What causes time dilation in gravitational fields?

[Gravitons]

Im having a hard time understanding gravitational time dilation. I have two examples I've heard(from shows on the science channel): a theoretical experiment is you leave Earth in a spaceship and orbit outside the event horizon of a black hole for 1 year, its possible that when you come back to Earth its been 10 years or even 100 years on Earth when its been only 1 year for you. This shows that as gravity increases time slows down for the person next to the black hole because of the black holes large mass? But this contradicts the fact that when astronauts orbit the Earth in the space station they are technically, however small the measurement, younger than us on earth, so they age slower? Because the farther away from Earth you are the less stronger gravity is? So this is saying that the less gravity the more time slows, which contradicts the black hole experiment that says more gravity has this effect on time. Can someone please explain this relationship.

 

[WannabeNewton]

The astronauts age relatively slower because they are orbiting the Earth at high speeds not because they are in a stronger gravitational field. The Earth's gravitational field is too weak to cause any kind of significant time dilation.

 

[Gravitons]

Oh thankyou i understand now. So does that mean the theoretical experiment about the black hole is true?

 

[WannabeNewton]

I don't know the exact number but yes the premise is very true.

 

[Oldfart]

The astronauts age relatively slower because they are orbiting the Earth at high speeds not because they are in a stronger gravitational field. The Earth's gravitational field is too weak to cause any kind of significant time dilation.

I read somewhere on PF that atomic clocks on Earth can detect a height difference of as little as three feet.

 

[bcrowell]

The astronauts age relatively slower because they are orbiting the Earth at high speeds not because they are in a stronger gravitational field. The Earth's gravitational field is too weak to cause any kind of significant time dilation.

This is incorrect. The gravitational and kinematic time dilation effects are of comparable orders of magnitude for satellites in Earth orbit. For satellites in low Earth orbit (which includes almost all crewed activity), the kinematic effect dominates. But for satellites in higher orbits (e.g., GPS and geosynchronous satellites), the gravitational effect dominates.

-Ben

 

[PAllen]

Oh thankyou i understand now. So does that mean the theoretical experiment about the black hole is true?

The black hole case would combine two sources of differential aging. Consider there is a black hole a light year away, that is stationary relative to sun (say, by doppler definition). Ship A goes near the black hole (not too close), circles a while, and comes back to earth. Ship B goes a light year in the opposite direction, circles similarly* and comes back to earth. Both pilots will have aged less than their Earth colleagues, but A pilot will have aged less than B pilot.

*Similarly: Near the black hole, measure speed of A relative to a momentarily coincident (NOT comoving) radial free fall frame (with zero instantaneous radial velocity compared to a coincident stationary observer). In the opposite direction, measure speed (in presumably empty region), relative to sun. The aim is to measure speeds from local Minkowski frames.

 

[pervect]

One interesting side-note. You can't really get much differential aging due to "gravitational time dilation" if you insist on orbiting a black hole, because the photon sphere is at r=3M, and the "gravitational time dilation there" is sqrt(2M/r) = sqrt(2/3).

While you could get a long time dilation orbiting a black hole near the photon sphere, this would come from your velocity more than the gravitational effect.If you consider traveling deep in a black hole's gravity well using rocket thrust, rather than orbiting it, you can get large time dilations due to the gravitational effect.

The gravitational effect is not due to "gravity", but is better (though someone loosely) described as being due to "gravitational potential". For instance, you'll have a maximum value of time dilation due to gravity on Earth at its center, even thought the gravity there is zero.

The "gravitational time dilation" is really due to curvature of space-time, but as long as you only consider static observers it's not too terribly misleading to use coordinate time as your base for time and think of physical clocks as ticking faster or slower than coordinate clocks. Pretty much everyone does this, I think.

Philosophically, though, there's a lot to be said for thinking of the physical clocks as being the "more real" clocks, in which case they always tick at 1 second per second. With this point of view, it's the coordinate clocks that are "off" due to the effects of curvature.

 

[WannabeNewton]

This is incorrect. The gravitational and kinematic time dilation effects are of comparable orders of magnitude for satellites in Earth orbit. For satellites in low Earth orbit (which includes almost all crewed activity), the kinematic effect dominates. But for satellites in higher orbits (e.g., GPS and geosynchronous satellites), the gravitational effect dominates.

-Ben

My apologies.

 

[yuiop]

The astronauts age relatively slower because they are orbiting the Earth at high speeds not because they are in a stronger gravitational field. The Earth's gravitational field is too weak to cause any kind of significant time dilation.

This is incorrect. The gravitational and kinematic time dilation effects are of comparable orders of magnitude for satellites in Earth orbit. For satellites in low Earth orbit (which includes almost all crewed activity), the kinematic effect dominates. But for satellites in higher orbits (e.g., GPS and geosynchronous satellites), the gravitational effect dominates.

-Ben

Just to make it clear, WN is correct that astronauts (usually in low orbit) would age slower than people on the ground, but erred a bit when he said Earth's gravitational time dilation effect is insignificant, because gravitational time dilation can dominate at higher orbits. However if you were to be charitable, you could interpret WN to mean gravitational time dilation is less significant than kinematic time dilation, in low orbits where astronauts usually work.

 

[PAllen]

One interesting side-note. You can't really get much differential aging due to "gravitational time dilation" if you insist on orbiting a black hole, because the photon sphere is at r=3M, and the "gravitational time dilation there" is sqrt(2M/r) = sqrt(2/3).

While you could get a long time dilation orbiting a black hole near the photon sphere, this would come from your velocity more than the gravitational effect.

Right, which is why I proposed circling with a rocket, rather than orbiting. That way you can make either components (speed, gravity) towards differential aging a large as you want.

One question is that I get sqrt(1/3) for the innermost unstable circular orbit, sqrt(2/3) for the innermost stable circular orbit. It is the former where the orbital velocity approaches lightspeed. I could have goofed, so let me know.

 

[yuiop]

Philosophically, though, there's a lot to be said for thinking of the physical clocks as being the "more real" clocks, in which case they always tick at 1 second per second. With this point of view, it's the coordinate clocks that are "off" due to the effects of curvature.

I am not sure about the philosophical desirability of this this interpretation. Let us say we have a clock (A) very far from a gravitational source that remains stationary and call this the coordinate clock.

Now let us lower another clock (B) close to the gravitational source such that clock A seems to be ticking 10 times faster than clock B from B's point of view and clock B appears to be ticking 10 times slower from A's point of view. We interpret this as clock A speeding up by a factor of 10 while clock B continues to tick at 1 second per second. (clock B undergoes no change).

Let lower one more clock (C) even closer to the gravitational source so that from A's point of view C's clock is ticking 100 times slower and from C's point of view A's clock is ticking 100 times faster. We interpret this as clock A speeding up by a factor of 100 while clock C continues to tick at 1 second per second. (clock C undergoes no change).

Now we have agreed that neither clock B nor clock C have undergone any sort of change and yet they are ticking at different rates to each other when initially they were ticking at the same rate when they were adjacent to each other. They have changed, but they have not changed. A bit paradoxical.

Meanwhile clock A, that has remained stationary all the while, is now the one that is really ticking 10 times faster relative to B and ticking 100 times faster relative to C. Since clocks B and C have undergone no change, clock A must be doing all the changing even though it is the only clock that that has no reason to change because it has not changed its velocity or gravitational potential. If A was originally ticking at 1 second per second what is its clock rate now? Is it 10 seconds per second which is what B says it is or is it 100 seconds per second which is what C says it is? Again, a bit paradoxical. Alternatively we say all clocks tick at one second per second (in their own rest frame) independent of their relative motion or gravitational potential which makes things a lot simpler, but completely glosses over the fact that clocks are measured to run at different rates.

To me it makes a whole lot more sense to say that the tick rates of clocks B and C change because they are the clocks that have changed their location in the gravitational field. This explains why the tick rates of both B and C have changed relative to each other (from everyone's point of view). Clock A, that has undergone no change in velocity or gravitational potential undergoes no change in tick rate, because it has no reason to. I think the main reason this common sense interpretation is avoided, is because when followed to its conclusion, it implies that clocks stop ticking at the event horizon and that is a bit awkward.

 

[bcrowell]

However if you were to be charitable, you could interpret WN to mean gravitational time dilation is less significant than kinematic time dilation, in low orbits where astronauts usually work.

Not trying to be too hard on WN. Charitability isn't one of my strong points :-)

 

[yuiop]

Not trying to be too hard on WN. Charitability isn't one of my strong points :-)

The help you give people here and the educational information you provide on your website seems pretty charitable to me

 

[pervect]

I am not sure about the philosophical desirability of this this interpretation. Let us say we have a clock (A) very far from a gravitational source that remains stationary and call this the coordinate clock.

Now let us lower another clock (B) close to the gravitational source such that clock A seems to be ticking 10 times faster than clock B from B's point of view and clock B appears to be ticking 10 times slower from A's point of view. We interpret this as clock A speeding up by a factor of 10 while clock B continues to tick at 1 second per second. (clock B undergoes no change).

Time for one of my favorite analogy.

You're on the surface of the Earth, and you mark off coordinates for lattitude and longitude. You have a sailing ship on the equator, and it covers 20 arc-minute of longitude in 1 hour.

You move up to closer to the north pole - and you observer it covers 40 arc-minutes of longitude in 1 hour.

If we followed the same rules that we did for time dilation we'd be talking about "distance contraction" as the ship moved further up north.

This idea wouldn't be totally wrong, at least not for navigational purposes, but aside from navigation, it'd be pretty confusing to think of your meter stick as changing as you moved north and south. One might even say it was wrong, for anything except navigational purposes. And, we don't actually do that. Nor do we say that "ships go faster near the North pole", or anything like that. We recognize that the "real" speed of the ships is the same near the poles and near the equator, that this speed is independent of the coordinates we use to describe the surface of the Earth, and that a meter is also independent of the coordinates, and that what happens is that we need to convert coordinate arc-minutes into physical meters by a conversion factor that depends on lattitude - the spatial "metric" of the Earth.

And we might well explain this phenomenon briefly just by saying that the paths we draw in order to compare the distances are curved.

In relativity, it's the concept of a static observer that allows us to compare the distant clocks at all, and it's this particular concept of time comparison, the particular concept of simultaneity used by static observers, that makes the physical clocks deeper in the gravity well appear to run slowly when measured according to "coordinate time".

 

[harrylin]

Commenting on:
"Philosophically, [..] there's a lot to be said for thinking of the physical clocks as being the "more real" clocks, in which case they always tick at 1 second per second. [..]"

I am not sure about the philosophical desirability of this this interpretation. Let us say we have a clock (A) very far from a gravitational source that remains stationary and call this the coordinate clock.
[..]
Now we have agreed that neither clock B nor clock C have undergone any sort of change and yet they are ticking at different rates to each other when initially they were ticking at the same rate when they were adjacent to each other. They have changed, but they have not changed. A bit paradoxical.

Meanwhile clock A, that has remained stationary all the while, is now the one that is really ticking 10 times faster relative to B and ticking 100 times faster relative to C. Since clocks B and C have undergone no change, clock A must be doing all the changing even though it is the only clock that that has no reason to change because it has not changed its velocity or gravitational potential.[..]

I fully agree - but hey it appears to be a matter of how one's brains are wired.

Pervect commented:

Time for one of my favorite analogy.
You're on the surface of the Earth, and you mark off coordinates for lattitude and longitude. You have a sailing ship on the equator, and it covers 20 arc-minute of longitude in 1 hour.
You move up to closer to the north pole - and you observer it covers 40 arc-minutes of longitude in 1 hour.
If we followed the same rules that we did for time dilation we'd be talking about "distance contraction" as the ship moved further up north.

This idea wouldn't be totally wrong, at least not for navigational purposes, but aside from navigation, it'd be pretty confusing to think of your meter stick as changing as you moved north and south. One might even say it was wrong, for anything except navigational purposes. And, we don't actually do that. Nor do we say that "ships go faster near the North pole", or anything like that. We recognize that the "real" speed of the ships is the same near the poles and near the equator, that this speed is independent of the coordinates we use to describe the surface of the Earth, and that a meter is also independent of the coordinates, and that what happens is that we need to convert coordinate arc-minutes into physical meters by a conversion factor that depends on lattitude - the spatial "metric" of the Earth.[...]

I don't see that example as support for "always 1 second per [nominal] second". In this example it would be "always N meters per degree longitude". And that's obviously not true. So, my brain is wired differently from yours.

Moreover the interpretation that clocks near mass tick slower than clocks far from mass (ceteris paribus), is independent of the observer and independent of the units.

Harald

 

[nitsuj]

Time for one of my favorite analogy.

You're on the surface of the Earth, and you mark off coordinates for lattitude and longitude. You have a sailing ship on the equator, and it covers 20 arc-minute of longitude in 1 hour.

You move up to closer to the north pole - and you observer it covers 40 arc-minutes of longitude in 1 hour.

If we followed the same rules that we did for time dilation we'd be talking about "distance contraction" as the ship moved further up north.

This idea wouldn't be totally wrong, at least not for navigational purposes, but aside from navigation, it'd be pretty confusing to think of your meter stick as changing as you moved north and south. One might even say it was wrong, for anything except navigational purposes. And, we don't actually do that. Nor do we say that "ships go faster near the North pole", or anything like that. We recognize that the "real" speed of the ships is the same near the poles and near the equator, that this speed is independent of the coordinates we use to describe the surface of the Earth, and that a meter is also independent of the coordinates, and that what happens is that we need to convert coordinate arc-minutes into physical meters by a conversion factor that depends on lattitude - the spatial "metric" of the Earth.

That is a really good analogy, requires a fair bit of background knowledge. But conceptualy really gets the main points across.

 

[pervect]

Commenting on:

I don't see that example as support for "always 1 second per [nominal] second". In this example it would be "always N meters per degree longitude". And that's obviously not true. So, my brain is wired differently from yours.

Moreover the interpretation that clocks near mass tick slower than clocks far from mass (ceteris paribus), is independent of the observer and independent of the units.

Harald

The interpretation that clocks near mass tick slower than clocks far away is not independent of the observer, if one includes relativistically moving observers. It is only for the special class of static observers that it really works, when there's a "special" method of comparing them that defines simultaneity.

One of the points of the analogy is that the Schwarzschild coordinates (r, theta, and phi) are just coordinates, like lattitude and longitude.

To put the coordinate description before the actual physics of what you measure with real instruments is quite literally putting DesCartes before the horse :-).

 

[bcrowell]

To put the coordinate description before the actual physics of what you measure with real instruments is quite literally putting DesCartes before the horse :-).

Oh...no...

 

[harrylin]

The interpretation that clocks near mass tick slower than clocks far away is not independent of the observer, if one includes relativistically moving observers. It is only for the special class of static observers that it really works, when there's a "special" method of comparing them that defines simultaneity. [...] To put the coordinate description before the actual physics of what you measure with real instruments is quite literally putting DesCartes before the horse :-)

Evidently an elaboration is necessary: I wrote ceteris paribus and that includes relativistically moving observers. Surely all observers agree that clocks tick slower near co-moving masses; this is the actual physics of what you will measure with real instruments.
Else you would get the kind of contradictions that the OP imagined.

 

[pervect]

Evidently an elaboration is necessary: I wrote ceteris paribus and that includes relativistically moving observers. Surely all observers agree that clocks tick slower near co-moving masses; this is the actual physics of what you will measure with real instruments.
Else you would get the kind of contradictions that the OP imagined.

I don't see how taking "all things equal" applies here, especially not to the point I'm trying to make about the requirement for a stationary observer to define a notion of simultaneity in order to be able to compare clocks.

In general, if you have two observers A and B in relative motion, they can't agree whether A's clock is faster or whether B's clock is faster. This is true even in flat space-time, and remains true in curved space-time. This is because they have different notions of simultaneity.

Graphically, I think of it rather like the attached diagram below (which is for flat space-time) where one observer uses red lines to compare the clocks, and the other the green lines. (Add: I tried to upload this, don't see it, and it won't let me re-up).

The purpose of the stationary observer is to define the "set of lines" on the space-time diagram that define simultaneity which is a pre-requisite in order to be able to compare the clock's rate.

I've also seen a LOT of confusion in the past over this issue, related to the issue of what a relativistically infalling observer to a black hole sees. If one takes the "time slows down" argument seriously, one would think that an infalling observer sees time "slow down" just like a stationary one, and that since a stationary observer sees the future of the universe play out in a flash as, so does the infalling observer.

The actual situation is that the infalling observer does NOT see the future of the universe play out in a flash. IIRC, a detailed calculation shows that for an observer free-falling from infinity, the clock at infinity appear to be slower than his own from his (infalling) viewpoint, not faster (as judged by the doppler shift of received signals that the infalling observer receives).

That's happens because the infalling observer has a different notion of how to compare clocks (i.e a different notion of simultaneity) than the stationary observer - though one can explain it in other terms. The whole "rate of time" idea doesn't really hold up reliably when you have speeding observers. In flat spacetime, or curved, it's pretty common to see the "slow/slow" case, where both observers think the other's clock is slow.

 

[pervect]

let's see if this gets the diagram up...

 

[PAllen]

Which is why I proposed to deal with the OP's questions always in terms of clocks that start and end colocated, with different paths through spacetime. The, no notion of simultaneity or distinguishing what you optically see from some interpretation imposed on it.

 

[harrylin]

I don't see how taking "all things equal" applies here, especially not to the point I'm trying to make about the requirement for a stationary observer to define a notion of simultaneity in order to be able to compare clocks. [...]

The OP asked about a clock's rate which according to all distant (=unaffected) reference systems will be less in the presence of a heavy mass than in the absence of that mass, all other things equal (in particular identical motions).

I have seen a LOT of confusion in the past over this issue, related to the issue of what a relativistically infalling observer to a black hole sees.

That is quite a different question from the one of this thread, and to which yuiops' answer #12 is not related. Confusing different questions leads to confusions.
Note that I don't know why yuiop thinks that clocks should stop ticking at the event horizon, but that's again a different topic.

[...] In flat spacetime, or curved, it's pretty common to see the "slow/slow" case, where both observers think the other's clock is slow.

The OP's question as I understood it is about the effect of gravity (thus "curved spacetime") on observed clock rate; that made it a straightforward and unambiguous question.
Experimenters have found it useful from the start (Hafele and Keating) to distinguish between the effects of gravitation and speed. The introduction with references of Wikipedia may be useful for the OP (http://en.wikipedia.org/wiki/Time_dilation).

 

[yuiop]

Time for one of my favorite analogy.

You're on the surface of the Earth, and you mark off coordinates for lattitude and longitude. You have a sailing ship on the equator, and it covers 20 arc-minute of longitude in 1 hour.

You move up to closer to the north pole - and you observer it covers 40 arc-minutes of longitude in 1 hour.

If we followed the same rules that we did for time dilation we'd be talking about "distance contraction" as the ship moved further up north...

Here is an alternative analogy. Let us say we have some hour glasses filled with treacle. At room temperature they take one hour to empty, but they are temperature sensitive because the treacle get more viscous at lower temperatures. Now let us say we also have a fridge with a glass door so we can see what happens inside the fridge. We place an hour glass and observer in the fridge and superficially the clock inside the fridge appears to be ticking slower than the clock outside the fridge. The observer inside the fridge says "No!, my clock is continuing to tick at on hour per hour!". To prove this he places another treacle filled hour glass inside the fridge alongside his original one and indeed they tick at the same rate inside the fridge seemingly proving his assertion. This is not unlike the observer very close to a black hole declaring his clock continues to tick at one second per second. He can only prove this by putting another clock next to his original one, but it proves nothing because both clocks in the gravitational case are equally affected by the gravitational field just as both clocks in the fridge are equally affected by temperature. Our observer in the fridge further claims it is impossible that his clock his slowing down because that would imply that a absolute zero temperature everything would stop. "How absurd!" he exclaims. He then further claims that the clocks outside the fridge (and everywhere else in the universe) actually speed up as a result of him and his clock entering the fridge. That (as far as the fridge observer is concerned) is the only logical explanation because he has already demonstrated that his fridge clock continues to tick at a rate of one hour per hour independently of temperature. He is also completely un-swayed by the observer outside the fridge pointing out that he can prove that the clocks outside the fridge also continue to tick at a rate of one hour per hour. The observer outside the fridge starts to wonder if the cold temperatures inside the fridge are actually slowing down the brain functions of the fridge observer and let's him out to warm up.

To put the coordinate description before the actual physics of what you measure with real instruments is quite literally putting DesCartes before the horse :-).

There was also a third observer outside the fridge who could see the clocks both inside and outside the fridge and could compare their different tick rates directly. He sides with the external observer, saying he saw the fridge observers clocks slow down when they entered the fridge and he saw no change in the tick rate of the clocks that remained outside the fridge. The fridge observer (who has not fully thawed out yet) says the third observers observations do not count because the third observer is just a coordinate observer (or book-keeper) and it well known that coordinate measurements do not have physical significance.

 

[pervect]

Einstein's "heated disk" example is similar to your refrigerator example.

You can make a flat disk curved if your rulers all uniformly change their length via some local field (temperature, in the example).

If you can make the geometry flat, it might even be worth the hassle (at least for someone who doesn't have the math to deal with curvature) though the abstract clocks and rulers that wouldn't be affected by gravity don't actually, physically, exist, and one would constantly need to be converting one's measurments back into what physical clocks would measure.

Einstein gave up on that approach, though, deciding instead to go for the geometrical one, because it was easier. So, it's an interesting idea that nobody has quite spelt out , at least not at any very basic level.

But if one can't accomplish anything useful by introducing non-physical clocks, I don't see the point. At the moment, I don't personally see that you're accomplishing anything as useful as eliminating curvature via your approach - the curvature is still there in your approach yet.

However, going back to the example at hand, there is one vitally important thing at least I don't think you've addressed (as well as some other things that are probably not quite as vital,though important in their own way).

This is the fact that if clocks are moving relative to each other, you can't tell which is running faster, they both seem to run "slow". Even if they are right next to each other momentarily.

In fact,I think you (or one of the other posters) objected to the point that you had to set up a preferred observer in order to compare clock rates. But it is really pretty obvious when you think about it - at least I think it should be.

Other issues are fairly minor, like you pretending that all the clocks that slow down are of one particular type, rather than the fact that every clock type known is affected in just the same manner. Which leads to a potnetially interesting point that if you think about it, what you actually experience is equivalent to what the physical clocks all measure, not what your coordinate clocks might "meaure".

 

[yuiop]

However, going back to the example at hand, there is one vitally important thing at least I don't think you've addressed (as well as some other things that are probably not quite as vital,though important in their own way).

This is the fact that if clocks are moving relative to each other, you can't tell which is running faster, they both seem to run "slow". Even if they are right next to each other momentarily.

Agree that observed behaviour in SR is slightly "odd", but if the two observers moving relative to each make totally symmetrical measurements then I think we can all be satisfied that no clock is physically running slower than the other. Nevertheless, fair comment about appearances being deceptive in some situations. However in the fridge and gravity examples the situation is not symmetric.In the gravity case:

The lower observer agrees that he measures the higher clock to be running faster.
The upper observer agrees that he measures the lower clock to be running slower.
Both observers agree the upper clock appears to be running faster than the lower clock.

If we lower a clock close to the event horizon and then bring it up again it will have lost time relative to the upper clock when they are alongside each other again.

If we raise a clock to higher level and then bring it down again it will have gained time relative to a clock that remained lower down when they are alongside each other again.

How can anyone be any doubt that clocks lower down run physically slower than clocks higher up, given the above?

In fact,I think you (or one of the other posters) objected to the point that you had to set up a preferred observer in order to compare clock rates. But it is really pretty obvious when you think about it - at least I think it should be.

Not quite sure what you are getting at here. The Schwarzschild "coordinate observer" is an arbitrarily chosen "preferred observer" but we could chose just about any observer that is static relative to the gravitational field as the preferred observer and obtain the same result, i.e. clocks lower down run faster than clocks higher up.

Other issues are fairly minor, like you pretending that all the clocks that slow down are of one particular type, rather than the fact that every clock type known is affected in just the same manner.

Well, it just an analogy and all anolgies have limitations, even the one you gave earlier It would be interesting if ALL clocks and physical processes slowed down with temperature. If that was the case, we would probably be seriously debating whether clocks in the fridge really slow down or continued to tick at "one second per second". If that was true then the fridge would be a very good analogy of gravitational time dilation.

Which leads to a potentially interesting point that if you think about it, what you actually experience is equivalent to what the physical clocks all measure, not what your coordinate clocks might "measure".

Let us say that a magician casts a spell on you in your room that slows down all physical processes by an extreme amount or even stops time. If your room is windowless you would be completely unaware of the time slowdown. You would not "experience" it. However, when you came out and noticed that the world had advanced several years you would agree that what you experience is not always the "whole truth" and when all your measuring devices are equally effected by the physical process they are trying to measure, then the only objective measurements are relative or coordinate measurements.

 

[pervect]

Agree that observed behaviour in SR is slightly "odd", but if the two observers moving relative to each make totally symmetrical measurements then I think we can all be satisfied that no clock is physically running slower than the other. Nevertheless, fair comment about appearances being deceptive in some situations. However in the fridge and gravity examples the situation is not symmetric.In the gravity case:

The lower observer agrees that he measures the higher clock to be running faster.
The upper observer agrees that he measures the lower clock to be running slower.
Both observers agree the upper clock appears to be running faster than the lower clock.

As long as all observers are static, you don't get too badly misled. When you start to try to extend the notion to non-static observers is the place where I've observed people start to get into trouble.

If we lower a clock close to the event horizon and then bring it up again it will have lost time relative to the upper clock when they are alongside each other again.

If we raise a clock to higher level and then bring it down again it will have gained time relative to a clock that remained lower down when they are alongside each other again.

How can anyone be any doubt that clocks lower down run physically slower than clocks higher up, given the above?

It's really pretty easy. You just give up the last vestiges of the notion of "absolute time". In order for one clock to be faster or slower than the other, you need a way to compare them. A static observer gives the comforting illusion of absolute time-but in the end the only way to compare clock rates is to have them next to each other for an extended period of time, so they must not be in relative motion.

So, when I think about the whole clock rate thing, I think "yes,that's something that works when the clocks aren't moving, or aren't moving rapidly, but it won't give me the right picture otherwise."

In the general case,when the clocks move, you really can't tell who is faster, or who is slower. You give up on the idea of even trying. And when you realize that there's really no reason to worry about it, because simultaneity is relative, you've made a breakthrough.One more question, on something you said earlier about coordinates. Do you have any problems in working one problem in Cartesian coordinates, and another in cylindrical, and a third problem in spherical coordinates?

If so, how do you get around realizing that the coordinates don't actually matter to the physics?

Is it perhaps a comfort thing,where there's some small class of coordinate systems you feel comfortable with, but you've got a small list of "acceptable coordinate systems", and if it's not on the list you don't use it?

I'm sort of guessing here,but I don[t quite see how you can actually be serious about thinking coordinates are real. Perhaps I'm misunderstanding something.

 

[cosmik debris]

Yulop, in order to measure a quantity like time or length at a distance you have to propagate some sort of vector from say the clock in the gravity well to the one at a distant point. As you move the vector from one place to another along some path in spacetime it's components will change. Note the vector as a whole doesn't change, it's invarient but it's components do. That is what constitutes a remote measurement. Nothing physical happens to the clocks or rulers.

In SR the apparent time dilation of two co-moving clocks is no more than an illusion, just like when we stand apart you look shorter to me and I to you. This is not the same as a traveling clock measuring less elapsed time.

If you have two roads that go from one place to another by different routes and they have markings every kilometre and you count the markings as you go down each road, you will get different answers for each road. You don't then say the markings must be a different distance apart, the obvious conclusion is that the roads are of different length, this is how it is with spacetime only distance is measured with a clock.

 

[yuiop]

As long as all observers are static, you don't get too badly misled. When you start to try to extend the notion to non-static observers is the place where I've observed people start to get into trouble.

Agree. I thought I would just add that most people have not given much thought to defining how we know when observers are static. For example if an object free falls to a BH horizon then according to local static (relative to the gravitational field) observers, its velocity tends towards the speed of light very close to the event horizon. To the Schwarzschild coordinate observer the velocity of the falling object tends towards zero as the event horizon is approached. Who is right?

It's really pretty easy. You just give up the last vestiges of the notion of "absolute time". In order for one clock to be faster or slower than the other, you need a way to compare them. A static observer gives the comforting illusion of absolute time-but in the end the only way to compare clock rates is to have them next to each other for an extended period of time, so they must not be in relative motion.

So, when I think about the whole clock rate thing, I think "yes,that's something that works when the clocks aren't moving, or aren't moving rapidly, but it won't give me the right picture otherwise."

In the general case,when the clocks move, you really can't tell who is faster, or who is slower. You give up on the idea of even trying. And when you realize that there's really no reason to worry about it, because simultaneity is relative, you've made a breakthrough.

In the example I gave I was primarily concerned with gravitational time dilation and although motion was involved it was intended to be minimal. It was supposed to be focused on the gravitational effect on time, since that is the subject of this thread. Let me give a more precise thought experiment for your consideration.

Imagine we have twins initially at rest wrt each other and the gravitational field. One is lowered down very close to the event horizon very slowly (quasi-statically) over a period of say 10 years according to the coordinate observer very far away from the gravitational source. After a further 10 years coordinate time, the second twin is lowered down very slowly over a period of 10 years coordinate time in an identical manner to the first. Now when they are both adjacent to each other and stationary near the event horizon and both at rest wrt to each other they note that the first twin has aged say 21 years and the second twin has aged say 29 years. How do we account for the missing 8 years of the now younger twin? We agree they have gone through identical motion phases for the same period of time and that the motion was so slow that special relativistic effects would be insignificant. The only remaining explanation is that time was passing slower for the first twin while he was low down in the gravitational field than for the twin who remained higher up for 10 coordinate years. I don't see how you can disagree with that conclusion, unless you are suggesting that the laws of the universe or time itself somehow changed between the first and second twin's journey down.

Note that both twins agree they saw identical proper times elapse on their own clocks as they traveled downwards.

One more question, on something you said earlier about coordinates. Do you have any problems in working one problem in Cartesian coordinates, and another in cylindrical, and a third problem in spherical coordinates?

None at all.

If so, how do you get around realizing that the coordinates don't actually matter to the physics?

Similarly I have to question why you think local or proper measurements are superior? Let us say we have observer in a small closed lab. He has no idea if is stationary far out in empty space or rapidly free falling towards a large mass. Similarly, if he feels proper acceleration he has no idea if he is stationary on the surface of a large mass or far out in empty space in an accelerating rocket. The coordinate observer has the "bigger picture" comparing measurements from different observers and different places and piecing it all together.

Is it perhaps a comfort thing,where there's some small class of coordinate systems you feel comfortable with, but you've got a small list of "acceptable coordinate systems", and if it's not on the list you don't use it?

I guess we are all guilty of that. I feel comfortable with the Schwarzschild coordinate system and I guess most "senior" members here feel more comfortable with alternative coordinate systems like the KS chart, suggestng that the KS system is superior and the Schwarzschild system is inferior, when as you have already suggested, all valid coordinate systems should be equal and compatible with each other.

I'm sort of guessing here,but I don[t quite see how you can actually be serious about thinking coordinates are real. Perhaps I'm misunderstanding something.

I am saying that by giving it some thought it can actually be demonstrated that clocks really do slow down lower in a gravitational field and there is an undercurrent of belief in this forum that gravitational time dilation is just "an illusion" or "artifact" brought about by the distorted/ inaccurate/ /misleading/ unfortunate Schwarzschild coordinate system. That I think is a mistake. Final question. In the above thought experiment, will the second twin have aged more than the first, or not?