Activity

Scott, I posted you’re corrected PDF up at the top with the other notes (I colored it green to make it stand out). If you want to link to it, it’s:

https://physicscafe.org/wp-content/uploads/2025/12/One-Form-Transformation-in-2D.pdf

I’ve prepared a document summarizing the one-form transformations discussed last meeting, and then included the specific transformations and partial derivatives required to transform between 2D Cartesian and Polar coordinates. We can use this as background in the meeting later today to derive and transform gradients between systems. I’ve confirmed…[Read more]

Today I mentioned I wanted to post an example of why I find time dilations problems often more confusing than problems about length contraction.

Suppose I observe a spaceship whiz by. Without looking at formulas, I know I will observe its length shortened in the direction of motion, and I will observe its time running slowly.

Suppose further I…[Read more]

Oh yes, I don’t think my solution is quite what we’re looking for here. I should have been more clear that I was posting it in the spirit of sharing errors that I don’t understand rather than asserting the correctness of a derivation.

That being said, I’ve been thinking a lot about where I went wrong and I think there are two primary elements.…[Read more]

I’ve come around to agree that it’s 4 round-way trips, regardless of whether the direction is parallel or perpendicular. I worked this out mathematically, but I realize there’s a more straightforward way to come to the same conclusion (which is probably equivalent to what Mike was saying today)…

Namely, I can forget how the light clock is…[Read more]

Video posted up at the top.

Oops – I missed that you had already acknowledged the issue.

Ahh….

I interpreted the question as the observer moving parallel to the plane of a mirror, whereas your Observer Frame depicts the observer moving perpendicular to the plane of a mirror.

I think Scott’s solution matches your picture and your above description.
I think the posted solution matches my interpretation. (There is an effect if the…[Read more]

> If the observer was traveling … how to say it … “along* one of the mirrors(?) … the I don’t think there would be any effect at all.

I guess I take that back. It seems like there would be the time effect in that case also. This problem obviously deserves more time than I gave it and I’m not all that confident in my answer at this point.