Recent content by Cadaei

Thanks so much, that makes sense.

I tried googling a good resource for this but it was difficult to think of good keywords. Are we always allowed to do this, or is it just for plane waves, linear media, conductors, etc? My intuition is that it's fine in all circumstances since we can Fourier decompose most any function into...

You wouldn't ever know, that was one of my points. If it had sufficient explanatory power and elegance, it might be reasonable, though. Or would it? And is it even likely that we'd arrive at such a theory?

Yes that's pretty much the canonical response to threads such as this, and why they get derailed on whether or not string theories merit consideration. But let us not go there. It's just strange to me that the typical response is "do not seek a complete description of reality, be entertained...

So it wouldn't bother you as an ant to know your knowledge is forever incomplete and approximations to unknowable things? I get your pragmatism, it's basically the only thing you can do. But surely you think that many if not most cosmologists seek a complete description of the universe? Also...

Imagine an intelligent ant living in a sealed glass tank, with nothing inside but sand and himself, for his entire existence. He has the intelligence of a human but no way to escape, and nothing to see outside of the glass tank. The temperature never changes, the air is static, the source of...

Wave functions in QM. So I guess you're saying that canonical QM formalism just doesn't apply to this regime, requiring QFT? I think you misunderstand. My beef is that the electron would appear to have traveled faster than c. The wave function does not propagate, but to know how far the...

1) If µ were > than ϵ0, the occupation number would be negative for ground states. 2) Your question here is unclear to me. As µ -> ϵ0, n_j -> infinity for j = 0, if that's what you mean by "macroscopic number of particles."

I don't know if it has a name but it simply comes from your non-hermitian operator, which as I understand it are only used as a mathematical convenience in quantum mechanics. What matters is that they have real eigenvalues so they can correspond to observables. The choice of normalization...

Suppose you have a free election and you make a measurement of its position r_0 at time t = 0. You then wait some time t required for the wave function to evolve out of its collapsed eigenstate. The electron now supposedly has a wave function expanding to infinity in all directions, albeit with...

Thank you for your help, I understand now.

If operators are simultaneously diagonalizable, then they commute -> no uncertainty relation.

I think I'm missing something extremely simple here... why is dotting ⟨X_I| into |psi_i⟩ the same as evaluating psi_I at X_I?

The wave function itself is a mathematical construct - you cannot "observe" a wave function (they're complex in the sense of complex numbers). What you can observe are the eigenvalues of wavefunctions for a given operator, which are used to represent all dynamical variables such as position...

Spin is an intrinsic angular momentum of a particle. The name is misleading because the particles aren't actually "spinning" in a classical sense. Really, you should think of it as a property of matter like charge. Electrons have an intrinsic charge, mass, etc. Spin is just another one of these...