A question about time dialation

[Johnny R]

I understand that clocks move slower as they approach c.

I also understand that clocks move slower on more massive bodies.


My question is are these two phenomena consistent and cumulative?

For example. We have two masses of significantly differeing masses and both have clocks on them. Both of these clocks are accelerated at the same rate and will slow down accordingly.

My question is will the slow down be consistent with both clocks or will the clock on the larger mass slow more slowly until their rates merge just before c?

Thanks

 

[Mentz114]

I understand that clocks move slower as they approach c.

You've missed the main point of relativity - all motion is relative - so the above does not make sense unless you say in which frame ( ie who) is measuring the speed of the clock. If the clock was in someones pocket, they would not notice any change. Only an observer in a frame moving relative to the clock *sees* it running slower. It actually isn't running slower.

 

[MeJennifer]

Johnny R, are you asking something like this:

Consider a massive non-rotating object M and a test particle T approaching or moving away from each other with relativistic speeds. Do we have to add both the gravitational and kinematical effects to calculate the perceived time dilation at M as observed by T or does the gravitational effect already include the kinematical effect?

Is it this you want to know? If so then the answer is that in general relativity the kinematics is built-in already.

Consider spacetime, while in special relativity it is possible to think of spacetime as some kind of 4 dimensional fixed ice surface on which particles trace paths without friction, this is not the case in general relativity. In general relativity, spacetime is exactly the complete configuration of all the particles including their masses and energy. Looking at it through time, spacetime continuously reshapes itself. Each particle's relative position, mass and energy contributes to the overall shape of spacetime. So when particles move with respect to each other, the spacetime shape changes. All these configurations of spacetime are actually all the same but just in a different form, a bit like all the different appearances of a Rubic's cube.

 

[Johnny R]

You've missed the main point of relativity - all motion is relative - so the above does not make sense unless you say in which frame ( ie who) is measuring the speed of the clock. If the clock was in someones pocket, they would not notice any change. Only an observer in a frame moving relative to the clock *sees* it running slower. It actually isn't running slower.

You are right, I am missing a major point here.

A clock on Earth ticks faster than a clock in orbit around the earth. A clock on Earth ticks faster than a clock on the Sun.

My question is that you have two masses in which one is much larger than the other and I assume that from a third person position the clock on the smaller mass body will tick faster. Now if you accelerate the two bodies at the same rate would the time dilation be consistent for the two bodies or would the clock on the smaller mass body show a more rapid rate of time dilation as they approach c?

 

[JesseM]

You are right, I am missing a major point here.

A clock on Earth ticks faster than a clock in orbit around the earth.

This situation is less ambiguous because the motion is non-inertial (although you could find frames where at certain moments during a satellite's orbit its clock would be ticking faster than a clock on the Earth, even though the average rate of ticking over a complete orbit would be slower), but when two clocks are moving inertially, at constant velocity relative to one another (constant speed and direction), relativity says that in each clock's rest frame, it is the other clock that is ticking slower, and that neither perspective is more correct than the other.

 

[Johnny R]

This situation is less ambiguous because the motion is non-inertial (although you could find frames where at certain moments during a satellite's orbit its clock would be ticking faster than a clock on the Earth, even though the average rate of ticking over a complete orbit would be slower), but when two clocks are moving inertially, at constant velocity relative to one another (constant speed and direction), relativity says that in each clock's rest frame, it is the other clock that is ticking slower, and that neither perspective is more correct than the other.

So let's explore a triplets problem.

One triplet in on a space station, one is on a highly massive spaceship and the third is on a spaceship the same size as the space station. The two ships take off together traveling at the same rate, say 3/4c. Who would be young, younger and youngest when they get back?

 

[JesseM]

So let's explore a triplets problem.

One triplet in on a space station, one is on a highly massive spaceship and the third is on a spaceship the same size as the space station. The two ships take off together traveling at the same rate, say 3/4c. Who would be young, younger and youngest when they get back?

Well, I assume by "highly massive" you mean "enough to cause noticeable gravitational time dilation", right? If so this is a problem for general relativity rather than special relativity, but in this case I think the answer would be that the combination of traveling on a non-inertial path and experiencing gravitational time dilation would make the twin on the massive ship youngest, while the twin on the station would be the oldest. In the case of your other question:

My question is that you have two masses in which one is much larger than the other and I assume that from a third person position the clock on the smaller mass body will tick faster. Now if you accelerate the two bodies at the same rate would the time dilation be consistent for the two bodies or would the clock on the smaller mass body show a more rapid rate of time dilation as they approach c?

I would think that if you take a large-scale view where most of the curvature is confined to the immediate neighborhood of the masses and spacetime is almost flat farther from them (the term for this is an 'asymptotically flat' spacetime), then you could treat this like two clocks that have been artificially slowed down by different amounts (to simulate gravitational time dilation) in SR, which means that one clock will continue to run slower than the other by the same ratio in any frame where they are moving together at relativistic speeds (but although the ratio would be the same in all frames, of course the actual rate of ticking of each clock would be slower in frames where their velocity was closer to c). I don't know enough general relativity to be able to verify that it would actually work this way in the case of real gravitational time dilation as opposed to just simulated time dilation, but I'm pretty sure it would.

 

[Mentz114]

The time dilations of the moving ( wrt space station) triplets is caused by their accelerations and decelerations during their trips. If gravity is indistinguishable from acceleration, then I go with JesseM's ranking -

massive ship youngest
other ship
space station oldest

 

[Johnny R]

In the case of your other question: I would think that if you take a large-scale view where most of the curvature is confined to the immediate neighborhood of the masses and spacetime is almost flat farther from them (the term for this is an 'asymptotically flat' spacetime), then you could treat this like two clocks that have been artificially slowed down by different amounts (to simulate gravitational time dilation) in SR, which means that one clock will continue to run slower than the other by the same ratio in any frame where they are moving together at relativistic speeds (but although the ratio would be the same in all frames, of course the actual rate of ticking of each clock would be slower in frames where their velocity was closer to c). I don't know enough general relativity to be able to verify that it would actually work this way in the case of real gravitational time dilation as opposed to just simulated time dilation, but I'm pretty sure it would.

I know that when a clock reaches c (it can't because it would require and infinite amount of energy) it will stop. So the clock with the greater mass would stop before the one with the lesser mass. Does this mean that there is a lower speed limit for more massive objects at some speed less than c? Does a greater mass reach the point where it needs an infinite amount of energy to increase velocity before an object of lesser mass?

 

[JesseM]

I know that when a clock reaches c (it can't because it would require and infinite amount of energy) it will stop. So the clock with the greater mass would stop before the one with the lesser mass.

No, that doesn't follow. Like I said, I think the ratio would be constant--so suppose one clock in space ticks at 1 tick per second according to my own clock when I am at rest relative to it, while another clock near a massive object ticks at half that rate, or 0.5 ticks per second of my clock when I am at rest relative to it, due to gravitational time dilation. Then if the two clocks accelerate until they are moving at 0.6c in my frame, the first clock would tick at 0.8 ticks per second of my clock due to ordinary velocity-based time dilation, while the second clock would continue to tick at half that rate, or 0.4 ticks per second, due to the combination of velocity-based and gravitational time dilation. Then if both clocks accelerate to 0.8c in my frame, the first clock ticks at 0.6 ticks per second while the second ticks at 0.3 ticks per second; if they accelerate to 0.9165c in my frame, the first clock ticks at 0.4 ticks per second and the second ticks at 0.2 ticks per second; and so on and so forth, with the second clock always ticking at half the rate of the first, and both clocks ticking slower and slower in my frame as they approach a speed of c relative to me. But there is no velocity under c where the second clock will have a rate of 0 ticks per second! Since half of zero is zero, and the second clock is always ticking at half the rate of the first, the second clock will only have a rate of 0 ticks per second when the first does too, which only happens in the limit as both clocks approach c.

 

[phyti]

time dilation

This answer is based on you being the observer.
Clock A on the large mass object, will initially be running slower
than clock B on the small mass object because of gravitation.
If both clocks experience the same acceleration to light speed c,
with a final frequency of zero, clock B with the highest frequency,
will have to slow down at a faster rate than A for the duration of the test.

 

[Mentz114]

phyti, that is good logic. What if the gravitational masses of the ship also showed a kinematic increase ? This might account for the different rates.

I offer this tentatively. I will try a calculation later or maybe the Relativity Police will intervene and tell me.

 

[Johnny R]

So the slow down due to acceleration is not constant for both masses in an absolute sense. So the larger the mass the less relative time dialation. I have learned something here, thank you very much.

Johnny