Recent content by vanhees71

A very detailed derivation can be found in Sommerfeld, Lectures on theoretical physics vol. 3.

I don't understand your problem with simply calculating ##\vec{E}## and ##\vec{B}## as it is done in the standard textbooks. You don't need artificial splits or at least you can't use arbitrary splits in gauge-dependent parts to interpret them physically. Of course, you use the potentials (in...

That's the point. If ##\vec{\nabla} \times \vec{E}=-\partial_t \vec{B} \neq 0## there is no potential field, and induction as in a transformer doesn't work in the static case, where the electric field has a potential. Of course you can decompose any vector field in a potential and a solenoidal...

Yes, of course the math is the math the real world is the real world, but the math accurately describes the real world according to the observations. So the samples you prepare with a preparation procedure are described by the formalism correctly, i.e., they are proxies of the ensembles...

That's what I also say the whole time, and you get this statistical sample by preparing single electrons (using Ballentine's example for the argument) repeatedly in the same way, i.e., with a preparation procedure referring to a quantum state. This is even emphsized by Ballentine himself in...

@gentzen obviously understands it as I mean it.

But then you couldn't use the formalism to describe real-world experiments. That's for sure not what Ballentine implies.

My interpretation falls in group I, because for me all the state describes concerning the properties of the systems prepared in a state are the statistical properties, which of course refer to an ensemble of equally prepared systems. I just say the same as what Ballentine says with different words.

But he says that the preparation procedure refers to a single electron. A bit later he even emphasizes that the so defined ensembles are different from preparing a bunch of electrons at once. I think it's pretty clear that the preparation procedure must relate to single electrons, if you want to...

I quoted Ballentine verbatim. Where can this be wrong? Here it is again from the RMP by Ballentine: It's an ensemble of single electrons being prepared by a procedure (to be specified for each state). So why do you claim it's wrong?

Yes, that's the theoretical formulation, but in practice you must work with finite samples and do a corresponding statistical analysis to ensure that the predicted probabilities agree with the measured "frequencies". Practice shows that in the here discussed experiments, which probe the...

I think, it's time to do the math. Let's consider a closed system of two particles interacting via a central-potential force. Then you have the full Galilei symmetry and thus all standard conservation laws fulfilled. Here we consider energy and momentum. The equations of motion read...

What is not helpful? I tried to explain what I mean when I say a state represents a preparation procedure for a single system and at the same time describes the statistical properties for the outcomes of measurements on an ensemble of equally so prepared systems.

The great appeal of the Dirac formulation is that this confusion is avoided from the very beginning. There are vectors in Hilbert space, which are completely independent of any choice of the basis. The wave function is then a component of these vectors with respect to a (generalized) basis of...

I don't know, what you are discussing here about. Which light cones are you referring to? If you mean "travelling" in the sense of "propagation of the em. field", it's all fine. You only must not think of photons in terms of little bullets moving along a trajectory. Photons cannot be localized...