to work hard to achieve success, whether it’s graduating, publishing papers, or making a Nobel Prize-worthy breakthrough.

In other words, perspective can be everything. Case in point, psychologists at Penn State, William Paterson University, New York University, and Columbia University published a new study showing that scientists who are known for their hard work — like Thomas Edison — are more inspiring than those typically recognized for their genius talent, like Albert Einstein.

“There’s a misleading message out there that says you have to be a genius in order to be a scientist,” said Daniel Hu, a doctoral student at Penn State and co-author of the new study. “This just isn’t true and may be a big factor in deterring people from pursuing science and missing out on a great career. Struggling is a normal part of doing science and exceptional talent is not the sole prerequisite for succeeding in science. It’s important we help spread this message in science education.”

Hu and colleagues performed three experiments involving 176, 162, and 288 young participants each. While previous studies that investigated the impact of effective models focused on their qualities, the new study looked at how aspiring scientists’ own beliefs might affect their motivation.

In the first study, the participants read the same story about the struggles a scientist had to overcome during his career. Half of the volunteers were told the story was about Einstein, while the other half believed it was about Edison.

Those who were told the story was about Einstein were more inclined to believe talent was the reason behind his success despite the fact that the two stories were identical. Meanwhile, those who thought the story was about Edison were more motivated to solve a series of math problems.

“This confirmed that people generally seem to view Einstein as a genius, with his success commonly linked to extraordinary talent,” Hu said. “Edison, on the other hand, is known for failing more than 1,000 times when trying to create the light bulb, and his success is usually linked to his persistence and diligence.”

In the second study, the participants were again asked to read a different story about the struggles of an up-and-coming scientist. Half were told it was about Einstein, while the other half was informed that the story was about Mark Johnson, a fabricated name that was unfamiliar to them. Those who thought the story was about the unfamiliar scientist were less likely to believe natural brilliance was necessary to succeed in science and were more likely to score better on math problems.

In the final study, the participants pitted the two types of stereotypical role models — genius for Einstein and hard work/perseverance for Edison — against a control. In this case, the control was an unknown scientist.

Like in the previous studies, the participants read a story that was attributed to Einstein, Edison, or some unknown scientist they had never heard of before. Compared to the control, Edison motivated the participants while Einstein actually demotivated them.

“The combined results suggest that when you assume that someone’s success is linked to effort, that is more motivating than hearing about a genius’s predestined success story,” Hu said. “Knowing that something great can be achieved through hard work and effort, that message is much more inspiring.”

This sort of insight could prove useful in an educational setting when designing programs meant to inspire students of all ages. Young people and children, in particular, are very susceptible to role models and often mimic those around them whom they look up to. The key message has to be that struggling for success is the norm, not an exception.

The findings appeared in the journal Basic and Applied Social Psychology.

Credit: Max Pexels.

Mindbending ‘Spooky Action at a Distance’ experiment involving 100,000 gamers proves Einstein wrong

Credit: Max Pexels.

Credit: Max Pexels.

It’s hard to find a stranger, more exotic phenomenon in physics than quantum entanglement — the idea that two entangled particles can influence each other’s state instantly even when they’re light-years apart. The whole idea is so baffling that Einstein famously referred to it as ‘spooky action at a distance.’

The physicist had a lot of qualms with quantum entanglement, such as the fact that it contradicts so-called  “local realism” — the idea that things have properties whether or not you observe them. Now, the most sophisticated experiment of its kind to date has confirmed quantum entanglement, proving Einstein wrong.

The randomness of humanity

The huge international collaboration involved more than 12 teams of researchers in 10 countries as well as 100,000 volunteer gamers. Scientists called the experiment the Big Bell Test — a Bell test is an experiment designed to test the validity of quantum entanglement.

Such tests were first introduced during the 1960s by the Irish physicist John Bell who proposed testing quantum entanglement by comparing randomly chosen measurements, like the polarization of two entangled particles that exist in different locations. If the number of times that the state measurements of the two particles mirror each other goes above a certain threshold, this suggests the separated particles enter their state only at the moment they are measured. The immediate consequence is that the particles can communicate instantly with each other. Spooky, indeed!

At the same time, this behavior contradicts the principle of local realism (upon which classical physics is based) –– the idea that phenomena and objects function irrespective of whether someone’s watching or not.

The problem with Bell tests, however, is that what you choose to measure has to be truly random. Even a computer random generator isn’t truly random, which is why scientists had to think outside of the box to design this experiment. Humans are pretty random and when they collectively number in the thousands, we humans can be unpredictable enough to fulfill the strict criteria for a Bell test.

The physicists recruited a staggering 100,000 people who were invited to play a smartphone game called the Big Bell Quest. Each player had to press two buttons on a screen, with respective values of one and zero. All of these random choices were used by different labs across five continents to select measurement settings for comparing entangled particles. Each lab performed a different experiment using different particles. For instance, single atoms, groups of atoms, photons, and so on.

When all the results were aggregated and compared, they suggested that local realism is not universally valid, confirming spooky action at a distance.

“We showed that Einstein’s worldview of local realism, in which things have properties whether or not you observe them, and no influence travels faster than light, cannot be true — at least one of those things must be false,” Morgan Mitchell, a professor of quantum optics at the Institute of Photonic Sciences in Barcelona told Live Science.

There are two possible explanations of these findings: either our observations actually change the state of the observed or particles are communicating with each other through some unbeknownst means that is yet invisible to us.

“What is most amazing for me is that the argument between Einstein and Niels Bohr, after more than 90 years of effort to make it rigorous and experimentally testable, still retains a human and philosophical element. We know that the Higgs boson and gravitational waves exist thanks to amazing machines, physical systems built to test the laws of physics. But local realism is a question we can’t fully answer with a machine. It seems we ourselves must be part of the experiment, to keep the Universe honest,” Mitchell said in a statement. 

All of this is quite a lot to swallow in one go but, at the end of the day, it’s impressive how far science has come and how much we can learn about the universe if we collaborate. Imagine what one million or one billion minds would be able to achieve when they put their minds to it.

“I also particularly enjoyed the outreach and public involvement side,” said Geoff Pryde from Griffith University in Australia.

“I enjoyed that we gave people an opportunity to do something which influenced how the experiment ran.”

Scientific reference: Challenging local realism with human choices, The Big Bell Test Collaboration, Nature 2018. 

Einstein's two notes on living a quiet and modest life sold for $1.8 million combined. Credit: Barath Tripard/Twitter.

Einstein tipped a Japanese bellboy with notes on living a happy life. They’ve now sold for $1.8 million

Albert Einstein

Credit: Public Domain.

By 1922, the 43-year-old Albert Einstein was already regarded as the most famous physicist alive. At the end of that fateful year, the brilliant scientist was touring Japan for a lecture series for which he was paid 2,000 pounds by his Japanese publisher. On the way from Europe, Einstein learned that he had been awarded the Nobel Prize in physics “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.” News traveled fast and his lectures gathered crowds of thousands of Japanese looking to catch a glimpse of a Nobel laureate in person.

A different kind of tip

Einstein's two notes on living a quiet and modest life sold for $1.8 million combined. Credit: Barath Tripard/Twitter.

Einstein’s two notes on living a quiet and modest life sold for $1.8 million combined. Credit: Barath Tripard/Twitter.

One night, exhausted by all the publicity, Einstein was gathering his thoughts in his room at the Imperial Hotel in Tokyo. A messenger knocked on his door with a delivery. According to AFP, the messenger either “refused to accept a tip, in line with local practice, or Einstein had no small change available.” Instead, Einstein handed the man two notes scribbled with his words of wisdom on how to live a happy life.

On Tuesday, the two notes sold for $1.8 million combined at a Jerusalem auction house.

The first note simply stated “a quiet and modest life brings more joy than a pursuit of success bound with constant unrest.” Bidding opened at $2,000 but in only 20 minutes two potential buyers escalated the bid over the phone until it eventually sold for a dazzling $1.56 million. The auction house didn’t expect to earn more than $8,000.

The second note contained a familiar aphorism: “where there’s a will, there’s a way.” This one eventually sold for the more ‘modest’ sum of $240,000.

Both buyers and sellers have chosen to remain anonymous but according to AFP the previous owner of the notes lives in Hamburg, Germany, and is a relative of the Japanese messenger.

Though short, the two notes possibly open a window into Einstein’s thoughts during a time in his life when things were moving mighty fast. We can infer from his work and early struggles as a patent clerk that Einstein firmly believed “where there’s a will, there’s a way.” The most expensive note also shows that Einstein, though certainly impressed, didn’t let over-night fame get the better of him. Despite his status as the most brilliant living physicist to the end of his days, Einstein never rested on his laurels. The physicist continued to perform ground-breaking science, gave lectures around the world, and was very involved with world peace activism.

“What we’re doing here is painting the portrait of Einstein—the man, the scientist, his effect on the world—through his writings,” said Roni Grosz, the archivist in charge of the world’s largest Einstein collection at Jerusalem’s Hebrew University, in a press release.

“This is a stone in the mosaic.”

One can only wonder, however, what Einstein would have thought of news that his hastened scrambling on living ‘a quiet and modest life’ sold for an obscene amount of money. With a smirk, the physicist might ironically note that people still haven’t learned to listen even a hundred years later. Millions of years might not be enough.

Two merging neutron stars were detected on Aug. 17 in the galaxy NGC 4993m about 130 million light-years from Earth. Credit: NASA.

Why the gravitational waves splashed by the merger of two dying stars spells a revolution in astronomy

Two merging neutron stars were detected on Aug. 17 in the galaxy NGC 4993m about 130 million light-years from Earth. Credit: NASA.

Two merging neutron stars
were detected on Aug. 17 in the galaxy NGC 4993m about 130 million light-years from Earth. Credit: NASA.

In a galaxy far, far away, some 130 million years ago, two neutron stars smashed into each other in an event called a ‘kilonova’ event, which astronomers have just witnessed for the first time. The collision sent out a burst of gamma rays and ripples through space-time known as gravitational waves. On August 17, both signals, which travel at the same speed of light, reached Earth, where they were picked up by the LIGO and Virgo detectors in the US and Italy, respectively. This was the first time signals originating from the same source were detected with both traditional telescopes that detect light, and gravitational wave detectors that sense wrinkles in the fabric of space-time.

A milestone in astronomy

The existence of gravitational waves, which were first predicted by Einstein’s Theory of General Relativity about a hundred years ago, was confirmed only last year. The event was recorded by the Laser Interferometer Gravitational-Wave Observatory (LIGO), whose founders were awarded this year’s Nobel Prize in Physics. 

Gravity waves are essentially ripples in the fabric of spacetime that are generated by interactions between very massive accelerating cosmic objects, such as neutron stars or black holes. Physicists liken gravity waves to the waves generated when a stone is thrown into a pond.

LIGO was founded in 1992, so it took them 25 years to prove their existence. That’s because detecting a gravity wave is no easy feat. To spot gravitational waves directly for the first time, scientists had to measure a distance change 1,000 times smaller than the width of a proton using interferometers, which are essential mirrors placed 4 kilometers apart.

In the case of the September 14, 2015 observation which was announced on February 11, 2016, scientists observed gravitational waves produced by the collision of two black holes. This week’s announcement marks not one but a number of unprecedented observations in science. This was the first time astronomers witnessed a new type of nova called a kilonova, which is a large explosion following the merger of two neutron stars. A neutron star is the collapsed core of a large star — they’re the smallest and, at the same time, densest stars we know of. Kilonovas are 1,000 times brighter than a typical nova, which is already intense. Their existence was purely theoretical until this summer.

The biggest hype around this week’s announcement is that both light and gravitational waves were observed from the same source. At 8:41 a.m. Eastern time on August 17, a gravitational wave hit the Virgo detector in Italy and, 22 milliseconds later, set off the LIGO detector. Later, over several days, the source was detected from its light emissions at many different wavelengths, ranging from gamma-rays through to radio waves. 

The black dot on the right shows where the kilonova signal comes from. The left image shows the same patch of the sky taken by the Hubble telescope in April, before the two neutron stars collided. Credit: Swope Supernova Survey, UC Santa Cruz.

The black dot on the right shows where the kilonova signal originated. The left image shows the same patch of the sky in an image taken by the Hubble telescope in April before the two neutron stars collided. Credit: Swope Supernova Survey, UC Santa Cruz.

Within 24 hours of the initial readings, telescopes all over the world were directed towards the same patch of the sky. Astronomers eventually managed to find the source around a galaxy called NGC 4993, located 130 million light-years away. The event was named Swope Supernova Survey 2017a (SSS17a), after the telescope which first detected it.

At this point, it’s not clear what was left in the wake of the kilonova event. It could be that the two stars merged into a single neutron star or if the two bodies collapsed into a black hole, which can’t be detected directly.

This week’s discovery could revolutionize astronomy, since measuring both optical and gravitational signals from the same source could vastly improve how scientists measure the expansion of the universe. Edwin Hubble first realized in 1929 that the further away you look, the faster galaxies recede from us. By measuring the distance and velocity of a large number of stars, it’s possible to infer the age of the universe. Being able to sense gravitational waves and light from the same source at the same time will enable scientists to keep the error bar low for this estimate. As more and more gravitational waves are detected, scientists hope that within 10 years they’ll be able to determine the age of the universe from these sorts of signals alone, which they can then compare to traditional methods to spot inconsistencies.

All in all, this was an amazing week in science, with more than a dozen published papers about various aspects of SSS17a. We’ve likely only seen a glimpse of what gravity waves can teach us.

gravitational lensing

Another Einstein predication is confirmed by scientists: gravitational lensing measures star’s mass for the 1st time

In an unprecedented new study, astronomers working with the Hubble Space Telescope have measured the mass of a white dwarf star using a cosmic phenomenon first predicted by Albert Einstein. The technique is essentially centered around an optical illusion called gravitational lensing. For more than 100 years, scientists have proposed that it’s possible to precisely measure a star’s mass using this quirk of General Relativity, though Einstein himself doubted it. Finally, the debate is put to rest with this breakthrough study.

Zooming in

Famed physicist Albert Einstein predicted, as a result of his Theory of General Relativity, that whenever light from a distant star passes by a closer object, gravity acts like a magnifying lens bending the distant starlight but also brightening it. This effect has been documented extensively around very massive structures such as galaxies. Captioned below is the great galaxy cluster Abell Cluster 2218. Notice the giant, stretched arcs? Those are actually background galaxies that get distorted and magnified by the giant cluster which bends the light. That’s analogous to how normal lenses such as the ones in a magnifying glass or a pair of spectacles work by bending light rays that pass through them in a process known as refraction, in order to focus the light somewhere (such as in your eye). In fact, astronomers often use gravitational lensing as a natural telescope, to great effect.

gravitational lensing

Image credit: ESA, NASA, J.-P. Kneib and Richard Ellis.

What we’re looking at is called strong gravitational lensing, which is very rare because it implies a fortuitous alignment between a foreground mass and a background galaxy. To understand gravitational lensing we need to go back to Einstein’s theory of general relativity which posits that space is not fixed. Instead, it’s merged with time in a four-dimensional continuum called space-time which is morphed by gravity. Massive objects like a black hole or star create curves in space-time much like a bowling ball causes a dent if you place it on a mattress. It follows that if a ray of light passes near such a massive object, it will follow the distorted curve in space-time and veer away from its straight path.

The deflection directs more light to the observer causing background objects to become brighter. Sometimes the effects create a ring of bright light around the foreground object which scientists refer to as an Einstein right.

The schematic below explains in graphic detail how it all works.

Credit: Starts with a bang!

Credit: Starts with a bang!

In 1919, measurements of starlight curving around a total eclipse of the Sun provided one of the first convincing proofs of Einstein’s general theory of relativity. But in a 1936 article in the journal Science, Einstein added that because stars are so far apart “there is no hope of observing this phenomenon directly.” Even Einstein can be wrong though.

An international research team directed by Kailash C. Sahu found it is possible to measure the extremely small displacement caused relative light objects like stars (light compared to a black hole or galaxy) using sensitive instruments mounted on the Hubble Space Telescope. They did so for a white dwarf star called Stein 2051 B located only 18 light-years away from Earth. This star caused a displacement of only 2 milliarcseconds on the plane of the sky, or about equal to the width of a quarter seen from 1,500 miles (2,400 kilometers) away. At such a resolution, it’s no wonder Einstein deemed the feat almost impossible given the technology available during his time.

“Einstein would be proud. One of his key predictions has passed a very rigorous observational test,” said Terry Oswalt of Embry-Riddle Aeronautical University, who was not involved in the research.

The gravity of the white dwarf star warps space and bends the path of light from a more distant object. Credit: ESA/Hubble & NASA

The gravity of the white dwarf star warps space and bends the path of light from a more distant object.
Credit: ESA/Hubble & NASA


This is the first report of  “gravitational microlensing” by a star other than the sun. The discovery required eight measurements between October 2013 and October 2015 of the shifts in the apparent position of a distant star as its light was deflected around the white dwarf star Stein 2051 B.

“The ring and its brightening were too small to be measured, but its asymmetry caused the distant star to appear off-center from its true position,” Oswalt says. “This part of Einstein’s prediction is called ‘astrometric lensing’ and Sahu’s team was the first to observe it in a star other than the Sun.”

During the close alignment, the distant starlight appeared offset by about 2 milliarcseconds from its actual position. This deviation is so small that it is equivalent to observing an ant crawl across the surface of a quarter from 1,500 miles away. From this measurement, astronomers calculated that the white dwarf’s mass is roughly 68 percent of the sun’s mass. Credit: NASA, ESA, and K. Sahu (STScI) .

During the close alignment, the distant starlight appeared offset by about 2 milliarcseconds from its actual position. This deviation is so small that it is equivalent to observing an ant crawl across the surface of a quarter from 1,500 miles away. From this measurement, astronomers calculated that the white dwarf’s mass is roughly 68 percent of the sun’s mass. Credit: NASA, ESA, and K. Sahu (STScI) .

The observation revealed Stein 2051 B has a mass that is about two-thirds that of the sun, indicating it formed from a star about 2.3 times the mass of the sun. Previously, another method measured the white dwarfțs mass to 0.5 times the mass of the sun, which didn’t sit well with what we know about white dwarf formation.

“This new tool for determining masses will be very valuable as huge new surveys uncover many other chance alignments over the next few years,” Oswalt said.

“At least 97 percent of all the stars that have ever formed in the Galaxy, including the Sun, will become or already are white dwarfs – they tell us about our future, as well as our history,” the physicist concluded.

Journal reference: K.C. Sahu el al., “Relativistic deflection of background starlight measures the mass of a nearby white dwarf star,” Science (2017). science.sciencemag.org/cgi/doi/10.1126/science.aal2879

How Albert Einstein broke the Periodic Table

In a study published in the January 19, 2016 issue of the Journal of the American Chemical Society (JACS), scientists at Tsinghua University in China confirmed that something very unusual is happening inside extremely heavy atoms, causing them to deviate from their expect chemical behavior predicted by their place on the Periodic Table of Elements. Due to the velocity of electrons in these heavy elements getting so close to the speed of light, the effects of special relativity begin to kick-in, altering the chemical features observed.

The study shows that the behavior of the element Seaborgium (Sg) does not follow the same pattern as the other members of its group, which also contain Chromium (Cr), Molybdenum (Mo), and Tungsten (W). Where these other group members can form diatomic molecules such as Cr2, Mo2, or W2, using 6 chemical bonds, diatomic Sg2 forms using only 4 chemical bonds, going unexpectedly from a bond order of 6 to a bond order of only 4. This is not predicted by the periodic nature of the table, which itself arises from quantum mechanical considerations of electrons in energy shells around the nucleus. So what’s happening here? How does relativity throw off the periodic pattern seen in our beloved table of elements?

The Periodic Table of elements was initially conceived by Dmitri Mendeleev in the mid-19th century, well before many of the elements we know today had been discovered, and certainly before there was even an inkling of quantum mechanics and relativity lurking beyond the boundaries of classical physics. Mendeleev recognized that certain elements fell into groups with similar chemical features, and this established a periodic pattern to the elements as they went from light weight elements like hydrogen and helium, to progressively heavier ones. In fact, Mendeleev could predict the very specific properties and features of, as yet, undiscovered elements due to blank spaces in his unfinished table. Many of these predictions turned out to be correct when the elements filling the blank spots were finally discovered. See figure 1.


Mendeleev's 1871 version of the periodic table. Blank spaced were provided where predicted new elements would be found.

Figure 1.   Mendeleev’s 1871 version of the periodic table. Blank spaced were provided where predicted new elements would be found.


Once quantum theory was developed in the early 20th century, the explanation for the periodic behavior of the table became apparent. The electrons in the atom are arranged in orbital shells around the nucleus. There are several different orbital types, again based on predictions from quantum mechanics, and each type of orbital can hold only a specified number of electrons before the next orbital has to be used. As you go from top to bottom in the Periodic Table, you use orbitals of progressively higher energy levels. Periodic behavior arrises because, although the energy levels keep getting higher, the number of electrons in each orbital type are the same for each group, going from top to bottom. See figure 2.


Figure 2. Group 1 as an example of a group in the Periodic Table. As the group goes from top to bottom the energy levels get higher and the elements get heavier.

Figure 2.   Group 1 as an example of a group in the Periodic Table. As the group goes from top to bottom the energy levels get higher and the elements get heavier.


The other great area of physics developed in the early 20th century was relativity, which didn’t seem to have much importance on the scale of the very small. Albert Einstein published his ground breaking paper on Special Relativity (SR) in 1905, which described the effects on an object moving close to the speed of light. In 1915 he developed the General Theory of Relativity (GTR), describing the effects due to a massive gravitational field. It is SR that becomes an important consideration in the very heavy elements due their electrons reaching velocities at a significant percentage of the speed of light.

Einstein showed that as the velocity of an object approaches the speed of light its mass increases. This effect is too small to be noticeable at everyday speeds, but becomes pronounced near light speed. It can also be shown that the velocity of an electron in orbit around an atom, is directly proportional to the atomic number of the atom. In other words, the heavier the atom, the faster its outer electrons are moving. For the element hydrogen, with atomic number 1, the electron is calculated to be moving at 1/137 the speed of light, or 0.73% of light speed. For the element gold (Au) with atomic number 79, the electrons are moving at 79/137 the speed of light, or 58% of light speed, and for Seaborgium (Sg) with atomic number 106, the electron is going at an impressive 77% of light speed. At these speeds the crazy effects of special relativity kick-in making the electron mass significantly heavier than it is at rest. For gold this makes the electron 1.22 times more massive than at rest, and for Seaborgium the electron’s mass comes out to be 1.57 times the electron rest mass. This, in turn, has an effect on the radius of the electron’s orbit, squeezing it down closer to the nucleus.

Some relativistic effects have already been known for certain heavy elements. The color of gold, for instance, arises due to the effects of relativity acting on it’s outer electrons, altering the energy spacing between two of it’s orbitals where visible light is being absorbed, and giving gold it’s characteristic color. If not for these relativistic effects, gold would be predicted to appear whitish.

For the elements in Group 6 of the Periodic Table (Cr, Mo, and W) (see Figure 3.) that were studied in the JACS article, they each have five d-orbitals and one s-orbital capable of forming bonds with another atom. Sg breaks the periodic pattern because it’s highest energy s-orbital is so stabilized by the effects of it’s relativistically moving electron, it doesn’t contribute to bonding. Due to the intricacies inherent in molecular orbital theory, this drops the number of bonding orbitals from 6 in Cr, Mo, and W, to only 4 in Sg (even though Sg is a group 6 member). It also means that the bond between Sg and Sg in the Sg2 molecule is 0.3 angstroms longer than expected, even though the Sg radius is only 0.06 angstroms bigger than W. If relativity didn’t have an effect, then the Sg2 molecule would be joined together by 6 orbital bonds, like any respectable Group 6 element should be! The same effect was also found in the Group 7 elements, with Hassium (Hs) showing the drop in bond order due to relativistic effects, just as Sg.


Figure 3. A modern version of the Periodic Table of Elements. Notice the Group 6 elements Cr, Mo, W, and Sg.

Figure 3.   A modern version of the Periodic Table of Elements. Notice the Group 6 elements Cr, Mo, W, and Sg.


The periodic table of elements is an impressive scientific achievement, who’s periodicity reveals an underlying order in nature. While this periodicity works remarkably well, the few exceptions to the rule also uncover important principles at work. Einstein’s theory of relativity breaks the periodic table in some interesting and unexpected ways. It’s the very heavy elements on the chart that don’t show good “table” manners, thanks to Einstein.


Journal Reference and other reading:
1. Relativistic Effects Break Periodicity in Group 6 Diatomic Molecules Yi-Lei Wang, Han-Shi Hu*, Wan-Lu Li, Fan Wei, and Jun Li*
Department of Chemistry & Key Laboratory of Organic Optoelectronics and Molecular Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China  J. Am. Chem. Soc., 2016, 138 (4), pp 1126–1129 DOI: 10.1021/jacs.5b11793 Publication Date (Web): January 19, 2016

2. Relativistic effects in structural chemistry Pekka Pyykko Chem. Rev., 1988, 88 (3), pp 563–594 DOI: 10.1021/cr00085a006 Publication Date: May 1988

3. Why is mercury liquid? Or, why do relativistic effects not get into chemistry textbooks? Lars J. Norrby J. Chem. Educ., 1991, 68 (2), p 110
DOI: 10.1021/ed068p110 Publication Date: February 1991

galileo pisa

Dropping weights in space to test Einstein’s general relativity

Extraordinaire experimental physicist  Galileo Galilei allegedly climbed hundreds of step to reach the top of the Leaning Tower of Pisa’s – which wasn’t so leaned as it is today – and dropped  pairs of balls of different weights and materials onto the ground. The experiment was meant to prove in front of the crowd of scholars and students gathered in front of the tower that regardless of an object’s mass, whether it’s wood or lead, all objects fall with the same acceleration. If there were no friction, a feather and a cannon ball would reach the ground at the same time. It’s unclear if the whole story is merely a legend or not, but needless to say it’s an inspiring anecdote. Now, Galileo’s experiment will be adapted in ways the great classical physicist could never have imagined, as the ultimate test for one of Einstein’s general relativity caveats.

galileo pisa

Image: North Country Public Radio

Called the Drag-Compensated Micro-Satellite for the Observation of the Equivalence Principle (MicroSCOPE), the experiment will contain two free-floating weights of different materials and will monitor whether one feels a stronger tug from Earth’s gravity than the other. If this were to happen, it would violate the mass equivalence principle which posits inertial mass and gravitational mass are absolutely one of the same time, independent of material composition or mass. The mass equivalence principle is a key assumption made by Einstein to draft his theory of general relativity which states acceleration and gravity are essentially the same thing.

One mass

There are actually several types of mass. The kind that most corresponds to our intuitive sense of mass is inertial mass which describes resistance to acceleration. If you push two objects of different inertial masses with the same force, the one with the less inertial mass will accelerate more. A two tonne truck has more resistance than a wheel chair. Another type of mass is known as gravitational mass. Gravitational mass is what (in Newton’s gravity) causes the gravitational attraction between objects. When you step on a scale in the morning, you are measuring your gravitational mass. The third type of mass is known as relativistic mass. This stems from Einstein’s theory of special relativity and the equivalence of mass and energy (the famous E equals m c squared). In that famous equation, E is the energy of a particle, and c is the speed of light. So if you divide the energy of a particle by the speed of light squared, you get a “mass”, known as the relativistic mass of the particle.

MicroSCOPE satellite

MicroSCOPE satellite. Image: CNES/DAVID DUCROSS, 2012

General relativity isn’t completely reconciled with quantum mechanics – the physics of the small scale. Basically, some observed phenomena in quantum mechanics couldn’t be explained by the mass equivalence principle. The team behind MicroSCOPE, thus, want to test mass equivalence with unprecedented precision because even a minute variation between the two masses would mean that the equivalence principle does not apply in all cases.  Spotting a violation would definitely mean that there is some sort of physics beyond Einstein’s theory. This might help physicists make a breakthrough. Otherwise, it could prove equally useful since physicists can finally stop worrying about whether or not the mass equivalence is true or not.

Of course, the mass equivalence has gone through countless tests and experiments – not one proved a violation. The most precise experiment to date was made by Eric Adelberger, a physicist at the University of Washington, Seattle, and colleagues in the Eöt-Wash Group, named after 1800s Hungarian physicist Loránd Eötvös who pioneered the method used by the group. According to Science author Adrian Cho:

“Eötvös used a small dumbbell of weights of different materials suspended horizontally from a thin fiber. Gravity pulls each weight toward the center of Earth. But Earth also spins, so the inertia of the weights creates a tiny centrifugal force that flings them away from the planet’s axis. The sum of the two forces, which align only at the equator, defines the direction “down” for each weight. If the equivalence principle holds, then the centrifugal force on each weight is locked into proportion to the gravitational one, so down is the same for both weights. Then, the dumbbell will rest pointing in any direction.

But if inertial and gravitational mass are different, then the flinging will affect the weights differently and the net force on each one will point in a slightly different direction. “If the equivalence principle is violated, then every material has its own down,” Adelberger says. That difference would cause the dumbbell to twist toward a particular orientation. In 1889, Eötvös saw no such sign and confirmed the equivalence principle to one part in 20 million.”

Of course, today the experiment is a lot more refined. Eöt-Wash researchers have been constantly tweaking the method for the past 25 years. Their current rig consists not of a dumbbell but of a nearly cylindrical shell studded on either side with weights of different materials. Likewise, instead of being based on a static twist, the whole rig rotates. The scientists then just have to look for periodic twisting of the cylinder. Using beryllium and titanium, they found gravitational and inertial mass equal to one part in 10 trillion, as they reported in Physical Review Letters in 2008. The MicroSCOPE will test the equivalence principle to one part in a quadrillion.

The MicroSCOPE satellite will host two cylindrical shells inside: one the size of a toilet paper roll and made of titanium and a smaller one inside it made of platinum-rhodium. If the equivalence principle holds, both will glide on precisely the same orbit. If not, one should slip Earth-ward relative to the other.

According to models made by the MicroSCOPE researchers, the probe has a chance of seeing a strong signal, meaning it might show a violation of the mass equivalence principle. But nothing’s certain until the €200 million mission will reach Earth’s orbit in April 2016 – and not even then.


`Relatively Simple

Book review: “Einstein Relatively Simple: Our Universe Revealed”

`Relatively Simple

Einstein Relatively Simple: Our Universe Revealed
By Ira Mark Egdall
World Scientific Publishing Company, 300pp | Buy on Amazon

In 1687, Isaac Newton published his groundbreaking Philosophiæ Naturalis Principia Mathematica, where he outlined his Three Laws of Motion and law of Universal Gravitation. For more than 300 years these were accepted without question because they predicted sufficiently accurate how mechanical systems would behave. This was the status quo until the beginning of the last century. That’s until Albert Einstein’s seminal papers revolutionized the way scientists think about space and time.

Albert Einstein shook the foundations of physics with the introduction of his Special Theory of Relativity in 1905, and his General Theory of Relativity in 1915. The first paper showed that Newton’s Three Laws of Motion were only approximately correct, breaking down when velocities approached that of light. The second showed  that Newton’s Law of Gravitation was also only approximately correct, since gravity is directly influenced by how strong gravitational fields are.

Today, Einstein is perhaps the most easily recognized scientist in history. His most famous equation E=mc2, which proves the equivalence of mass and energy, is extremely rampant in popular culture, encountered everywhere from TV cartoons to etched baseball caps. Yet, ask most people who share Einstein’s quotes on facebook what does E=mc2 stand for or what his theories of relativity imply, and they’ll shrug. “Einstein’s a genius – I’ll never understand his work,” some might wrongfully say. Well, here’s an Einstein quote to get you started “It’s not that I’m so smart, it’s just that I stay with problems longer.”

However, to understand Einstein’s most fundamental theorems you need not experience the same mental strain Einstein went through. Countless books have been written that seek to explain special and general relativity to the general public, and I’ve yet to found a more reader friendly book on relativity than Ira Mark Egdall’s “Einstein Relatively Simple: Our Universe Revealed.” The whole book is riddled with real life examples that almost anyone can relate to, all set in a humorous tone. Most of all, the language is so clear that even a fifth grader will come to understand relativity – in fact, Egdall hints in one of his chapters how primary school kids will be studying Einstein’s theories just as they do Newton’s today. The intellectual gap between the two views, one classical, the other relativistic, lies more in perception, than in genuine intellectual stress. It’s all relative!

Of course, you’ll find some equations, but they’re well explained physically such that laymen might grasp the essence without becoming lost in the mathematical details. Seasoned readers who aren’t afraid of math and hardcore physics have quite a few annex sections where they can delve deeper into Einstein’s process.

Understanding relativity becomes easier if we understand Einstein too. Filling his shoes, if just for a brief moment, brings us closer to his process, his creative thinking and ultimately grants access to the well of information the great physicist revealed to the world. Egdall follows these thoughts and is sure to fill is on some of Einstein’s most important personal turning points, whether it was his relationship with his parents or wife, or his conflictual episodes with conventional education and academia. All without turning the book into a 2nd rate biography. It stays true to itself – it’s a book on relativity!

All in all, I’d recommend this book to anyone who wants to grasp some of the most important works in modern physics, for ultimately without relativity we would never had learned about the Big Bang, black holes and our view of the universe would have been significantly poorer.

The history of physics in a short, neat animation

Physics is a branch of science that interestingly enough developed out of philosophy, and was thus referred to as natural philosophy up until the late 19th century – a term describing a field of study concerned with “the workings of nature”. Here’s a short, very interesting and nice animation showing a short history of physics, from Galileo to Einstein. Hope you like it – I sure did.

BBC Science Club – Physics from Asa Lucander on Vimeo.


three-dimensional (right) graph shows the relationship between three different velocities: v, u and U, where v is the velocity of a second observer measured by a first observer, u is the velocity of a moving particle measured by the second observer, and U is the relative velocity of the particle to the first observer. (c) Hill, Cox

After extending Einstein’s theory of relativity to greater than light velocities, the laws of physics alter

 three-dimensional (right) graph shows the relationship between three different velocities: v, u and U, where v is the velocity of a second observer measured by a first observer, u is the velocity of a moving particle measured by the second observer, and U is the relative velocity of the particle to the first observer. (c) Hill, Cox

three-dimensional (right) graph shows the relationship between three different velocities: v, u and U, where v is the velocity of a second observer measured by a first observer, u is the velocity of a moving particle measured by the second observer, and U is the relative velocity of the particle to the first observer. (c) Hill, Cox

When last year scientists at CERN reported how neutrinos traveled a few tens of nanoseconds faster than the speed of light, the whole scientific community was left in shock, since it defied even the most elemental restriction of modern-day physics, a cornerstone without which physicists would have to rebuild the Standard Model. Still, some researchers, even after the whole event was disproved on account of a measurement glitch, were intrigued about the possibility of traveling at faster than light speeds; a range of “what ifs” surfaces. Two researchers at the University of Adelaide sought to find out what would happen to Einstein’s special relativity theory if it wasn’t limited by the speed of light, and mathematically described their findings. Apparently, in an environment where velocities greater than the speed of light exist, the laws of physics are dramatically altered.

Einstein’s special relativity theory, first pronounced in 1905, states that speed is relative. A moving observer will register an object’s velocity with a different value than that registered by a stationary observer. Also, special relativity postulates that as your travel with a higher velocity, time dilation occurs. Remember the famous twin paradox? One twin stays on Earth, while the other orbits the planet in spacecraft. After many years, the twin from Earth would have aged more.

Special relativity, however, limits the relative velocity of two objects (A and B) when their speeds approach that of light. Apart from the Newtonian limit, velocities are not additive quantities, so the differential velocity between A and B is not equal to their relative velocity and particularly has a smaller absolute value. However, Professor Jim Hill and Dr Barry Cox in the University’s School of Mathematical Sciences have developed new formulas that allow for travel beyond this limit. Of course, these formulas aren’t practical in the world, but provide an interesting view to a world where faster than light speeds are possible.

“Since the introduction of special relativity there has been much speculation as to whether or not it might be possible to travel faster than the speed of light, noting that there is no substantial evidence to suggest that this is presently feasible with any existing transportation mechanisms,” said Professor Hill.

“Our approach is a natural and logical extension of the Einstein Theory of Special Relativity, and produces anticipated formulae without the need for imaginary numbers or complicated physics,” says Professor Hill.

Their formulas extend special relativity to a situation where the relative velocity can be infinite and can be used to describe motion at speeds faster than light. In this new, imaginary world, the laws of physics are sensibly different, like one might expect. For instance, if a spaceship were to travel at ever-increasing, faster than light velocity, it would lose more and more mass, until at infinite velocity, its mass becomes zero.

“We are mathematicians, not physicists, so we’ve approached this problem from a theoretical mathematical perspective,” said Dr Cox. “Should it, however, be proven that motion faster than light is possible, then that would be game changing.

“Our paper doesn’t try and explain how this could be achieved, just how equations of motion might operate in such regimes.”

Both Cox and Hill have confidence in human ingenuity to surpass the light barrier, as many other breakthroughs managed to overcome other popular beliefs. If this will ever happen, indeed only time will tell. The findings were reported in the journal  Proceedings of the Royal Society A: Mathematical and Physical Sciences.

This digitized image made from a screen shot of a new iPad app, provided Sept. 24, 2012 by the National Museum of Health and Medicine Chicago.

Einstein’s brain: now available on iPad

This digitized image made from a screen shot of a new iPad app, provided Sept. 24, 2012 by the National Museum of Health and Medicine Chicago.

This digitized image made from a screen shot of a new iPad app, provided Sept. 24, 2012 by the National Museum of Health and Medicine Chicago.

After the most recognized physics figure in the world, Albert Einstein, past away on April 18, 1955, the whole world was left in shock, seeing how he was even by then considered the most famous physicist in history. His dying wish was that of being cremated, however an eccentric physician by the name of Thomas Harvey, a Princeton Hospital pathologist, removed Einstein’s brain without any kind of permission, either from the authorities or Einstein’s family. He quickly sliced Einstein’s brain in 200 cubes and left them in formaldehyde for preservation. Now, 57 years after Einstein’s passing, the same slices were sampled, scanned, digitized and made available to general public under the form of an iPad app.

Yup, you’ve heard it right – Einstein’s grey matter is now on iPad, and while some of you might rejoice at the thought of exploring through one of humanity’s greatest minds, some might find it offensive. Whatever may be the case, it’s done and over. Einstein’s brain walk-through was made after 350 brain slices taken from the collection bequeathed to the National Museum of Health and Medicine Chicago by the Einstein family estate in 2010 were digitized.

Now, the view itself is extremely interesting as you might imagine, just like you’d observe the slices by a microscope, however they’re no where near as detailed as modern brain scans via MRI’s, which can render a 3-D model. So, while things like cellular structure and tissue definitions are clearly visible, the developers didn’t highlight which parts of the brain you’re looking at.

Possibly the world’s greatest mind

Was Einstein’s brain different from the typical human one, though? Well, an investigation led by Harvey himself, whose results were subsequently published in the journal Lancet in 1999, found that Einstein’s parietal lobe, the part of the brain associated with our processing of mathematics, language, and spatial understanding, was 15 percent wider then normal. Also, small parts of Einstein’s brain were missing according to Harvey’s slices, like the Sylvian fissure and parts located in the frontal lobe.

According to Sandra Witelson, who worked on the paper, “This unusual brain anatomy may explain why Einstein thought the way he did… Einstein’s own description of his scientific thinking was that words did not seem to play a role. Instead he saw more or less clear images of a visual kind”.

The new iPad app may allow researchers to dig even deeper by looking for brain regions where the neurons are more densely connected than normal, said Dr. Phillip Epstein, a Chicago-area neuroscientist and consultant for the museum

It’s not clear whether these physical discrepancies helped Einstein develop such a powerful intellect, still considering his brain is now freely available to the public – well, sort of, since the app is priced at $9.99 – scientists from all over the world may study it and possibly find hints that suggest a superior mind.

via Wired

Faint galaxy sheds light on the dawn of the Universe – many more to be found

The first galaxies formed very fast after the Big Bang – in cosmic time, that is. It’s estimated that the earliest ones appeared some 500 million years after the Big Bang, a period about which researchers know very little.

How they observed it

Source: The CLASH team/Space Telescope Science Institute

Even though they are typically very bright, such galaxies are quite hard to observe because they are very far away and only a small fraction of their light can make its way towards Earth, a fraction so small it’s almost impossible to pick up. However, the Hubble telescope managed to detect light from a small galaxy emitted just 500 million years post-Big Bang, a period when the Universe was still in its infancy.

The telescope was able to do this thanks to a phenomena called gravitational lensing: basically, when you have an observe (Hubble), a distant source (the galaxy) and a certain distribution of matter (a galaxy cluster for example), the light emitted by the source can be bent and the observer can observe it easier; gravitational lensing is one of the predictions involved by Einstein‘s general theory of relativity. Basically, the massive gravity of the galaxy cluster acts just like a lens.

In this case, astronomer Wei Zheng and colleagues using the Hubble and Spitzer Space Telescopes reported light was magnified 15 times, making it just strong enough to be observed. Even so, the galaxy MACS 1149-JD appeared as a mere blob, and only after repeated measurements were they able to conclude that it is most likely a galaxy.

How they know its age

The Universe is expanding; galaxies produce light with specific spectral properties, based on the stars and gas they contain. Combine these two facts, and you can understand that light emitted by early galaxies was stretched shifting the entire spectrum into a different wavelength range, a phenomenon called cosmic redshift. All electromagnetic types of radiation (light included) have an electromagnetic spectrum – the range of all possible frequencies of electromagnetic radiation. Cosmic redshift means light seen coming from an object that is moving away is proportionally increased in wavelength, or shifted to the red end of the spectrum.

So, using multiple measurements from the Spitzer and Hubble telescope, they estimated that the light was emitted 490-505 million years after the Big Bang. But their conclusions are perhaps even more interesting. Instead of suggesting MACS 1149-JD is a special snowflake, astronomers believe there are many more such galaxies, formed in the same era, the ‘first’ era, just waiting to be discovered.

Scientific article was published in Nature