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The quantisation of the electromagnetic field, proposed originally by Planck, blurs the distinction between particles and fields. 'Point' particles become fuzzy and subject to a wave equation. Also, the field takes on a particle-like nature (photon) which is otherwise classically represented as a continuum.

Then, if we have charged particles interacting through the electromagnetic field, is there an essential distinction between them?

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    $\begingroup$ Fields are sections of a fibre bundle, in a nutshell. Particles are irreducible representations thereof. Also, there is no photon in quantum mechanics. $\endgroup$ – gented May 28 at 7:51
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    $\begingroup$ @gented What do you think single-photon sources generate and single-photon detectors detect? $\endgroup$ – Mark Mitchison May 28 at 8:35
  • $\begingroup$ @MarkMitchison I don't understand your comment (sarcasm probably?). My point was that the concept of photon arises in QFT and QM per se' doesn't involve them at all. $\endgroup$ – gented May 28 at 9:03
  • $\begingroup$ @gented Ah, I see what you meant. My comment was a genuine question, I thought you were saying that photons don't exist in quantum theory. Note that QFT is just quantum mechanics with fields as the degrees of freedom. It's a bit of an anachronism to refer specifically to single-particle non-relativistic quantum mechanics just as "quantum mechanics". $\endgroup$ – Mark Mitchison May 28 at 13:02
  • $\begingroup$ @MarkMitchison "QFT is just quantum mechanics with fields as the degrees of freedom" of course, and that makes all the difference :). $\endgroup$ – gented May 28 at 13:16
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'Point' particles become fuzzy and subject to a wave equation

One must not confuse the wave equations of classical mechanics with the wave equations of quantum mechanics. Mathematically they have sinusoidal solutions, but it is the variable assignments on the mathematics that describe measurable physical quantities.

The classical solutions of Maxwell equations describe the variations of energy in space and time, the Poynting vector and the power carried by the classical electromagnetic waves.

The solutions of the quantum mechanical wave equations do not describe energy transfer and are chosen by the postulates of quantum mechanics, , basic of which is that the wavefunction

wavefunction

It is the probability that waves, as seen in the double slit experiments one particle at a time

The same behavior is seen for photons .

Photons wavefunctions obey a quantized maxwell's equation.

Then, if we have charged particles interacting through the electromagnetic field, is there an essential distinction between them?

At the particle level the classical electromagnetic field does not exist, it is interactions between photons and the rest of the particles that holds, and yes, there is a difference if a photon hits an electron or a proton for example. The study of scattering processes is explored by quantum field theory which is a meta level in calculations, based on the underlying quantum mechanical solutions of free particles. It leads to Feynman diagrams which allow calculations for many body problems.

Using the tools of quantum field theory one can show that the classical electromagnetic wave emerges from the underlying zillions of photons , a quantum mechanical superposition of zillions of photons.

There is no essential distinction between particles, of which the photon is one, except their masses, spins and other quantum numbers. The photon is one of the elementary particles in the standard model.

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  • $\begingroup$ "The solutions of the quantum mechanical wave equations do not describe energy transfer" I do not agree. You can write a Schrödinger lagrangian and then obtain the Noether conservation laws of energy-momentum, charge and angular momentum for the Schrödinger wave function. $\endgroup$ – my2cts Jun 27 at 6:46
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    $\begingroup$ @my2cts These laws apply , but it is not the mass or the energy of the particles that is "waving", i.e. display sinusoidal behavior, but the probability of measuring a particle with given energy and momentum. $\endgroup$ – anna v Jun 27 at 7:26
  • $\begingroup$ That is interpretation. The Noether conservation laws give us the distribution of energy etc. in a probabilistic sense. The same is true for Maxwell's equations. The difference is that the number of particles can be very large in the case of photons, which is what we call "classical". $\endgroup$ – my2cts Jun 27 at 8:26
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    $\begingroup$ @my2cts Well,I think you are not thinking mainstream quantum mechanics, which depends on its postulates as extra axioms, , not just the mathematics. google.gr/… . how about single electron at a time?en.wikipedia.org/wiki/… . the energy-momentum would be a fourier transform of the wavefunction in space and time. $\endgroup$ – anna v Jun 27 at 8:59
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    $\begingroup$ @my2cts in refusing to understand that the quantum mechanics postlates/axioms interpret the wave equation differently, that it is a different framework., ruled by probabilities, not determinism. $\endgroup$ – anna v Jun 27 at 9:28

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