What does symmetry of time dilation really mean?

[Chenkel]

Hello everyone,

I've been studying Morin's book and the case for time dilation makes sense, a clock in the rest frame of the moving body counts to $T_A$, and a clock in the lab frame counts to $T_B$ and we find $T_B = {\gamma}{T_A}$

What I might be failing to do is understand what the symmetry of time dilation really means.

There is a clock that is not moving, the lab clock, and there is a clock that is moving, the traveling clock, the traveling clock ticks less than the lab clock.

I get this and it makes sense, but why would we say the lab is moving and the traveling clock is the stationary clock for analysis?

In this latter case I see that time dilation is used to explain length contraction of the lab relative to the traveler based on Morins explanation, so maybe that's how time dilation is symmetric?

Maybe if I get good at spacetime diagrams it will make sense.

Looking forward to any help on this matter, thank you.

 

[Dale]

a clock in the rest frame of the moving body counts to $T_A$, and a clock in the lab frame counts to $T_B$ and we find $T_B = {\gamma}{T_A}$

a clock in the rest frame of the moving body counts to $\tau_A$, and a pair of synchronized clocks in the lab frame count to $t_B$ and we find $t_B = {\gamma}{\tau_A}$

What I might be failing to do is understand what the symmetry of time dilation really means.

a clock in the rest frame of the lab counts to $\tau_B$, and a pair of synchronized clocks in the rest frame of the moving body count to $t_A$ and we find $t_A = {\gamma}{\tau_B}$

 

[Ibix]

I get this and it makes sense, but why would we say the lab is moving and the traveling clock is the stationary clock for analysis?

Think of a long straight road with mile markers along it. Another straight road crosses the first one at an angle $\theta$.

On the first road, at the marker one mile after the crossing point, which mile marker on the other road are you level with?

On the second road, at the marker one mile after the crossing point, which mile marker on the other road are you level with?

 

[PeroK]

I get this and it makes sense, but why would we say the lab is moving and the traveling clock is the stationary clock for analysis?

Why not? Why would you assume that a lab, on the rotating surface of the Earth, orbitting the Sun, orbitting the galactic centre, on a collision course towards the Andromeda galaxy is the only valid reference frame in the universe?

 

[Mister T]

What I might be failing to do is understand what the symmetry of time dilation really means.

You keep asking the same question in different threads that you've started. It's actually a very good question, but the answer is subtle.

Since the previous answers involving relativity of simultaneity and spacetime diagrams don't seem to have landed, try focusing on the concept of proper time. Think in terms of events. Let's have two reference frames, $A$ and $B$ moving relative to each other. If two events occur in reference frame $A$ at the same place, then the time that elapses between them is the proper time $\Delta \tau_A$. Likewise, for two events that occur in the same location in $B$, the time that elapses between them is $\Delta \tau_B$.

You seem to be under the impression that time dilation is a relationship between $\Delta \tau_A$ and $\Delta \tau_B$. It is not!

 

[Chenkel]

a clock in the rest frame of the moving body counts to $\tau_A$, and a pair of synchronized clocks in the lab frame count to $t_B$ and we find $t_B = {\gamma}{\tau_A}$

a clock in the rest frame of the lab counts to $\tau_B$, and a pair of synchronized clocks in the rest frame of the moving body count to $t_A$ and we find $t_A = {\gamma}{\tau_B}$

What do you mean by a pair of synchronized clocks?

 

[PeroK]

What do you mean by a pair of synchronized clocks?

See section 1.3 of Morin's book.

 

[Chenkel]

See section 1.3 of Morin's book.

I'm aware that loss of simultaneity happens in certain reference frames in the theory.

 

[Vanadium 50]

And we're on Thread #4. At least.

You got some good advice in previous threads. It might be a better idea to try and follow this advice than to start a brand new thread where you will likely get the exact same advice.

 

[Chenkel]

And we're on Thread #4. At least.

You got some good advice in previous threads. It might be a better idea to try and follow this advice than to start a brand new thread where you will likely get the exact same advice.

Relativity seems like an accepted idea, but time dilation being symmetric and happening in both rest frames seems like it might be contradictory to me. Maybe I just haven't studied enough.

 

[Chenkel]

a clock in the rest frame of the moving body counts to $\tau_A$, and a pair of synchronized clocks in the lab frame count to $t_B$ and we find $t_B = {\gamma}{\tau_A}$

a clock in the rest frame of the lab counts to $\tau_B$, and a pair of synchronized clocks in the rest frame of the moving body count to $t_A$ and we find $t_A = {\gamma}{\tau_B}$

So the first paragraph chooses the lab as the rest frame for analysis, and the second paragraph chooses the moving body as the rest frame for analysis?

Why do two different analysis lead to two equations that are inconsistent?

 

[PeterDonis]

I'm aware that loss of simultaneity happens in certain reference frames in the theory.

It's not "loss of simultaneity", it's relativity of simultaneity. That means simultaneity is different in every inertial frame, not just "some".

@Vanadium 50 has made a valid point: you keep starting new threads asking the same question. And the answer keeps being the same.

Why do two different analysis lead to two equations that are inconsistent?

They don't when you do the analysis correctly. Doing that requires using the full Lorentz transformation equations, which you are not doing. You need to do that. This has already been discussed in your previous threads.

 

[Orodruin]

Relativity seems like an accepted idea, but time dilation being symmetric and happening in both rest frames seems like it might be contradictory to me. Maybe I just haven't studied enough.

For the unpteenth time: You are missing the relativity of simultaneity. You will not understand relativity until you internalize it.

 

[Orodruin]

Why do two different analysis lead to two equations that are inconsistent?

They are not, they are comparing different things.

 

[Chenkel]

They are not, they are comparing different things.

I just don't see how both clocks can think the "other" is ticking slower, seems inconsistent. But I don't know, Albert Einstein is a genius, who am I?

 

[PeterDonis]

I just don't see how both clocks can think the "other" is ticking slower, seems inconsistent.

At this point we have done our best to explain it to you. If you still don't get it, the only advice we can give you is to take the time to learn SR from a textbook.

But I don't know, Albert Einstein is a genius, who am I?

Someone who does not understand how relativity works the way Einstein did. At this point we can do nothing more to help you fix that, but that's what you need to fix.

This thread is closed.

 

[Dale]

What do you mean by a pair of synchronized clocks?

I mean two inertial clocks, at rest with respect to each other, that have been synchronized using Einstein’s synchronization convention. This process of synchronizing a set of inertial clocks is the basis of an inertial reference frame.

So the first paragraph chooses the lab as the rest frame for analysis, and the second paragraph chooses the moving body as the rest frame for analysis?

Yes.

Why do two different analysis lead to two equations that are inconsistent?

They don’t. There is nothing inconsistent with The equations I wrote:
$t_B = {\gamma}{\tau_A}$
$t_A = {\gamma}{\tau_B}$
This is a perfectly consistent set of equations.

You had written
$T_B = {\gamma}{T_A}$
$T_A = {\gamma}{T_B}$
which is inconsistent. But that is not what I wrote.

I just don't see how both clocks can think the "other" is ticking slower, seems inconsistent.

That is why I carefully wrote it the way I did. In each frame the two synchronized clocks read more coordinate time than the one clock’s proper time. There is nothing inconsistent about that.

This thread is closed.

Oops, sorry I didn’t notice the closure when I started replying.