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I'm reading the book $[1]$ (which is not a scientific communication book, rather a student-friendly introduction to Quantum Mechanics).

Jakob $[1]$ then writes:

Many people unfamiliar with quantum mechanics may wonder how an electron could be a partile and a wave at the same time. Please ignore this kind of idle speculation. The situation is not as crazy as some would lead you believe. Electrons, photons and all other elementary particles are particle. Period. This is what every experiment tell us. Our detector make "click, click, click"$^{(*)}$. Waves are merely one convenient mathematical tool for describing the behavior of these particles.

$^{(*)}$Here the author is talking about the double slit experiment using electrons.

Considering the realization of the author, I can conclude that, when the books (modern physics mostly and some introductory texts on quantum mechanics also) said the famous idea "the nature of particles in quantum mechanics have a dual behavior: a electron can be a wave and a particle at the same time! This is called particle-wave duality" they acctualy want to mean: Electrons, photons and all other elementary particles are particle. Period. This is what every experiment tell us (...) Waves are merely one convenient mathematical tool for describing the behavior of these particles.

So, can I say that particle-wave duality is mostly a mathematical formalism rather than a huge physical fact?

$$ --\circ --$$

$[1]$ Jakob Schwichtenberg. No-Nonsense Quantum Mechanics. No-nonsense Books. 2ed. 2020.

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    $\begingroup$ Re, "our detector make 'click, click, click,'" That evidence supports the idea that electrons exhibit particle-like nature in some circumstances. It does not support the idea that electrons cannot exhibit wave-like nature in other circumstances. The math that predicts where those 'click, click, clicks' will happen is wave mathematics. Something is waving. Something that (as far as we know) is inseperable from the 'click, click, clicks.' Draw your own conclusions, but also, try to recognize when your pondering crosses the line from Physics into Philosophy. $\endgroup$ Nov 16, 2020 at 17:28
  • $\begingroup$ @SolomonSlow Right. So, firstly, can I conclude what I conclude? Secondly, Jakob then was too harsh saying: "the electron is a particle. Period."? $\endgroup$
    – M.N.Raia
    Nov 16, 2020 at 17:32
  • $\begingroup$ Maybe I misread what you wrote. I agree with your assesment that the author was "too harsh." $\endgroup$ Nov 16, 2020 at 17:33
  • $\begingroup$ @SolomonSlow maybe this "too harsh" can evolve to a "the author is wrong"? $\endgroup$
    – M.N.Raia
    Nov 16, 2020 at 17:34
  • $\begingroup$ I am not actually a physicist. This stop is where I get off of the train. $\endgroup$ Nov 16, 2020 at 17:41

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The definition of particles in QFT is a bit technical than our usual notion of particles. A particle is an excitation of a field. For example, the Higgs boson is an excitation of the Higgs field. With this notion, we can say electrons are particles. However, the wave notion is also built-in in the excitation part of the definition.

In the usual sense, we cannot say that electron is only a particle and the wave nature is just a mathematical tool. This is not a correct statement. In some experiments, it behaves as a particle and it some other experiments it behaves as a wave. This is because neither description is the full fledged QFT description of electrons. The price we pay is we have to choose the electron either as a particle or as a wave according to the needs, while in truth they are not two different things.

For example, if you consider that the electron is a particle, you cannot have double slit experiment (just put a detector on one of the slits and the pattern will be destroyed) , and if you consider electron as waves in the usual sense, photoelectric effect cannot be explained.

While the author is correct in saying that electrons are particles, his emphasis on the wave nature being just a mathematical convenience is a bit oversimplification to make the book readable to beginners, a trait that is often found in these books but can be harmful sometimes.

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I think most in quantum physics would say just the opposite, that there are no "grains of sand". Rather, Caltech theoretical physicist Sean Carroll put it this way: “To understand what is going on, you actually need to give up a little bit on the notion of particles..... The universe is full of fields, and what we think of as particles are just excitations of those fields, like waves in an ocean. An electron, for example, is just an excitation of an electron field.

So particles, as we know them, are nothing more than waves in the field. It is the excitation of the field that we consider to be a particle.

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The EM field governs every thing we see, feel, remember, it governs all the chemical interactions of matter including all the reactions that cause our brains to function.

Water waves show how energy can move from one place to another and there are some similarities as well as differences to the EM field. In water we have many many particles that form the waves, the waves spread, superimpose, usually caused by wind they eventually transfer their energy by crashing to the shore. In the EM field we have virtual photons and real photons, enmasse they spread like water (like radio waves) but we can also study them as single particles to better know their behaviour. Every real photon emerges from at atom and is eventually absorbed by an atom. Virtual photons are force carriers, like when you hold 2 magnets apart or feel static electricity, no energy is transferred.

Maxwell gave us an equation for the propagation of light in the EM field, its solution was based on the fact that a magnetic force is generated at 90 degrees whenever there is a electric field generated, the solution was a sinusoidal. You can think of this as trying to run down a road on a day with a mysterious wind. When you try and run forward the wind blows with an equal force at 90 degrees, you would end up going in circles, but if you try and run in a sine wave pattern you can actually have a net vector down the road!

Now combine the fact that most of our scientific experiments are based on observation using the EM field, and that most of the experiments involve interaction of matter which is also molecules and atoms surrounded by electrons using the EM field to govern all the interactions. The EM field, i.e. photons, can only act sinusoidally, that puts a lot of wave behahior into the nature of interaction of matter.

Consider an electron in the DSE, before it even leaves the emitter it has already caused virtual photons and is feeling out a path to travel before it even gets started. Certain paths are ideal, they resonate with the field and the eventual absorbing atom, resonance is also ideal when the path length is a multiple of the wavelength (Feynman path integral).

So do not think of matter as some inert chargeless ball of mass, matter is something that exists in the EM field and is even made up of particles the have EM properties of their own.

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