# Relativity Of Simultaneity Problem

1. Feb 3, 2014

### Trojan666ru

Imagine a 2.3 Ly long box. At the middle of the box there's a half silvered mirror (S) which splits laser beam into two and reflects to the both end of the box which is also mirrors that are facing each other (mirror A & B). Another observer (O) is placed 1.15 Ly away from mirror A in a series position. O A S & B are in series. Total distance between O and B is 3.45 Ly
O sends a laser pulse S (takes 2.3 years), it splits and reflects both beam towards A & B and reaches there simultaneously (in 3.45 years)
After that O starts his instantaneous acceleration towards the box and reaches at 90%c in his 1hr.
Now from his point of view, the beam that reflected from A moves towards the laser earlier than the laser that reflected from B. So the laser A hits the Centre of box earlier than laser B. Isn't that a paradox?

2. Feb 3, 2014

### PAllen

It would be a paradox if true. It isn't. See if you can figure out why. Start by showing how you calculated that it would happen as you think. Writing it down may help you see the issue.

3. Feb 3, 2014

### Mentz114

No. If the lasers hit simultaneously according to one clock, they can be non-simultaneous by another clock. That is relativirty of simultaneity.

Why are you wasting your time trying to find paradoxes where there aren't any ? Try to understand SR without this futile searching.

4. Feb 3, 2014

### PAllen

I believe the proposed paradox is that after reflecting at A and B, the beams meet in the center simultaneously - at a single event - per one frame, and not per another. That would, indeed, be a paradox, if true. The issue is that it is false.

5. Feb 3, 2014

### Trojan666ru

There's a problem because if the laser is a bomb that works on simultaneity it will explode in the observers frame

6. Feb 3, 2014

What false?

7. Feb 3, 2014

### Mentz114

I admit that I made no attempt to analyse the 'problem' so I'm not surprised !

8. Feb 3, 2014

### PAllen

I want you to try to figure it out, if you have interest in learning physics. Show your precise line of reasoning and calculation. My belief is that will help you see your error. If not, it will show you tried, and also help others help you.

9. Feb 3, 2014

### Staff: Mentor

No, it will explode in *any* frame. The laser beams reflected from mirrors A and B will meet back at S at the same event in *any* frame. That's why there is no paradox.

10. Feb 3, 2014

### JesseM

As PAllen suggests, try working out the numbers. Specifically, work both out both the position and time coordinates of the following four events in the frame that is moving at 0.9c relative to the box (you can assume the box is oriented parallel to the x-axis, and is moving only in the x-direction, so that you don't have to worry about the y and z coordinates which will always be the same, and can just define the "position" of each event in terms of the x-coordinate in this frame):

1. The event of the laser beams leaving the center of the box
2. The event of one beam reflecting off mirror A
3. The event of the beam that reflected off mirror A reaching the center of the box
4. The event of the other beam reflecting off mirror B
5. The event of the beam that reflected off mirror B reaching the center of the box

If you do the math correctly you'll see that there's no paradox. If you do get numbers that suggest a paradox, people can look at your numbers and point out the first one you made a mistake on.

P.S. you might want to change the velocity of the moving frame from 0.9c to 0.8c, it'll make the numbers work out neater--in the frame moving at 0.9c the length of the box will be Lorentz-contracted by a factor of 0.43588989 but in a frame moving at 0.8c it'll be Lorentz-contracted by a factor of exactly 0.6

Last edited: Feb 3, 2014
11. Feb 3, 2014