Special relativity question?

Question

The lorentz transformations can be (probably invalidly) derived using simple algebra. The idea is to use the postulate that there is no "right" frame of reference, all are equally valid, to show that there is no contraction in the directions perpindicular to motion. Two equal sized (at rest) rings travel towards each other. If contraction occurs perpindicular to direction of motion, one ring becomes smaller and fits inside the other. That ring is at rest in its frame and sees the other ring as contracting and fitting inside of it. Why is that argument flawed (if it is) in proving that the direction perpindicular to motion doesnt contract and is a simple logical algebraic derivation based on that not mathematically sound even if it produces the correct transformations.

Answer 1

Two rings of the same size (at rest) cannot pass through each other because the Lorentz contraction is ONLY in the direction of travel.

So, if the ring is traveling "forward", it only shrinks in the "front-to-back" direction. It will never shrink in the "side-to-side" direction, so it will never be able to fit inside the other ring.

Answer 2

*dusts off brain*

I think that your derivation is flawed in several places.

First of all, you haven't actually proved anything, your argument is missing steps - this can't actually be an argument.

Lets walk through your steps 1 by 1.

You laid out your hypothesis, "The lorentz transformations can be derived using simple algebra." - good.

The description of your setup was a contradiction, "Two equal sized (at rest) rings travel towards each other" - two rings at rest AND traveling? Did you mean the rings are at rest with respect to the frames of reference based upon their center point, traveling with the same velocity?

Next sentence, "If contraction occurs perpindicular to direction of motion, one ring becomes smaller and fits inside the other." - Ok, I follow this one, you are explaining what to look for if a contraction occurs; however, this doesn't belong in a proof except to say, "... so, since one ring would fit inside the other, a contraction has occured, which is impossible...".

Next sentence, "That ring is at rest in its frame and sees the other ring as contracting and fitting inside of it." - Ok, this was just a restatement of the last sentence and could have been included.

The next sentence is asking why this argument is flawed?

Where is the step where you show me that I use algebra to derive the transformation?

What you described was more of an "In an ideal setting, we might be able to witness a transformation if..." type of post.

Furthermore, you based your argument on the premise that lorentz transformations happen! You assumed what you were trying to prove to me - this is a bad mistake in logic.

You must come from the premise that something happens when these rings travel towards each other and "show" me that nothing happens or vise versa.

Please rethink what argument you want to convey and edit your post.

You must SHOW me something.

*Two days later*

You still have not SHOWN me anything.

If you are asking whether or not this would be a good test of the Lorentz Contraction - I think that it would be a fine way of proving that there are no contractions perpendicular to the plane of motion.

I think, ultimately, this is what you were asking...