Recent content by akhmeteli

Yes, this is the Schrödinger's article that I referred to (looks like it is in open access). My previous post (#43 in this thread) is about https://www.hep.phy.cam.ac.uk/~chpotter/particleandnuclearphysics/AppendixE.pdf , where they prove gauge invariance of the non-relativistic Schrödinger...

Yes, there seems to be a conflict between the title and the content of the reference, but the content clearly includes a proof of gauge invariance of the non-relativistic Schrödinger equation in electromagnetic field. Moreover, I don't think you dispute that this non-relativistic equation is...

I don't see why it is important that the Klein-Gordon equation is not used in non-relativistic QM, because the gauge transformation that Schrödinger used can be straightforwardly used for the non-relativistic Schrödinger equation in electromagnetic field as it is also hauge-invariant.

Again, I don't see how the difference between "field" and "wave function" is problematic in the context of this thread. Obviously, Schrödinger wrote about a non-second-quantized wave function (which is often regarded as a classical field that nevertheless has quantum properties). He explicitly...

I did not say that the Klein-Gordon equation describes electromagnetic field, I was talking about the Klein-Gordon equation in electromagnetic field: $$ (\partial^\mu+ieA^\mu)(\partial_\mu+ieA_\mu)\psi+m^2\psi=0.$$ It describes the matter field ##\psi## in electromagnetic field ##A_\mu##. Note...

This is not obvious. I usually cite Schrödinger's Nature, 169:538 (1952). He noticed that the wave function for the Klein-Gordon equation in electromagnetic field can be made real (rather than complex) by a gauge transformation. His comment: "That the wave function ... can be made real by a...

Sorry, I did not provide the link. The article is actually in open access.

Lohmiller W, Slotine J-J. 2026 On computing quantum waves exactly from classical action. Proc. R. Soc. A482:20250413 Abstract: "We show that the Schrödinger equation can be solved exactly based only on classical least action. Fundamental postulates of quantum mechanics can in turn be derived...

M. O. Scully, M. S. Zubairy, Quantum Optics, Cambridge University Press, 1997 "as we shall see in later chapters of this book, there are many processes associated with the radiation-matter interaction which can be well explained by a semiclassical theory in which the field is treated classically...

Thank you for the information. By the way, what you describe seems similar to US patent 10625842 by Nathan Rapport.

Maybe your approach is better than mine, maybe it's worse, who knows. Are any details publicly available? I guess buckling is critical to your approach too.

And I am trying to do that, but it takes (a lot of) time. Making a vacuum balloon is hard: the idea is 350+ years old, but it has not been realized yet. As for our design, one of the challenges is making thin boron carbide plates (say, 0.1-0.2 mm thick). I cannot disclose what has been done in...

I don't know, maybe I completely misunderstand what you have in mind, but this is how it looks to me at the moment. Your design is supposed to withstand 88% of atmospheric pressure at sea level and also to be buoyant at high altitude, where air density is, say, one tenth of that at sea level...

So you seem to consider water vapor just as a means to prevent failure of the vacuum balloon on its way from the Earth's surface to its (high) design altitude. However, condensation strongly limits the water vapor pressure. If I am not mistaken, unless we have some exotic conditions, saturated...

Still, this is pain in the neck. It is one of the problems with helium ballons, besides helium being pretty expensive, nonrenewable, penetrating through pretty much any envelope. So I believe there can be at least some niche applications for low-altitude vacuum balloons.