# Is the Earth’s Core Younger than the Crust?

There was a rather interesting announcement recently: three Danes calculated that the centre of the earth is 2.5 years younger than the crust ( U I Uggerhøj et al. The young centre of the Earth, European Journal of Physics (2016). DOI: 10.1088/0143-0807/37/3/035602 ). The concept is that from general relativity, the gravitational field of earth warps the fabric of space-time, thus slowing down time. This asserts that space-time is something more than a calculating aid and it brings up a certain logic problem. First, what is time and how do we measure it? The usual answer to the question or measurement is that we use a clock, and a clock is anything that has a change over a predictable period of time, as determined by some reference clock. One entity that can be used as a clock is radioactive decay and according to general relativity, that clock at the core would be 2.5 years younger than a clock on the surface; another is the orbit of the Earth around the star, and here the core has carried out precisely the same number of orbits as the crust. Where this becomes relevant is that according to relativity all clocks must behave the same way towards velocity, otherwise you could take your rocket ship and by comparing two different types of clocks you could measure your absolute velocity. So, does that mean gravitational time dilation is conceptually different from velocity time dilation? I believe this matters because it brings into question exactly what is space-time?

The above does not mean that time dilation does not occur. It is unambiguous. Thus we know that the muon travelling at relativistic velocities has its lifetime extended relative to a stationary one. If we assume that the process of decay is unaffected by the velocity, then the passage of time has to have slowed down. But that raises the question, is the assumption valid? An analogy might be, suppose I have a clock that is powered by a battery, and as the voltage drops, the clock slows. I would argue this is because the lower voltage is inadequate to keep the mechanism going at its previous rate, and not that time itself has slowed down.

Now, consider the mechanism of muon decay. If apparent mass increases according to velocity, why should not the rate of decay of a muon slow down, after all, it has accumulated more mass/energy so it is not the same entity? Is the accretion of mass equivalent to the change of gravitational potential?

Perhaps what relativity tells us is the rate at which clocks move indicates their altering the scale of the passage of time, rather than time itself slowing down. By that, I mean that when a clock hand completes one period, we say an hour has passed, but at relativistic speeds it might say that γ hours have passed per clock period, where γ = 1/√(1 – v2/c2). In terms of gravitational fields, it is not that time slows down, but rather clocks do, together with the rate of physical processes affected by the gravitational field.

That suggests we take our concept over to inertial motion. If a body travels near the velocity of light, then our equations tell us that time appears to dilate, but has time really slowed, or is it the process that leads to the decay that has slowed? Does it matter? In my opinion, yes, because it is through understanding that we are more likely to make progress into new areas.

The reason it is asserted that it is time itself that slows down comes from the principle of relativity, first (as far as I can tell) loosely stated by Galileo, used as the basis of his first law by Newton, and perhaps more clearly stated by Poincaré: the laws of physical phenomena must be the same for a fixed observer as for an observer who has uniform translational motion relative to him, so that we have not, nor can we possibly have, any means of discerning whether or not we are carried along in such motion. When added to the requirement from Maxwell that the velocity of light is a constant, we end up with Einstein’s relativity.

The question is, is the principle correct? It has to be in Galilean relativity, as it is the basis of Newtonian dynamics. If velocities are added vectorially, there is no option. But does it translate over into Einstein’s dynamics?

My argument is that it does not. There is an external fixed background, and that is the cosmic microwave background. The microwave energy comes almost uniformly from all directions, and through the Doppler shift one can detect an absolute velocity relative to it. (The accuracy of such determinations at present is not exactly high, but that is beside the point.) Very specifically, at 1977 our solar system was travelling with respect to this black body radiation at 390 +60 km/s in the direction 11.0+ 0.6 h right ascension and 6o +10 o declination. (Smoot et al., 1977, Phys Rev Lett. 39, 898 – 901). So we DO have the means of discerning whether or not we are carried along with such motion.

If we can measure an absolute velocity, it follows there is an absolute time, and as I have noted before, we can always measure when we are by determining the age of the Universe. Therefore I am reasonably confident in saying that the core of the Earth has aged at precisely the same rate as the crust once the Earth formed, and since there has not been complete mixing, it is more likely the core is older, as it on average would have accreted first. One the other hand, isotope decay there should have been held back by about two and a half years.

## 23 thoughts on “Is the Earth’s Core Younger than the Crust?”

1. Dear Ian:
As the article is behind a pay wall (something that should be unlawful with research paid with public funds), I could not check the computation. However, notice that the core itself has no gravitation. So actually the slowing down of light clocks is a function of depth.

I have argued for decades that the Cosmic Background Radiation gave an absolute frame. However, the situation is a bit more subtle than that. Galileo argued that a laboratory in the bowels of a ship cannot provide an indication of motion.

I recently dug around and found the argument came initially from bishop Oresme, a student and collaborator of Buridan. Both were major philosophers, mathematicians and physicists of the Fourteenth Century in Paris. Oresme considered the principle of relativity self-obvious. However that was as long as one was in the bowels of a ship, and not looking at heavenly bodies. He said. Because Oresme argued the diurnal motion of Earth around itself could not be detected inside a lab (that turned out to be false: Foucault’s pendulum).

So can we find a sort of Foucault pendulum of absolute motion? General Relativity insists on what Newton already knew: the Earth falls around the Sun. Can we detect this rotation inside a mine, 2 kilometers down? In theory, yes: the CBR will slow down the Earth sometimes, and push it, at other times. A supersensitive accelerometer could detect that.

Nor can we do away with the likes of a CBR like reference frame. The simple fact that there are galactic clusters all around and they generate the gravitational field defines a state of rest relative to it.

The formalism of Quantum Physics already has an absolute time for all to see. That absolute time is what enables the non-local effects.

So is physics finished? No. Will the philosophical approach help? Of course (roll over, Feynman!). It took 32 years for physicists to realize that the potential was on the right side of the De Broglie-Schrodinger equation of 1924… That provided immediately with an experimental confirmation, the Bohm-Aharanov effect…

Keep with the good work…

• I would argue the core has gravitational potential – just no net force. And yes, it has depth.

And I do not believe physics is finished either – or anywhere near finished. But I do fear we are in danger of entering a period where dogma rules.

2. I gave an argument why local time really slows down. Moreover, if local time, as given by light clocks, were different from local time given by the weak force (radioactive decay), then one could tell absolute motion easily from the inside the bowels of the ship lab……

• Dear Patrice,

Disagree. If you had two different clocks giving different readings, and there was nothing wrong with the clocks, yes, you could tell there was a motion, but I am unconvinced it would tell you it was absolute. It may also tell you there is something strange about the environment. However, i think relative to the cosmic microwave background does give you an absolute motion (leaving aside the possibility of multiverses) because it is coming uniformly from all parts of the universe, and its own uniformity tells us the Universe expanded symmetrically. So the CMB is effectively a background on which the parts of the Universe move.

The difference between local time slowing and local clocks slowing is an interesting one, and not easy to resolve,

• I do not disagree that the CRB gives an absolute frame, de facto. I pointed out that Oresme would have said, more than six centuries ago, that it needed to be detectable in the bowels of the ship.
And:
1) I showed how that can be done without looking outside. Using an accelerometer works in the case of orbital motion. It also works for linear motion (the CRB will exert a constant force, hence acceleration).

2) Even if there was no CRB, the CGB, the Cosmic GRAVITATIONAL Background would provide with an unavoidable equivalent. (Notice the close relationship with Mach’s Principle.)

3. Reblogged this on Patrice Ayme's Thoughts and commented:

Inner parts of the Earth are younger than the surface by an appreciable amount. Richard Feynman made this point first. But he underestimated the effect 100 times! As the Danes who just discovered that put it: “The pedagogical value of this discussion is to show students that any number or observation, no matter who brought it forward, must be critically examined”.

Local Time is a theory invented by Poincaré, to make sense of Lorentz’s work. Local Time became famous when Einstein, a German, advertized it, and was himself advertized by Kaiser nationalists such as Max Planck. A gravitational field slows down (Local) Time. (The proof is easy.)

Notice that the core itself has no gravitation. So actually the slowing down of light clocks is a function of depth.local time really slows down.

Local time, as given by light clocks, has to be the same as local time given by the weak force (radioactive decay). If not, one could tell absolute motion easily from the inside the bowels of the ship lab. That would contradict the Principle of Relativity.

I have argued for decades that the Cosmic Background Radiation gave an absolute frame. However, the situation is a bit more subtle than that. Galileo argued that a laboratory in the bowels of a ship cannot provide an indication of motion (as long as one does look outside!)

.

I recently dug around and found the argument came initially from bishop Oresme, a student and collaborator of Buridan. Both were major philosophers, mathematicians and physicists of the Fourteenth Century in Paris. Oresme considered the principle of relativity self-obvious. However that was as long as one was in the bowels of a ship, and not looking at heavenly bodies. He said. Because Oresme argued the diurnal motion of Earth around itself could not be detected inside a lab (that turned out to be false: Foucault’s pendulum).

So can we find a sort of Foucault pendulum of absolute motion? General Relativity insists on what Newton already knew: the Earth falls around the Sun. Can we detect this rotation inside a mine, 2 kilometers down? In theory, yes: the CBR will slow down the Earth sometimes, and push it, at other times. A supersensitive accelerometer could detect that.

Nor can we do away with the likes of a CBR like reference frame. The simple fact that there are galactic clusters all around and they generate the gravitational field defines a state of rest relative to it.

The formalism of Quantum Physics already has an absolute time for all to see. That absolute time is what enables the non-local effects.

So is physics finished? No. Will the philosophical approach help? Of course (roll over, Feynman, go back to your computations!). It took 32 years for physicists to realize that the potential was on the right side of the De Broglie-Schrodinger equation of 1924… That provided immediately with an experimental confirmation, the Bohm-Aharanov effect…
Patrice Ayme’

4. Ian, Patrice,

(a little garbled. My computer ate the first effort)

Yes different clocks run at different rates, but what would be an absolute time? We perceive it as change and measure it as frequency. What would be an absolute rate of change, or frequency?

“There is an external fixed background, and that is the cosmic microwave background. The microwave energy comes almost uniformly from all directions, and through the Doppler shift one can detect an absolute velocity relative to it.”

While we can use the CMBR to measure a universal frame, is it this radiation which actually provides the resistance of a universal frame? If so, than any other fields, such as gravity, would be equally complicit.

Could it be the only universal frame is the vacuum of space itself, mediated by all these fields?

Then the fastest rate of change would be a frame in equilibrium with this vacuum, so that the motion of a frame relative to this equilibrium would be subtracted from velocity within the frame and that would be the basis of time dilation.

Remember the speed of light is measured relative to the vacuum of space. So it is the velocity of light in the vacuum(not any particular field) which is the basis of any concept of a universal time. Yet that is still activity in space. Time is a measure of activity, even if it is light. So the only absolute time would be similar to a temperature of absolute zero. No activity and no change.

Which goes to a point I keep making; That time has far more in common with temperature, than space and that temperature is actually more elemental. In that it arises from frequency and amplitude, while time is just a measure of frequency. Just that we are intellectually biased toward time, such sequence is the basis of rational thought.

• I am not sure I understand the point you are making, but for me, an absolute time is such that irrespective of your history, everybody agrees, when using it, of when you are. That is why I say there is one – because everyone can determine the age of the Universe, and all should get the same answer at the same time, irrespective of where they are. Of course as clocks go, it is not exactly one of the more sensitive and the observational uncertainties are awful, but that does not eliminate the concept that at least it is possible conceptually to do that. An absolute time is still changing regularly – everything still ages, but may not all age at the same rate.\ wishing that absolute time scale.

I guess for me a frame of reference is defined by a thing, but it itself is merely a concept, a geometrical construct, and hence fields exist in it, but they are not part of it. This is where space-time becomes somewhat complicated, because it is treated as a thing by some, being warped, etc, whereas I consider the so-called warping merely a geometric way of manipulating the equations, which ar either right or wrong (and which we believe to be generally right).

I may have misinterpreted what you were saying. if so, sorry.

• Ian,

Space as three dimensional is basically the xyz coordinate system, the center point of which is really the basis. So that when any such point and its coordinate system is moving relative to the vacuum of space, its clock rate is slowed proportionally.
As you asked, is this due to some fundamental dimensionality of time, or is it simply a slowing of the actions being measured and nothing more.
Your argument is that while is is a slowing of the particular action, there is still some underlaying absolute time, starting with the beginning of the universe.

As a side note, on previous occasions, I’ve argued the Big Bang Theory is faulty.

Among quite a few other reasons, the most mathematically basic is that the premise of redshift due to a doppler effect of galaxies moving away from each other overlooks the fact this assumes a stable speed of light in a vacuum that is otherwise distinct from the perceived expansion. To wit, if there are more lightyears between galaxies to cause this redshift, what is this vacuum on which C is based, if it is not space!

If this vacuum is space and it expands, there would only be stretched lightyears and no redshift. So there are two metrics being assumed and contrasted. One based on the speed of intergalactic light and the other based on the redshifted spectrum of the very same light.

While we perceive time as the narrative sequence, from prior to succeeding events, it is activity creating and dissolving those events, such that they go future to past, i.e., come into being and dissolve. Thus there is only the present state and separate clocks are simply separate actions and while it is useful to synchronize them, they don’t have to be.

In fact, a faster action/clock will essentially use energy quicker and so recede into the past faster. Much as animals with faster metabolism will age and die quicker than those with slower metabolism.

So time is an effect within the present state, not external to it.

So while we agree that spacetime is just a useful mapping device, my point is that time is an effect of activity, not some fundamental dimensionality. We could use ideal gas laws and coordinate the relationship between volume and temperature in a similar way.

• “Time is a measure of activity, even if it is light. So the only absolute time would be similar to a temperature of absolute zero. No activity and no change.”
The same reasoning proves that light is no activity and no change.

Contemplate more what I said about Quantum Physics before gravely insulting time… 😉

• Patrice,

Isn’t the point that at the speed of light, all other activity would be cancelled out, because it would have to be faster than light, since it would be C+activity.
So it’s not the light isn’t itself moving, but that it precludes all additional motion.

5. Brodix, I see several points here. Yes, we agree what space is, although I suppose we cannot totally rule out additional dimensions.

As for the rate of expansion of the Universe, I disconnect that from time itself. As far as we can tell, if we correct for the Doppler shift, the spectra, e.g. hydrogen line spectra, are the same as now, which requires the permittivity and permeability of space, and Planck’s quantum of action, to be constant. If so, c is constant. Yes, there is that wretched red shift correction. I have never carried out a calculation to see if that could be partially due to different values of the “constants”, so my case is not exactly strong.

As for the light year “expanding” as space expands, that seems to assume that c is not constant. Maybe, but I would like to see some evidence before I take that on. I simply consider that as the galaxies move apart, the number of light years increases.

Since we can only measure time through some activity, I suppose it is difficult to falsify your concept, but for me the second law of thermodynamics seems to provide a requirement for a dimension, although I suspect you will say it is just more activity

• Ian,

“Yes, we agree what space is, although I suppose we cannot totally rule out additional dimensions.”

As a coordinate system, the actual coordinates would have to be specified, otherwise it is just a fuzzy concept. Yet if they are, then multiple such maps can be applied to the same space. So space itself is infinitely dimensional. Each of us is the center point of our own coordinate system and there is no universal coordinate system. Assuming coordinates are fundamental to space would be like assuming longitude, latitude and altitude are fundamental to the surface of the planet.

” I simply consider that as the galaxies move apart, the number of light years increases.”

Remember C is the speed of light “in a Vacuum.” So what is this Vacuum, if it is not the space that is expanding, since there presumably are more lightyears between galaxies?

• Brodix,

Mathematically you can have infinite dimensions, but not if you ask them to correspond to something measurable physically. And there may be more light years between galaxies because they are moving apart, but that does not alter the speed of light. Velocity is distant over time – if the distance grows by a factor of x, then c is constant if the time also increases by x, and as far as I am aware, there is no physical evidence that it does not.

6. Dear Patrice,

Yes, there would be a differential force from the CMB, but I doubt you could tell from the bowels of the ship because microwaves do not pass nicely through metal.

A differential gravitational effect. I am not so sure of that one, but I guess in principle, yes.

7. Ian,

“Mathematically you can have infinite dimensions, but not if you ask them to correspond to something measurable physically.”

Yes, but you are asking them to correspond to space! If it has no physical properties, then it would not be bound, bent, or unstable, so its only qualities would be the non-physical attributes of infinity and equilibrium.

“And there may be more light years between galaxies because they are moving apart, but that does not alter the speed of light.”

So it would be an expansion in space, not of space, given the “ruler” is C. The reason this was originally rejected, for the notion that space itself expands, is because cosmic redshift increases proportional to distance, with no appearance of lateral motion. Which gives the impression that we are at the center of this universe. So the argument became that space itself expands and so every point would appear as the center.

Yet they still need this stable ruler to measure the effect.

Now we are at the center of our view of the universe, so it may be more logical to surmise that redshift is an optical effect and we really can’t fully test what happens to the spectrum of light that has been traveling for billions of years.

Though this is an interesting possibility;

Click to access 2008CChristov_WaveMotion_45_154_EvolutionWavePackets.pdf

• No, I am not asking dimensions to correspond to space. I am asking them to act as a scale so I can proportionately relate observations, thus B is 2 km north of A; C is 4 km east of A. The km is a scale unit within the dimensions. The point I was trying to make is you have to be able to relate things outside of space, at least for me.

If everything moves away uniformly at a velocity proportional to the distance, again you appear to be at the centre. You do not require space to be a physical thing that is expanding; you can still have it as a background on which everything else is placed.

I may be mistaken, not having read your link properly, but a casual glance (before I go out) seems to indicate it is a version of the tired light concept.

• Ian,

So do you agree dimensions are a mapping device, not an underlaying property of space and time? That seemed to be the essence of your original post. I was just trying to break down what space and time are, if the “fabric of spacetime” is only a mapping of events, not the basis of them.

“You do not require space to be a physical thing that is expanding; you can still have it as a background on which everything else is placed.”

Yes, but then it is a stable volume, in which case, the expansion is “in” space. So either we are at the center of the expanding universe, or it is an optical effect.

The premise of the paper seemed to be that we have only really studied single spectrum photons, in terms of what causes redshift, but that multi spectrum photons behave differently. So that when you have light traveling for billions years, to the point that entire galaxies have been reduced to a few photons being received by the telescopes, they will be a sample of the broad spectrum of light, not just particular bands, as would be with stronger sources..

Now if redshift is an optical effect, then it would seem the cosmic background radiation would actually be the solution to Olber’s paradox. The light of infinite sources, shifted off the visible spectrum. Which would be why it comes from the edge of the visible universe.

8. Brodix,

Yes, I consider dimensions as a device to aid mapping. And I do consider our being at the centre as likely to be an optical effect. I may be wrong, of course.

Sorry, but I haven’t really looked at that paper – just got home 🙂 However, at present I think on balance the red shift is likely to be a Doppler shift. That does not mean it is, but (and this is outside my expertise) I would like to see evidence that requires me to change my mind. I am assuming that the experts can unravel the spectra, but in fairness I have recently heard a talk by a cosmologist who more or less maintained that distances greater than red shift = 1 have quite error – ridden data, mainly, as you mention, due to the fact that there are so few photons.

• Ian,

Keep in mind the Big Bang Theory is based on the idea of space expanding, not an expansion in space and this relies on four dimensional spacetime, i.e. the ‘fabric of,” being physically real. So it is being assumed that space itself is being created by this expansion. Yet the assumption remains that light just happens to travel at a constant rate, relative to the “vacuum” and this is unaffected by the expansion.
Which is complete and utter nonsense, as light is not exactly separate from our understanding of space.

Spacetime as a physical explanation for the math of GR is about like giant cosmic gearwheels as a physical explanation for the math of epicycles. Your original post examines how time is affected by normal actions, not some underlaying geometry.

So if redshift is due to the doppler effect, we are at the center of this universe.

Gravity is described as the bending of space, but it also amounts to a normal lensing effect, that warps light around gravitational fields. So if there is this inward warping, due to gravity, could there be an outward warping in the absence of gravity? It would fulfill Einstein’s Cosmological Constant, as a balance to gravity and that effect might be what Hubble actually discovered.

• Brodix,

Yes, it is often felt that the Universe is expanding through an expansion of space, but that does not make it so. Don’t forget that if space is “something” then the Uncertainty principle is argued to have fluctuations, and from the gravitational effect of the energy you can predict the expansion rate, and be out by 120 orders of magnitude! Me, I believe the expansion is movement through space.

You do not need to bend space to have a light trajectory bend. In fact Newton predicted that light would bend in a gravitational field. He got the amount out by a factor of two, but he still predicted light bending. And the Doppler shift does not put us at the centre. If everything is expanding, we still get the same effect as long as we cannot see an edge.

9. Ian,

The situation is that it is doppler shifted evenly, proportional to distance, in all directions. If we were not at the center, then we should still be able to calculate about where the center is and we have. It’s right here.
Now an optical effect would seem logical, as we are at the center of our point or view, otherwise….