This is from a classic textbook by Chandrasekhar, called Radiative Transfer. Li First published in 1950!

Here, ds is distance along direction ω, dω is differential solid angle.
κ is mass absorption coefficient of the scattering material, ρ is its density, and p is the so called phase factor.

Genius people problems :)
But it resonates on the normie level. High achievers lose their edge unless they keep their humility, and they keep it by realizing that their work is greater that they will ever be themselves.

I do not understand this on any level, yet the algorithm decided that I should see it. Can anybody find the charitable impulse to explain this to a hypothetical 70 year old grandfather?

Are you kidding? You know how much those footlongs cost these days? Those thugs aren’t worth it. A bag of chips maybe but no more.

That’s why the universities need older guys like me. I’m immune.

Can't do justice to this in a 300 char tweet. For the right stuff, see Misner, Thorne and Wheeler, Gravitation, chapter 20.4. My favorite, but it is covered in any good treatment!

This stems from the Equivalence Principle. You can always choose a local inertial frame where the effects of gravity vanish. In that frame, the gravitational field energy is locally zero.
Total energy of system? Sure! It can be defined on the boundary. Not a boundary condition. Boundary property.

Reagan understood economics because he had the good sense to hire the best advisors in the nation. Trump’s economics are a sham for the opposite reason.

Well he had to. It was not garish and gauche enough!

It’s an apt metaphor no doubt.

America wins by rebuilding on the sound counsel of scientists and professionals. There are those who must take political stands, but to be effective scientists must stand above.

The more apolitical we are the greater our credibility compared to the ideologues.

For standard message queuing RabbitMQ is pretty good. It may have more features than you need but they may come on handy some time. For example it supports mirroring and transaction semantics if you ever find that you need more reliability.

I have physics dreams like that…details, you don’t want to know… it means that you truly have a passion and you are looking for more ways to make a real contribution.

See cs.uwaterloo.ca/~watrous/TQI/ where Watrous spends the first 100 pages setting it up in a totally admirable rigorous way!

And finally he will ask "expected values are done with operators sandwiched between bras and kets, not this simple thing that reduces to a trace of products."

All *very* good questions, by the way. But it turns out we are just doing box standard QM in a disguised form. It all comes out in the wash.

Subtle? Yes. A student of physics seeing this for the first time will say, "What is this, a state is a vector in Hilbert space, not this operator", and "a QM measurement tells us what state we are in, might be an expectation of a projection, but what is this thing with operator-valued measures?"