# A doubt in simultaneity

1. Jul 22, 2008

### novice2000

Hi everyone,

I got interested in physics recently and started reading a book called "relativity simply explained " by martin gardener. when i was going through the book i got some doubts in relativity of simultaneity.

my problem is described below

o>>> ---------------------------<< 0
1---------------B-------------------2
----------------C --> V
Point 1 and 2 are light sources equidistant from observer B . There are clocks at point 1 and 2 each.The moment the light is sent from point 1 clock at point 1 is set to zero and the moment the light is sent from point2 clock at point 2 is set to zero.

B receives the light from both point1 and point 2 simultaneously. Can he conclude that clocks at 1 and 2 are synchronized ?

C is an observer moving w.r.t to B Can he actually see that light from both sources reaching B at same time??

I have a few more queries

hoping to get a reply soon

2. Jul 22, 2008

### Staff: Mentor

It depends on whether those clocks are moving with respect to B or not. If the clocks are not moving, then he can conclude they are synchronized. (Assuming they are working properly.)

If you mean will a moving observer C agree that the light from both sources reached B at the same time: Yes. All observers will agree on that.

3. Jul 22, 2008

### novice2000

Doc Al thanks for the reply

As you have mentioned the clocks are not moving w.rt to B and he concludes that clocks are synchronized.

Observer C sees that light from both sources reaches B at the same time.

o>>> ---------------------------<< 0
1---------------B-------------------2
----------------C --> V

the observer C is moving to the right with a speed V. He observes that light from 2 has to travel more distance and since speed of light is same in both directions he is forced to conclude that clock at 2 is set ahead of clock at 1

is my conclusion correct?

4. Jul 22, 2008

### Staff: Mentor

Yes, that is correct.

5. Jul 22, 2008

### novice2000

Oh great!!!

if i repeat the same experiment with two tennis balls instead of light source. ie i will release two tennis balls from both 1 and 2 with same speed say "w".

the two balls will arrive observer B at the same moment and he will conclude that clocks are synchronized. right?

C will see that both balls arrive observer B at the same moment.

o--> w--------------------- w<----- 0
1---------------B--------------------2
C --> V

if i take speed of ball from 1 as w-v ( relative speed . is this correct???)

and speed of ball from 2 as w+V .

is'nt it possible for observer C to back calculate and conclude that both clocks are synchronized??

i know there is some error. But cant figure out

6. Jul 22, 2008

### Staff: Mentor

Hi novice2000,

The error is just that you need to use the http://www.math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html" [Broken] formula, not the Gallilean one.

Last edited by a moderator: May 3, 2017
7. Jul 22, 2008

### Staff: Mentor

Right.

Right.

No, as DaleSpam already pointed out, this is not correct. You must combine speeds relativistically to get the correct answer. (That's why relativity thought experiments always use light beams--they always go at the same rate in any frame. Much easier to switch from one frame to another.)

The transformation of velocities that you used to get w-v and w+v is only true in Newtonian physics, not Einsteinian. (That transformation is called Galilean relativity, after Galileo.) Using that transformation, you would be able to conclude both clocks are synchronized: But that's no surprise--in the Newtonian world time is the same for any frame.

If you used the proper relativistic transformation (see DaleSpam's link), you'd find--once again--that simultaneity is relative.