3 ms·

Magnetic vector potential is actually directly measurable with a somewhat esoteric experimental setup.

deleted 4y ago
[deleted]
Elpis1 4y ago
It's not quite measurable; the magnetic potential is gauge invariant, which means, among a great deal many other things, that it has no well-defined measurable value. However, it is certainly physical; things like the Aharonov–Bohm effect prove that.
- wnoise 4y ago
  You're missing a "not".
  - Elpis1 4y ago
    Where?
    - wnoise 4y ago
      in "the magnetic potential is gauge invariant". It differs for different gauges, so is not gauge-invariant, but gauge-dependent. A choice of A _is_ a choice of gauge. The theory using it (i.e. E&M Lagrangian) is what is gauge-invariant. This is a hyper-correction; in practice physicists apply the term in places adjacent to where it should be all the time.
      - Elpis1 4y ago
        Ah, sorry about that! You're right, of course; my brain slipped a bit.
  - deleted 4y ago
    [deleted]
mikewarot 4y ago
Yes, I'd like to own a few SQUIDs to play with. I've got some old Tesla patent drawings (bifilar coils) I'd like to understand better.
aether-regained 4y ago
Is this what you are referring to?: FLP-II-15–5 The vector potential and quantum mechanics https://www.feynmanlectures.caltech.edu/II_15.html#Ch15-S5 https://www.feynmanlectures.caltech.edu/II_15.html#Ch15-S5 " Precisely this experiment has recently been done. It is a very, very difficult experiment. Because the wavelength of the electrons is so small, the apparatus must be on a tiny scale to observe the interference. The slits must be very close together, and that means that one needs an exceedingly small solenoid. It turns out that in certain circumstances, iron crystals will grow in the form of very long, microscopically thin filaments called whiskers. When these iron whiskers are magnetized they are like a tiny solenoid, and there is no field outside except near the ends. The electron interference experiment was done with such a whisker between two slits, and the predicted displacement in the pattern of electrons was observed. In our sense then, the A-field is “real.” You may say: “But there was a magnetic field.” There was, but remember our original idea—that a field is “real” if it is what must be specified at the position of the particle in order to get the motion. The B-field in the whisker acts at a distance. If we want to describe its influence not as action-at-a-distance, we must use the vector potential. "

deleted 4y ago

[deleted]

It's not quite measurable; the magnetic potential is gauge invariant, which means, among a great deal many other things, that it has no well-defined measurable value. However, it is certainly physical; things like the Aharonov–Bohm effect prove that.

wnoise 4y ago
You're missing a "not".
- Elpis1 4y ago
  Where?
  - wnoise 4y ago
    in "the magnetic potential is gauge invariant". It differs for different gauges, so is not gauge-invariant, but gauge-dependent. A choice of A _is_ a choice of gauge. The theory using it (i.e. E&M Lagrangian) is what is gauge-invariant. This is a hyper-correction; in practice physicists apply the term in places adjacent to where it should be all the time.
    - Elpis1 4y ago
      Ah, sorry about that! You're right, of course; my brain slipped a bit.
- deleted 4y ago
  [deleted]

mikewarot 4y ago

Yes, I'd like to own a few SQUIDs to play with. I've got some old Tesla patent drawings (bifilar coils) I'd like to understand better.

aether-regained 4y ago

Is this what you are referring to?: FLP-II-15–5 The vector potential and quantum mechanics https://www.feynmanlectures.caltech.edu/II_15.html#Ch15-S5 https://www.feynmanlectures.caltech.edu/II_15.html#Ch15-S5 " Precisely this experiment has recently been done. It is a very, very difficult experiment. Because the wavelength of the electrons is so small, the apparatus must be on a tiny scale to observe the interference. The slits must be very close together, and that means that one needs an exceedingly small solenoid. It turns out that in certain circumstances, iron crystals will grow in the form of very long, microscopically thin filaments called whiskers. When these iron whiskers are magnetized they are like a tiny solenoid, and there is no field outside except near the ends. The electron interference experiment was done with such a whisker between two slits, and the predicted displacement in the pattern of electrons was observed. In our sense then, the A-field is “real.” You may say: “But there was a magnetic field.” There was, but remember our original idea—that a field is “real” if it is what must be specified at the position of the particle in order to get the motion. The B-field in the whisker acts at a distance. If we want to describe its influence not as action-at-a-distance, we must use the vector potential. "