Understanding Time Dilation: A Closer Look at Relativity and Relative Motion

[KingOrdo]

My understanding is that if X moves relative to a 'stationary' observer Y (say in direction +x), at close to the speed of light, time will pass 'more slowly' for X. That is to say, when X returns to Y, Y is older than X.

But, isn't it just as accurate to say that Y is moving relative to X (in direction -x)? That being the case, Y would experience time dilation, and when X & Y meet up again, X should be older than Y.

What gives?

 

[radou]

This should help: http://theory.uwinnipeg.ca/mod_tech/node135.html"

 

[leright]

This is known as the twins paradox and a lot of smart people broke their heads over it in Einstein's day. The key is that there is a change in the inertial reference frame when X turns around, which is a no-no in relativity.

 

[KingOrdo]

Okey, let me put it another way:

My understanding is that, when Y moves relative to a 'stationary' observer X, time passes more slowly on Y's watch than on X's.

But isn't it just as accurate to say that X is moving relative to Y, and therefore Y's watch would tick "more slowly" than X's? Why would there be any net change?

 

[JesseM]

My understanding is that, when Y moves relative to a 'stationary' observer X, time passes more slowly on Y's watch than on X's.

But isn't it just as accurate to say that X is moving relative to Y, and therefore Y's watch would tick "more slowly" than X's? Why would there be any net change?

The usual rules for time dilation in SR only apply to inertial observers, ie observers moving at a constant speed and direction (if you accelerate, you'll know you're not moving inertially because you'll feel G-forces). For a non-inertial observer, it's not true that a clock moving relative to her must always be ticking slower in a coordinate system where she's at rest.

 

[KingOrdo]

Right. . . .

But the point is that, regardless of the accelerations involved, an entity Y will have its clock run IN SOME FASHION slower than X, if Y has a velocity relative to X.

But, isn't it just as accurate to say that X has the velocity relative to Y, and consequently X would undergo the time dilation? Certainly, they can't both undergo time dilation because then there would be no net difference. . . .

What gives?

 

[JesseM]

But the point is that, regardless of the accelerations involved, an entity Y will have its clock run IN SOME FASHION slower than X, if Y has a velocity relative to X.

I don't think that's right. For example, if from the perspective of some inertial frame Y is at rest while X is traveling in a circle around it at constant speed, then I think in some reasonably-constructed non-inertial rotating coordinate system where X is at rest while Y is the one moving, Y would be ticking at a constant rate faster than X.

 

[KingOrdo]

Well, let's look at it this way:

Whatever the specifics, Y moves relative to X in direction +x, and therefore undergoes time dilation; time passes more slowly for Y.

But isn't it just as accurate to say that X moved relative to Y, in an identical fashion except in direction -x? And consequently, X would have time pass more slowly?

 

[JesseM]

Whatever the specifics, Y moves relative to X in direction +x, and therefore undergoes time dilation; time passes more slowly for Y.

But that's exactly what I just said is wrong. If the specifics are that the x-axis is part of a non-inertial coordinate system, then movement along this axis could cause Y to speed up rather than slow down in this coordinate system, and the rate of time dilation wouldn't necessarily just be a function of Y's velocity in this coordinate system either, even if Y moves at a constant rate it might be running faster at some times and slower at others.

 

[KingOrdo]

Well, certainly you concede that we can have a situation where Y is moving relative to X and Y undergoes time dilation.

But why can we not say that it was X that moved relative to Y and X underwent the time dilation; where does the asymmetry come from?

 

[JesseM]

Well, certainly you concede that we can have a situation where Y is moving relative to X and Y undergoes time dilation.

Huh? That's what I keep saying is incorrect! Are my posts unclear?

edit: sorry, I missed that you said "we can have a situation..." So yeah, I agree that you could have a non-inertial frame where Y was moving and its clock was slowed down. But this wouldn't be true at all times in a non-inertial frame of the traveling twin, for example--if you set up the non-inertial frame correctly, you'll still end up predicting that the earth-twin's clock shows more elapsed time, meaning at some point in the trip it must have been ticking faster rather than slower.

 

[bernhard.rothenstein]

My understanding is that if X moves relative to a 'stationary' observer Y (say in direction +x), at close to the speed of light, time will pass 'more slowly' for X. That is to say, when X returns to Y, Y is older than X.

But, isn't it just as accurate to say that Y is moving relative to X (in direction -x)? That being the case, Y would experience time dilation, and when X & Y meet up again, X should be older than Y.

What gives?

If you are interested in time interval measurement by accelerating observers have a look please at

arXiv.org > physics > physics/0608010

 

[KingOrdo]

Let's look at it this way: Y moves with a constant velocity, 0.5c, on a great circle path on a sphere. No accelerations involved in this example at all. The circumference of the sphere is 1 light year. X sits on the great circle, 'stationary'.

In Y's reference frame, every 2yr it passes X. Yet in X's reference frame, Y passes it every 3yr or so due to time dilation. So after ten passes, X is ten years older than Y.

But isn't it just as accurate to say that X is moving and Y is the stationary observer? In that case, every time X and Y meet, time dilation has caused Y to be a year older; accordingly, after ten passes, Y is ten years older than X. But then every time they meet, it would seem there is no net change in their ages: depending on the reference frame, one aged faster than the other.

 

[JesseM]

Let's look at it this way: Y moves with a constant velocity, 0.5c, on a great circle path on a sphere. No accelerations involved in this example at all.

Inertial motion refers exclusively to movement at constant speed and in a straight line--since velocity is a vector, any change in direction represents a change in velocity, even if speed is constant. And you can tell you're not moving inertially when you move in a circle at constant speed, because you'll feel G-forces (known in Newtonian physics as 'fictitious forces' because they are not genuine forces in inertial frames...see here and here)--in this case, the "centrifugal force". An observer moving inertially will always feel weightless.

 

[Flatland]

moving in a circular path = acceleration. Acceleration is not just a change in speed, it's a change in direction also. While constant motion is relative, acceleration is not.

 

[KingOrdo]

Is a body moving along a geodesic on the 2-sphere with a constant velocity not a inertial observer? I'm not talking about a higher-dimensional embedding: I'm saying that X (or Y) has constant velocity: no change in speed, no change in direction. He just happens to reside on S^2 instead of in Euclidean space.

 

[JesseM]

Is a body moving along a geodesic on the 2-sphere with a constant velocity not a inertial observer? I'm not talking about a higher-dimensional embedding: I'm saying that X (or Y) has constant velocity: no change in speed, no change in direction. He just happens to reside on S^2 instead of in Euclidean space.

A geodesic in curved spacetime is indeed "locally inertial", but once you introduce curved spacetime you can't assume the SR rules of time dilation will still apply outside of a local (infinitesimally small) region of spacetime. Also, it'd probably be better to talk about positively-curved 3-space, since my understanding is that general relativity would be seriously modified in 2-space (no gravitational waves, for example).

 

[yogi]

A down to Earth example (to make a play on words) is a GPS satellite clock - it is in an inertial frame - it experiences no acceleration since it is in free fall - and if you placed a clock on a tower at the North pole at the same elevation - the satellite clock will ACCUMULATE LESS TIME DURING EACH ORBIT than the north pole clock as it passes by - but the satellite clock really doesn't run slower - that is where the confusion arises - it simply has a space increment and a time increment that must be combined pathagorean like to total the time increment accumulated by the North Pole clock during each pass of the satellite - both clocks run at the same rate in their own frame.