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Scott, I agree with your first paragraph, but I don’t see why that means t₀ will have elements of both x and t in its calculation.

After looking at this yet again, I concluded that our approach to #1 is equivalent after all, but not our approach to #2. The key to understanding this is that when x and t are measured in the same frame,
x = vt.…[Read more]

I pasted a more readable version of what I’ve got below. I think the discrepancy here has to do with how v is conceptualized. v captures the relative velocity of two different frames. From the Earth frame, v captures the measured velocity of the muon, but it’s not going to be the velocity of the muon in it’s own frame of reference! For the muon,…[Read more]

Here’s my answers in a nicer format:

I worked problem 1 differently, but got the same answer (after accounting for significant digits).

1.) v = 0.99c

γ = 1 1 – v 2 c 2
= 7.09

t = 6.73 µs
t₀ = t / γ (t₀ is the proper time)
= 0.949 µs

————————-

I worked problem 2 differently, and got a very different answer.
2.) 
v = .99c = .99 * 3*10⁸ m/s

= 2.97*10⁸ m/s



t₀ =…[Read more]

Problems 3-5:

v = 4/5 LY/Y
d = 4 LY

————————-
3) time in Earth’s frame:
t = d/v
= 4 LY / (4/5 LY/Y)
= 5 Y
————————-
4) time in ship’s frame:
γ = 1 / √(1 – v²/c²)
= 5/3

t = t’/ γ (t, or proper time, is in frame where events happen at same place => ship’s frame)
= 5 Y / (5/3)
= 3 Y
—…[Read more]

Given:
v = .99c
x = 2000m
t = 6.73us

lambda = sqrt(1/[1-{v/c}^2]) = sqrt(1/[1-0.99^2]) ~= sqrt(50.25) ~= 7.1

1) t’ = lambda * (t – vx/(c^2)) = lambda * (t – .99x/c) ~= 7.1 * (6.73us – .99*(2000m)/(3*10^8 m/s)) = 7.1*(6.73us-6.6us) = 7.1*0.13us = 0.92us
2) x’ = lambda * (x – vt) ~= 7.1 * (2000m – .99(3*10^8 m/s)(6.73*10^-6 s)) = 7.1 * (2000m -…[Read more]

It’s 3:00pm West Cost time. I believe that’s 4:00pm Denver and 6:00pm Eastern.
The meetings are (almost) always Sunday at that time.
If we do a different day or time we’ll make sure to let everybody know.

Hi, Mike. What time is the meeting? I’m on Eastern Daylight Time.

–Joel

Transcription follows. [Apparently the site I use started adding time stamps and its guess as to who’s speaking.]

00:00:07 [Speaker 2]
Good afternoon.
00:00:09 [Speaker 2]
Thank you for continuing with our derivation of the black body radiation formula and the ultraviolet catastrophe.
00:00:20 [Speaker 2]
So having gone on a long digression,…[Read more]

Transcription:
—————————

So last time we left off in the main lecture, we had just introduced the concept of entropy, how it’s the logarithm of the multiplicity. Long numbers turn the very large numbers of multiplicity into merely large numbers. 10 to the twenty third is supposed to 10 to the power of 10 to the 23, and it makes…[Read more]

I think I just realized something else that addresses a big part of my confusion. I think it was more-or-less stated in the talks, but I wasn’t getting it.

When we discuss the k-vector, where each n must be at least 1, we are talking about the composite standing wave (the superposition of individual waves), and only this wave, correct?

I was…[Read more]

Based on this image from Stephan’s slide, I’ve concluded I’ve had a fundamental misunderstanding of the waves we’ve discussed.

Both the left and right images show a wave that exists in 2-D. The left image uses a 3rd dimension to show the value of the wave in each 2-D location, and the image on the right uses color.

To truly picture the 3-D…[Read more]