Time Measurement in Moving Frames: Synchronization and Experimental Techniques

[wizrdofvortex]

Two doubts...

1. Consider two frames S and M, the latter moving at constant velocity v wrt S. I know that it's possible to synchronize clocks at different positions in a particular frame. But is it possible to synchronize a clock in S and another in M, and if so, how to do it?

2. Suppose we represent coordinates by x, t in S and X, T in M. For t = 0, T = 0, and at t = T = 0, the origins of the two systems coincide.

Now an observer in M can measure the time of an event at distance X1 as follows: if he receives a light signal from that event at time T1, the time of that event will be (T1 - (X1/c)).

My question is, how can an observer in S at the origin of S experimentally measure the time of the same event (by PHYSICAL reasoning and not using Lorentz transformation)?

Thanks in advance

 

[_PJ_]

What's the distance between S' origin and X1?
Can it be assumed to be (X1-(v*T))?

 

[wizrdofvortex]

What's the distance between S' origin and X1?
Can it be assumed to be (X1-(v*T))?

I'll clarify: X1 is the position (x-coordinate) of the event as measured by an observer in M. I don't think it can be assumed to be (X1-(v*T)).

 

[ghwellsjr]

My question is, how can an observer in S at the origin of S experimentally measure the time of the same event (by PHYSICAL reasoning and not using Lorentz transformation)?

There is no consistent or meaningful physical or experimental way for an observer to measure the time of a distant event (it doesn't matter whether it is of a moving object or not) without making an arbitrary assumption. Einstein's synchronization convention is based on one such arbitrary assumption, that the time it takes for light to travel from the observer to the distant event is the same time as it takes for light to travel from the distant event to the observer. Once this convention is established for multiple frames in relative motion, you can use the Lorentz Transform to see what the co-ordinates in one frame look like in another frame. There is no physical or experimental way to sidestep an arbitrary establishment of a convention to resolve the problem of defining the time of a distant event.

 

[_PJ_]

Okay, to see if I'm understanding you correctly, I made a simple graph (don't laugh, I'm no artist :D )

http://homepage.ntlworld.com/mickyandlaura/graph.jpg

Distance is on the X axis, and Time on Y, with the event occurring at Y=0, X1
The future light-cone for the event is visible to M at T(M) and to S at T(S). S is stationary at X=0, whilst M moves at constant velocity, v

The gradient of the light-cone sides have magnitude c

TS=SQR((v*T(M)-c^2)) + T(M)

Provided S knows M's velocity, then T(M) can be calculated by S.

There's no guarantee of synchronicity of their clocks, though, since M is moving wrt S

 

[Mike_Fontenot]

[...]
My question is, how can an observer in S at the origin of S experimentally measure the time of the same event (by PHYSICAL reasoning and not using Lorentz transformation)?

https://www.physicsforums.com/showpost.php?p=3106767&postcount=38 .

 

[wizrdofvortex]

There is no consistent or meaningful physical or experimental way for an observer to measure the time of a distant event (it doesn't matter whether it is of a moving object or not) without making an arbitrary assumption. Einstein's synchronization convention is based on one such arbitrary assumption, that the time it takes for light to travel from the observer to the distant event is the same time as it takes for light to travel from the distant event to the observer. Once this convention is established for multiple frames in relative motion, you can use the Lorentz Transform to see what the co-ordinates in one frame look like in another frame. There is no physical or experimental way to sidestep an arbitrary establishment of a convention to resolve the problem of defining the time of a distant event.

I see... actually I was trying to arrive at a derivation of Lorentz transformation without using Minkowski space-time diagrams.

I came across the following in relation to that:

(Again using the same convention, x, t for S and X, T for M:)

for X = 0 and arbitrary T as measured in M,
x = vt (OR x = (v/c)*(ct) ) (1)

and for T = 0 and arbitrary X as measured in M,

x*(v/c) = ct. (2)

(1) and (2) were arrived at by referring to Minkowski diagrams (c/v being the slope), but I wanted to understand how these equations are arrived at using physical reasoning (also Minkowski diagrams do not reflect the complete physical picture). That is to say, how would one arrive at these relations without the assistance of such diagrams?

 

[ghwellsjr]

x*(v/c) = ct. (2)

Shouldn't this be x*(c/v) = ct ?

 

[wizrdofvortex]

Shouldn't this be x*(c/v) = ct ?

No, with units taken such that c = 1, the equations were :

vt - x = 0, for X = 0, which becomes : (v/c)*ct = x (T-axis in Minkowski diagram)

vx - t = 0, for T = 0, which is : (v/c)*x = ct (X-axis in Minkowski diag)