back to article Earth's core is younger than its crust surface

Back in the early 1960s, physicist Richard Feynman remarked that the centre of the Earth had to be a little younger than the surface, since it would experience gravitational time dilation. Now, boffins from two Danish universities have put a value to that difference, and while they agree with his hypothesis, they've corrected …

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So Feynman was a bit off - probably because he never got around to sit down and do the math properly. Which, in the 1960ies, may have been based on a different perception of the solar system's age, so even his proper math might have been off by today's baselines.

The amazing thing is to come up with this in the first place. Honestly, who even thinks about stuff like this? Gravitational effects, yes, but the focus there usually is black holes or other singularities* or space travel. But thinking about the effects on the very rock you're standing on - that guy was one serious thinker.

* A plural for singularity, now that feels kinda funny.

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A bit off?

Just out of curiosity, does any of the calculations take in to account the fluidity of the earth's core? So that something in the core could come up and away from the core and then recycle and flow back to the core?

Just going out on a limb but the further away from the core, the less of a factor the time dilation effect, so that it could be that Feynman is closer to the truth?

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Anonymous Coward

" Honestly, who even thinks about stuff like this?"

Lots of people. GPS signals wouldn't work without accounting for it either, it's not just the big things you highlighted.

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Re: A bit off?

There's very little exchange of material from the core as it's overwhelmingly made of dense metals (80% or so of which is believed to be iron). That core is believed to have formed very early on when the Earth was still molten and the relatively small amount of material that has moved since is really not going to make a significant differences to the calculations.

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Facepalm

"* A plural for singularity, now that feels kinda funny."

...only if you never learned any maths, wherein thoroughly non-remarkable functions (like the humble "tangent(x)") can have a dozen of them before you even reach 0 on the x axis...

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Anonymous Coward

Re: A bit off?

"There's very little exchange of material from the core as it's overwhelmingly made of dense metals"

Not sure what density has to do with exchange of materials? The inner core is believed to consist primarily of a nickel-iron alloy. However, a iron-nickel alloy under core pressure is denser than the core, implying also the presence of lighter elements in the core.

It is likely that the outer core at least has extensive exchange of material as it's liquid...

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Re: A bit off?

Material doesn't really leave the Core. As well s the Inner Core being a giant ballbearing of solid iron/nickel alloy, there's also a profound density difference across the Core Mantle boundary which means that convection can't take place.

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Re: A bit off?

The density matters because the mechanism for movement will be largely convection and the denser elements will tend to remain at the core. That's why the core is much more dense than the layers above, not because it's under a lot of pressure (which will be a relatively minor matter compared to the density difference between different elements).

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Anonymous Coward

What is time

You realize that time, t, is just a parameter we used to define our equations-of-change. It made it easier for us to describe those equations in terms of t.

It's phrased in terms of human perception, so the unit of seconds is a time scale that we perceive, its not nano-seconds, or centuries which would be too short or too long to perceive.

And since we all live on the surface of earth, it is defined to be constant regardless of gravity because we perceive nothing else.

So Einsteins fixup to time is really a difference between human perception of time and the truer underlying measure of change, but we didn't understand that when we first defined t.

And you can ask "why can't we go back in time", but of course if we did, we would 'unperceive' change. The electronics of our brains would 'unlearn' as we did. The neuron signals would go outward away from the brain to the eyes and the senses. Rather than inwards to learn from the change.

Asking instead "why doesn't time go 1 million times faster..." well of course it does, its only us that perceive change in terms of seconds not centuries. If our brains could perceive change at the much slower rate, time would appear to be going much slower than seconds.

So it really does go k times faster, and even negative k, but our perception of it can only ever be of +ve values of k near the value +1.

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Re: What is time

Each observer has its own ‘proper time’ and for everyone their proper times clock at exactly the same speed, as far as any time-like factors in laws of physics are concerned. Beside that you can define more or less arbitrary space-time coordinates, which is done routinely in general relativity, but they are just that, arbitrary coordinates.

You can observe that proper times of distant objects go slower or faster (i.e. physical processes appear to be slower or faster) -- which is exactly the difference between the crust and core times here.

Humans simply experience their proper times because that is the physical time determining the evolution of everything. In principle you can imagine a time difference for instance between your head and limbs, but for any non-negligible difference the corresponding tidal forces would be enormous.

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Re: What is time

>In principle you can imagine a time difference for instance between your head and limbs

That's actually been shown experimentally! Seriously, physicists as NIST have observed difference in reading between two nuclear clocks, one 0.33 m higher than the other. The difference is as theory predicted, and it is equivilenet to 90 billionths of second over the course of a 79 year lifetime.

http://www.nist.gov/public_affairs/releases/aluminum-atomic-clock_092310.cfm

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Re: What is time

You can observe that proper times of distant objects go slower or faster (i.e. physical processes appear to be slower or faster) -- which is exactly the difference between the crust and core times here.

It's not a matter of distance per se. If you are deeper in a gravity well then space-time is being distorted more. To an observer higher up in the well, your time appears to them to be passing more slowly than does theirs.

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Anonymous Coward

Re: What is time

See my comment about dog years below (when it gets posted, post-time is not in sync with real time).

My point is, that to be useful as a measure of change, delta-t at the earths surface has to be equal to delta-t at the core. Because the earths core and earths crust regularly interact, and its silly to have each layer of the earth in a different time scales.

@"proper times because that is the physical time determining the evolution of everything"

Proper? Well no, we could define change in all manner of parameters, so for example if I throw a ball its path is parabolic, i.e. y = ax + bx^2, a parabolic curve defined as a function of x. That equation is not actually true, it treats gravity as fixed and constant, if we'd defined it properly, we'd have a much longer equation.

Then when we parameterize that equation for a 'change' value the correctly deals with gravity, (which we'll call tReal ), we then have a definition which we could then use BOTH at the crust, AND at the center of the earth and everywhere inbetween. There's nothing special about our perception of time that makes it the proper perception. But all that physics *we* defined in terms of t, where t is time defined in terms of our incorrect perception of it.

Why is it incorrect?

Put it this way, the dog years thing:

I was there at the birth of my dog. My dog is older than me in dog-years. This is because dog-years is not a real measure of change, its an arbitrary scaling of my dogs years as a measure of how old it is in human age terms. Which leads to impossible faults like me being at its birth and it being older than me. Or like the earths core being younger than the earth. The fault, (which Jake below notices but doesn't understand the implications) is such a major flaw in a parameter intended to be the measure of change.

Hence using t, a human perception of time, is an incorrect measure of change.

The earths core really isn't younger than the crust, its just the incorrect way we defined t.

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Re: What is time

> That's actually been shown experimentally!

Sure, it has been *measured* thanks to the insane precision of nuclear clocks. I was talking about direct sensory input, ‘feeling’ that time goes differently in different pats of your body. Which should be a funny feeling, except for the terrible tidal forces killing you instantly.

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Pint

Re: What is time

R11: "If you are deeper in a gravity well then space-time is being distorted more."

Which leads to the following thought experiment...

You're inside a box (like Einstein's elevator). The box is either floating 'weightless' alone in the interstellar void, or it's hovering 'weightless' in the hollow exact-center of a very huge mass (deep in a huge gravity well). What experiment can you perform inside your sealed box to distinguish these two?

Conclusion: We're in a conceptually similar box called The Universe. This is where some of the fundamental constants (e.g. 'c') come from.

Maybe. Maybe not.

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Coffee/keyboard

@ Jeffy Poooh ... Re: What is time

You didn't happen to take your cat along with you in to the box, now did you?

You didn't happen to catch his name? (Schrodinger was it? )

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jzl

Re: What is time

"So Einsteins fixup to time is really a difference between human perception of time and the truer underlying measure of change"

Nope.

Stick to commenting on politics, where actual facts don't matter. Leave the physics alone.

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Happy

Re: What is time

Indeed a timeless question.

As a kid I spent a lot of time in a library during the winter. I had my fair share of Biggles, Tarzan and such but I soon found out adults have more interesting book to read like science, and stuff one had to hide from parents at home. Anyway, one book I still remember after 60 years, Cosmos (1 and 2) was written by some guy (not Sagan) who left Russia for the USA and started to write about science in a "popular" way.

Writing about Einstein and why it took other "boffins" so many years to understand him he claimed one reason is that we understand things like a kg a meter and speed as an physical experience but we are rubbish at understanding time.

To explain his point he has this simple and straightforward example.

There is a river and a boat goes upriver downriver from A to B and then from B to A with no current in the river. And then the same trip but with a stable current, say 2 knots while the ships speed is 20 through the water in both cases. No hidden agenda here just pure mathematics/logic.

Now his question is this - does it take more, less or equal time with the current.

Take your pic but then prove it on paper and then prove your answer with one spoken sentence (pure logic) and you will understand why I still remember it.

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Re: What is time

Lars.. can you expand on this..

It takes the same time surely - what am I missing?

Something to do with derivative of speed against time and distance?

Too old for this.

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Happy

Re: What is time

@ myhandler

Try paper and pen and you get it. Time.

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jzl

Re: What is time

If you go upriver twice as slow, you have to come back twice as fast to take the same time, but the speed downstream can't be the inverse of the speed upstream. Basically, (22/20) <> (20/18)

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Re: What is time

Thanks.. ok.. but no light bulbs gone off.. why is this meant to be revelatory?

There I was pondering the extra 2 miles an hour increasing the mass as it approaches the speed of light, and vice versa, but that seemed contrived

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jzl

Re: What is time

It's not revelatory. Lars is pretty pleased with himself for understanding some GCSE arithmetic :)

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Happy

Re: What is time

@ myhandler and jzl

Thanks for responding to my time rant.

The reason I still remember that "time example" is that while I knew the answer as I read the book, I still had to check it on paper because I went for the equal time answer and I just did not get it.

The whole idea with this example is to prove that we are rubbish when it comes to understanding time.

But then I got it, and yes jzl, I was very very proud about my self, I was eleven and I felt a genius. Hasn't happened much often since then.

The solution in one sentence is that the time against the disadvantage (against the current) is always longer than the time during the advantage (down stream). The stronger the current the greater the difference. But what we idiots do is to add 18 to 22 and then we divide by 2 and we get 20 and we will say the time is equal. We suddenly forget that speed is the relation between distance and time. We don't get the time at all.

The funny thing is that some guys are so totally convinced the time must be equal that they even refuse to do the calculation. For them I have invented a modern version that you can solve in your head. Goes like this. You have a trip to do of 200km in your car. Then you decide you will use 2h driving 100km/h and everything is fine. But then after having made that first 100km you realize that your average speed was in fact 80km/h. Cleaver as you are you then decide you drive the rest of the trip, 100km at 120km/h to make it in 2h. But when your 2h are up you are still 10km short of the 200km. That you can work out in your head.

Now, I am not obsessed with this, but during my "barfly" -period, long ago, often short of beer, I found that one can win a beer or two with that silly question. Only once did I have to avoid a punch in the nose.

Regards Lars

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Lack of critical thinking, methinks ...

The Earth was molten for how long?

The heavy elements (mostly iron) became the core while the Earth was molten, right?

The core developed before the crust developed, by definition, right?

How many hundreds of millions of years was it between "molten" and "crust development? It certainly wasn't a couple of years. In fact, it's still going on as the Earth cools ...

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Anonymous Coward

Re: Lack of critical thinking, methinks ...

"I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."

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Re: Lack of critical thinking, methinks ...

Even if it was a few hundred million years that's a single digit percentage against the age of the Earth. Take a single digit percent off 2 1/2 years and you get ... maybe 2 1/3 years. Not enough to worry about, especially since this was never going to be an exact calculation to begin with.

That doesn't even get into the question of when you start the clock for the Earth's age. Is it when mass starts to coalesce in the orbit we occupy? When it finishes that process and is a sphere about the size of today's Earth? When the surface begins to solidify into a crust?

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Re: Lack of critical thinking, methinks ...

It would appear you have picked the stick up from the wrong end.

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In partial defence of jake:

This Reg article has used the word 'crust' in error. The authors of the paper did not use the word 'crust', only 'surface'. Jake is correct - the crust took tens of millions of years to form in the first place, and has been recycled through tectonic activity many times since.

That said, jake should know better than to trust the Reg at face value - it's important to check the source material directly.

The purpose of the paper, as the authors intended it, was as a teaching aid for undergraduate students to challenge established views. Feynman would have approved.

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Re: Lack of critical thinking, methinks ...

>"I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."

The Reg made an error in its reporting, and introduced the word 'crust' when it wasn't present in the source material. Just like using Wikipedia, it's important to check the references yourself.

Welcome to the internet.

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Re: Lack of critical thinking, methinks ...

Abstract

We treat, as an illustrative example of gravitational time dilation in relativity, the observation that the centre of the Earth is younger than the surface by an appreciable amount. Richard Feynman first made this insightful point and presented an estimate of the size of the effect in a talk; a transcription was later published in which the time difference is quoted as 'one or two days'. However, a back-of-the-envelope calculation shows that the result is in fact a few years. In this paper we present this estimate alongside a more elaborate analysis yielding a difference of two and a half years. The aim is to provide a fairly complete solution to the relativity of the 'aging' of an object due to differences in the gravitational potential. This solution—accessible at the undergraduate level—can be used for educational purposes, as an example in the classroom. Finally, we also briefly discuss why exchanging 'years' for 'days'—which in retrospect is a quite simple, but significant, mistake—has been repeated seemingly uncritically, albeit in a few cases only. 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.

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Anonymous Coward

Re: Lack of critical thinking, methinks ...

This is the "time dilation effect" i.e. gravity affects time, since gravity inside the center of a sphere is lower and effectively zero at the center, time is faster.... wait.... shouldn't that make it older from our perspective?

Oh no matter, basically we have a measure of change that has an error in it, since it doesn't account for gravity. That error means you can't compare two times at two different gravity values. Even though they clearly interact regularly, at t = 0, {t= 1, tcore=1.1}, {t=2, tcore=1.2}... the time definition for each is messed up.

It's like measuring time in dog years, we know its wrong to scale time by the average human life over the average dog life, its arbitrary and clearly broken, but well my dog is "older" than I am (in dog years), yet I was there are his birth. That fact clearly demonstrates the error in the time unit I'm using. And in a similar way, a younger core that was created before the outer core illustrates the problem with our time unit.

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Re: Lack of critical thinking, methinks ...

""I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.""

I think the word you were looking for was "comprehend".

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Re: Lack of critical thinking, methinks ...

Having now read your correction to a famous quote in the history of computer science, I look forward to your edits of Defoe, Darwin, Newton, Ruskin, and Shakespeare.

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Coat

Re: Lack of critical thinking, methinks ...

"I think the word you were looking for was 'comprehend'."

To aprehend - to grasp or understand a concept.

A most appropriate verb to use when so many comments here demonstrate a complete failure to grasp one of the basic concepts of general relativity i.e. time is relative and not constant.

Though it begs the question, if a higher gravitational potential at the Earth's surface causes relative time dilation, what implications does this have for the turtle at the bottom?

I know, I know, I'm being silly, there cannot be a turtle at the bottom. It's turtles all the way down...

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Gravity

I'd have thought that the gravitational field at the centre of the earth is zero, assuming a spherical earth. You can only treat a planet as a point source of gravity if you're outside it, or just on the surface. Under the surface, you have to do an integration involving slices of the planet 'above' and 'below' you. At the centre, everything cancels out and you have what is effectively a one body Lagrangian point.

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Re: Gravity

The time dilation between two points depends on the difference of the gravitational potential between them, not on the field strength at either point. The centre of the earth has a zero field, but a low potential relative to the surface (if you drop something down a tube to the centre of the earth, all that kinetic energy has to come from somewhere!).

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Have an upvote

for asking a good question which elicited an excellent answer.

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Pitching for down votes... ;-)

So, the age of the earth is dependent on where you measure it from, because it's all relative. Measured from the surface, the centre is the same age as the surface. Measured from the centre, the surface is the same age as the centre. The difference between the two, which would have a single start point about 4.5 billion years ago, is down to the way atoms and particles and everything else in the centre are slowed down by gravitational dilation while at the surface they move just a little faster because there's less gravitational effect.

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Anonymous Coward

Re: Pitching for down votes... ;-)

Pitching AGAINST the down votes:

No, its Physics as an unchallengable religion, that can't face up to a few thought experiments that point to the problems.

As if down-voting make the problem go away.

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Coat

So ...

Dateline 22 October 4004 BC, about 3:30 pm: Place the planet Magrathea:

Two figures stand on a construction gantry surrounded by partly assembled dinosaur skeletons and surplus firmament.

"Right that's the crust finished, shall we call it a day?"

"Nah, we'll pour the core in before we go. It'll only take a couple of hours or so to heat it up."

"OK, but I'm taking tomorrow off for a rest."

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Unhappy

My brain hurts, can we have an article about kittens please.

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"My brain hurts, can we have an article about kittens please."

Here you go.

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Coat

> My brain hurts, can we have an article about kittens please.

OK, fine. Do you want kittens in low or in high gravity?

Mine is the one with the 13 volumes of "Annoying questions that will make you hugely unpopular" in the pockets.

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Quite a large pachyderm in the room

Seems to me like nobody considered a little thing called plate subduction, wherein the earths tectonic plates constantly move, when forced against each other one plate will be forced under the other, as that plate is pushed further into the underlying magma it in turn "melts" once again becoming magma itself. At areas where the plates pull apart, new land is formed by upwelling magma (Hawaiian island chain is a good example of this).

Long story short - the earths crust is much much younger than the core as it is constantly being "recycled". This scientific hypothesis which states the opposite is only relevant in a static earth model where there is no subduction or upwelling to recycle the crust.

Currently Mars has no plate tectonics, but the hypothesis doesn't even work there, as Mars did have plate tectonics in the past meaning that even its crust is in fact younger than its core.

I guess this is a problem specific to when physicists try to work out geology.

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Re: Quite a large pachyderm in the room

No. The rocks themselves may be younger, but the material they are made of is not. Those same atoms have been cycled around through various different rocks. Just because they have been melted and re-solidified does not make them physically younger.

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Re: Quite a large pachyderm in the room

Some plates manage to get deep enough to interface with the magma-core boundary and dredge up core material, the materials from the crust mix with the cores due to these interactions at the the magma-core boundary which is why there are heavy elements for us to mine in the crust. Which would make crust and core the same age. So again screwing the hypothesis, and how about the new material from space which is constantly added to the crust (160+ tonnes per year according to NASA)? That adds up to a metric fuck-ton over geological timescales.

If you really want to stick to atomic age and not material age then answer me this- How old is the earth? Because if you answer 4.543 billion years then you would be wrong (by your reasoning) as that is the "material age" the atoms were formed long long before that in the hearts of long dead stars from atoms which were created long long before that yadda yadda etc.

I say it again, the hypothesis only works for a static earth model.

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Re: Quite a large pachyderm in the room

Irrespective of how many times some particular stuff has actually been at the surface it's still the same stuff. You're really only looking at the difference between the time dilation effect at the surface vs just below the surface and the time spent at various depths. In terms of the overall size of the Earth it's not a great deal. What's more, the paper points out that as the Earth isn't homogeneous the effect varies depending on depth and even ignoring vertical movements, is negligible for several hundred kilometres (fig 3).

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Re: Quite a large pachyderm in the room

"Some plates...the materials from the crust mix with the cores due to these interactions at the the magma-core boundary which is why there are heavy elements for us to mine in the crust."

And overall, just what proportion does this amount to for the core & for the crust?

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