Question About Lorentz Contraction: Red vs Blue?

[AdirianSoan]

TL;DR

Is the distribution of contraction constant across a moving object?

I have a question which I've found very difficult to Google.

The easiest way to frame it I can think of is this:

Given a cylinder moving lengthwise by an observer at some significant fraction of C, with the forward half of the cylinder (relative to the direction of motion) painted red, and the backward half painted blue, would there be a difference in the observed length of red, and the observed length of blue, portions of the cylinder?

My understanding suggests the red portion will appear slightly shorter than the blue to the observer.

 

[Ibix]

Depends what you mean by "observed". As it is typically used in relativity, meaning that the observer is assumed to correct for varying light speed delay, then both halves are the same length. If you mean what you would actually see directly with a camera (i.e., not correcting for the varying tracel time of light from different parts of the rod), then exactly what you see depends where you stand and what direction the cylinder is moving relative to you. If this is what you were interested in, where were you thinking of standing?

 

[Nugatory]

What exactly do you mean by “appear”? In this context it could mean what you actually see as the light leaving different parts of the moving object at slightly different times reaches your eyes at the same time, or it could mean what you determine the lengths to be by considering where the two ends and midpoint of the object are at the same time.

Lorentz contraction refers to the second meaning, and in this sense the red and blue sections will have the same length.

 

[PeroK]

Summary:: Is the distribution of contraction constant across a moving object?

I have a question which I've found very difficult to Google.

The easiest way to frame it I can think of is this:

Given a cylinder moving lengthwise by an observer at some significant fraction of C, with the forward half of the cylinder (relative to the direction of motion) painted red, and the backward half painted blue, would there be a difference in the observed length of red, and the observed length of blue, portions of the cylinder?

My understanding suggests the red portion will appear slightly shorter than the blue to the observer.

Suppose you look closely and realize that it's not one cylinder but two cylinders glued together. You've painted the first cylinder red and the second blue. Why is the red cylinder more length contracted than the blue one?

 

[phinds]

@AdirianSoan think about it this way: the Lorentze contraction between two objects depends on their relative speeds, NOT where they are relative to each other. So in the frame of reference of an object A, the Lorentz contraction for the ends of and object B, regardless of how long it is, depends only on the speed of the ends relative to object A.

SO ... if object B is in uniform linear motion relative to A, it's the same for both ends.