Understanding Time Dilation: Whose Clock Ticks Faster in Special Relativity?

[Toftarn]

I have just started studying special relativity, and there is one thing I really don't understand:

Suppose you have two observers, A and B, in space, and that these are moving relative to one another. Due to time dilation, their clocks will tick at different rates. But how do you know whose clock ticks faster?

In other words, if a spaceship travels at a speed near c away from the earth, why do the astronauts age less than someone who stays at the Earth and not vice versa? Couldn't you instead say that the Earth travels away from the spaceship?

 

[JesseM]

I have just started studying special relativity, and there is one thing I really don't understand:

Suppose you have two observers, A and B, in space, and that these are moving relative to one another. Due to time dilation, their clocks will tick at different rates. But how do you know whose clock ticks faster?

In other words, if a spaceship travels at a speed near c away from the earth, why do the astronauts age less than someone who stays at the Earth and not vice versa? Couldn't you instead say that the Earth travels away from the spaceship?

Yes, there is no objective truth about whose clock ticks faster, different inertial frames have different opinions and all are equally valid. Are you familiar with the idea of the relativity of simultaneity? If we are moving apart at 0.6c, with both our clocks set to zero at the moment we departed, then in my inertial rest frame the event of my clock reading 10 years will be simultaneous with the event of your clock reading 8 years, but in your inertial rest frame the event of your clock reading 8 years is simultaneous with the event of my clock reading 6.4 years, so each of us says the other's clock is slowed down by a factor of 0.8. Of course, the symmetry only holds when both observers are moving inertially (constant speed and direction), if either one turns around so they can reunite and compare clocks then the symmetry is broken, and the one who accelerated will have aged less--this is the classic twin paradox.

 

[peio]

While someone gives you a batter answer, as I'm also a beginner, you can check http://en.wikipedia.org/wiki/Twin_paradox"

Basically both observers see that the other is ageing less, but if the astronaut is to return to the same place he will have to change of reference frame, and in that case everything changes and the typical time dilation doesn't apply.

 

[neu]

You should think of it in terms of one inertial reference frame at a time if you get confused.There is no universal inertial frame of reference. Everything is relative to one's own reference frame. Hence your question of "which clock ticks faster?" is counter productive.

Say you have two people in two separate inertial ref frames moving reltive to each other.

Person A and B will both experience time as constant in their own ref frame but will observe the space/time dilation in the other persons ref frame.

i.e. Person A will observe Person B's watch to tick slower by an amount proportional to their volocity relative to A (and visa versa), Hence in this scenario your selection of ref frame determines whose watch ticks slower.

 

[Toftarn]

I see. So in the example with the two astronauts, whose clock will tick faster depends on the frame of reference you choose, and to both of them it will look as if the other astronaut's clock ticks slower?

And in the case with a spaceship traveling near c, the astronauts will age less not just because of time dilation in special relativity, but because of something that has to do with their acceleration?

 

[JesseM]

And in the case with a spaceship traveling near c, the astronauts will age less not just because of time dilation in special relativity, but because of something that has to do with their acceleration?

A good analogy here is with spatial paths on a 2D piece of paper. If you draw two paths between a pair of points, the straight-line path on the paper (analogous to an inertial path through spacetime) will always have a shorter length than a path with a bend in it (analogous to a path through spacetime involving an acceleration), because the straight line is the shortest distance between points. That doesn't mean that the bent path accumulated all the extra distance during the bendy segment, the extra length is due to the geometry of the entire path. And similarly, if you draw a cartesian coordinate grid over these paths, then depending on how you orient your y-axis, the rate at which each path is accumulating length as you vary the y-coordinate can be different, but all coordinate systems agree on the overall lengths of the two paths. I expanded on this analogy a bit in this post if you're interested.