The time for 2 light pulses in a moving vehicle

[Dale]

The minus sign means that it happens before a nearby O frame synchronized clock reads t=0.

 

[powermind]

Is this logical?!

Suppose M turns the lights on at t’. At this time (t'), O will calculate his time so that t = $\gamma$t’. Definitely the lights should be turned on not before the time (t) according to O.

But we notice that A is switched on before t according O which is not logical!

Can you please explain what the wrong is?

 

[Dale]

Is this logical?!

Yes, it is logical. You are simply forgetting to include the relativity of simutaneity.

Suppose M turns the lights on at t’. At this time (t'), O will calculate his time so that t = $\gamma$t’.

This is only correct for x'=0. The complete formula is $t=\gamma(t'+vx'/c^2)$. For x'=0 that simplifies to what you wrote, but A and B are located at $x'=\pm L_0/2$, not at x'=0, so you cannot use the simplified formula.

Can you please explain what the wrong is?

My recommendation is to avoid the simplified formulas. Always use the full Lorentz transform formulas (http://en.wikipedia.org/wiki/Lorentz_transformation#Boost_in_the_x-direction). They will automatically simplify to the appropriate formulas when they do apply, but you will avoid mistakes like this from using the simplified formulas when they don't apply.

 

[powermind]

DaleSpam,

Q. When did M switch the light on?
A. At t'.

Q. At t' what was the time according to O?
A. t = $\gamma$t'. (x' = 0 or using time dilation equation)

I think you agree right now!

So, the switching event happened at t' according to M or at t according to O.

Is there any problem?

Ok! how was the light A switched on before t?
How can I say "O sees the light A before it is switched on" ??! This is very strange!

You can believe in the relativity of simultaneity but not on that way, can't you?!

 

[Dale]

Q. At t' what was the time according to O?
A. t = $\gamma$t'. (x' = 0 or using time dilation equation)

I think you agree right now!

No, I definitely disagree. As I already explained, that equation doesn't apply here since x'≠0 for A and B. The correct equation is $t=\gamma(t'+vx'/c^2)$.

You cannot use an equation when it doesn't apply, and you cannot neglect the relativity of simultaneity when it suits you. Always use the Lorentz transform. It includes all relativistic effects, and will automatically simplify to the time dilation equation when it is applicable, which it isn't here.

Neglecting the relativity of simultaneity by improperly using the time dilation equation is a key mistake that you have been repeatedly making since the beginning of the thread. I don't know how to be more clear about it. You have been corrected on this point multiple times by multiple people.

 

[Nugatory]

Ok! how was the light A switched on before t?
How can I say "O sees the light A before it is switched on" ??! This is very strange!

You can believe in the relativity of simultaneity but not on that way, can't you?!

For M, the A light source was switched on at t', and the flash of light reached M's eyes at his time $t'+\frac{d'}{c}$ where $d'$ is the distance between where the light source was when the light was switched on and where M's eyes are when the flash of light reached them. It's easy for M to measure $d'$ because the light source and M's eyes are both at rest relative to M.

For O, the A light source was switched on at t, and the flash of light reached O's eyes at his time $t+\frac{d}{c}$ where $d$ is the distance between where the light source was when the light was switched on and where O's eyes are when the flash of light reached them.

Although ${t}\neq{t'}$ and $d\neq{d'}$ both observers see something perfectly reasonable: the light source is switched on, the flash of light travels from the light source to their eyes at speed $c$, and they add the travel time to the emission time to get the arrival time.

 

[powermind]

DaleSpam, sometimes generic talking can not transfer an idea in correct way. Nugatory has clarified what is my mistake. Unluckily I knew that before his post :)

After Nugatory's post we can make a scenario: O will see light A first then M will see A and B at the same time finally O will see B. I hope I am correct

I would like to thank you all, PeterDonis, Nugatory, DaleSpam and all who help me. Thank you for your patience.

Thank you very much.
Will see you back ...

 

[Dale]

Excellent. I am glad that Nugatory's comments were helpful.