What causes time dilation in gravitational fields?

[yuiop]

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.

So how do you explain the difference in the twins's ages in the post #30 thought experiment if nothing physical happens?

In SR the apparent time dilation of two co-moving clocks is no more than an illusion,

if they are co-moving there will be no apparent time dilation, only if they have relative motion

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.

Its not scientific to jump to the "obvious conclusion" without checking all possibilities first. Let me give the fridge analogy again. We have two hour glasses filled with treacle that take one hour to empty at room temperature. We place on in the fridge. To a coordinate observer the clock in the fridge appears to be running slower. We now place the warm clock that was outside the fridge alongside the one already already in the fridge and let their temperatures equalise. We now see that that two clocks inside the fridge are running at the same rate and that the coordinate observer was suffering from a book-keeping delusion and that treacle does not get more viscous at lower temperatures and no physical processes are slowed down by lower temperatures. The problem is that we are using equipment (clocks and rulers) that are affected by the environment they are measuring (eg gravitational effects) just as the treacle clocks are affected by the environment in the fridge (i.e temperature effects).

 

[cosmik debris]

So how do you explain the difference in the twins's ages in the post #30 thought experiment if nothing physical happens?

if they are co-moving there will be no apparent time dilation, only if they have relative motion
Its not scientific to jump to the "obvious conclusion" without checking all possibilities first. Let me give the fridge analogy again. We have two hour glasses filled with treacle that take one hour to empty at room temperature. We place on in the fridge. To a coordinate observer the clock in the fridge appears to be running slower. We now place the warm clock that was outside the fridge alongside the one already already in the fridge and let their temperatures equalise. We now see that that two clocks inside the fridge are running at the same rate and that the coordinate observer was suffering from a book-keeping delusion and that treacle does not get more viscous at lower temperatures and no physical processes are slowed down by lower temperatures. The problem is that we are using equipment (clocks and rulers) that are affected by the environment they are measuring (eg gravitational effects) just as the treacle clocks are affected by the environment in the fridge (i.e temperature effects).

Yes, I'm sorry I was addressing the problem of measuring the tick rate of a clock at a remote distance. Yes the one in the well ages less, because they have taken a different path through spacetime and the elapsed time on the clock is the integral along the worldline.

I think with all of this we are getting confused by the difference between what we see from a distance and what we see when we are co-located. In relativity clocks do not tick at different rates in gravity wells or when they move relatively, a second is a second, when you integrate the times over a path in spacetime then you get different answers, just as in the road example. This is a real effect.

This is for relativity, note that for various LET (Lorentz Ether Theories) clocks and rulers are physically affected. These theories are experimentally indistinguishable from relativity only the explanation differs. These theories after all are just models, one picks the easiest, usually.

 

[DrGreg]

yuiop, I think you should apply the equivalence principle and consider a Born-rigid accelerating rocket, with clocks at the top and bottom. An on-ship observer at the bottom says the top clock is going faster than his own clock. An on-ship observer at the top says the bottom clock is going slower than his own clock. Both attribute this to gravitational time dilation.

But an external inertial observer explains this as just relative motion between the top and the higher-acceleration bottom.

Now in this situation I can throw some of your own comments and see if you still agree with them in this context. (I have made some minor changes, all highlighted in red, to adapt to the new context.)

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

For example if an objects free falls to a [STRIKE]BH [/STRIKE] Rindler horizon, its velocity tends towards the speed of light very close to the [STRIKE]event [/STRIKE]Rindler horizon according to local static (relative to the [STRIKE]gravitational field[/STRIKE]rocket) observers. To the [STRIKE]Schwarzschild [/STRIKE]Rindler coordinate observer the velocity of the falling object tends towards zero as the event horizon is approached. Who is right?

Imagine we have twins initially at rest wrt each other and the [STRIKE]gravitational field[/STRIKE]rocket. One is lowered down very close to the [STRIKE]event [/STRIKE]Rindler horizon very slowly (quasi-statically) over a period of say 10 years according to the coordinate very far [STRIKE]away from the gravitational source[/STRIKE]above the rocket. 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 [STRIKE]event [/STRIKE]Rindler 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 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 pseudo-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.

I feel comfortable the [STRIKE]Schwarzschild [/STRIKE]Rindler coordinate system and I guess most "senior" members here feel more comfortable with alternative coordinate system like the [STRIKE]KS[/STRIKE] Minkowski chart, claiming that the [STRIKE]KS [/STRIKE]Minkowski system is superior and the [STRIKE]Schwarzschild [/STRIKE]Rindler system is inferior, when as you have already suggested, all valid coordinate systems should be equal and compatible with each other.

I am saying that by giving it some thought it can actually be demonstrated that clocks really do slow down lower in a pseudo-gravitational field and there is an undercurrent of belief in this forum that pseudo-gravitational time dilation is just "an illusion" or "artifact" brought about by the distorted/ inaccurate/ /misleading/ unfortunate [STRIKE]Schwarzschild [/STRIKE]Rindler coordinate system. That I think is a mistake. Final question. Will the second twin have aged less than the first is the above thought experiment. If the answer is yes, then the "all clocks continue to tick at one second per second, wherever they are" might be true in terms of proper time but generally misleading in the bigger picture.

You may counter by saying that there is a difference between true gravity and the pseudo-gravity of acceleration, but that difference is a second-order tidal effect, whereas gravitational time dilation is first order effect and the dominant term (especially for extremely large black holes).

 

[yuiop]

Yes, I'm sorry I was addressing the problem of measuring the tick rate of a clock at a remote distance. Yes the one in the well ages less, because they have taken a different path through spacetime and the elapsed time on the clock is the integral along the worldline.

Yes, I understand that concept. The twin that remains higher up "travels" through a greater arc through curved spacetime than the lower twin. However, I find it very abstract, because after all they both traveled down the same lift shaft down the same radial coordinate at the same rate, just at different times. Also, you might note that even if one twin stays high up and the other stays low down and never get together, they travel different distances through spacetime. The differential ageing of the gravitational twins is asymmetric and not symmetric as in the SR case. They both agree on whose clock is ticking slower and they can prove it objectively by coming together. The confusing symmetry of SR is just not there, even when comparing from a distance.

I think with all of this we are getting confused by the difference between what we see from a distance and what we see when we are co-located. In relativity clocks do not tick at different rates in gravity wells or when they move relatively, a second is a second, when you integrate the times over a path in spacetime then you get different answers, just as in the road example. This is a real effect.

I guess that is the formal interpretation. For those that have an interest in the ether in its modern interpretation, you might be interested in looking up the "ether on steroids" paradigm of Wilkczec who won a Nobel prize for his work on the strong force.See https://www.amazon.com/dp/0465003214/?tag=pfamazon01-20 , http://effectiveclass.org/video/sci...eing-mass-ether-and-the-unification-of-forces etc.

 

[harrylin]

Yes, I'm sorry I was addressing the problem of measuring the tick rate of a clock at a remote distance. Yes the one in the well ages less, because they have taken a different path through spacetime and the elapsed time on the clock is the integral along the worldline.

Similarly, I was addressing, as was yuoip perhaps, the problem of measuring the tick rate of a clock at the same distance and speed, for the case that a mass is nearby compared with the case that the mass is not there. Only that tells us "Gravity's Effect on Time".
A good example is the bending of star light near the Sun: that is not a non-effect, and it was first calculated based on Einstein's interpretation (using Huygens) that light waves propagate more slowly near the Sun than at a slightly greater radius. We thus measure the effect of the Sun on the light waves by measuring with and without the Sun, all other things equal. Do you claim instead that the trajectory of the star light is not affected by the Sun? If so, then how can we measure the effect?

[..] In relativity clocks do not tick at different rates in gravity wells [..] These theories after all are just models, one picks the easiest, usually.

Now Einstein's model is not any more relativity?! As a reminder, he held that a clock "goes more slowly if set up in the neighbourhood of ponderable masses" (1916).
But yes, we pick the models that we like, either for calculation or for making sense of it - and different people prefer different models.

 

[harrylin]

[...]
You may counter by saying that there is a difference between true gravity and the pseudo-gravity of acceleration, but that difference is a second-order tidal effect, whereas gravitational time dilation is first order effect and the dominant term (especially for extremely large black holes).

The equivalence principle served its purpose, but many clues help us to distinguish between gravitation and acceleration (even looking out of the window!). If we follow the reasoning that we should ignore the clues that we receive from small effects, then we should prefer Newton's theory.

 

[Quickless]

Time is invariant with respect to regime. It is not time that is changing but the measurement of time. Consideration should be given to whether time is a thing in and of itself or just a measurement.

 

[pervect]

I've been a bit distracted by other things recently, but there was one thing I thought of that I did want to mention.

That is , if you consider "Einstein's elevator", it's widely recognized that there's a "gravitional field" in the eleveator's frame (if it's small enough), or in the elevator's Fermi-normal coordinates (if the elevator is a bit too large to have a frame we replace the frame with the fermi-coordinates0.

So the clock "higher" in the elevator ticks faster. We might also say that the Rindler metric describes the space-time of the elevator, and that the time dilation is described by g_00 of that metric.

However, it is a definite error to imagine that this gravitational time dilation effect exists in the inertial frame which also exists and can be used to describe the elevator's motion.

The Rindler metric has g_00 vary with position, but the Minkowskii metric of flat space-time has a constant g_00.

In the inertial frame, there is absolutely no gravity field,and absolutely no gravitational time dilation,either. (But there is the usual relativistic doppler shift in the inertial frame, which is sufficient to explain allthe observed reception and transmission times. However, we can't say that one clock ticks faster or slower in said inertial frame, though we can say that there are doppler shifts, red shifts for light signals traveling from back-front for instance.

So, it's fairly easy to show that a simple change of coordinates or viewpoint causes "gravitational time dilation" , considered in isolation, to either appear or dissapear. In other words, gravitational time dilation is not a geomoetric object or tensor, it's just a piece of one.

So, that's one last reason why NOT to think of g_00 as "time slowing down". It's too simplistic, when you consider the whole picture, it's part of something bigger. The metric coefficeints depend on what coordinate systems one uses.