### Is interference a quantum effect?

Consider the famous double-slit experiment with photons. This experiment can be performed in two regimes: the low intensity (Feynman) regime and the high intensity (Young) regime. In the Feynman regime, photons are released one-by-one, the image on the screen is built one dot at a time, and the explanation of the interference picture is given by quantum mechanics of particles - photons. In the Young regime, the interference picture is exactly the same as in the Feynman regime (after enough dots were accumulated on the screen, so that a continuous distribution of the intensity emerged), however, the explanation of the interference is radically different. Classical electrodynamics describes light as a continuous electromagnetic field. One interference picture, two different explanations. Which one is correct?

Note that there is no any significant difference between these two regimes apart from the intensity of light or the number of emitted particles. Therefore it would be not correct to say that the Young regime arises in some kind of classical limit, i.e., when the Planck constant can be neglected. The same physical mechanism works in both regimes, and the theoretical explanation should be also the same. The only explanation that works in both cases is the view that light is a flow of particles - photons, and that the wave properties of light are manifestations of the quantum nature of these particles.

This brings up interesting questions. Are we making a mistake when calling Maxwell's wave theory of light a "classical theory"? Is wave theory of light, in fact, a surrogate attempt to describe quantum effects? I think the answers to both these questions should be "yes". Newton's rings, Grimaldi's diffraction, and Young's interference are genuine quantum effects, and their correct description requires the machinery of quantum mechanics: Hilbert spaces, wave functions, etc.

Newtonian ray optics in which light corpuscles move along well-defined trajectories is the only truly classical description of light.

Note that there is no any significant difference between these two regimes apart from the intensity of light or the number of emitted particles. Therefore it would be not correct to say that the Young regime arises in some kind of classical limit, i.e., when the Planck constant can be neglected. The same physical mechanism works in both regimes, and the theoretical explanation should be also the same. The only explanation that works in both cases is the view that light is a flow of particles - photons, and that the wave properties of light are manifestations of the quantum nature of these particles.

This brings up interesting questions. Are we making a mistake when calling Maxwell's wave theory of light a "classical theory"? Is wave theory of light, in fact, a surrogate attempt to describe quantum effects? I think the answers to both these questions should be "yes". Newton's rings, Grimaldi's diffraction, and Young's interference are genuine quantum effects, and their correct description requires the machinery of quantum mechanics: Hilbert spaces, wave functions, etc.

Newtonian ray optics in which light corpuscles move along well-defined trajectories is the only truly classical description of light.

## 7 Comments:

The following paragraph deserves major revision.

"Note that there is no any significant difference between these two regimes apart from the intensity of light or the number of emitted particles. Therefore it would be not correct to say that the Young regime arises in some kind of classical limit, i.e., when the Planck constant can be neglected. The same physical mechanism works in both regimes, and the theoretical explanation should be also the same. The only explanation that works in both cases is the view that light is a flow of particles - photons, and that the wave properties of light are manifestations of the quantum nature of these particles."

The first sentence can be understood misleadingly. Interference exists for water and other waves, too, where certainly no quantum effects take place. Classical bodies don't display interference. The so-called wave-particle duality is an artifact which has been slept-in from classical physics (due to the historical development of QM). Although SchrÃ¶dinger, de Broglie and Heisenberg have argued against, it's repeated again and again (incl

Further, you wrote "Newtonian ray optics in which light corpuscles move along well-defined trajectories is the only truly classical description of light." What about the wavefronts in Hamilton-Jacobi's description of motion of classical bodies, a quantum theory?

Peter:

The first sentence can be understood misleadingly. Interference exists for water and other waves, too, where certainly no quantum effects take place.Water waves, acoustic waves, their interference, and their diffraction are classical effects which involve periodic movements of a large number of classical particles. Light waves are completely different. In my opinion, they are just the "waves" of the probability amplitudes related to quantum particles - photons. So, the interference of light is a pure quantum effect. If we set the Planck constant to zero, then the interference of light will disappear, and the Newtonian corpuscular optics will become the accurate description of light.

My major point was the following: if you assume (as written in textbooks) that light is a classical continuous electromagnetic wave and that the interference of light has nothing to do with quantum mechanics, then how would you explain that the interference picture is exactly the same in both the high intensity regime (where the classical wave theory of light is supposed to work) and in the low-intensity single-photon regime, (where the continuous wave description of light doesn't work)? You would need to have two different physical reasons for the same effect, which I find rather suspicious.

If one assumes that light is a classical continuous electromagnetic wave, then the interference picture is independing of the intensity, and there is no need at all to discriminate between high and low intensities.

peter:

The problem is that classical wave description of light does not work at low intensities. When the intensity of light is so low that individual photons can be distinguished, the interference picture is no longer continuous as in Young's double-slit experiment. The low-intensity interference picture consists of individual dots scattered across the screen. The dots are places where individual photons hit the screen. This is what I call Feynman's regime. This dotty interference picture is not explained by the classical theory at all.

Maxwell's classical light model is not physics.

See Maxwell stuff, crackpot gearcog and idler wheel models made in 1861 to "predict" that light speed is the square root of two electromagnetic constants, a fact Maxwell already knew because Weber had discovered it empirically in 1856. None of Maxwell's derivations for electromagnetism have stood the test of time, and even his equations are wrong because he sets up continuous differential equations to represent fields and energy flows, when the reality is quantum (photons, discrete units of charge).

Maxwell's greatest prediction, made in an Encyclopedia Britannica article, was that the velocity of light is

absolute. This prompted the Michelson-Morley experiment, which failed to detect absolute motion in a Maxwellian aether. Einstein credits Maxwell with an invariant velocity of light by ignoring Maxwell's model and focussing on the Heaviside vector equations which are now falsely called "Maxwell's equations".The worst part of Maxwell is his illustration of a light ray in one dimension (direction of propagation) with two orthagonal axes representing electric field and magnetic field.

This is a longitudinal wave, not a transverse wave. Nothing is shown as varying transversely to the propagation direction, as the two orthagonal axes depict

not transverse oscillationsbut just field strength variations along the propagation direction.(Most people glancing at the diagram automatically mis-understand it to be a plot of light waving in three space dimensions, not merely one.)

As for the Young double slit experiment, focus on what happens at the

dark fringes.Young is wrong, because he claimed two light rays land out of phase at the dark fringes, thereby somehow "cancelling out".

Aside from the fact that the experiment works with individual photons and not merely with large numbers on the statistical average, Young's claim would violate the conservation of energy!

What is physically happening in the double slit experiment is clear when you remember that the slits have to be close together, and that it still works when you fire one photon at a time. The photons are complex transverse propagating waves in the background field of Yang-Mills exchange radiation in space and some of the transverse component from a single photon is able to enter each slit if the slits are close together. Hence interference.

I know a lot about fields "cancelling out", white noise, etc. The late Dr Lynch who was a leading expert on microwave signal beaming showed vey simply that although you can pass electromagnetic radiation through itself in opposite directions and cancel out the observable electric and magnetic fields perfectly, the energy is still there.

All that happens is that the superimposed field strength is zero, which is different from having nothing.

Think of it like this: if you have are $1 in debt and have $1 in your pocket, you are in a different situation PHYSICALLY from simply having $0 debt and $0 cash.

A simple mathematical answer does not always automatically reflect the underlying physics, which may be more complex.

Hello Eugene,

I would like to note that the interference of a photon with itself was first anticipated and desribed by H. Poincare in his "Last essays", The Quantum Theory: "It is therefore each quantum which really interferes with itself;..."! He made this conclusion just by considering the low intensity regime.

Vladimir Kalitvianski.

Hi Vladimir,

thanks for the info.

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