[gem (OP)]

 It is  said that a atomic clock runs faster at altitude proving time runs faster the weaker the gravity field,

 so if you placed an atomic clock at the centre of the earth and ignoring the gravitational effects of the sun and the moon, it would run considerably faster because it would seem to the atomic clock that the mass of the earth did not exist

 now if you placed a hour glass egg timer along side it, it would not run at all so doing the total opposite as regards our ways of measuring the passage of time.

 So which method should i use to cook my eggs when visiting the centre of the earth


[straight lines in curved space time or force field].

[flr]

Not sure you need to worry about how to cook an egg when visiting the centre of the Earth because as soon as you get past the solid crust (roughly 30Km depth) you will encounter liquid lava at 1200degree Celsius and as you go deeper and deeper the temperature rises up to 4000-5000 degrees.
Aside from the enormous pressures, at these temperatures the egg will perhaps get very cooked regardless of the relativity effects of time.

[gem (OP)]

Does that mean you prefer the atomic clock method ?

[JP]

First, any slowing of the clock due to the earth's mass is going to be very small, simply because the earth isn't all that massive.  The difference per day from a satellite to the ground is about 45 microseconds, that's 45 one-millionths of a second (http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html)!

Second, if you put both your atomic clock and your egg at the center of the earth, they'd both be experiencing the same rate of time (since they're both at the same place in the earth's gravitational field), and therefore the egg wouldn't even notice the tiny slow-down.  It's only when the clock and egg are at two different places that the timer and egg experience time differently. 

The atomic clock would work best.  Any gravity-based clock (an hourglass or a pendulum-style clock) would have problems.

[gem (OP)]

The atomic clock would work best.  Any gravity-based clock (an hourglass or a pendulum-style clock) would have problems.

I agree the atomic clock at earths center  would run closer to another atomic clock on the surface compared to a hour glass at the centre measured against one at the surface.

I liked your link but looking at what they say about relativity are they not just talking about the accuracy of the clocks in different strengths of force field

[JP]

Aren't you just asking about the accuracy of the clocks in different places in the gravitational field?

[Geezer]

Assuming they are decent clocks, they are always accurate. Good clocks keep track of time in a particular place, even when time varies form one place to another.

[JP]

True.  The question (I assume) is about the disagreement of clocks at different places in the earth's gravitational field, which should be tiny (fractions of a second) compared with the time it takes to actually cook the egg no matter you are in the earth's gravity. 

[Geezer]

Eggs are pretty good clocks too.

Assuming we can maintain a constant temperature of, say, 100C (which is highly unlikely under the circumstances), there would be no difference in the time required to boil the egg.

[gem (OP)]

Aren't you just asking about the accuracy of the clocks in different places in the gravitational field?

Its the concept of time i am wanting to address i am struggling with it in some areas of physics.

[straight lines in curved space time or force field].

on the link you provided it said that a atomic clock ran 45 micro seconds a day faster at an altitude of 20000km and the way that gravitational force is calculated at present that means it is experiencing a force equal to a acceleration of 575 mm a second squared.

[note i believe the way gravitational force is calculated at present may not be correct ]

so not down to zero as it would be at earths centre, but close enough for the principle we are discussing.

One question that i would like to clarify before i go much further is it presently believed that because an atomic clock runs faster at lower gravity then time runs faster also?

[JP]

Time seems to run the same for you when you're at further away from the earth, but if you compare your clock with the clock of someone on the earth, yours appears to be running faster.  Relativistic effects on time are all about comparing clocks, so you can only really talk about how fast time is going relative to someone else's clock (hence why it's called relativity).

[Geezer]

It's quite hard (least it was for me) to get ones mind around the idea that time does not march along at a constant rate throughout the Universe. It actually does vary at different locations under different conditions. Everything at that location behaves according to that "local" time, so it is impossible to detect the effect at that location.

As JP said, small differences in atomic clocks are quite measureable. 45 microseconds does not sound like much, but to a digital engineer, it's an incredibly long interval. GPS systems must take account of these variations in time. If they didn't, they would not be much use.

[gem (OP)]

It's quite hard (least it was for me) to get ones mind around the idea that time does not march along at a constant rate throughout the Universe.

I agree i am finding it hard to accept and will try to test it with different scenarios if members Patience will allow, but i will try to go one step at a time because i have lots of questions.

firstly does the theory of relativity therefore postulate that mass at the centre is older than mass at the surface.

[yor_on]

As gravity slows time the surface of our earth have a slower 'clock' than what the exact middle should have, but I'm not really sure. As everything else it falls back on definitions. In fact it should make a nice proof for SpaceTimes geodesics if it was so, as we then would have to accept that gravity isn't an 'energy'..

So as time 'ticks slower' at the surface you could, as an observer, have a good discussion about it, at the very least. But no matter where you are,as long as you're alive, your heart will tick, let's say, eighty times per minute as checked by your own watch. And that will be true everywhere, in the middle of the Earth or on the surface. And the reason why is that we can loosely say that you and your arm where your clock resides is in the same 'frame of reference' being 'at rest' versus each other.

If you now was passing the Event Horizon of a black hole, or a neutronstar, rotating it wouldn't be true any more. The more gravity and momentum/relative mass the more 'geometrically compressed' those frames of reference being 'at rest' versus each other (your molecules, atoms, quarks etc) will become, and the more 'gravitational forces' will act at every point in every defined 'system', like your body.

And here comes the discussion about 'systems' and 'frames of reference' in. Can we really say where one frame end and another starts. No, not really. We can define them and at some times they are easy, like with acceleration, but there is no clear borderline between where you, according to me watching outside from the moon, can be said to suddenly start to 'live slower or faster'. It is only at extremely high energies, like traveling very near light that those differences become clear. And only if returning to that 'frame of rest' relative you accelerating & journeying away and back (like the twin experiment).

So 'times arrow' is a very diffuse thing. Although always macroscopically pointing in the same direction at 'all times', and according to you, always giving you the 'same time' no matter what you do.

[JP]

firstly does the theory of relativity therefore postulate that mass at the centre is older than mass at the surface.

Yes, that's a result of the theory.  As an example, if you had some radioactive element at both the surface and the center of the earth that you expected to decay in 200 years, the element at the center would decay slightly later.  (Again, we're talking about tiny fractions of a second per day). 

[gem (OP)]

So therefore does that mean the theory of relativity postulates that the mass at the centre is travelling at a different speed?

[JP]

So therefore does that mean the theory of relativity postulates that the mass at the centre is travelling at a different speed?

No.  There are two theories of relativity.  Special relativity describes how lengths and clocks measure things differently when objects are moving with constant (but different) speeds.  General relativity describes how gravity works and describes how clocks measure things differently when objects are at different places in a gravitational field.  The effects I'm talking about are based on the general theory of relativity, so it just has to do with things at different points in a gravitational field, without accounting for their relative motion.  They measure time differently even if they're standing still with respect to each other.

[yor_on]

Jp why would it decay slower in the middle of the Earth?

The closer you come to a neutron star the slower your clock will be relative the rest of the universe, right? Are you saying that if I burrowed my way into the exact middle of that neutron star, I would get an even slower clock? Although gravity would be 'nulled' in there?

As I think of it you will have the highest gravity on the surface, therefore also the slowest clock, any direction chosen, up or down from that surface, will give you a faster clock relative the observer 'at rest' with the surface as gravity goes down both ways? If it is as you say that the middle will give me a slower clock, then you need to explain why to me

As I then will have to reconsider my idea of SpaceTimes geodesics, well, at least it seems so to me.
==

This should be possible to test with two radioactive samples and some really deep shaft in South Africa. Is there any experiments done proving this?

[yor_on]

What you're saying seems to involve a situation where the equivalence principle isn't correct then?  And we're still speaking general relativity? That one is strange to me, I didn't knew this was a proved fact?
==
Some more wondering's.

If that is correct then the weightlessness inside the middle of the Earth isn't equivalent to a weightlessness outside Earths gravitational field? Or if they are seen to be equivalent and both are a form of free fall' then? If this one is correct, a 'uniform free fall' doesn't exclude different time rates inside that frame of reference. Can you see what I mean there? that the same 'body' would be weightless in both cases but in one being 'trapped' in a gravitational field. And in that case have no direction of least effort or 'energy'. Would that mean that to be 'at rest' relative something it suddenly isn't enough with having f.ex the same uniform velocity?

[gem (OP)]

  The effects I'm talking about are based on the general theory of relativity, so it just has to do with things at different points in a gravitational field, without accounting for their relative motion.  They measure time differently even if they're standing still with respect to each other.

If this were true IE two points that were measuring time differently but were standing still with respect to each other and these points were contained within the sphere of the earth which is in motion around the sun at a average orbital speed of 107218 k/m per hour.

It would mean that the clock at the center of the earth would measure one revolution of the earth relative to the sun slightly longer than a clock at the surface, meaning that the mass at the centre is travelling slower at over a kilometre every time the sun reaches its zenith relative to a fixed point,[one day] so is it not time running slower but just accuracy of the clocks in different strengths of force field.

As I then will have to reconsider my idea of SpaceTimes geodesics, well, at least it seems so to me.
=

If gravity is a force field i would totally agree. i am still with newton on this one [mass moving in straight lines unless acted on by a force]