Credit: Pixabay.

Why the Earth’s core is two and a half years younger than the crust

Credit: Pixabay.

Credit: Pixabay.

The closer you are to a source of gravity, and the stronger that source of gravity, the slower you experience time relative to someone further away. This is a basic tenant of the theory of relativity, first postulated by Albert Einstein.

To illustrate time dilatation, famous physicist Richard Feynman would often tell his students during lectures that Earth’s core, which is a lot denser than its surface and hence exerts a stronger gravitational pull, is younger. That’s despite the whole planet, as a whole, clumped together some 4.5 billion years ago.

Feynman used to say, probably out the back of his end, that the core is a few days younger. The physicist was so influential and right most of the time that everyone just ate that cookie whole. To this day, you can find his statement reproduced across classrooms all over the world and even in textbooks.

Well, someone actually crunched the numbers and found Feynman was off — by two and a half years. That’s not to say that we should be too harsh on Feynman — we’re all to blame. Even Ulrik Uggerhøj from Aarhus University in Denmark, the physicist who calculated the ‘aging’ effect of the Earth’s core, confesses he cited Feynman’s “couple of days younger” in his papers. He later realized no one actually confirmed the statement. It was like a myth, and he took it upon himself to bust it.

The calculations he published are “accessible at the undergraduate level and can be used for educational purposes, as an example in the classroom,” Uggerhøj wrote.

E = mc2

Spacetime fabric distortion by a massive object. Credit: Giphy

Before Einstein, everyone thought that time was a river that flowed at the same rate from everyone’s perspective. If I had a watch and you had the same watch, each would tick at the same rate no matter where you are or how fast you travel. Also, there is no limit to how fast anything can travel. Or so we thought.

Post-Einstein, we now know that the laws of physics are the same in all “inertial frames of reference” and that nothing can travel faster than light. Moreover, light always travels at a constant speed, often denoted by the letter ‘c’.

Time dilatation enters the picture when an object is moving faster than another object. Say I’m on a train and you’re on the platform; as the train’s velocity approaches the speed of light, from your point of view you will notice that time is running slower and slower inside the train. You would see me moving slow-motion, for instance. From my point of view, I would see people moving on the platform very, very fast, but the people inside the train with me are all acting normal.

This is what Einstein called Special Relativity, and he later showed that the same effect applies when gravity is involved — in systems with acceleration (Special Relativity only deals with uniform speeds). The Theory of Relativity says that time and space are not separate and instead form an interwoven continuum called spacetime.

The more massive an object is, the more it distorts the spacetime fabric causing time to pass more slowly in the vicinity of the gravitational pull. In our case, time at the Earth’s core has been lagging by 0.0000000003 of a second. That seems negligible but not if you factor in the age of the Earth, which is 4.5 billion years. This is how the scientists eventually got to 2.5 years. Strikingly, the sun’s core is 40,000 years younger than its surface.

Note: We know Feynman said the ‘earth’s core is a couple days younger’ from transcripts of his lectures. It’s possible he was actually right, saying ‘years’ only to be transcribed in ‘days’ by a typist who didn’t think too much of it. 

 

 

22 thoughts on “Why the Earth’s core is two and a half years younger than the crust

  1. David Bofinger

    "lagging by 0.0000000003 of a second" probably should read "lagging by 0.0000000003 of a second per second" or something like that. It's lagging by a fraction of time elapsed, not by an absolute amount. A very rough back of the envelope calculation: depth of gravitational energy well is roughly Earth radius times gravity divided by two, divide that by c^2 to get the distortion as a bit over 3*10^-10. Multiply by 4.5*10^9 years to get something like 18 months. Real answer appears to be a bit longer, not sure why. Still, when a basic scribble like this gets us so close it's strange a mistake as large as a factor of a few hundred was around so long, didn't anyone give this to their undergraduates as a problem?

  2. Gnarlodious

    I say Feynman is wrong. The core may be maximum density due to extreme pressure, but at the very center there must be zero gravity. After all, its mass that sucks up gravity, so once gravity has traveled to the center of a mass, there's no more of it to push stuff around.

  3. Tibi Puiu

    Hey David,

    Yes, you're completely right. If you run the numbers, you'll get 18 months. But according to the researchers, once you factor the difference in density between the core and the crust, you get 30 months.

  4. Xinhang Shen

    General relativity is totally non-sense! Einstein’s relativity theory has already been disproved both theoretically and experimentally (see “Challenge to the special theory of relativity” March 1, 2016 Physics Essays). The most obvious evidence is the absolute time shown by the universally synchronized clocks on the GPS satellites which move at high velocities relative to each other while special relativity claims that time is relative (i.e. the time on each reference frame is different) and can never be synchronized on clocks moving with relative velocities.

    Time is absolute and space is 3d Euclidean. Even if gravitation can slow down atomic clocks, it slows down the frequency of the clocks, not the time. Can you say that high temperature can accelerate time because in tropical area plants grow much faster than in arctic area? Of course not. For example, a pendulum clock on the moon will go much slower than on the earth while an atomic clock will go faster on the moon. Then, what can we say: time goes faster or slower on the moon? There are many things can influence clocks, but they just influence the frequency or speeds of specific processes employed by clocks, not time. The concept that time is relative is the most preposterous idea in the world created by Einstein, which can never be realized in any circumstance.

  5. Xinhang Shen

    No, you are wrong. Clocks on the GPS satellites are corrected just to make them universally synchronized, nothing to do with relativity. On the other hand, the universal synchronization of clocks with relative velocities directly denies that claim of special relativity that time is relative and can never be synchronized on clocks with relative velocities. The daily sync of the clocks is to correct the errors of the atomic clocks which are still not very stable.

  6. Xinhang Shen

    Why don't you use your own brain to make a judgement? I have told you that all these explanations are already outdated and completely wrong.

  7. Brian

    You told me? and HOW ARE YOU? where are you links, your references, your proof? You nonsense that any group would pay more and risk more to bribe more people on a committee than they had too. Hillary takes in million for secrete talks to bankers, and you still want to kiss her ring.

  8. Brian

    The accuracy of the satellites clocks is thousands of times better than the the calculated adjustment they make to keep them synchronize. NS versus usec errors.

    Relativity never said you could not calculate the relative times, just that they are dependent the acceleration of the object.

  9. Xinhang Shen

    No, the time of special relativity is relative to the inertial reference frame, not depending on the acceleration.

  10. Xinhang Shen

    This is the place for discussing the physics. If you do find anything wrong from my paper, you can refute it here, and I will definitely respond.

  11. Xinhang Shen

    I have never tried to impress you with such funny logic. All I want to tell is for people who can think with their own brain: the time shown by the universally synchronized clocks on the GPS satellites with huge relative velocities is the same absolute time, but special relativity says that time is relative and can never be synchronized on clocks with relative velocities. Please don't respond, Brian! This is not for you.

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