[Geezer]

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.

It's not a question of accuracy. Time actually differs, so everything from electrons to elephants moves according to that time. Therefore, the speed of the centre of the Earth is not different, because speed is a measure of distance in time.

It's counterintuitive to accept that time is not constant. Try thinking of it this way; because time is different at the two places, the subatomic activity of atoms at the two locations (all other conditions being equal) actually "run" at different rates relative to each other. However, because literally everything is affected at those locations, it is impossible to detect any difference at the locations. That can only be done by some sort of relative comparison.

[gem (OP)]

First a little correction please ignore this figure

 the mass at the centre is travelling slower at over a kilometre every time the sun reaches its zenith

I believe i may have slightly upped the figure above, for the distance traveled by the earth in the time it takes to perform one rotation 107218 k/m hr times 24 =2573232 km divided by the amount of seconds in one rotation 86400 divided by 1oooooo.[one million] equals 30 millimetres .     oops [] []
But the principle is still the same .

because speed is a measure of distance in time.

how can the time actually differ to travel the same the same distance and the two masses still be stationary relative to each other.

Also when i pick up a mass on earth am i feeling earths gravitational force or a bending of space time?

[JP]

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?

Oops.  You're probably right--the situation would be reversed now that I think about it.  Time would go faster in the center of the earth as compared to the surface for the reason you say: gravity is negligible there which should be equivalent to being in space far from any gravitating bodies. 

[yor_on]

JP I'm not stating that you're wrong, I've seen others arguing that it comes naturally from the mathematics involved, and few arguing the other way around, it's just me walking around in blissful ignorance . I would really like to see some real experiments done about it though, proving it one way or another.

That as it to me seems to point to how to look at gravity, maybe I haven't thought it through but I still wonder how SpaceTimes Geodesics and being weightless inside the 'middle' of a 'gravity field' goes together. If the concept holds and the situation in the middle is equivalent to a free fall?

Or if it won't hold? What will gravity be then, some 'magnetic monopole'? But I know that there are several physicists seeing it exactly as you did there. It's just me not knowing how to see it

[JP]

I actually think you're right, though. 

The usual description of time slowing down as you move towards a massive object assumes you're outside of the object.  The equations have problems once you pass through the outer crust of the massive object.  I think it makes sense that at the center, where you're essentially in free fall, you should experience the same passage of time as in empty space.  I don't know GR well enough to be 100% sure, but it makes sense to me as an educated guess.

[yor_on]

Would you agree to it having an importance to what one should see those SpaceTime geodesics as, any which way? It seems so to me. If I assume that there is an equivalence to it, what will it do that 'rubber sheet' analogy? And if it isn't, what would that mean? That you can be weightless without free falling? Isn't that a 'anti gravity' concept?

Well JP, I have patience, I can wait those few hours it will take you to read in the rest of that math of general relativity, you might feel needed. And as it is so truly general (Why else would they call it 'general'?) I surely can expect it to be a fairly quickly process, Ain't that right?

So the time is, ah, nine pm here locally. Yep, I'm sure you can do it on your coffee break, it's alway nice to have something to do there

Don't worry, I can wait an hour more, if needed.. )

Hmmm.

[gem (OP)]

Would you agree to it having an importance to what one should see those SpaceTime geodesics as, any which way? It seems so to me. If I assume that there is an equivalence to it, what will it do that 'rubber sheet' analogy? And if it isn't, what would that mean? That you can be weightless without free falling? Isn't that a 'anti gravity' concept?

I actually think you're right, though. 

The usual description of time slowing down as you move towards a massive object assumes you're outside of the object.  The equations have problems once you pass through the outer crust of the massive object.  I think it makes sense that at the center, where you're essentially in free fall, you should experience the same passage of time as in empty space.  I don't know GR well enough to be 100% sure, but it makes sense to me as an educated guess.

I refer to my first post on this matter

[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].

[gem (OP)]

maybe there will be little raised bits in the rubber sheet where the mass is

[yor_on]

Yes Gem, you and me seems to have that intuitively reached concept together

As for me teasing JP on general relativity and the math surrounding it, I understand that math to be amongst the hardest there is to set your teeth in So I can easily understand why there is discussions ongoing on this. Special relativity seems somehow easier to understand, than to use the whole shebang as 'general relativity' describes (spaceTime).

As for your egg timer I'm not sure what you mean? Are you thinking of a glass one, using sand for its time measures? Or are you thinking that 'times arrow' will change as compared to something outside its 'frame of reference'?

There is a strangeness to the concept when considering times arrow. F.ex you can have different free falling orbits around the earth, right? closer and further away from it, would you then argue that there will be only one concept of 'times arrow' for all those geometrically different orbits? That they all share the same 'rate of time' as observed/compared from an far observer?

And the time inside that Earth? What if we changed/compared it to a neutron star instead? Would you argue that the 'time' then would be the same at both places, inside that exact middle?

So we have two scenarios here. The first one is testable, the other one? Naah
But I agree, it's one of the weirdest phenomena I've thought of in some time. If the first scenario would be answered, such as all free falls (orbits) are the same, would that then guarantee a answer to the question about the middle of our planet?

I don't think so? We need to test that one for itself.

Assuming we test both ideas, orbits and that 'deep shaft' and get conclusive evidence stating that time do 'speed up' inside the middle, and that all free falling orbits around the Earth is the same 'Time wise', as observed from an 'far observer', then we would have something I think, that is, or not, possibly too )

(And I can't understand what's taking JP so long? Two hours already:)

[yor_on]

To sum it up, we know that different velocities will present us with different time, we can see that with muons falling in on our Earth. They are surviving longer than is possible considering their 'normal' life length on Earth. Thinking of it they are in a way 'uniformly accelerating' into Earths gravity field, or as I see it, taking the shortest possible path through Earth's (SpaceTimes) geodesics, free falling into a gravity well if you like. That will to the far observer at rest with Earth seem as an acceleration, but with the difference of there being no energy expenditure for in-falling muon. And there it seems to me, to be an crucial difference between acceleration spending energy, and what we now discuss, a 'free fall'? So then, to me it seems quite plausible that different orbits will have to be adjusted for different time dilations relative Earth (GPS)?

And if that is so then we know that being isolated (black box) in a free fall tells us nothing about the time, It's only when compared from another far observer (another frame of reference) there will be a 'difference' measured. Inside that black box it won't matter what uniform motion you have relative anything else, your time frame won't differ. What difference there is, will then be the relation expressed between you comparing and what you compares your frame of reference too. As with two uniformly moving rockets passing each other near light speed, as observed by each other.

So, looking at it that way, assuming that we can call the situation inside the middle for equivalent to a free fall, what would you then think of the scenario Earth versus a Neutron Star? To me intuitively it seems as if 'time' would be able to differ there as you when you're doing it actually compare one 'free falling' frame against Earth in one case, a neutron star in the other.

Well, that's my take on it?
But it is so lovably weird
==

I will stop looking at it now, or I will find even more 'clarifications' I need to do )
Sh*

[gem (OP)]

Assuming we test both ideas, orbits and that 'deep shaft' and get conclusive evidence stating that time do 'speed up' inside the middle,

The deep shaft test may not be conclusive one because the shaft would have to be very deep and two the earths core is thought to be a lot denser than the rest of the planet.

I like the way you are thinking and you have posted lots of relevant questions and i will discuss these and other issues later, at the moment i have family coming for dinner [mothers day]

[fontwell]

Just to say something on the issue of the zero gravity at the earth's centre versus 1G at the surface. I think the bending of space-time and slowing of clocks is due to mass, not gravity. Gravity is an effect of curved space-time. The centre of the earth is at the bottom of a local curve and so there is no gravity there. However, the actual curve is at its lowest point so the time is most slowed down. I think.

[yor_on]

A subtle but penetrating idea fontwell. So what are distances? Are they also 'brought upon us' from mass? Assuming a place of no mass, then there can be no distance either?

[gem (OP)]

As for your egg timer I'm not sure what you mean? Are you thinking of a glass one, using sand for its time measures? Or are you thinking that 'times arrow' will change

The egg timer i was using as an example was the glass and sand one, the reason i used this and the atomic clock was to demonstrate opposite effects of gravitational force on systems we call clocks to make a clear definition of the physical dynamics at the center of a mass [planet].

Because when discussing time and times arrow i am still not convinced it is not just a mathematical construct to measure cause and effect in the physical world.

If it really is a bending of time and their are peaks in the fabric of space time in the centre of the mass of planets then the fact that the mass at the centre travels at the same speed as the rest of the planet should mean there should be a physical stress/strain happening within the planet similar to tidal stresses.
[are tidal stresses already called difference in space time stresses in the theory of relativity ?]

However if a clock was designed that was unaffected by gravitational interaction and it ran at the same speed where ever it was in space what would that do to the concept of curved space time

 We would still have the issues of thermodynamics at the macro level and atomic particle level effected by the strength of gravitational interaction having a direct effect on the speed of change on the level of entropy.It is wether we need to tie time to one specific physical happening is one of the things concerning me.

Next generation clocks to replace caesium fountain clocks are said to be optical clocks i don't know to much about how they work but i wonder if they are using a design that is effected less by gravitational force.

One other question that comes to mind is how much faster is time sopposed to go in Zero gravity in a day compared to 1 g one earths surface 50 millionths 60 millionths of a second?.

I am not to sure of your meaning in regard the same rate of time for bodies in different orbits other than they will be experiencing different gravitational acceleration.

I will leave it there for tonight look forward to any thoughts

[yor_on]

I'm still not sure I understand the concept we’re discussing Gem Sometimes I think I do but then, just as sudden, I feel that I lost all sight of it again. Consider two uniformly moving clocks in space, both being in what we call a 'free fall'. They are equivalent in that motto, except for one thing. It was us that sent them out, and we gave them two different 'uniform motions' relative Earth.

One has double the speed of the other. For those very small gnomes marking times passage inside those clocks, having no windows and no interest in looking out either, time passes as it always have done inside their clock, as I understand it. But assume that they are returning at some point. Naturally it will mean that the one traveling fastest relative Earth will use more energy returning (acceleration), but my question here is if you really can ignore their time of uniform motion and only see their time dilation as a result of acceleration?

To make it, hopefully, clearer, as I see it there will be no difference in energy spent by their returning after one years travel, compared to them spending ten years before turning back, as observed by Earth.  But will that uniform motion for nine more years change their time rate relative each other, and us? And yes, the exact same clocks with the exact same twin-gnomes. So, do 'uniformly motion' have an importance to clocks time rate relative their origin (Earth)?

So how do we define objects being at rest versus each other? If we by being 'at rest' only defines it as being stationary relative to a particular frame of reference, or another object? Then we allow for different time perspectives as those two objects can have a different invariant mass, although sharing the same velocity. And then I could argue that those two objects can be arbitrarily far placed from each other and still be seen as a 'system being at rest’ versus each other? And if so, it seems silly to argue that they somehow share 'gravity' with each other, don't it? As they can be a thousand light years apart I mean, or more.

So it seems to me that we know that ‘time rates’ have nothing to do with being in a free fall, aka uniformly moving. Am I making sense here?  There can be different time rates for objects being at rest with each other. If we now look at the clock inside our Earth it is at rest relative Earth but its time rate can differ, but in which direction? There we have one, possibly two possibilities that I can see. Gravitational time dilation, by which I mean the effect mass have on SpaceTime (geodesics), which also includes its own invariant mass. And possibly the effect of ‘uniform motion’?

That it is at rest with Earth won’t exclude the uniform motion it share with Earth. And where you want to draw the ‘limits’ of what motions one should include there I don’t know What we do know is that it seems to be ‘free falling’, equivalent to something traveling in a uniform motion without any mass acting at it. At least I understands it that way? If you don’t accept that definition you will have to define how it can be weightless, but yet not ‘free falling’ And that seems to me to come near a concept of ‘antigravity’ if so? And if my reasoning holds I also guess that this clock will have the same time as an object of its mass would have moving uniformly through space on its own, possibly? With the addition that its uniform motion also might have a role for its time rate. Not that it will differ in this case as they are at rest versus each other. So we can have different ‘time frames’ even when being at rest with another frame. Which having two different invariant masses at rest with each other seems to be good examples of.

When it comes to time introducing a stress on matter I’m not sure how you mean Gem? If what I think is correct then, possibly uniform motion, acceleration and mass are what defines time for us. Inside our own frame of reference time won’t change, the only thing we might notice is an increased mass, made by acceleration and/or invariant mass, but even when getting ripped apart by tidal forces at a black hole your time will be ‘as always’ to you when taking your pulse as it happens, which would be quite a feat btw

I think you are wondering about the same thing as me, but you speak about time and speed. Speed is defined as a measurement in time over a distance. Inside your frame one meter will be one meter no matter where you are, it is only in the comparison with another frame you might notice a difference, and that difference will always be the other frames ‘difference’, not yours. That we know that the other frame will notice the same thing about you tells us something, it tells us that distances is a very Copernican thing, always getting defined from your own frame. If that is so then times arrow and distances doesn’t fight each other, they cooperate in a very plastic way and there won’t be any ‘stresses’ due to that.

But it sure makes one wonder about what a ‘distance’ then should be defined as in our new world. As it will change with acceleration, uniform motion and mass. There is a subtle strangeness to, as I see it, comparing your frame to SpaceTime outside that frame. When you’re accelerating, time outside your frame speeds up relative you, and the meters outside ‘shrink’ too, not because you’re driving faster but because SpaceTime actually becomes smaller as compared to your frame, as I understands it. And you can imagine several accelerating objects at the same time, all observing different SpaceTime’s and measuring different distances between the same objects. And you can also imagine someone back at Earth watching them all, never losing sight of them and getting yet another distance measuring  the same objects.  Time is an ethereal thing to me but distance seems more ‘real’ But in this case neither of them are so, right?

So maybe my reasoning hold so far. If you see SpaceTime as fontwell, graphical curves describing invariant mass bending space, then the question seems to become if that curve then can have a ‘spike’ in it Or is it is us missing something when looking and thinking of space?  Maybe we’re looking at it from a false perspective. If we assume that you and me are correct in our expectation how would one then describe SpaceTimes geodesics? If the ‘shortest path’ is the one a photon describes when observed, what would it describe inside that middle? Then Space in some ways act as if matter is no ‘barrier’ for that ‘straightest path’?

[JP]

Now it is somewhat easier to do the calculation if you consider that you're always outside of the earth and you make some approximations: (1) that the earth is a sphere, (2) that the earth isn't rotating and (3) that the earth is the only source of gravity in your system.  Even though these aren't strictly true, I think the result is going to be fairly accurate.  Under those assumptions, you can write down a (fairly simple) solution to Einstein's field equations of GR rather than having to rely on numerical simulations.

The solution is called the Schwarzschild solution (in honor of the first person to work it out) and if you're trying to measure the time between two events and time dilation is given by (from Wikipedia).  Here, G and c are the gravitational constant and the speed of light.  M is the mass of the earth and r is the earth's radius.  t_f is a tick on a clock infinitely far from the earth where gravity is negligible and t₀ is a tick on the clock at the earth's surface.  

I plugged in the constants and I get roughly 60 microseconds of disagreement per day as measured by the person infinitely far away from the earth.  

[JP]

By the way, I'm not sure how correct this is, but if you assume that you can model diving into the earth the same way that Newtonian gravity does, i.e. by considering that only the mass within a sphere centered at the center of the earth and with radius equal to your distance from the center, then time measured at the center is the same as time measured infinitely far away.  Here's a plot of the time difference (in microseconds) versus distance from the center of the earth (in meters) for the above assumptions.  You'll notice the biggest difference is at the earth's surface and it dies away in both directions. 

 [ Invalid Attachment ]

[yor_on]

You are giving us an approximation to the difference of time-rate between being placed 'outside' Earth's geodesics (gravity) and being on the surface JP?

Very nice:)
And that would then be our possible difference inside that middle too?
JP, so very cool. I kind'a love it..

(I was actually joking before, but you came through anyway)

[JP]

Well I still don't know what the correct way to model gravity inside the earth is.  I just made a guess based on how Newtonian gravity does it by only using some of the earth's mass contained in a smaller sphere.  This may not be right because all the stuff I've ever seen on the Schwarzschild metric says you are outside of the object.  In the plot, the right-hand part of the curve is certainly right within the Schwarzschild approximations.  The left-hand part is what I'm unsure on...