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If a photon of 475nm strikes my retina, my brain registers it as "blue," whereas a photon of 650nm is "red." If I ask the question "what is oscillating, and therefore causing the change in wavelength (and thus frequency) that I observe?" I'll receive an answer invoking alternating orthogonal electric and magnetic fields. Since a single photon is itself a quanta of the EM field, there is an easily understood relationship between the wavelength of light that I access directly when my eyes register the color "Blue," and the QED entity described by "the photon has a wavelength of 475nm."

My question is this:

Why is the wavelength of a photon discussed and treated as a physically real component of the world, while the de Broglie wavelengths of other (massive) particles are dismissed as "waves of probability."

The color blue registered by my retina is the product of very real wavelength in an EM field, which is itself composed of (built up of) field quanta of the same wavelength (within uncertainty distribution). Why do we alter the way we conceptualize de Broglie wavelengths when we speak about particles/atoms/molecules, when diffraction and other characteristics remain, and the maths remain the same as well?

This is a follow-up to "Reality" of EM waves vs. wavefunction of individual photons - why not treat the wave function as equally "Real"?

Qmechanic
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JPattarini
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2 Answers2

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That's a complete misunderstanding of the statement of how matter waves work, and in particular it is a confusion regarding the role of wavelength and amplitude in waves. If you take a standard sinusoidal wave with waveform $$ f(x,t) = A \sin(kx-\omega t), \tag 1 $$ then the wavelength is $\lambda=2\pi/k$, and the amplitude is $A$.

  • For visible light, as detected by your eyes, the colour that you will perceive is determined by the frequency $\omega$, which is tied to the wavelength via $\omega=2\pi c/\lambda$. The amplitude $A$ determines, through its square $|A|^2$, the intensity of the light.
  • For matter waves, the probability aspect is described via the squared amplitude, $|A|^2$, which describes the peak probability density for finding the particle in that region. The wavelength, on the other hand, acts separately, through the de Broglie relation $p=h/\lambda=\hbar k$, and it is directly tied with the momentum of the particle. And, as far as the wave characteristics of matter go, such as its ability to diffract of of apertures, the de Broglie wavelength acts exactly in the same role that the wavelength of diffracting light does.

Thus, the role of the wavelength in the wave dynamics remains completely unchanged. The only change in going from light to matter waves is that the quantity that is actually doing the oscillations (along $f$ and along $A$) changes to a probability amplitude with all the conceptual problems that brings with it, but those have been treated to death elsewhere and there's no point in rehashing them here.

Emilio Pisanty
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Color is a property of light, classical electromagnetic wave, as perceived by the receptors in our eye. So the perceived color is not always the color of the spectral frequency. So let us narrow it down to the colors of the spectrum that have one to one correspondence with the frequency.

A photon is an elementary particle,the quantum of electromagnetic radiation, and has only energy , momentum and spin. The formula E=h*nu assigns a frequency to a photon which is the frequency that the classical electromagnetic wave will have when composed by an enormous number of superposed photons of this energy.

With this in mind:

Why is the wavelength of a photon discussed and treated as a physically real component of the world, while the de Broglie wavelengths of other (massive) particles are dismissed as "waves of probability."

the phrase "wavelength of a photon" refers to its energy in the one to one correspondence of E=hc/λ . There is no electric and magnetic field associated with a real photon. There exists a wave function of a photon, which is the solution of a quantized maxwell equation, which carries information of the electric and magnetic fields , and its complex conjugate square will give the probability of finding the photon at (x,y,z,t).

In this sense, the photon also has a debroglie wavelength which will describe its probability locus, given by λ=h/p, the same as for the electron or another particle.

It just happens that the ensemble of superposed zero mass photons builds up a classical electromagnetic wave that has a one to one correspondence with the optical spectrum, but an ensemble of ( for example) protons make a beam of protons at the LHC. The superposition is additive for massive particles.

So both an electron and a photon have a probability associated with them, it so happens that the photon supeposed ensembles have a macroscopic collective behavior that is wavelength dependent and is perceived as color.

anna v
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