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Of course I know photoelectric effect, as well as Compton effect, blackbody spectrum, and other things. My problem is: in my personal opinion, all these facts only prove that THE INTERACTION is quantized, not that a particle flies from source to revelator.

Why it is quantized, and why the energy acquired from the electron is proportional to frequency...this is something else I would like to know. Quantum mechanics doesn't prove it, it takes it as a matter of fact. Where does h (Planck's constant) come from? The speed of light, for example, another very important constant in physics, is explained from classical electromagnetism: c^2=1/mu(0)*epsilon(0), but h is not.

The subject you have raised is indeed a perplexing one, which has generated great debate. One thing we need to keep in mind is that although the wave particle behavior is something difficult for the average person to make any sense out of, the mathematics describing it are very well developed. If we really want to have any hope of understanding this subject, we need to look closely at the math. In particular, a study of the Schroedinger "wave" equation is in order. When we look at that, we see that although it is a "wave" equation, it is an equation markedly different than any of the other wave equations we traditionally run into in physics (sound, water, classical electromagnetism). It differs markedly especially in the fact that the number of independent variables (coordinates or dimensions) over which the wave is formed, is not 1, 2, or 3 as in classical equations, but typically much larger. That means that when we calculate a "wave" from it, it is not a wave in the classical sense. That means we can't use it as the basis of conventional wave thinking untill we have somehow extracted from it an expression which is over 1, 2, or 3 conventional dimensions that has some resemblance to a classical wave.

If this sounds like I am saying that what is propagated in the double slit experment may not actually be the wave we think it is, that is what I am saying.

Another view of this problem can be had by examining how quantum electrodynamics is mathematically constructed. The quantization of the electromagnetic field, (to boil it down to its simplified essence) originates in the results which quantum mechanics gives us for the behavior of a particle confined within a potential well, in this case a parabolic well. A parabolic well corresponds to the situation in which the particle is confined to the vicinity of a point by a force which is proportional to the distance -- the simple harmonic oscillator problem. Quantum mechanics replaces the "particle" with a wave equation within the well, such that the wave's rate of propagation varies with the "speed" of the particle at any point, such that the wavelength is shorter in regions of high speed (near the origin) and longer near regions of low speed, and becomes imaginary beyond a certain distance away. This creates a standing wave within the well, the width of which depends upon what energy is assumed for the particle. Owing to the need for discrete solutions of this problem, only certain solutions are possible, meaning that only certain energy levels are possible. In turns out that in this sitiation, the energy levels are spaced equally apart in energy. As to the position of the particle: the absolute square of the wave function at any position and moment, is proportional to the probability that an operation to detect a particle would be successful at yielding the registration of a particle, if carried out at that point. Other than that, we know nothing about the position of the particle. As to the energy of the particle: We have said that the quantum hypothesis and the assumption that there must exist a Schroedinger wave, requires that onlyh certain energies are possible. More exactly, that means that if an operation to measure the energy is carried out, it can yield only one of the discrete permissible values. However, the wave principle also tells us that any linear combination of wave states that are valid, is also a valid solution, so that the particle is capable of existing in several energy states at once, so long as no operation to measure the energy exactly, is carried out. So in other words, we have a situation in which the classical quanties of position and energy are, in general, apparently indefinite, and become definite only when an operation to measure one or the other is carried out, and (because a wave state corresponding to a definite location cannot be a wave state correspoinding to a definite energy and vice versa) the two quantites cannot both be simultaneously definite.

What quantum electrodynamics does is say that this law (behavior of a particle in a situation where the energy varies as the square of the amplitude, as with a particle held by a linear spring) applies to

*any* variable the square of which is proportional to a classical energy. In particular, it applies to the electromagnetic field strength. Solving the equations in an analogous manner (although the situation is somewhat more complex here because of the possibilities of various field polarizations) yields analogous, and profoundly signficant, results: The electromagnetic field strength, like with the position of a particle in a parabolic potential, is, in general, of indefinite value, and for any particular spatial wavelength is capable of existing only in discrete energy levels, and zero is not a permissible observable and fixed value of the field. For an electromagnetic field which has a particular direction of propagation, polarization, and spatial wavelength, the phase of oscillation is indeterminant, and the "value" of the field remains time-invariant but multivalued, assuming a whole range of values between some effective maximum and the negative of the same. This is a very important point to note, because this description of the electromagnetic field is quite unlike the classical view, in which it has, at any one point in space and time, definite strengths and directions (electrostatic and magnetic), which oscillates according to a well defined function through all phases, in definite relation to time. Another key point to note is that the "width" of the parabolic curve (energy as a function of field strength) varies with spatial wavelength in such a way that the spacing between energy levels is simply h times the frequency -- which of course is nothing other than the photon energy. The conclusion is inescapable therefore that the "photon" is nothing more or less than the difference in energy between one permissible eigenstate of the field at that wavelength, and the next adjacent one (up or down).

So when you talk about the photon being, I understand, some artifact of the process of detection, that is only part of the story; you have to get into an understanding of what a quantized radiation field looks like, and that shows us that the wave propagating from transmitter to detector is in fact not structured the way a classical wave is structured, but has features unimaginable to classical physics.

Of course, this new picture of the electromagnetic field raises many questions, which, however, I will not attempt to deal with here.