Recent content by abszero

The physical justification is that it works. Dave, what you've said would imply that the Uncertainty Principle is a purely experimental phenomena. In fact, it is absolutely necessary for our current formulation of quantum mechanics, and is a consequence of the formal structure, not just some...

This is not a true statement. It is equivalent to Newton's laws in cases where forces of constraint do no work, which is not every problem. This is an important distinction. Newton's laws deal stupidly with constraints to motion regardless of their form, whereas Lagrange's equations do not...

Your statement is ambiguous, so nobody knows what to say. How can collapse not be "defined"? As I understood it, it's not particularly hard to "define", it's just an experimental result obtained for quantum mechanics.

If you have a holonomic constraint, then it means that there is a constraint on the problem of the form f(\overline{q}, t) = 0. Nonholonomic constraints are the rest. The papers I cited mention a few examples. The point is that the calculus of variations coupled with the usual treatment given...

I think it's probably important to note that Hamilton's principle does not lead to Newton's equations, it's the other way around. To see an example of the failings of Hamilton's principle to obtain Newton's equations, I recommend reading "Nonholonomic Constraints: A Test Case" in the Am. Jour...

In most modern texts I've seen it derived by looking at the generators of rotations, and then concluding the commutation relations [L_\imath, L_\jmath] = \imath \epsilon_{\imath \jmath k} \hbar L_k and then realizing that, like how momentum is the generator of space translations, angular...

Bell's inequality is intimately related to EPR type things, since it declares that quantum mechanics is locally complete. This is clearly related to your "instantaneous transmission of information" idea.

Which means that useful information did not get transmitted faster than light. You can only transmit information faster than light in a way that violates relativity if they can know each other's experimental results without any other communication between them aside from the entangled units...

Objects with spin rotate in different ways. Fermions and bosons pick up different phases with rotations, so it depends on what your real space wave function is producted with in terms of spinors. To get a full rotation, you have to have the rotation operator in both real space and spin space...

It's the definition of the inverse of a function f(x). For example, y = 2x and y^-1 = 1/2 x

Be double careful that you don't multiply by zero and stumble across a solution that actually does not exist.

The thing is, if you use the symmetry-based deduction, it sets you up quite well for thinking about Noether's Theorem, so in that sense it's quite useful. The Schrödinger equation arises out of some postulates of quantum mechanics, particularly that observables are generators of some sort of...

The way that you "derive" the Schrödinger equation is that you assume that the hamiltonian is the generator of finite time translations. As for the form of the hamiltonian, it comes from making a classical correspondence and introducing operators that obey the canonical commutation relations, or...

If it's a thermal reservoir, then the temperature is assumed to remain constant.

photon-photon scattering as I understand is a fourth order effect, where you have two pair productions, the pairs interact then annihilate, and the emitted photons appear to be scattered from the original two. Is this correct?