I am doing some programming and will eventually have to deal with this same complicated problem. Here is my take. I'm going to strip it down into 2 manageable pieces.
First, the trivial piece. No rotations. It appears the OP has already solved this version, but I will summarize here...
So you think I am trolling. Whatever that means, I will stop posting. You must know that you and the other senior members of this forum have a communications problem with the sincere laymen who visit here. All we have is the basic SR for sophomore college. I took the course. In frustration...
Dropping the relevance of acceleration by making it negligibly short doesn't work. As the turnaround time gets smaller the magnitude of the acceleration gets bigger. You know that. The contribution of relative aging to the problem stays the same. Consider fuel consumption for the space trip...
Potential Energy formula? What's the purpose for introducing the potential energy formula into this thread? Are you saying the traditional method for solving the twins paradox in textbooks is wrong? Do you recognize that the traditional method gives an incompatible answer to the answer in...
I have not read every post by FactChecker, but I agree with this one.
Given two inertial observers, each must consider the other's clock to be running slower (or the same). Each must consider the other guy ages slower (or the same). That's basic SR.
Why can't people just agree on this?
The...
Here is my 3d vector version for velocity addition. I have used it successfully for all kinds of 3d problems.
http://www.relativitysimulation.com/Documents/VelocityTransform.pdf
makphi, everyone is trying to point out to you the same problem. When I first learned SR I went round and round that same problem too. Here is how I finally resolved it for myself.
http://www.relativitysimulation.com/Documents/DeterminingTheLengthOfMovingObject.html
I have not compared the data you listed to that generated by my program, but the diagram looks consistent with my video of the Car with Observer on the road. Kudos.
Perhaps I did not explain my position accurately.
Below are 2 videos of a simulated car, one where the observer is at rest with respect to the road and one where the observer is at rest with respect to the car.
I have seen both versions on various web sites.
My versions were produced by my own...
Yes, I am. That's the reason the Ehrenfest paradox isn't a paradox. I can only assume that Ehrenfest didn't know how to transform points very well because he and everyone who read his material assumed behavior that is not predicted by the Lorentz Transformation.
If a 1m rule is pinned to a...
I was referring to the geometry of the disk as defined in Newtonian geometry books. If I specify a disk of 1m diameter and you draw a circle on a piece of paper and labeled the diameter 1m, I would say you have drawn the correct geometry. If I specify a 1m square moving with x-velocity of...
Uh?
Consider a disk at rest with respect to an inertial observer at its center. Then transform to a rotating reference frame still at the center of the disk.
There is no relativistic geometry change.
Note: The common formula for relativistic length contraction was derived for the condition...