Recent content by Elemental

Rest in Peace, Jim Hardy! One of his posts on this forum that convinced me that a shunt-type motorcycle voltage regulator (which basically shorts out the alternator windings when charging current is not needed) does not waste power, as is commonly believed. Saved me the expense of buying a new...

Thanks, PeterDonis. Agree that if the distant masses didn't accelerate, then their retarded effects do the job. But then you can't reverse the situation and say (based on the analogy) that there is no difference whether the local body accelerates or the rest of the universe accelerates instead...

Ciufolini and Wheeler give an interesting analogy from electrodynamics in chapter 7 of their book. If a charged body is suddenly accelerated, its electric field lines are deformed from radial into a roughly spherical shell at large distances r = ct from the region of the charge's acceleration...

Thanks for the references, Demystifier! So I do see a lot of similarities with Hegerfeldt's theorem. It looks like G. N. Fleming attempts to overcome Reeh-Schlieder localization problems by postulating Newton-Wigner fields, which appear local very much like Newton-Wigner states are local in...

Thanks for the clarifications! Well, I don't think I'll "stop now" because I "know" I have free will, so instead I'll keep plowing through these intractable papers.

Hegerfeldt's theorem holds under extremely general conditions, including special relativity, as shown, e.g., in his paper G.C. Hegerfeldt, Phys. Rev. D 10, 3320 (1974), so it is certainly not limited to the non-relativistic regime. The theorem basically states that in any first quantized theory...

It is a misconception to assume that in general orthogonal eigenstates of an observable have distinct eigenvalues. Frequently they do but there may be degeneracies. Even the one-dimensional free particle has a degenerate energy spectrum, since eigenstates of momentum ##\hat p## with respective...

I think this was meant to read ##A|\psi_1\rangle=\lambda_1 |\psi_1\rangle## and ##A|\psi_2\rangle=\lambda_2 |\psi_2\rangle## (may be a problem with my viewer). Translating to plain English, I concur that orthogonality of states with different eigenvalues for the same Hermitian operators does...

As mentioned, several corporations, including mine, have quantum computers actually in use on practical problems, but I've not seen dramatic success stories to date. I was fortunate to get an in-depth briefing on this technology a couple of years ago. The idea is that each qubit is in a quantum...

Typo, I meant ΔpΔq = ħ/2, and carrying though the correction, the sentence toward the bottom should read, "But the uncertainty from the forgoing calculation for particle B’s momentum is just mΔVi, which is a factor of m/M smaller than ħ/2Δq!" Anyway, the point I tried to make is that, sticking...

There is something that has bothered me for a long time about Bohr’s response, and 80+ years after his paper this looks like a good thread to bring it up. In Bohr’s example two particles, whose initial states are known, pass through separate slits of known separation in a diaphragm. This...

Position and momentum are definitely not on an equal footing in relativistic quantum mechanics. Momentum eigenstates are easily represented, but position representations are fraught with problems. At least for massive particles one has Newton Wigner states which are strictly localized at one...

Geometric Algebra definitely promises greater insights into Pauli and Dirac equations than traditional vector algebra because of the intrinsic geometric interpretations allowed by Clifford algebra. The drawback I find with Hestenes' approach is that he introduces more than the required number...

Thanks for the post; I concede this space-time is flat. Back to Mach's principle, Ciufolini and Wheeler discuss it at length in Gravitation and Inertia (Princeton University Press, 1995). They provide an analogy from electrodynamics. The electromagnetic radiation from a suddenly accelerated test...

I apologize for the confusion and agree there is no intrinsic curvature to the trajectory. Assuming that the space-time defined by the frame of reference of the falling body is flat, it still should be flat when re-expressed in a rotating coordinate system even though a space-like hyper-plane in...