Hi Justin,
There are many many other wagers in physics over history. We're working on a feature about it in symmetry magazine already so we'll have a bunch to tell you about coming up. They include the SLAC National Accelerator Lab bet book, a bunch of bets at Caltech, and various others...
You might be interested in the contest that ran at the SLAC Summer Institute this year that asked: "What will be the first evidence to demonstrate that Einstein's theory of General Relativity (GR) must be revised, and when will that be found?"
The...
New issue of http://www.symmetrymagazine.org/cms/?pid=1000183" is about the Snowmass meeting to work toward designing the International Linear Collider.
Other stories:
http://www.symmetrymagazine.org/cms/?pid=1000191": An experiment with polarized electrons probed the strength and asymmetry...
If you want to work in quantum optics, you don't NEED any of these in any real sense depending on exactly what you do. However, you would be well-advised to get a grounding in QFT and techniques in mathematical physics.
That said, I would advise you to take as much theory as you can handle...
As Tom points out, the value is local. But it depends on more than just your radius because there are local effects that distort the gravitational field. Indeed, detecting these distortions is one goal for people looking for deposits of minerals, ore, oil, etc.
The varying can be quite...
You don't seem to have explicitly factored in that the slope is changing in time. (There is no alpha dependence in your equations.) What this also means is that the velocity of the particle is not as simple as it seems, and is not along the inclined plane in the lab reference frame anyway. For...
Although not conserved separately, I am sure you realize.
Where does this equation come from? It's not a wave equation in the usual sense (unless you mean that x is a time variable). It certainly doesn't have anything to do with a hydrogen atom. Or am I misinterpreting and is supposed to be...
I think we need more information about the model to say anything sensible. What is the reference for this? Giving that metric by itself doesn't indicate a solution to the hierarchy problem in any meaningful way without more information.
It's not clear exactly what you mean by this but if you are just looking at a (non-interacting) hydrogen atom, then there is a well-defined Hamiltonian which gives a conserved energy.
If you are referring to something to do with Heisenberg's uncertainty principle, then it might get subtle...
I guess you realize that Bell didn't do the experiments himself. The landmark experiment was done by Alain Aspect and collaborators in 1981.
Here is the paper you should read to start with:
A. Aspect et al., Experimental Tests of Realistic Local Theories via Bell's Theorem, Phys. Rev...
It will indeed separate so then you just have to be careful about counting modes, etc. and degeneracies. If it is truly cubic (the lengths of each side are the same), then there there are 3 degenerate modes for the first excited state.
Are you really interested in whether they can form a superposition or whether they can form a bound state? Matter and antimatter can form bound states, for example. See this article which talks about positronium. It's very short lived but can exist. It's not really clear from your question why...
You are definitely on the right track but you have to be more explicit about the statement "a vector that satisfies the conditions of a subspace of U and W, (the intersection of U and W) then it is part of the U u W" - you need to give the details there.