# Concerning the platform and the carriage in uniform translatory motion

1. Jul 31, 2005

### paco1955

all our judgments in which time plays a part shall always be judgments of simultaneous events.

if at the point x of space there is a clock, an observer at x shall be able to determine the time values of events in the immediate proximity of x by finding the positions of the hands which are simultaneous with these events.

if there is at the point y of space another clock in all respects resembling the one at x, it shall be possible for an observer at y to determine the time values of events in the immediate neighborhood of y.

it shall not be possible, however, to compare, in respect of time, an event at x with an event at y.

if the "time", however, required by light to travel from x to y equals the "time" it requires to travel from y to x, a common "time" for x and y shall have been established, and the two clocks synchronize. let a ray of light depart from x at the time tx, and be reflected at y at the time ty, and reach x again at the time t'x. if ty - tx = t'x - ty, then the clock at y shall synchronize with the clock at x.

2xy / (t'x - tx) = c

(1) the principle of relativity:

the laws by which the states of physical systems undergo change shall not be affected, whether these changes of state be referred to the platform or the carriage in uniform translatory motion.

(2) the principle of the constancy of the velocity of light:

any ray of light shall move in the platform with the determined velocity c, whether the ray be emitted by a stationary or by a moving carriage.

let the carriage be stationary relative to the platform; and let its length be l as measured by a measuring-rod which is also stationary. we now imagine the axis of the carriage lying along the axis of x of the platform, and that a uniform motion of parallel translation with velocity v along the axis of x in the direction of increasing x is then imparted to the carriage. we now inquire as to the length of the moving carriage, and imagine its length to be ascertained by the following two operations:

(a) an observer moves together with the given measuring-rod and the carriage to be measured, and measures the length of the carriage directly by superposing the measuring-rod, in just the same way as if all three were at rest.

(b) by means of stationary clocks set up in the platform and synchronizing, the observer ascertains at what points of the platform the two ends of the carriage to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated "the length of the carriage."

the length to be discovered by operation (a) we shall call "the length of the carriage in the moving system", and shall be equal to the length l of the stationary carriage.

the length to be discovered by operation (b) we shall call "the length of the moving carriage in the platform". this length shall be determined on the basis of the principle of relativity and the principle of the constancy of the velocity of light, and it shall differ from l.

a moving carriage at the epoch t shall not in geometrical respects be perfectly represented by the same carriage at rest in a definite position.

imagine that at the two ends x and y of the carriage, clocks are placed which synchronize with clocks on the platform, that is to say that their indications correspond at any instant to the "time of the platform" at the places where they happen to be. These clocks are therefore "synchronous in the platform."

imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established for the synchronization of two clocks. Let a ray of light depart from x at the time tx, let it be reflected at y at the time ty, and reach x again at the time t‘x.

Taking into consideration the principle of the constancy of the velocity of light we find that

ty - tx = rxy/(c - v) and t’x - ty = rxy/(c + v)

where rxy denotes the length of the moving carriage--measured in the platform.

why is it that ty - tx = rxy/(c - v) and t’x - ty = rxy/(c + v)?

Observers moving with the moving carriage would thus find that the two clocks were not synchronous, while observers in the platform would declare the clocks to be synchronous. why?

we shall not be able to attach any absolute signification to the concept of simultaneity.

two events which (viewed from the platform) are simultaneous, shall no longer be looked upon as simultaneous events when envisaged from the carriage which is in motion relatively to the platform

Last edited: Jul 31, 2005