# Non-linear length contraction

1. Oct 4, 2011

### artkingjw

hey forum,

first of all, i'm a high school kid so forgive me if this is stupid. i've been thinking about relativity for some time now, and the issue with simultaneity.

Einstein proposed that length contracts as you approach the speed of light. Assume for a second that a train is going close to the speed of light and there are 2 bulbs at each end of the train, with an observer in the middle, outside there is an observer as well. so when the train passes the observer outside the two lights turn on at exactly the same time and the observer outside sees the event as not simultaneous whilst the observer inside sees it at simultaneous.

what i propose is, instead of the usual picture of linear contraction in the direction of motion (where such a paradox holds true), think of the contraction as non linear (hyperbolic or exponential perhaps?) where a test length in front and at the back contract with differing amounts although the overall contraction of the train is still according to einsteins length contraction equation. So if the front shortens more than the back, the paradox can be solved.

thoughts???

once again i'm a kid... forgive me if i'm wrong

2. Oct 4, 2011

### ghwellsjr

But there's no paradox that needs to be solved. You should try to learn and understand relativity before you try to explain it.

3. Oct 4, 2011

### artkingjw

ok so the accepted theory is that the events are not simultaneous, but there is no paradox cuz everything you observe depends on your frame of reference. (Tell me if i'm correct at this point, call it A)

point B, what if, there need not be non-simultaneity if my hypothesis were true.

don't answer point B if A is false or incomplete. Thank you.

4. Oct 4, 2011

### harrylin

Why do you think that non-linear contraction could help with synchronization? It would just mess up things. From the way you formulate your A, I'm not sure if what you mean with it is correct or not.

Anyway, the accepted theory is, as Einstein expressed it in 1907:

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated."

The essential feature of doing like that, is that the laws of nature work fine with respect to such an inertial system, just as with classical mechanics.

A direct consequence of such a synchronization is that distant clocks that appear in sync in one reference system, will appear out of sync in a system that is moving relative to the first system (except for clocks that are at the same position perpendicular to the line of motion).

Does that help?

Harald

Last edited: Oct 4, 2011
5. Oct 4, 2011

### artkingjw

Yes wow thank you i get it thank you harald and ghwellsjr

6. Oct 4, 2011

### ghwellsjr

What you observe does not depend on having a frame of reference or the Theory of Special Relativity. SR is an explanation for all the things everyone observes by establishing the concept of a Frame of Reference where time and distances are defined a particular way. Then you can talk meaningfully about things you cannot observe, like, what time is it over there? or when did the light get to a particular place? But it's all according to your previously agreed on FoR. Use a different FoR with its own definitions of time and space and you get a different set of values for those questions.