Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: gem on 08/03/2010 21:22:21
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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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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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Does that mean you prefer the atomic clock method ?
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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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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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Aren't you just asking about the accuracy of the clocks in different places in the gravitational field?
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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.
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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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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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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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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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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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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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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.
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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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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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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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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.
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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?
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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?
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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?
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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.
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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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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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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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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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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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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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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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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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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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maybe there will be little raised bits in the rubber sheet where the mass is
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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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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 :)
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I will stop looking at it now, or I will find even more 'clarifications' I need to do ::))
Sh*
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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]
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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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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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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
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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’?
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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 (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fmath%2F1%2F2%2Fb%2F12b6af8d31abe31378245988a0e74f66.png&hash=38131a4a68c8978cbb927449fe35c2a2) (from Wikipedia (http://en.wikipedia.org/wiki/Gravitational_time_dilation)). 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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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 ]
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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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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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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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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:)
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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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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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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
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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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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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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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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?
"Damn that doctor.." he mutters as he has to run again.
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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
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(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fd%2Fd9%2FGravityPotential.jpg%2F300px-GravityPotential.jpg&hash=848f35613bf74f8f41fe54b2817d5567) (https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fnrumiano.free.fr%2FImages%2Fbh_warp1_E.gif&hash=a7489b4a43454dc83dcd0c694307eec8)
Having hunted around it seems to be accepted that mass bends space-time, and bends in space-time cause gravity e.g. see http://en.wikipedia.org/wiki/Gravity#General_relativity -> "the effects of gravitation are ascribed to spacetime curvature"... "Einstein proposed that spacetime is curved by matter." By 'matter' he implies mass.
I have only found a few places where they explicitly say the gradient (derivative) of space-time is gravity but it always seems to be understood this way.
Famous quote: ‘Matter tells space how to curve. Space tells matter how to move.’
Translation: Mass bends space-time. Bent space-time causes gravity.
I feel pretty confident to say:
Mass curves space-time, the gradient of the space-time curve is gravity. Time dilation is a function of the space-time curve's magnitude, not its gradient.
To be honest, I haven't ever come across any discussions on GR where anyone thought other than this, its just mainstream GR isn't it?
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No worrys :) it's just that I haven't thought of it that way before, I have always seen those geodesics as the true 'straight paths' sort of. To me mass and space are very much the same thing, I haven't really thought to separate them. Like we say that a black hole (Schwarzwild solution) opens to infinite (?) distances inside the EV according to some thoughts, and even more so for a spinning one. To me it seems that they go together (Space and mass), so when you used the sheet analogy this way it made me curious. I can see the idea, but then my thought visually became how to set this flat sheet 'pulled together' and wonder how mass could be represented from such a view. That is if we assume that a free fall is equivalent to another free fall, no matter internal time rates differing, and that both represent the same 'flat sheet' ?
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Or is there some way of describing that 'weightlessness' without using the idea of a free fall? Uniform motion for example, when the motion is zero relative something else, like we have in those innards of our earth, we can still say that A even if at rest with B still have a uniform motion when compared to C, right? So that thingie in the middle do have an uniform motion, even if not relative Earth? So in one way you might say that it share a free fall with our Earth, but as it also is 'weight less' relative Earth its equivalence seems to have more to do with 'space' than with our Earth?
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Doesn't time dilation/length contraction have to do with how you measure space-time distances, which is in turn defined by the metric tensor? http://mathworld.wolfram.com/MetricTensor.html The metric tensor appears to measure curvature, which involves derivatives, rather than magnitudes.
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By the way, I think there is an error in my previous reasoning about drilling into the earth, as the Schwarzschild solution assumes that you're solving the equations in a vacuum (where the stress-energy tensor is zero). Inside the earth, this wouldn't be the case. I don't know what the proper form of the solution would be or if it's solvable without numerical simulations.
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I saw an explanation on it somewhere where every 'bit' of matter was treated as having, that is if I remember right now, an equal effect on every other bit? I think it was a Newtonian concept though? But it came to the conclusion that in the middle they would 'negate' the 'attraction', or as we say the 'bending of space'? Hyperphysics takes this approach when digging a hole (http://hyperphysics.phy-astr.gsu.edu/Hbase/mechanics/earthole.html) to the problem.
Another question relating to that middle of out Earth? If I assume that it is equivalent to a free fall, can there be a pressure acting at that point? There can, right? As it is a part at rest in a bigger system Earth / 'It' :) Analogous to your black box can be inside a bigger pressurized black box..
As for the metric tensor JP? Want to explain how you think for us more , ah, solid ones there? No, not 'thick headed' solid I said. By 'curvature involves derivatives' you would then mean that? It measures difference instead of magnitude for those points in space? Or am I getting it all wrong? That's a subtle one JP :)
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I saw an explanation on it somewhere where every 'bit' of matter was treated as having, that is if I remember right now, an equal effect on every other bit? I think it was a Newtonian concept though? But it came to the conclusion that in the middle they would 'negate' the 'attraction', or as we say the 'bending of space'? Hyperphysics takes this approach when digging a hole (http://hyperphysics.phy-astr.gsu.edu/Hbase/mechanics/earthole.html) to the problem.
That works in Newtonian gravity. That's what I tried to apply to GR. I have a feeling you can't simply apply those ideas to GR, though.
As for the metric tensor JP? Want to explain how you think for us more , ah, solid ones there? No, not 'thick headed' solid I said. By 'curvature involves derivatives' you would then mean that? It measures difference instead of magnitude for those points in space? Or am I getting it all wrong? That's a subtle one JP :)
A metric tensor is a mathematical object that tells you about the curvature of a "surface" (or in mathematics what is called a manifold) at a point in space. You use it to define lengths on that manifold.
In general relativity, you have to measure "lengths" in space-time, and they are called intervals, since they involve events separated in time and in space. The metric tensor tells you how to define intervals locally (the definition depends on your reference frame). Since you're measuring intervals in space and time, it therefore tells you how the definitions of length and of time differ. The definition of the metric tensor involves derivatives, and derivatives tell you about slopes instead of magnitude. It seems to me that because the metric tensor involves derivatives, it's probably based on how space-time curves rather than on the magnitude of the space-time curve. By the way, there's a number called curvature that you can calculate from the metric, which isn't what we're talking about here.
In addition to the link I posted above, there's this description: http://en.wikipedia.org/wiki/Metric_tensor_%28general_relativity%29#Local_coordinates_and_matrix_representations
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If it helps, try to imagine that instead of being solid, the earth was made out a big sphere of liquid (which is probably true near the centre anyway. If you were at the centre you would be crushed by the pressure of all the mass but still feel no gravity.
Although this is a dubious way to think about the situation here it does indicate how mass can have an effect that is not detectable by measuring local gravity.
The idea of every piece of matter affecting every other piece by a gravitational pull is a Newtonian way to sum the net effects of masses. This kind of calculation results in a Newtonian explanation for zero gravity at the centre of a mass. But in GR gravity is caused by the bending of space-time and the bending of space-time is caused by mass. So in GR we do not ask how every piece of matter affects each other, we ask how do all the pieces curve space-time. Gravity is then derived from the curvature of space-time.
Really, this whole thing comes down to this; Is time dilation caused by mass, which bends space-time, thus making the centre of mass the most dilated place? Or is it caused by gravity, which is caused by the curve of space-time?
Well, the GR view of gravity is that it is only an effect of curved space-time. The GR view is that mass curves space-time. And the equations for time dilation refer to the centre of mass. The clock at the earth's centre is slowed by the combined pressure of all that mass around it. It does not care that it is in an inertial frame with zero gravity.
Also, distant orbiting satellites have faster clocks compared nearer to orbiting satellites, due to being further from the mass of the earth. But they also experience themselves as being in an inertial frame with zero gravity.
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If it helps, try to imagine that instead of being solid, the earth was made out a big sphere of liquid (which is probably true near the centre anyway. If you were at the centre you would be crushed by the pressure of all the mass but still feel no gravity.
Yes, and I think that what you're saying here agrees with the reason my earlier reasoning was wrong. The extra forces you're describing are likely components of the stress-energy tensor which we can't ignore within the earth. Therefore you can't just extrapolate from the solution outside the earth to get the solution within the earth--the form of the equations changes.
I also think I see how the timer within the earth should measure time differently than the timer in deep space. Even if things "curve" the same way at the center of the earth (since you're experiencing no net gravity), the entire space is squashed down. Think of a piece of graph paper in deep space. As you move down towards the center of the earth, it distorts because of the curvature and gets squashed, so it's no longer flat and the lines aren't parallel to each other. At the center of the earth, it's flat again and all the lines are parallel but it's been squashed to a smaller size. You can kind of see that if you look at the left-hand figure you show here: http://www.thenakedscientists.com/forum/index.php?topic=29156.msg304011#msg304011 .
I have to think a bit more to get it to make sense with the (little) mathematics of GR that I know, but it seems right...
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Even if things "curve" the same way at the center of the earth (since you're experiencing no net gravity), the entire space is squashed down. Think of a piece of graph paper in deep space. As you move down towards the center of the earth, it distorts because of the curvature and gets squashed, so it's no longer flat and the lines aren't parallel to each other. At the center of the earth, it's flat again and all the lines are parallel but it's been squashed to a smaller size
Yes!
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Yes, that's what I'm wondering too. Pressure and Gravity. You will have a pressure at the middle, that much seems clear but you can't equal that to a 'gravity', can you? Thanks for the explanations btw :) they're helpful. So one could say that in a mathematical sense the steeper the slope the slower the clock? And as all sides are extremely steep at a VMO f.ex you will have a very slow time where those slopes come together, no matter if they plan out there. Like some sort of 'gravitational vectors' pointing towards that 'flat point' in the middle of our VMO?
Hah I refuse to accept that, I just have to find some paper and a pencil, just wait and see:)
Nah, I'm sort of joking. But yes I can see how that view comes naturally from treating it as slopes with vectors pointing to the middle, that is if I got it correct ::)) But I still would like to see an experiment proving the concept?
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Ah, in the Jules Vernian sense I mean, measuring time differences. And then we have two different types of 'weightlessness' if this is correct, don't we? Or maybe not? You could compare it to an uniform acceleration giving you a constant gravity?? Nah, that's not being weightless, weightless is a 'free fall' as I understands it? In what way does that 'weightlessness' in the middle have anything to do with a free fall if so?? Awh..
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Yes, that's what I'm wondering too. Pressure and Gravity. You will have a pressure at the middle, that much seems clear but you can't equal that to a 'gravity', can you?
Correct, you can't. But it makes the point that an effect due to mass (pressure) can occur in a region where there is no gravity. Indicating that time dilation due to mass can occur in a place with no gravity.
So one could say that in a mathematical sense the steeper the slope the slower the clock?
No. Not if you mean the slope of curved space-time. You could say the steeper the slope the stronger the attraction of masses - which we observe as gravity. Gravity would be the steepness, time dilation would be the amount of stretch.
Ah, in the Jules Vernian sense I mean, measuring time differences. And then we have two different types of 'weightlessness' if this is correct, don't we? Or maybe not? You could compare it to an uniform acceleration giving you a constant gravity?? Nah, that's not being weightless, weightless is a 'free fall' as I understands it? In what way does that 'weightlessness' in the middle have anything to do with a free fall if so?? Awh..
Exactly!
As I understand it 'weightlessness' is 'weightlessness' but also 'mass' is 'mass' :)
By which I mean, free fall and being weightless in the centre of a large mass are the same in that an observer in either condition can't do a local experiment which would give different results (to him).
However, the presence of mass is a real thing which makes the two situations unequal. They will both agree on who has the faster clock - the one furthest from the mass. This is unlike inertial frames in SR where both parties observe the other to have a slow clock. Mass allows the situation to be absolutely unbalanced.
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So in what way would I be able to differ the weightlessness inside my black box at the middle of our earth, against being in a free fall? You could argue that pressure will do it, but you can set up a equal situation in a free fall I think, creating that pressure, can't you?
Either it will differ or?
Consider the definition of gravity as being equal to a uniform accelerating?
This one is still strange to me, even though your point of view makes eminent sense Mr fontwell :)
And the idea of equivalence doesn't build on looking at a situation with 'the eye of a God' as I understands it? It builds on the opposite, being in a black box unable to define anything except from your own frame?
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So in what way would I be able to differ the weightlessness inside my black box at the middle of our earth, against being in a free fall? You could argue that pressure will do it, but you can set up a equal situation in a free fall I think, creating that pressure, can't you?
Either it will differ or?
Consider the definition of gravity as being equal to a uniform accelerating?
This one is still strange to me, even though your point of view makes eminent sense Mr fontwell :)
And the idea of equivalence doesn't build on looking at a situation with 'the eye of a God' as I understands it? It builds on the opposite, being in a black box unable to define anything except from your own frame?
I agree, to my understanding, inside a block box there is no difference between the two situations, that is why relativity is still 'relativity'.
The difference is that near a mass everyone agrees clocks run slower than further away. But this does not create a privileged position, just different positions. The clock near the mass still measures local seconds but he measures clocks further away as running as too fast. Who is correct? There is no correct.
It is like we look at the clock on a GPS satellite and correct it to our local time. But the Sun affects us both, so the Sun thinks we are both too fast. But the centre of the Galaxy thinks the Sun is too fast. Even our observable universe is perhaps too fast for someone else!
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Yep :)
You're all to fast for me.
*Oh no, Those men in their white coats again, where do they grow them?*
Ah, gotta run now Mr Fontwell :)
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I'll be back ::))
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Hi all
gosh you have all been busy, font well certainly has helped clarify space time theory a little clearer for me as to how it can come to the same conclusions for different reasons. such a lot to take in i have read through every ones posts but will have to read through some more to make sure i have understood it all properly,
At the moment my grasp on it is 'newton' mass causes gravitational attraction force and when within a sphere of mass the attraction vectors cancell each other giving a resulting zero force on a body within.
Einstein separates gravity from the mass, gravity does not attract and the reason mass acceleration diminishes as you get nearer the center is because the curve of space becomes less
one question that comes to mind straight away though is about this statement that G R postulates
The difference is that near a mass everyone agrees clocks run slower than further away. But this does not create a privileged position, just different positions. The clock near the mass still measures local seconds but he measures clocks further away as running as too fast. Who is correct? There is no correct.
It is like we look at the clock on a GPS satellite and correct it to our local time. But the Sun affects us both, so the Sun thinks we are both too fast. But the centre of the Galaxy thinks the Sun is too fast. Even our observable universe is perhaps too fast for someone else!
Does this mean there is not a universe standard law of conservation of energy [work heat equivilance] ?
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I'm glad you are finding this helpful :)
Does this mean there is not a universe standard law of conservation of energy [work heat equivilance] ?
I'm pretty certain that conservation of energy is one of the few laws that always works. I'm not really very clear about energy in SR or GR but isn't it the case that everything works due to differences in potential energy (what ever that is!). So if it turns out that we are all affected (more or less) the same by a huge but distant mass it doesn't affect the local differences in potential.
This is actually our experience anyway - when we raise 1kg by 1m it takes 1Joule. We do not notice that this raising took place in the context of the Sun's gravity, that just adds an equal potential energy to both positions.
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We've had a few discussions about conservation of energy in GR lately. (There isn't a problem with conservation of energy in SR as far as I know.) Basically, GR has issues defining an energy, since when you include gravitational energy, the quantity that acts like a conserved energy doesn't transform appropriately when you change reference frames.
The two links I include below were useful in trying to understand this:
http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/GR/energy_gr.html
http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html
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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.
OK another question,
how is time slowest at the center ?
Because as i understand it Einstein used inverse square law and the earths radius, and one times one equals one. So it would seem to be the same as at earths surface, or am i missing something ? [i must be otherwise there would be no more down once your on earths surface]
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3 minites
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Well, the GR view of gravity is that it is only an effect of curved space-time. The GR view is that mass curves space-time. And the equations for time dilation refer to the centre of mass. The clock at the earth's centre is slowed by the combined pressure of all that mass around it.
I will say again in case the relevance of my previous question was not understood if the equations for time dilation were referring to the centre how is it possible that the time dilation is any different one radius away?, the values should be the same according to the radius squared part of the equation.
Meaning no curvature from the centre to the surface.
[Newton addressed this issue did Einstein]
Also i don't see how mass applies pressure other than as a consequence of gravity
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I will say again in case the relevance of my previous question was not understood if the equations for time dilation were referring to the centre how is it possible that the time dilation is any different one radius away?, the values should be the same according to the radius squared part of the equation.
Time dilation occurs wherever gravity curves space-time so that one point in space experiences a different rate of time than another. Since gravity starts curving space-time well outside of the earth and continues all the way down to the center, you would expect time dilation to occur between any two all radial points you chose. Only if you chose two points the same radial distance from the earth's center would you get the same rate of time. (And all this assumes the earth is a perfect sphere--in reality it would be slightly different.)
Also i don't see how mass applies pressure other than as a consequence of gravity
There's a term in the equations of general relativity called the stress-energy tensor. This is the term that tells space-time how to bend. Mass contributes to this term.
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OK another question,
how is time slowest at the center ?
Because as i understand it Einstein used inverse square law and the earths radius, and one times one equals one. So it would seem to be the same as at earths surface, or am i missing something ? [i must be otherwise there would be no more down once your on earths surface]
I'm not quite sure what you are asking. Inside the earth, distances from the mass of the earth are less than one earth radius. So time runs slower. There are some pictures near the top of the page in one of my earlier posts indicating the way that space-time is warped by mass. The warping isn't the same at the surface and the centre.
Also i don't see how mass applies pressure other than as a consequence of gravity
Of course. I may have confused the issue here by using an analogy comparing regular pressure of a liquid with the bending of space-time due to mass.
In a normal Newtonian way of thinking the pressure at the centre of the earth is huge. But there is zero local gravity (if you dropped a stone while at the centre it would not accelerate away from you). The only point of this is to show that just because a location has no gravity itself, it is not free from the surrounding effects of gravity and mass, even in Newton's world. So, just because there is zero gravity it doesn't mean we can say it is the same as a point at infinite distance, either for Newton or Einstein.
In GR thinking, mass bends space-time in an analogous way to the pressure inside a Newtonian Earth. But the GR curving isn't caused by being squashed under a mass by gravity. Space-time bending is caused purely by the presence of mass. A 'way you could think' about this is as a 'pressure' to due to mass - like in the pictures above. This is a mental model of 'pressure' due to mass, and this pressure slowing down time. But it isn't an actual pressure in the everyday meaning. The 'GR pressure' which bends space-time is highest at the centre of the Earth because in this location the effect of all the mass of the Earth is at is maximum (the sum of the 1/r^2 equations over all the mass), not anything to do with gravity.
Time dilation occurs wherever gravity curves space-time so that one point in space experiences a different rate of time than another...
Please! I thought we had agreed that mass curves space-time! Gravity doesn't do anything to space-time, it is a consequence of how curved it is.
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Please! I thought we had agreed that mass curves space-time! Gravity doesn't do anything to space-time, it is a consequence of how curved it is.
True. Poor choice of words on my part in trying to simplify things. To be more precise, the stress-energy tensor (which includes mass) is the source of the curvature and the curvature is a mathematical description of gravity.
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Right i have got the concept of mass pressure in the way it applies in general relativity, and it answers my question as to how it is postulated that time runs slowest at the centre.
So the difficulty is how to get nature to ask a question of both theory's that will separate out which one is closest to what is observed,
And because both theory's include the same dynamics happening, albeit for different reasons it would seem at first glance to be insurmountable.
However i can think of one which could isolate there differences
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Yep I can follow that thinking, gravity would then be the consequence of SpaceTimes geodesics (dips, bends and heights) called forward by the stress-energy tensor that is the direct result (expression) of mass acting on space.
The problem here being that both the geodesics and the stress energy tensor are mathematical descriptions versus gravity that really is what we feel :) I mean, we don't say, "Hey Alex, watch out for that stress energy tensor man, you're gonna fall !!" Do we, huh? ... "Why thanks Charles, that geodesic really took me by surprise."
:)
But it do make sense, all the way down to how to accept the idea that a free fall in the middle won't be equal to a free fall outside, time dilation wise that is. But then again, if they're not then it seems to me that the same should hold for free falling frames outside too. And if that would be right then different velocity in free fall (uniform moving) will be able to create different time dilations relative a common originator (like starting two rockets from Earth)?
Awh..
1+1= *White coats again? Why do they persecute me. "I'm innocent I say, innocent."*
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Anyway, I suspect Geo Driver is quite correct. If you want a three minute egg, time it for three minutes. (I'm assuming we are conducting the experiment at something close to one atmosphere and boiling the egg in water rather than molten iron.)
The timing device and the egg will both experience three minutes in, well, three minutes, or did we conclude the answer would be different?
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yor_on, you seem to have it in your grasp. The trouble is that some examples you use jump between GR and SR. A free falling body (or orbiting) compared to the Earth's surface (or centre) has time dilation due to the relative velocities (ignores mass). This is an SR effect. There is also another effect due to being near mass, this is a GR effect.
@Geezer, yes three minutes is three minutes but don't use an hour-glass style egg timer :)
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@Geezer, yes three minutes is three minutes but don't use an hour-glass style egg timer :)
Ah yes! I suppose any device that relied on gravity (pendulums etc) would be suspect [;D]
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@Geezer, yes three minutes is three minutes but don't use an hour-glass style egg timer :)
Not if it contravenes the laws of conservation of energy it isn't. below is an extract from a link J P provided in regards to wether G R voilated energy conservation ...........
An infinitesimal piece of spacetime "looks flat", while the effects of curvature become evident in a finite piece. (The same holds for curved surfaces in space, of course). GR relates curvature to gravity. Now, even in newtonian physics, you must include gravitational potential energy to get energy conservation. And GR introduces the new phenomenon of gravitational waves; perhaps these carry energy as well? Perhaps we need to include gravitational energy in some fashion, to arrive at a law of energy conservation for finite pieces of spacetime?.........
Looks to me like there turning gravity back in to a force field.
Anyone else come up with a way to test wether gravity is an attractive force or a bending of time ??
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We think we have indirect evidence of gravitational waves acting as a energy Gem.
"The smoking gun is a system of orbiting neutron stars with the catchy name PSR1913+16. Einstein's theory predicts that gravitational waves carry away energy. For a system of orbiting stars, such a decrease in total energy leads to an ever faster and closer orbit. Over decades, radio astronomers have monitored the time that it takes the stars of PSR1913+16 to complete each successive orbit, and lo and behold: this orbital period decreases over time exactly as predicted by general relativity. This is strong evidence that the speed-up is indeed due to the radiation of gravitational waves, and the reason Russell Hulse and Joseph Taylor were awarded the Nobel prize for physics for the year 1993." Gravitational waves. (http://www.aei.mpg.de/einsteinOnline/en/elementary/gravWav/sources/index.html)
But, what exactly is this 'energy' we're speaking of, is it the same type we find in our combustible engine? and furthermore, if there exist this kind of phenomena, why couldn't we speak about gravity as a 'force'?
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@Geezer, yes three minutes is three minutes but don't use an hour-glass style egg timer :)
Not if it contravenes the laws of conservation of energy it isn't. below is an extract from a link J P provided in regards to wether G R voilated energy conservation ...........
An infinitesimal piece of spacetime "looks flat", while the effects of curvature become evident in a finite piece. (The same holds for curved surfaces in space, of course). GR relates curvature to gravity. Now, even in newtonian physics, you must include gravitational potential energy to get energy conservation. And GR introduces the new phenomenon of gravitational waves; perhaps these carry energy as well? Perhaps we need to include gravitational energy in some fashion, to arrive at a law of energy conservation for finite pieces of spacetime?.........
Looks to me like there turning gravity back in to a force field.
Anyone else come up with a way to test wether gravity is an attractive force or a bending of time ??
Well, I'm not sure what it has to do with energy conservation, but I'm pretty sure if it was not three minutes, some other significant law would be violated. I'm not sure what the law is called (or if it even exists!) but, according to my understanding, it is impossible to detect any "variation" in time within a local space. In other words, if your egg required more or less than three minutes of boiling to "behave" like an egg that had been boiled for three minutes, you would have created a means of detecting a "variation" in time without reference to some other time frame.
I'm sure JP will straighten me out if this is not right.
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We think we have indirect evidence of gravitational waves acting as a energy Gem.
"The smoking gun is a system of orbiting neutron stars with the catchy name PSR1913+16. Einstein's theory predicts that gravitational waves carry away energy. For a system of orbiting stars, such a decrease in total energy leads to an ever faster and closer orbit. Over decades, radio astronomers have monitored the time that it takes the stars of PSR1913+16 to complete each successive orbit, and lo and behold: this orbital period decreases over time exactly as predicted by general relativity. This is strong evidence that the speed-up is indeed due to the radiation of gravitational waves, and the reason Russell Hulse and Joseph Taylor were awarded the Nobel prize for physics for the year 1993." Gravitational waves. (http://www.aei.mpg.de/einsteinOnline/en/elementary/gravWav/sources/index.html)
That's interesting. We know that the Earth manages to transfer energy to the Moon, but I don't think there is any need to invoke gravitational waves to explain the phenomenon.
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Why is energy conservation suddenly coming up and what does it have to do with time dilation? All you really need to know is what Geezer was saying--that if you put your timer and egg next to each other, then they should both agree on what three minutes is.
The gravitational wave stuff is nice, but it has to do with gravitational energy being carried far away from a gravitational system, doesn't it? Orbits might decay faster than normal as a result of this, but what does it have to do with timing an egg?
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Why is energy conservation suddenly coming up and what does it have to do with time dilation? All you really need to know is what Geezer was saying--that if you put your timer and egg next to each other, then they should both agree on what three minutes is.
The reason i brought energy conservation up was that to time and cook the egg you need a set amount of energy in a set amount of time
And a joule is a unit of energy in the International System of Units, It measures heat, electricity and mechanical work.
The joule is a derived unit equivalent to a newton-meter, or a kilogram-meter squared per second per second.
A joule is also:
A unit of electrical energy equal to the work done when a current of one ampere is passed through a resistance of one ohm for a period of time of one second.
A unit of energy equal to the work done when a force of one newton* acts through a distance of one meter.
In the meter-kilogram-second (MKS) system, a newton is the unit of force required to accelerate a mass of one kilogram one meter per second per second,
So you will notice time is a factor in the measurement of the work heat equivalence and as we have already noted earlier in this post at the center where in GR time is slower will the energy interactions there not disagree with the International System of Units as regards the laws thermodynamics.
similar to the fact that a particle at the centre of the earth would seem to travel faster than one at the surface according to G R, so distance travelled would disagree with the International System of Units.
But, what exactly is this 'energy' we're speaking of, is it the same type we find in our combustible engine? and furthermore, if there exist this kind of phenomena, why couldn't we speak about gravity as a 'force'?
Energy is Energy it just takes different forms and yes even in GR they must be trying to detect a variation in gravity as some kind of force or maybe they will detect a variation in the gravitational force.
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Could you minimize that post a little and make it clearer to me Gem. I sort of lose myself reading it? Are you saying that the units we use are wrong? I'm not sure I'm following you rightly here?
Thinking of the conservation of energy. It just states that we always will have an equivalence in our universe. It may change form when using it, like gasoline comes out as water, heat and CO2 etc, as it also goes up as 'energy' driving the pistons in our engine. but it doesn't come from nothing as far as we know, and it won't disappear into a nothingness. The gasoline just becomes unusable for 'new work', as its usable energy gets transformed into such things as water, CO2 and heat. And the idea is similar to thermodynamics idea of work and 'work done' describing 'usable energy' transforming to 'unusable' energy.
And looking at it that way the only thing requested of this egg in any frame of reference is that the 'work' will be equivalent to the same amount of 'work done', unusable to us after its transformation(s) for it to hold true. So it doesn't really have to do with time dilation or mass. It's a principle of equivalence to me, describing how we think our universe 'works' :)
Like we also speaks of our universe to be a 'closed one' instead of 'open ended'. and that statement have nothing to do with its 'inflation' or 'expansion' but is a statement saying the same as above, that we don't lose any energy, it only transforms, like being in a bubble of a sorts where the 'walls' won't allow any penetration of new 'energy'. At least that's my understanding? That's also why Hawking radiation is so interesting, as we on one side calls Black Holes enigmas and 'singularities' meaning that we can't look past the Event horizons of them, and that they are 'closed' to our universe, but on the other hand according to some theories, still would have some sort of 'information exchange' due to that radiation with our universe.
But I'm not really sure if that was what you were thinking of here Gem?
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So you will notice time is a factor in the measurement of the work heat equivalence and as we have already noted earlier in this post at the center where in GR time is slower will the energy interactions there not disagree with the International System of Units as regards the laws thermodynamics.
I think Gem is concerned that time dilation will affect the quantity of energy required to boil the egg.
Well, no. I don't believe it has any effect on the energy required. Everything at the center of the Earth runs a bit faster (or is it slower - I can never remember) than it does at the surface. By "everything" I really mean everything. All atomic activity, every chemical process, human thought, human metobilism, all physical motion etc. etc. is governed by the local time.
If it actually did require a different amount of energy, you would have invented a mechanism to detect time dilation locally, and that is a big no no. (Sorry for the less than scientific phrase.)
If you use an atomic clock to time your egg for three minutes, the atomic clock measures local time, so it will "tick" exactly the same number of times in three minutes, regardless of its location.
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You know Geezer, I think you're right. That thoughts too are regulated by time I mean. They seem so unrelated to what we deem as being materially 'there', as if they wasn't connected to anything materialistic, but they are.
That was a nice one.
Now, how about 'photons' ::))
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You know Geezer, I think you're right. That thoughts too are regulated by time I mean. They seem so unrelated to what we deem as being materially 'there', as if they wasn't connected to anything materialistic, but they are.
Well, I think thinking(!!) is mainly a chemical processes, so it would have to be governed by local time. I can't see why anything would be exempt - even photons. That's not to say the speed of light is any different. Light still travels the same distance in unit time. It would kind of have to, wouldn't you think?
(I'm not sure that the photon bit is necessarily correct. It sounds logical, but photons have a nasty habit of defying my logic. Let's see if JP thinks this is legit.)
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The general rule of thumb is that locally, space-time is flat, so you only need to use special relativity, not GR. In that case, everything should be governed by special relativity instead of general relativity and as long as things are moving fairly slow, everything is governed by the same "local clock" where the only time dilation you need to consider is from special relativity (i.e. if something is moving fast). Light you're watching move about should seem to do so at the speed of light no matter what with the appropriate doppler shift if you're moving with respect to the source.
Was that a long answer to a short question or what? :)
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Quite nice JP, and by flat you're using the idea that it is so vast (the universe I mean) that to us locally all 'curves' will be a straight line? Like we thought the Earth was too, some time ago (last year in my case::))
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The general rule of thumb is that locally, space-time is flat, so you only need to use special relativity, not GR.
I thought fontwell posted diagrams that showed that space time curves between the surface of a planet and the centre in G R.? And this from a link Jp provided seems to contradict.
An infinitesimal piece of spacetime "looks flat", while the effects of curvature become evident in a finite piece. (The same holds for curved surfaces in space, of course). GR relates curvature to gravity. Now, even in newtonian physics, you must include gravitational potential energy to get energy conservation.
And also if space time is flat locally there would be no gravity according to fontwell that is what happens only at the centre.
If you use an atomic clock to time your egg for three minutes, the atomic clock measures local time, so it will "tick" exactly the same number of times in three minutes, regardless of its location.
when the clock at the centre has ticked the same amount of times as the one at the surface it will have travelled further in its orbit around the sun.
And as mass according to G R is the cause of gravity where will the mass at the centre be bending space time compared to mass at the surface,If what you say below is correct.
By "everything" I really mean everything. All atomic activity, every chemical process, human thought, human metabolism, all physical motion etc. etc. is governed by the local time.
Please explain how ALL PHYSICAL MOTION IS GOVERNED BY LOCAL TIME because according to the atomic clocks the mass at the centre is traveling faster.
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And also if space time is flat locally there would be no gravity according to fontwell that is what happens only at the centre.
Not at all. Think about how the earth's surface looks pretty flat to you, even though the earth is (roughly) a huge sphere. Gravity and curvature come in when you look at how you travel from one tiny locally flat patch to another.
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Please explain how ALL PHYSICAL MOTION IS GOVERNED BY LOCAL TIME because according to the atomic clocks the mass at the centre is traveling faster.
Local time is time measured locally. The local time at the center faster than the local time at the surface. What's meant by that quote is that how something moves is related to the time that thing experiences, i.e. it's own local time. So if you put the timer and egg next to each other at the center of the earth, they would pretty much agree on what a second was. They wouldn't agree with someone on the surface or in deep space, however. The more curved space-time is the closer your timer and egg would have to be in order to "see" the same local time.
To really experience the exact same time, they'd have to be at the same point, but since the earth isn't a powerful source of gravity, being next to each other is "good enough." (Actually for egg timing, the time dilation of the earth isn't even important since microseconds don't matter).
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By "everything" I really mean everything. All atomic activity, every chemical process, human thought, human metabolism, all physical motion etc. etc. is governed by the local time.
Please explain how ALL PHYSICAL MOTION IS GOVERNED BY LOCAL TIME because according to the atomic clocks the mass at the centre is traveling faster.
It's not really correct to say it's travelling faster. Locally, it's travelling at the same speed. Speed is distance in time. Everything is governed by local time, so locally speed would be the same at the two locations.
If you had some amazing device that allowed you to observe the two egg timers simultaneously, if both started simultaneously, you would be able to observe that the one at the center of the earth would finish before the one at the surface.
However, locally, both eggs would cook for three minutes because three minutes of local time had elapsed. If you could see two objects moving at 10 mph at the two locations, you would observe that one was moving faster than the other from your perspective, but from the perspective of local observers, they would both be moving at 10 mph.
Don't worry. It only took me about twenty years to get my head around this strange situation. [:D]
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If you had some amazing device that allowed you to observe the two egg timers simultaneously, if both started simultaneously, you would be able to observe that the one at the center of the earth would finish before the one at the surface.
After
(Actually for egg timing, the time dilation of the earth isn't even important since microseconds don't matter).
No but for the integrity of the theory micro seconds do matter
Local time is time measured locally. The local time at the center faster than the local time at the surface.
Slower.
It's not really correct to say it's travelling faster. Locally, it's travelling at the same speed. Speed is distance in time. Everything is governed by local time, so locally speed would be the same at the two locations.
If you had some amazing device that allowed you to observe the two egg timers simultaneously, if both started simultaneously, you would be able to observe that the one at the center of the earth would finish before the one at the surface.
Can you not see the contradiction in those two statements.
For the clock to seem to be traveling faster it has to be running slow to allow it to travel further.
But the point of the contradiction is lets pretend earth is a vessel traveling through space at speed and on this vessel there are two atomic clocks running at different rates so giving a different velocity for the said vessel.
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Nope. I don't see a contradition and I don't think I can add any more to my explanation.
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Local time is time measured locally. The local time at the center faster than the local time at the surface.
Slower.
Touche. It still doesn't change the rest of the explanation, though.
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It's 'frames of reference' we're speaking of here right?
1. Your own 'frame' will always show you the same time, as measured by your wristwatch against your heartbeats, in any 'frame' you exist in.
2. To show a really large 'time dilation' you will have to do a 'twin experiment' more or less, but that it exist is already proved, by muons and GPS amongst others.
3. Without that 'twin experiment' whatever you will observe outside your 'frame of reference' will give you an answer time-wise, as related to you both, but without you being to measure any difference relative time-dilation (naively seen without foreknowledge.)
And 3. is the really remarkable thing to me, making us able to see the universe as a 'whole experience' no matter that according to the 'twin experiment' one of the returning twins won't have aged (accelerating one).
What one might say? Is that we have no way to 'slow down' the universe as a whole. It have it's own 'arrow of time' it seems(?) Ticking at a even pace. What we can do is to 'slow ourselves down' against the universe, and so, relative our place of origin, measure a time dilation.
But I can't see how we ever would be able to 'slow it down'?
That means you aging faster than the universe as a 'whole'.
That is, if you accept my definition of the universe as a 'whole experience' aging of course. Otherwise you might say that there are things/objects aging 'faster' than you. But if it is that way then the experience of being able to observe a 'whole universe' have to be explained from something else it seems to me?
Can you see what I think here? That what we call 'times arrow' then is a very localized phenomena and that our 'universal arrow of time' then becomes even more remarkable, as will all causality-chains observed, following our 'entropy'.
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welcome back yor on, i thought the white coats had finally caught up with you.
That is, if you accept my definition of the universe as a 'whole experience' aging of course. Otherwise you might say that there are things/objects aging 'faster' than you. But if it is that way then the experience of being able to observe a 'whole universe' have to be explained from something else it seems to me?
Can you see what I think here? That what we call 'times arrow' then is a very localized phenomena and that our 'universal arrow of time' then becomes even more remarkable, as will all causality-chains observed, following our 'entropy'.
And this from the man that helped bring Einsteins theory's to prominence in the scientific community
http://en.wikipedia.org/wiki/Arrow_of_time (http://en.wikipedia.org/wiki/Arrow_of_time)
Eddington then gives three points to note about this arrow:
1 It is vividly recognized by consciousness.
2 It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.
3 It makes no appearance in physical science except in the study of organization of a number of individuals.
Here, according to Eddington, the arrow indicates the direction of progressive increase of the random element. Following a lengthy argument into the nature of thermodynamics, Eddington concludes that in so far as physics is concerned time's arrow is a property of entropy alone.
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Not bad Gem, there is another guy that recently described gravity as a product of entropy too, if I remember right. Entropy is a very strange idea as it, as a product, don't have to be equal over the whole area it acts on, that is to my understanding. You can have limited areas with a decreased entropy, yet still with the overall effect being an increased entropy. If I lifted that up to the concept of times arrow, it then seems to state that if entropy and times arrow is the same, we c/should have areas where time 'ticked backwards'?
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"Why did you have to say it so loud" he screamed?
*Running as he* *
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Not bad Gem, there is another guy that recently described gravity as a product of entropy too,
Gravity is certainly not a product of entropy, it may contribute to some of the process that occur in the increase of entropy in some of the transformations of energy.
yet still with the overall effect being an increased entropy. If I lifted that up to the concept of times arrow, it then seems to state that if entropy and times arrow is the same, we c/should have areas where time 'ticked backwards'?
I believe that the laws of entropy and thermo dynamics say the total opposite that in these energy interactions and transformations you can not reverse every aspect of the dynamics of their interactions.
Put in a simple form its stating there is energy in its many forms, and its interactions and transformations that we observe as cause and effect and these are the process that we apply times arrow to. below is a statement from the supplied link
http://en.wikipedia.org/wiki/Entropy (http://en.wikipedia.org/wiki/Entropy)
Entropy is the only quantity in the physical sciences that seems to imply a particular direction for time, sometimes called an arrow of time. As we go "forward" in time, the second law of thermodynamics states that the entropy of an isolated system tends to increase or remain the same; it will not decrease. Hence, from one perspective, entropy measurement is thought of as a kind of clock.
and this is i believe is what time is, the clocks we use to measure these interactions are just that 'measuring devices' to help us put some values to what we observe in reality.
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Nope, or yes :)
Sorry if I got the wrong impression there, it was just that your writing reminded me of another guy, quite serious and interesting. But it's an misunderstanding, as I understands it, that entropy can't have patches where the entropy locally decreases as long as the overall effect is an increase. I know I wrote about that somewhere here before?
Ah, found it Entropy (http://www.infidels.org/library/modern/richard_carrier/entropy.html) and Entropy too :) (http://entropysimple.oxy.edu/)
As for that guy i was talking about. And I really need to try to read him, I'm lazy when it comes to sit down and really read it all through but he's quite heavy, as well as interesting TNS (http://www.thenakedscientists.com/forum/index.php?topic=28588.msg298571)