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@MartinBeckett you're right about ground water. My thesis advisor (I was measuring big G) told me about a grad student who'd searched for a signal that went crazy at like 11pm each night. Turned out it was sprinklers putting water into some nearby lawn.
You neglected to mention that if the energy of the photon must be higher than the work function of the metal, excess energy may be carried away by the ejected electron by the photoelectric effect.
This isn't an answer, but I had some friends in grad school who worked with the physics of bubbles. They always used nitrous oxide. I'm not sure why, but they did say, vaguely, that it made for better bubbles.
The tides will change, too. With less water to slosh around, the earth will transfer rotational energy to the moon more slowly. The moon's rate of outspiraling from the earth, and the rate of slowdown of the day, will probably decrease modestly.
I'm not sure you're correct. The inverse should map (0, 0, 1) to his original vector; it maps it to x⃗ =(-sin(ϑ)cos(φ),sin(ϑ)sin(φ),cos(ϑ)) (note the minus sine in the $\textbf {i}$ direction)
@SumukhAtreya Ah, yes, I was right in my guess. The weak form simply implies conservation of linear momentum, the strong form conservation of angular momentum. And for conservative, spherically symmetric fields centered on the point particles, you're right. You can't have a torque between two point particles if they can only push & pull each other along the line. Let them "shove" each other "sideways" (by which I mean perpendicular to the line joining them), and you still have an action/reaction pair, but it violates conservation of angular momentum.
oops, used p rather than r, sorry. I was learning the LaTex to make it look good, and went over the 5 minute deadline for re-editing. For $\textbf{p}$, please pretend it's $\textbf{r}$
Okay, I had never seen "weak" form applied to Newton's 3rd Law, and a quick googling doesn't give me the answer in the top 2 hits, but I assume you mean the case where the net force is zero, but the net torque is not. For example, suppose we have a 2-dimensional system, with particles at positions $\textbf{p}_1=1m \textbf{i}$ and $\textbf{p}_2=-1m \textbf{i}$, but forces $\textbf{F}_1=1N \textbf{j}$ and $\textbf{F}_2=-1N \textbf{j}$. This isn't made explicit, but it's not seen in nature. If seen, it would violate conservation of angular momentum.
