There is something about quantities "probability per unit [whatever]" that takes people aback the first time they encounter them.
It is easy to argue that they shouldn't, but it trips most folks at some point.
I can't count how many times I've had to patiently explain to a scorching bright grad student how the vertical extent of a histogram depends on the binning.
Hey, @dmckee, any clue on where I'm confusing myself on that exponential distribution?
We have probability per time of an event (say decay, or whatever) $\lambda$.
The probability of decay in time $dt$ is $\lambda dt$.
What's the probability of going time $T$ without decay, and then decaying at $T$?
Well, divide $T$ into $N$ intervals of length $dt = T/N$.
The probability of not decaying in one of those intervals is $(1 - \lambda dt)$.
The probability of not decaying in any of them is $$(1 - \lambda dt)^N \, .$$
We can write that as $$\left( 1 - \frac{\lambda T}{N} \right)^N$$ which tends to $\exp(-\lambda T)$ as $N \rightarrow \infty$.
I am confused in two ways: 1) That result isn't normalized, 2) I know that formula is almost the usual thing for exponential decay, but that "usual" formula is supposed to be the probability that you survive for time $T$ and then decay at $T$.
Is there an elegant proof of the existence of Majorana spinors?
No. Because they don't exist. The neutrino is not a Majorana spinor. It's a Weyl spinor. See Dirac, Majorana and Weyl fermions by Palash Pal. He said “the neutrinos had to be uncharged because of conservation of electric charge,...
Malcolm John Perry (born 13 November 1951) is a British theoretical physicist and professor of theoretical physics at the University of Cambridge. His research mainly concerns general relativity, supergravity and string theory.
== Biography ==
Perry attended King Edward's School, Birmingham before reading physics at St John's College, Oxford. He was a graduate student at King's College, Cambridge, under the supervision of Stephen Hawking. He obtained his doctorate in 1978 with a thesis on the quantum mechanics of black holes. In these early years, he worked on several very influential papers on...
Is the RHS solution just as general as the LHS? $e^{-\beta t}[Ae^{i\omega t} + Be^{-i\omega t}] =?= Ce^{i\omega t + \delta}$ To me it seems not, but it was used by the professor seemingly as if it was. It is the homogeneous solution of a damped oscillator.
I'm thinking, maybe because the general solution covers all three cases of dampening but in reality you always have $A$ or $B$ zero?
@0celo7 My first (of three) GR lecturers was definitely a physicist. He was so good, that a few students bought the textbook, despite him printing everything out for everyone and then got him to sign the textbook