how should i time my eggs

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Offline gem

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« on: 08/03/2010 21:22:21 »
 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].


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Offline flr

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« Reply #1 on: 08/03/2010 22:09:28 »
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.

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Offline gem

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« Reply #2 on: 09/03/2010 07:40:17 »
Does that mean you prefer the atomic clock method ?

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Offline JP

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« Reply #3 on: 09/03/2010 08:19:36 »
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.

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Offline gem

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« Reply #4 on: 09/03/2010 19:56:10 »



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



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Offline JP

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« Reply #5 on: 10/03/2010 00:38:53 »
Aren't you just asking about the accuracy of the clocks in different places in the gravitational field?

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Offline Geezer

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« Reply #6 on: 10/03/2010 06:32:57 »
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.
There ain'ta no sanity clause, and there ain'ta no centrifugal force æther.

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Offline JP

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« Reply #7 on: 10/03/2010 06:40:53 »
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. 

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Offline Geezer

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« Reply #8 on: 10/03/2010 07:28:51 »
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.
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Offline gem

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« Reply #9 on: 10/03/2010 20:07:56 »
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?

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Offline JP

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« Reply #10 on: 11/03/2010 00:46:36 »
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).

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Offline Geezer

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« Reply #11 on: 11/03/2010 03:18:12 »
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.
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Offline gem

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« Reply #12 on: 11/03/2010 19:58:25 »
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.

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Offline yor_on

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« Reply #13 on: 11/03/2010 21:19:14 »
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.
« Last Edit: 11/03/2010 21:35:06 by yor_on »
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Offline JP

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« Reply #14 on: 12/03/2010 01:13:51 »
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). 

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Offline gem

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« Reply #15 on: 12/03/2010 07:12:25 »
So therefore does that mean the theory of relativity postulates that the mass at the centre is travelling at a different speed?

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Offline JP

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« Reply #16 on: 12/03/2010 07:50:16 »
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.

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Offline yor_on

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« Reply #17 on: 12/03/2010 16:59:37 »
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?
« Last Edit: 12/03/2010 17:27:08 by yor_on »
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Offline yor_on

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« Reply #18 on: 12/03/2010 18:10:47 »
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?

« Last Edit: 12/03/2010 19:52:47 by yor_on »
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Offline gem

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« Reply #19 on: 12/03/2010 19:52:05 »

  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]

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Offline Geezer

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« Reply #20 on: 12/03/2010 21:14:59 »
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.
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Offline gem

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« Reply #21 on: 12/03/2010 22:49:41 »
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?

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Offline JP

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« Reply #22 on: 13/03/2010 02:09:27 »
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. 

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Offline yor_on

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« Reply #23 on: 13/03/2010 14:04:05 »
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 :)
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Offline JP

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« Reply #24 on: 13/03/2010 15:54:11 »
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.

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Offline yor_on

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« Reply #25 on: 13/03/2010 20:04:33 »
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.


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Offline gem

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« Reply #26 on: 13/03/2010 22:24:34 »
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

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Offline gem

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« Reply #27 on: 13/03/2010 22:25:50 »
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].



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Offline gem

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« Reply #28 on: 13/03/2010 22:33:16 »
maybe there will be little raised bits in the rubber sheet where the mass is

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Offline yor_on

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« Reply #29 on: 13/03/2010 23:11:16 »
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:)
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« Reply #30 on: 14/03/2010 00:08:54 »
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 ::))
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« Last Edit: 14/03/2010 00:54:42 by yor_on »
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Offline gem

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« Reply #31 on: 14/03/2010 13:08:46 »


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]
« Last Edit: 14/03/2010 13:57:28 by gem »

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Offline fontwell

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« Reply #32 on: 15/03/2010 11:00:20 »
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.

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« Reply #33 on: 15/03/2010 14:12:01 »
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?
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Offline gem

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« Reply #34 on: 15/03/2010 22:08:51 »

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
« Last Edit: 15/03/2010 22:11:19 by gem »

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« Reply #35 on: 16/03/2010 02:45:53 »
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’?
« Last Edit: 16/03/2010 02:53:27 by yor_on »
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« Reply #36 on: 16/03/2010 03:00:30 »
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.  tf 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.  

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« Reply #37 on: 16/03/2010 03:05:33 »
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. 

[attachment=11588]

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« Reply #38 on: 16/03/2010 03:31:35 »
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)
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« Reply #39 on: 16/03/2010 03:55:07 »
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...

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« Reply #40 on: 16/03/2010 06:51:27 »
Assuming minor details like temperature and pressure have negligible influence on gravity, would not the gravitational effect at the centre (of mass) of the Earth be almost the same as the gravitational effect at a very great distance from the Earth?

In either location, a body would be unlikely to alter its distance from the centre of the Earth because of the Earth.

Perhaps this is a fancy way of saying that the Earth produces no gravitational effects at its centre.
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« Reply #41 on: 16/03/2010 15:08:03 »
Are you thinking that the geodesics might look the same at a far spot in space, as it does inside the middle Geezer? I had that disturbing feeling too yesterday thinking of it, like a flat paper (two dimensional) with mass creating the three dimensions we see. Then mass could make a 3D description of a 2D space..

Kind of like that, although as I think of it, what we see as 3D is 'whole patterns', not 'cut & paste' So my universe would then be a 'flat-land', with matter creating 3D as times arrow binds it together for us into a seamless experience.

Ahem.. :)

with some weird kind of 'bumps' making up what we call 3D? Alternatively it could be times arrow that then produce the effect of what we call matter and also what we see as a 3D environment?

(Well, they're waiving at me over there, better go, the doctor gets so irritated when I don't:)
« Last Edit: 16/03/2010 15:09:54 by yor_on »
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« Reply #42 on: 16/03/2010 16:22:41 »
Yoron: My thought was a bit more Newtonian I'm afraid. [:D]

It was more along the lines of the net effect of gravity at the center of mass (due to the Earth) will be zero.
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« Reply #43 on: 16/03/2010 18:44:54 »
Ah well. Prosaic is cool too :)
And I can proudly say that I'm one step behind :)

My view is turning into an Copernican one ::))
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« Reply #44 on: 16/03/2010 22:39:25 »
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.
Sorry yor on that's probably my fault my  thinking of time is probably along the ethereal lines so i struggle with statements like ' time actually runs faster there or atomic clocks run faster showing that gravity bends time'.

hence the post to put space time theory to a few tests,[I think its my way of kicking the tyres of the vechicule that is space time before i buy in to the idea] when i mention time and speed at the back of my logic is the laws of conservation of energy and wether i can use them to show space time theory contravenes them.
 
Because it is said if a theory is right it gives the confidence to make other theory's [or question others ] and i believe the laws of conservation of energy hold in the physical world, so i will try and come up with a scenario of placing a horse in a space suit in different values of gravity and time and see if we get the same values as Mr Watt.

getting back to where  we are up to J p has summed up very nicely indeed in his last two posts, so we have to consider does what is postulated on this post have any  specific impact on space time theory by bringing newton physics in to space time theory. [has it really not been considerd before?]

Are you thinking that the geodesics might look the same at a far spot in space, as it does inside the middle Geezer? I had that disturbing feeling too yesterday thinking of it, like a flat paper (two dimensional) with mass creating the three dimensions we see. Then mass could make a 3D description of a 2D space..

On that note you have to consider that at the centre of earth the sun and the moons gravity field [space time] still exist UN altered and given that earths core is said to be a solid within a fluid it is probably held in place or comes up against the fluids pressure gradient {but i am straying in to something else there that i will be posting later] many thanks for the posts so far
« Last Edit: 16/03/2010 22:41:14 by gem »

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« Reply #45 on: 17/03/2010 06:46:19 »
Ah well. Prosaic is cool too :)
And I can proudly say that I'm one step behind :)

My view is turning into an Copernican one ::))

"Prosaic". Was that a typo? Perhaps you meant Prozac? http://en.wikipedia.org/wiki/Prozac
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« Reply #46 on: 17/03/2010 16:49:46 »
Ah?
Prozac??

Now, would that be a invitation, or a theory??

My dear friend, in a true Copernican manner I just have to state. "I am the world" That as I just follow it to the logical end, as did our first royal Copernican, Louis XIV when he stated "I am the state". He also said "There is little that can withstand a man who can conquer himself." Which I agree wholeheartedly too even though it sounds a mite lonely? Let me finish with his immortal words. "It is legal because I wish it." which should cover most of my views, I hope?
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« Reply #47 on: 17/03/2010 19:01:48 »
Just to repeat my previous post on this topic, I think that bending of space-time, and thus time dilation, is caused by mass. Gravity is an effect of bent space-time, not the other way round. And mass bends space-time.

The famous analogy is to place a heavy metal ball on a rubber sheet, or a  mattress, or even a rubber sheet on a mattress :) The sheet is only two dimensions but represents space-time for our purpose.

The heavy ball makes a dip in the sheet and also for some distance around it. This bending of the sheet is analogous to how a mass bends space-time in GR. We would see that objects roll down into this dip as if attracted to it. The way that objects fall down the dip is analogous to gravity in GR. They look as if they are attracted to the mass but actually they are following a path due to bent space-time. It just happens that the mass bent the space-time.

Note that near the ball the dip has a steep gradient. This really pulls objects in. Further away, the dip has less gradient and so the pull toward the dip is weaker. The gradient of the dip is analogous to gravity.

Note that if you just look at the shape of the dip, there is no gravity at the bottom of the dip because the sheet is flat at this single point. So just like with Newton we get zero gravity at the balls centre (or the earth's centre). However, at this same point, the sheet itself is at its most stretched, and it is the stretching that makes time appear to run differently.

I know that the ball and sheet thing is only an analogy and that you can stretch an analogy too far ;) but I think this is how it works. So, the time differences will continue all the way to the centre because that is where the space-time is most stretched, but gravity will fall to zero because it is caused by the gradient of the stretching.

The result is, don't use a gravity egg timer.

Also, I can't see it now but did someone ask how to tell if you are in an inertial frame? Well the answer is, you pick up the egg with your hand and then open your hand. If the egg moves away from your hand you are not in an inertial frame. If it stays inside your open hand you are in an inertial frame.


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« Reply #48 on: 17/03/2010 20:31:23 »
Fontwell, it's interesting the way you think of gravity. You seem to split it in stretching/stressing(?) SpaceTime and its gradient that then will equal an gravity?. Using that analogy seems to leave me two ways to see what we call that 'flatness' area. Either I associate it with 'levels' like invincible layers upon layers where the so called 'flatness' aka non gravity can exists on all levels, like our dip with that new 'flatness level' on its bottom. Or one could imagine one 'flatness level' only, and there I wonder how those gradients would look? It's intriguing. Is there anything speaking more in the favor of time moving faster or slower 'down there'? Like some analogue experiment pointing to one way or another? Or does it build on the math describing gravity. That as I've seen the same idea at other places. And Gem :) do you have any thought experiment drawn up yet?

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« Reply #49 on: 17/03/2010 23:15:04 »
Just to repeat my previous post on this topic, I think that bending of space-time, and thus time dilation, is caused by mass. Gravity is an effect of bent space-time, not the other way round. And mass bends space-time
 

If gravity is only an effect of space time what property of mass is bending space?

yor on, just a quick one because something in j p posts has got my attention
[Einstiens seems to have got a double error that got him closer than newton to what we actually observe will be posting in 'is this the source of the pioneer anomally' later this week]

Right, that horse or engine equal to one horse power forgive the imperial measurements but that's what watt used.

WE WILL USE THREE PLANETS ALL WITH THE SAME RADIUS AND  ROTATION SPEED AND THEY ALL ORBIT THE SUN AND THE ENGINE/HORSES WORK FROM DAY BREAK TO NIGHT FALL.

on earth one horse power is equal 550 foot pounds per second  now lets put that same engine on a planet with half the gravitational force that should mean that that same one horse power should be able to lift 1100 pounds per second ,

However if the atomic clock runs faster it would seem that the engine was not quite operating at its full 1 hp.

And if we reversed the scenario and placed the engine on a planet with a gravitational force twice times earth then the said same 1 hp should be able to lift 275 pounds per second  but the atomic clock is running slower and so it would seem that the 1 hp engine is operating at an efficiency greater than 1 hp.

So it would seem that space time theory contravenes the laws of conservation of energy
or does that stretchy rubber sheet help lift the mass in some way. 

so one which planet would i get more miles to the gallon
« Last Edit: 18/03/2010 20:37:15 by gem »