Tag Archives: singularity

Sir Roger Penrose has been awarded the 2020 Nobel Prize in physics for his work revolutionising our theories regarding black holes and reshaping general relativity. (Robert Lea)

Singularity Minded: The Black Hole Science that Won a Nobel Prize

The 2020 Nobel prize in physics has been jointly awarded to Roger Penrose, Reinhart Genzel, and Andrea Ghez for their contributions to our understanding of black holes — the Universe’s most mysterious and compact objects. Whilst Genzel and Ghez claim their share of the most celebrated prize in physics for the discovery of a supermassive compact object at the centre of our galaxy — an object that we would later come to realize was a supermassive black hole which was later named Sagittarius A* (Sgr A*) — Penrose is awarded his share for an arguably more fundamental breakthrough. 

Sir Roger Penrose has been awarded the 2020 Nobel Prize in physics for his work revolutionising our theories regarding black holes and reshaping general relativity. (Robert Lea)
Sir Roger Penrose has been awarded the 2020 Nobel Prize in physics for his work revolutionising our theories regarding black holes and reshaping general relativity. (Robert Lea)

The Nobel is awarded to Penrose based on a 1965 paper in which he mathematically demonstrated that black holes arise as a direct consequence of the mathematics of Einstein’s theory of General Relativity. Not only this; but for a body of a certain mass, the collapse into a singularity wasn’t just possible, or even probable. If that collapse could not be halted, singularity formation, Penrose argued, is inevitable. 

“For the discovery, that black hole formation is a robust prediction of the general theory of relativity”

The Nobel Commitee awards the 2020 prize in physics to Sir Roger Penrose

The fact that Penrose showed that black holes mathematically emerge from general relativity may seem even more revolutionary when considering that the developer of general relativity — a geometric theory of gravity that suggests mass curves the fabric of spacetime — Albert Einstein did not even believe that black holes actually existed. 

How Black Holes connect to General Relativity (Robert Lea)

It was ten years after Einstein’s death in April 1955 when Penrose showed that singularities form as a result of the mathematics of general relativity and that these singularities act as the ‘heart’ of the black hole. At this central–or gravitational–singularity, Penrose argued, all laws of physics displayed in the outside Universe ceased to apply. 

The paper published in January 1965 — just eight years after Penrose earned his Ph.D. from The University of Cambridge — ‘Gravitational Collapse and Spacetime Singularities’ is still widely regarded as the second most important contribution to general relativity after that of Einstein himself. 

Yet, Penrose wasn’t the first physicist to mathematically unpick general relativity and discover a singularity. Despite this, his Penrose Singularity Theorem is still considered a watershed moment in the history of general relativity. 

Black Holes: A Tale of Two Singularities

“A black hole is to be expected when a large massive body reaches a stage where internal pressure forces are insufficient to hold the body apart against the relentless inward pull of its own gravitational influence.”

Roger Penrose, The Road to Reality

Black holes are generally regarded as possessing two singularities; a coordinate singularity and an ‘actual’ gravitational singularity. Penrose’s work concerned the actual singularity, so named because unlike the coordinate singularity, it could not be removed with a clever choice of coordinate measurement.

That doesn’t mean, however, that the coordinate singularity is unimportant or even easy to dismiss. In fact, you may already be very familiar with the coordinate singularity, albeit under a different name — the event horizon. This boundary marks the point where the region of space defined as a black hole begins, delineating the limit at which light can no longer escape. 

The discovery of the event horizon occurred shortly after the first publication of Einstein’s theory of general relativity in 1915. In 1916, whilst serving on the Eastern Front in the First World War astrophysicist Karl Schwarzschild developed the Schwarzschild solution, which described the spacetime geometry of an empty region of space. One of the interesting features of this solution — a coordinate singularity. 

The coordinate singularity — also often taking a third more official name as the Schwarzschild radius (Rs) — exists for all massive bodies at r =Rs = 2GM/c². This marks the point where the escape velocity of the body is such that not even light can escape its grasp. For most cosmic bodies the Schwarzschild radius falls well within its own radius (r). For example, the Sun’s Rs occurs at a radius of about 3km from the centre compared to an overall radius of 0.7 million km.

Thus, the Schwarzschild radius or event horizon marks the boundary of a light-trapping surface. A distant observer could see an event taking place at the edge of this surface, but should it pass beyond that boundary — no signal could ever reach our observer. An observer falling with the surface, though, would notice nothing about this boundary. 

The passing of Rs would just seem a natural part of the fall to them despite it marking the point of no return. To the distant observer… the surface would freeze and become redder and redder thanks to the phenomena of gravitational redshift — also the reason the event horizon is sometimes referred to as the surface of infinite redshift.

The very definition of a black hole is a massive body whose surface shrinks so much during the gravitational collapse that its surface lies within this boundary. But, what if this collapse continues? When does it reach a central singularity at the heart of the black hole–r= 0 for the mathematically inclined?

Birthing a Black Hole

“We see that the matter continues to collapse inwards through the surface called the event horizon, where the escape velocity indeed becomes the speed of light. Thereafter, no further information from the star itself can reach any outside observer, and a black hole is formed.”

Roger Penrose, The Road to Reality

Penrose and other researchers have found that the equations of general relativity open the possibility that a body may undergo a complete gravitational collapse — shrinking to a point of almost infinite density — and become a black hole.

In order for this to happen, however, a series of limits have to be reached and exceeded. For example, planets are unable to undergo this gravitational collapse as the mass they possess is insufficient to overcome the electromagnetic repulsion between their consistent atoms — thus granting them stability.

What would it take for Earth to become a black hole? (Robert Lea)
(Robert Lea)

Likewise, average-sized stars such as the Sun should also be resistant to gravitational collapse. The plasma found at the centre of stars in this solar-mass range is believed to be roughly ten times the density of lead protecting from complete collapse, whilst the thermal pressure arising from nuclear processes and radiation pressure alone would be sufficient to guarantee a star of low to intermediate-mass stability.

For older, more evolved stars in which nuclear reactions have ceased due to a lack of fuel. It’s a different story. Especially if they have a mass ten times greater than the Sun.

It was suggested as early as the 1920s that small, dense stars — white dwarf stars — were supported against collapse by phenomena arising from quantum mechanics called degeneracy.

This ‘degeneracy pressure’ arises from the Pauli exclusion principle, which states that fermions such as electrons are forbidden from occupying the same ‘quantum state’. This led a physicist called Subrahmanyan Chandrasekhar to question if there was an upper limit to this protection.

In 1931, Chandrasekhar proposed that above 1.4 times the mass of the Sun, a white dwarf would no longer be protected from gravitational collapse by degeneracy pressure. Beyond this boundary— unsurprisingly termed the Chandrasekhar limit — gravity overwhelms the Pauli exclusion principle and gravitational collapse continues unabated.

Cross Section of A Black Hole (©Johan Jarnestad/The Royal Swedish Academy of Sciences)

The discovery of neutrons — the neutral partner of protons in atomic nuclei — in 1932 led Russian theorist Lev Landau to speculate about the possibility 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.

Again, neutron stars would 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.

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 
5000 km roughly that of the Earth. A neutron star of a similar mass though, that would have a radius of about 20km — roughly the size of a city.

By 1939, Robert Oppenheimer had calculated that the mass-limit for neutron stars would be roughly 3 times the mass of the Sun. Above that limit — again, gravitational collapse wins. Oppenheimer also used general relativity to describe how this collapse appears 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.

Straight to the Heart: The Inevitability of the cental singularity

“So long as Einstein’s picture of classical spacetime can be maintained, acting in accordance with Einstein’s equation then a singularity will be encountered within a black hole. The expectation is that Einstein’s equation will tell us that this singularity cannot be avoided by any matter in the hole…”

Roger Penrose, The Road to Reality

For Penrose, the mathematical proof of a physical singularity at the heart of a black hole arising from this complete collapse was not enough. He wanted to demonstrate the singularity and the effects on a spacetime that would arise there. He did so with the use of ‘light cones’ travelling down a geodesic — an unerringly straight line. In the process, he unveiled the anatomy of the black hole. 

Lightcones: A Physicist’s Favorite Tool (Robert Lea)

A light cone is most simply described as the path that a flash of light created by a single event and travelling in all directions would take through spacetime. Light cones can be especially useful when it comes to physicists calculating which events can be causally linked. If a line can’t be drawn between the two events that fits in the light cone, one cannot have caused the other.

We call a line emerging from a lightcone a ‘world-line’–these move from the central event out through the top of the cone–the future part of the diagram. The worldline shows the possible path of a particle or signal created by the event at the origin of the lightcone. Throwing a light cone at a black hole demonstrates why passing the event horizon means a merger with the central singularity is inevitable.

Penrose considered what would happen to a light cone as it approached and passed the event horizon of what is known as a ‘Kerr black hole.’ This is a black hole that is non-charged and rotating. Its angular momentum drags spacetime along with it in an effect researchers call frame dragging.

Far from the black hole, light is free to travel with equal ease in any direction. The lightcones here have a traditionally symmetrical appearance which represents this.

Using Lightcones to Probe Black Holes ((©Johan Jarnestad/The Royal Swedish Academy of Sciences))

However, towards the static limit — the point at which the black hole starts to drag spacetime around with it — the lightcones begin to tip towards the singularity and in the direction of rotation and narrow. Thus the static limit represents the point at which light is no longer free to travel in any direction. It must move in a direction that doesn’t oppose the rotation of the black hole. Particles at this limit can no longer sit still — hence the name static limit.

Yet, despite the fact the dragging effect is so strong, here that not even light can resist it, signals can escape this region — it isn’t the event horizon — but they can only do so by travelling in the direction of the rotation.

Interestingly, Penrose suggests that particles entering the static limit and decaying to two separate particles may result in energy leaching from the black hole in what is known as the Penrose process, but that’s a discussion for another time.

Probing Black Holes with Lightcones (Robert Lambourne/ Robert Lea)
Probing Black Holes with Lightcones (Robert Lambourne/ Robert Lea)

So as our light cone moves toward the event horizon, it begins to narrow and tip. But, something extraordinary happens when it passes this boundary. As long as one is using so-called Swartzchild coordinates, once ‘inside the black hole’ proper, the lightcone flips on its side, with the ‘future end’ of the cone pointed towards the singularity.

This can mean only one thing for the worldline of that event, it points to the central singularity signalling that an encounter with that singularity is evitable.

The Anatomy of a Black Hole

“It is generally believed that the spacetime singularities of gravitational collapse will necessarily always lie within an event horizon, to that whatever happens to be the extraordinary physical effects at such a singularity, these will be hidden from the view of any external observer.”

Roger Penrose, The Road to Reality

Black holes aren’t particularly complex in construction and posses only three properties –mass, electric charge, and angular momentum–but physicists working with light cones were able to determine the layers of their anatomy–and crucially, the bounded surfaces that exist within them.
This is what was revolutionary about Penrose’s concepts, they introduced the concept of bounded surfaces to black holes. 

The structure of a Kerr (rotating) Black Hole. (Robert Lambourne/ Robert Lea)

Looking back on this from an era in which a black hole has been imaged for the first time and gravitational waves are beginning to be routinely measured from the mergers of such objects, it’s important to not underestimate the importance of Penrose’s findings.

Before any practical developments surround black holes could even be dreamed of, Roger Penrose provided the mathematical basis to not just suggest the existence of black holes, but also laying the groundwork for their anatomy, and the effect they have on their immediate environment.

Thus, what Penrose’s Nobel award can really be seen as a recognition of moving these objects — or more accurately, spacetime events — from the realm of speculation to scientific theory.

The first-ever image of a black hole was released 2019 came decades after Roger Penrose demonstrated such spacetime events are inevitable in the ungoverned collapse of a star with enough mass. (Event Horizon Telescope collaboration et al)
The first-ever image of a black hole was released 2019 came decades after Roger Penrose demonstrated such spacetime events are inevitable in the ungoverned collapse of a star with enough mass. (Event Horizon Telescope collaboration et al)

Original research and further reading

Penrose. R., ‘Gravitational Collapse and Space-Time Singularities,’  Physical Review Letters, vol. 14, Issue 3, pp. 57-59, [1965]

Penrose. R., ‘The Road to Reality,’ Random House, 2004

Senovilla. J. M. M., Garfinkle. G., ‘The 1965 Penrose Singularity Theorem,’ Classical and Quantum Gravity, [2015].

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.

Photo: Masayoshi Son. Credit: Corporate Executives.

Japanese billionaire wants to raise $100 billion to be among the first to reach the singularity with a 10,000 IQ computer chip

Photo: Masayoshi Son. Credit: Corporate Executives.

Photo: Masayoshi Son. Credit: Corporate Executives.

Masayoshi Son, the CEO of SoftBank Group, is Japan’s second wealthiest person and a strong believer in the singularity — a sort of point of no return in which human civilization, rules, and technology become incomprehensible to previous generations. Some think the singularity is going to happen when we become immortal, others claim the singularity is the moment humanity becomes a spacefaring species. Most people, however, seem to agree that the singularity will happen right in that moment when artificial intelligence becomes sentient and Son wants to be right in the front row when this happens.

“I really believe this,” he said at a keynote speech at the Mobile World Congress in Barcelona on Monday. The growth in computer ability was “why I acquired ARM,” he said.

Son is not some dimwit and he sure is prepared to put his money where his mouth is. Recently, SoftBank acquired semiconductor and software firm ARM Holdings plc for a reported $32 billion. Son also contributed with a huge stake in a group investment in satellite startup OneWeb Ltd worth $1.2 billion. The plan is to have these investments converge into a chip that has an equivalent rated IQ of 10,000 — but Son’s investments aren’t enough, he reckons, which is why the Japanese billionaire is really upping the stakes.

On October 12, 2016, Son’s Softbank signed a memorandum of understanding with the Public Investment Fund of the Kingdom of Saudi Arabia (“PIF”) under which PIF considers becoming the lead investment partner in a huge fund aimed at developing the required tech for the singularity. Saudi Arabia said it would invest $45 billion over the next five years in the scheme with SoftBank bringing $25 billion to the table. The goal is to scale this fund to the $100 billion mark.

“With the establishment of the SoftBank Vision Fund, we will be able to step up investments in technology companies globally. Over the next decade, the SoftBank Vision Fund will be the biggest investor in the technology sector. We will further accelerate the Information Revolution by contributing to its development,” Son said in a statement.

Next Big Future reports Son is looking to close more deals by the end of the month for his Vision Fund. Besides his $25 billion and the Saudis’ $45 billion, there will also be contributions worth $1 billion each from Apple Inc., Qualcomm Inc. and Oracle Corp. Chairman Larry Ellison.

“We believe the singularity is inevitable and all businesses will be redefined as computers overtake humans in intelligence,” Son said at an earnings briefing in November.

Previously, the 59-year-old entrepreneur predicted the singularity will occur by 2047, in line with predictions made by the father of the singularity movement, Ray Kurzweil. With this new found momentum and huge piggybank, it looks like Son wants to accelerate this transition as fast as possible.

 

robot helper chat

Google just released a chatbot that’s trying to figure out the purpose of life

robot helper chat

Image: Wallpaper Vortex

Don’t you just hate it when you’re looking for support for a service or app you bought, only to be greeted by some monosyllabic robot ? Ok, that can happen just as well when dealing with outsourced tech support, but at least you know you’re talking to a real person. Well, that might change sooner than you might think. The singularity is getting closer by the moment. Just take a look at Google’s new chatbot which according to the developers has moderate “natural language understanding”. In other words, it can roll with the punches and continue the conversation by itself without following predefined question – answer. Of course, after a while you can still tell it’s not human (fails Turing test), but that doesn’t mean it isn’t entertaining. Have a look at how it answers to “what’s the purpose of life?”.

bot chat

The bot was developed by Oriol Vinyals and Quoc Le, both researchers at the Google Brain project. They claim their AI works by learning from previous sentences and predicting what comes up next. Essentially, the bot is trying to second guess where you’re going with your questions and frames the answers accordingly. However, after each question it re-arranges itself.

“We experiment with the conversation modeling task by casting it to a task of predicting the next sequence given the previous sequence or sequences using recurrent [neural] networks,” they wrote in a paper describing the experiment posted on the arXiv pre-print server. “We find that this approach can do surprisingly well on generating fluent and accurate replies to conversation.”

To learn “human speak”, the bot was fed with thousands of movie subtitles and a dataset from an online tech support chat. For instance, here’s how it behaves as a tech support assistant.

tech support bot
tech support bot

Not bad at all, quite lively. If you stick to simple, to the point questions – like when you’re trying to solve your tech problem – the bot is up to it without too much hassle. It might even fool some. When it gets too philosophical, it sounds like a drunken droid though.

philosophical bot
philosophical bot

Nevertheless, it’s still pretty freaking amazing! It doesn’t make those blatant noun-pronoun errors you typically see in other bots, and actually has a bit of “personality” (borrowed from the datasets – does the bot think he’s a movie star?). Just kidding. After all, it can’t think. This is still a mindless software, a child’s play, but most certainly a taste of what’s to come in the future as we see bots made to interact with information or even the physical environment not by acting on predefined instructions, but by improvising based on previous experience.

“In other words, it does not simply look up an answer by matching the question with the existing database,” they wrote. “In fact, most of the questions above do not appear in the training set.”

“It is surprising to us that a purely data driven approach without any rules can produce rather proper answers to many types of questions,” the researchers add.

There’s still a long way to go until we see the singularity breached, but until then these sort of artificial intelligence renderings might prove extremely useful.

“The model may require substantial modifications to be able to deliver realistic conversations,” the researchers wrote. “Amongst the many limitations, the lack of a coherent personality makes it difficult for our system to pass the Turing test.”