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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.

Right. I need to delete that “index” next time. It only works inside the notebook itself.

Oops, another ambiguity in the problem statement. The observer is supposed to be moving in the direction of *between* the mirrors. See that picture. 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.

Am I misreading what you’re saying? (Does the picture make sense?)

Small issue:

In Problems2-Notebook.pdf, the links are broken.
But of course we can still scroll to access the content.

Length is only contracted in the direction of motion. The distance between mirrors is perpendicular to the direction of motion. So I think the mirrors are 1 ls apart in both frames.

I agree with the posted solution if we tally round trips, or double that if we tally 1-way trips.

PS … Also remember that I made the pictures. So if I make a mistake, the pictures could be wrong.

The mirrors are indeed .8 ls apart in the moving frame. I’m not exactly clear on what’s happening when you do the ltrans on x at the end, but take a look at the picture on the third page of the “notebook” that I posted up at the top of the thread. See if that makes sense of things. The mirrors are moving in the observer’s frame, so the light takes…[Read more]

I’m not able to attend today, apologies! I’m doing a birthday party for my oldest. I’ll also be missing next week as I’ll be camping. Apologies!

I got the same answers for everything except 5. For that one, rather than evaluating time I went down the path of counting bounces by distance.

So:
d = distance between mirrors = 1 lightsecond
gamma =…[Read more]

Sorry about that. It wasn’t stated very clearly. What I had in mind was how many “round trips” (from one mirror to the other and back again). So, in other words (if I’m thinking clearly at the moment) then an observer traveling with the mirrors would see 5 “bounces” in 10 seconds. So, yes, the same mirror.

But of course the other interpretation…[Read more]

For problem 5, I interpreted the question
“How many times will the light pulse bounce between the mirrors”
as
“How many times will the light pulse bounce off any mirror”
whereas the solution appears to be answering
“How many times will the light pulse bounce off the same mirror”.

If it’s the former, the proper time between bounces is 1 second…[Read more]