I Is this a new theory, an enhanced theory or just philosophy?

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SP) does not represent an observable phenomenon. It is a correct mathematical starting point to derive the observable superposition effect (SE) as the nonlinear square modulus of the expression for the linear superposition principle. In spite of this existing knowledge, somehow we get systematic training to accept that individual “indivisible light quanta” interfere by themselves. The phrase, “indivisible light quanta,” represents energy “hν,” a quantum cup of energy that is exchanged between quantized materials and classical waves.
The paper which ftr posted above contains that text.

The author thinks that the wave function of a single photon does not "interfere with itself". There has to be matter (photographic screen) present, so that we can observe the interference pattern.

The claim "a photon does not interfere with itself" is vague, because one cannot test the claim.

A photon does not interact with itself in empty space. That is true, but interaction is not the same process as interference.
 

vanhees71

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It's utter nonsense to begin with. There's no "photon wave function" to begin with, because there's no position representation for photon states, because there's no photon position operator definable.

Ironically for photons you come very far with just thinking about them not as classical particles (which is far from their true nature which is only describable in QED) but as classical electromagnetic waves. Then there's nothing weird about interference effects like in the double-slit experiment. There in some mathematical sense simply "parts of the e.m. field" interfere though of course there's just one electromagnetic field.
 

ftr

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Bialynicki-Birula is definitely a serious theoretician who has a long record of multiple insightful works; I have read some of his work in the past. If one is willing to disparage his work as 'nonsense' then I believe practically no theorist is safe from criticism.
 
Maybe the author thinks this way: if the wave equation is perfectly linear, then waves will pass through each other with no interaction.

That is, if f1(t, x) and f2(t, x) are two solutions of the wave equation, then f1 + f2 is a solution, too. The waves are not disturbed by each other.

If the equation is not perfectly linear, then the waves will interact and various scattered waves will form.

Suppose that f(t, x) describes a photon and g(t, x) describes an electron close to t = 0 and x = 0.

If there is no electron, then g is identically zero, and the pair (f(t, x), 0) is a solution of the system.

Similarly, (0, g(t, x)) is a solution of the system.

But the sum of the above two,
(f(t, x), g(t, x)),
is not a solution of the system because the photon and the electron interact. The wave equation is not linear in this sense.
 
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But none of the above authors mention anywhere that ##f(t,x)## and ##g(t,x)## would represent two different kinds of particles...
 

A. Neumaier

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It's utter nonsense to begin with. There's no "photon wave function" to begin with, because there's no position representation for photon states, because there's no photon position operator definable.
I am no expert in the field but many papers like following seem to be genuine physics.
Bialynicki-Birula is definitely a serious theoretician who has a long record of multiple insightful works; I have read some of his work in the past. If one is willing to disparage his work as 'nonsense' then I believe practically no theorist is safe from criticism.
The confusion is explained by the fact that the term ''wave function'' is ambiguous.

If the term is reserved for the position representation with Born's probability interpretation then vanhees71 is right. But there is a wave function in the momentum representation with a proper probability interpretation, and Bialynicki-Birula discusses its Fourier transform, which also deserves the name ''wave function''. Though it doesn't have a probability interpretation it completely describes the state.
 
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