Understanding Simultaneity in Relativity: Common Doubts Addressed

[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

 

[Doc Al]

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

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.)

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

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.

 

[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?

 

[Doc Al]

Yes, that is correct.

 

[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 can't figure out


Please help

 

[Dale]

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 ... i know there is some error. But can't figure out

Hi novice2000,

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

 

[Doc Al]

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?

Right.

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

Right.

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 .

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.)

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

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.