Quantum Mechanics is Falsifiable.

One concept which exists in Science, is that certain theories are Falsifiable. This means that a given hypothesis will predict some sort of experimental outcome, which other theories would not predict, and then an experiment can be performed to test whether this outcome is according to the theory. If it is not, then this test will break the theory, and will thus falsify it.

Quantum Mechanics is often Falsifiable. If the reader thinks it is not, then maybe the reader is confusing Quantum Mechanics with String Theory, which is supposedly not falsifiable? And thinking that String Theory is just the same thing as Quantum-Mechanics, is a bit like thinking that Cosmology is just the same thing as Astronomy.

According to Quantum Mechanics, light can be polarized, just as it can according to the classical, wave-based theory of light. Only, because according to Quantum-Mechanics light is driven by particles – by photons – its explanation of polarization is quite different from polarized light, according to the classical, electrodynamic explanation.

According to wave-based light, plane-polarized light is the primary phenomenon, and circular-polarized light is secondary. Circular-polarized light would follow, when waves of light are polarized in two planes at right-angles to each other, but when these waves also have a 90⁰ phase-shift.

According to Quantum-Mechanics, the photon is in itself a circular-polarized quantum of light, of which there can trivially be left- and right-handed examples. According to Quantum-Mechanics, plane-polarized light forms, when left- and right-handed photons pair up, so that their electrostatic components form constructive interference in one plane, while canceling at right-angles to that plane.

From a thermodynamic point of view, there is little reason to doubt that photons could do this, since the particles which make up matter are always agitated, and since the photons in an original light-source also have some random basis. So a conventional plane-polarizing filter, of the kind that we used to attach to our film-cameras, would not be so hard to explain. It would just need to phase-shift the present left-handed photons in one way, while phase-shifting the present right-handed ones oppositely, until they line up.

But there exists one area in which the predictions of Quantum-Mechanics do not match those of classical wave-mechanics. If we are given a digital camera that accepts lens-attachments, we will want to attach circular polarizing filters, instead of plane-polarizing filters. And the classical explanation of what a circular polarizer does, is first to act as a plane-polarizer, which thereby selects a plane of polarization which we want our camera to be sensitive to, but the output of which is next circularly-polarized, so that light reaches the autofocus mechanism of the camera, which is still not plane-polarized. Apparently, fully plane-polarized light will cause the autofocus to fail.

This behavior of a polarizer is easily explained according to Quantum-Mechanics. The plane-polarized light which is at first admitted by our filter, already possesses left- and right-handed photons. After that, we could visualize sorting out the photons that are circular-polarized in the wrong direction.

But the opposite behavior of a filter would not be predicted by Quantum-Mechanics. According to that, if we first pass randomly-polarized light through a circular polarizer, and if we then pass the resulting beam into a plane-polarizer, we should not be able to obtain plane-polarized output from the last polarizer.

According to the classical explanation of light, this should still be an easy thing to do. Our circularly-polarized light is supposed to have two components at right-angles, and our plane-polarizer should only allow vibration in one plane. But according to Quantum-Mechanics, if the incident beam is already circularly-polarized, it should only consist of either left-handed or right-handed photons, and then a simple filter should not be able to conjure photons that are not present in the original beam. And so our circularly-polarized light should not be convertible into plane-polarized light.

Now, there is a tiny way in which Quantum-Mechanics makes an allowance for such situations, in which left-handed particles can be flipped into right-handed particles and vice-versa. But as far as I can see, this phenomenon may be possible in theory, but simply will not take place in simple filters. (It would be accompanied by some loss of energy.)

This is because in order for a photon to be left- or right-handed, it must not only have momentum, but is actually theorized to have angular momentum as well. And this property has been confirmed experimentally. In order for a left-handed photon to be flipped to being right-handed, for example, something needs to take place which conserves both energy and momentum. So in principle, a crystal would need to carry away the momentum, that changed in the photon.

The way crystals do this in Quantum-Mechanics, is by carrying away an actual phonon – a quantum of sound. The problem here is that this quasi-particle – the phonon – will also have energy. Thus, in the process of being flipped, a photon should be losing energy to a phonon. And what this would also mean, is that the color of light should get red-shifted, because of this loss of energy – from one photon.

This loss of energy can be reduced – but not entirely avoided – by making the crystal harder. But in practical polarizing filters, we do not see the behavior, that monochromatic green light turns red, etc.. We can see the behavior by which photons of different wavelengths will get sorted, or by which they could be absorbed with probabilities depending on several arbitrary variables, or by which they are phase-shifted, but not usually the sort of phenomena, by which the wavelengths of individual photons is changed or shifted.

And so it would seem that Quantum-Mechanics is easily falsifiable. And yet the body of Science available today embraces it, and does not reject it.

Dirk

P.S. I suppose that one question which an astute reader might ask would be: ‘If the conservation of momentum is important, why does a beam of light bend, as it enters a refractive substance?’ The answer which Quantum Mechanics offers, is much messier than the answer classical electrodynamic models would have offered: When a photon is passing through a medium, it is not exactly the same particle, as a photon traveling through a vacuum.

The way QM explains refraction is a fascinating world unto itself. Apparently, a photon needs to couple with another particle, which can either be a Plasmon, a Phonon, or an Exciton, in order for both to propagate through a medium. If the coupling succeeds, the result can be one of

  • A photon-plasmon (surface) polariton,
  • A photon-phonon polariton, or
  • A photon-exciton polariton.

The conservation of both momentum and energy is still basic, except that once inside the medium, the photon is now attached to a particle which was not there before. The combined momentum and energy of the resulting polariton need to equal those of the original photons.

One factor that makes Quantum Mechanics unaesthetic, is its over-reliance on quasi-particles.

And a philosophical question which follows but still has no answer, would be ‘What signals the event, by which the photon has crossed the boundary into a refractive substance, thus requiring it form a polariton, if all that matters finally is particles?’

While the QM explanation for refraction is ugly, it explains certain facts, such as that some metals – copper and gold in particular – have specific surface-coloration, which is referred to as ‘pink’. According to classical theories, either metal should be equally capable of reflecting light, the same way chicken-wire reflects radar echos. There do exist holes in the chicken-wire, but the wavelengths of the radars in question, are longer that units of the mesh.

Well according to that, the atoms of copper and gold should also form a mesh smaller than the visible wavelengths of light, and should just reflect it. But according to QM, they only reflect wavelengths much longer, than their inter-atomic distances. Which we can see in their not having a typical, neutrally-colored luster.


But this relates back to plane-polarized light. There are essentially two types of filters which produce it:

  1. A polarizing mirror, or
  2. A gel block.

Unless I am mistaken, Excitons are not circularly-polarized but rather form dipoles.

In case (2), the medium has been treated by old-fashioned means, so that repeated polarization along one axis loses energy – maybe because the gel has been made ohmic along that axis – while repeated polarization at right angles to that does not lose energy. But circularly-polarized photons still need to be coupled with the Excitons, to form Polaritons.

If there are only left-handed photons and no right-handed photons present, then regardless of along which axis the medium is lossy, the corresponding photon should constantly be polarized the wrong way, and should eventually be absorbed.

(Edit 04/26/2017 : )

I could engage in some speculative thinking.

When one photon couples with one exciton, the resulting polariton may remember in what direction the photon was polarized. Next, the medium could manipulate the polariton based on the orientation of its exciton. I.e., the medium could absorb most of the polaritons whose excitons were oriented along the disfavored axis.

Then, when the polariton reaches the opposite boundary of the medium, it could release its photon with the polarization it first had.

  • If the incident light was randomly polarized, it will emerge as plane-polarized in this case, because at the exiting boundary, the combined fields will be coaxial with the excitons.
  • If the incident light was circularly polarized, it will leave circularly polarized in the same direction as before.
  • If the incident light was plane-polarized in the disfavored direction, it will have produced polaritons at its entry-point, the excitons of which were also oriented along the disfavored axis of the medium, and therefore, most of the polaritons will have been absorbed in the given case.

I do not recommend that readers attempt to confirm this, using two circular-polarizing filters meant for photography, because the circularly-polarizing layer of the second filter, could happen to be in the opposite sense, from that of the first filter tried. I.e., a reader might mistakenly place a left-handed circular polarizer in front of a right-handed polarizer, especially since this aspect of how they are designed is usually not written in their product descriptions. And a false-positive conclusion might follow, that a linear polarizer does not transmit light which entered, circularly polarized.

It would be a suitable test on the light emerging from the second gel-block, for finding out whether it is linearly polarized, to try making circularly-polarized light out of it, in both directions. If light is transmitted, circular in either direction, then my hypothesis will be disproved.


I suppose that another reasonable question this subject could pose, is how it relates to birefringence. According to some public documentation, when randomly-polarized light impinges on a birefringent crystal, at least two beams form within it, those being the ordinary and the extraordinary beam. The same documentation states, that the direction of polarization of each beam is linear, but either against or along an axis of the crystal, or according to an axis of anisotropy.

This type of anisotropic layer can be applied at a 45⁰ angle, to a gel-block, which first applies plane-polarization to incident light. The thickness of this birefringent layer can be such, that light along one axis emerges ~ 90⁰ out-of-phase with the light emerging along the other axis. And so circularly-polarized light emerges.

I think that the public documentation on birefringence may be flawed, when it comes to depicting what will happen, if the light entering the birefringent is already circularly-polarized. In such a case, the crystal is only likely to sort the polaritons according to the direction of their excitons – again – and it will no longer be assured that the actual electrical polarization of each beam is still linear.

In fact, if the incident beam is circularly-polarized in the opposite direction of the present filter-combination, all that might result is that this light may cancel out, the same way light would generally cancel out, which is circularly-polarized in the direction opposing the current filter-combination. Only, if the incident beam is randomly polarized, then light circularly-polarized in the favored direction emerges.


Certain alternatives exist, to describe polarized light at the quantum level. One of them is, to state that a photon could be plane-polarized, or could be circularly-polarized. To my understanding, because a photon is a fundamental particle, it can be either one or the other, but not both. And so either alternative appears to offer absurdities.

It is an absurdity that light can be plane-polarized at one moment in time, but that it can enter a birefringent at a 45⁰ angle, and within some distance of travel, become circularly-polarized. And yet that is what happens. Do plane-polarized photons, or circularly-polarized ones, describe that best?

Also, in writing this posting, I did consider the possibility that photons and excitons could couple differently, to form polaritons. I considered this, because polarized light in a vacuum does not present many puzzles, only polarized light when refracted.

  1. One exciton could always be coupled with two photons, each spinning in opposite directions. The main problem with this would be, that circular polarization is preserved, when light is refracted many times through lenses etc. Is there something special about the dielectric that makes up a lens, which allows it to preserve this, but which dielectrics do not have, which have been tuned to modify the polarization of light?
  2. One photon could be grouped with more than one exciton. But then a dilemma which ensues, is the question of what exactly happens, when exactly one exciton is absorbed by the dielectric. If a plastic has been made ohmic along one axis, then excitons are in fact being absorbed when oriented along that axis. How would that affect a single photon, if that photon was coupled with several of them?

I felt it actually afforded the best consistency, if one photon – circularly polarized – was coupled with one exciton – that carrying the linear polarity of the dielectric. But then it would also seem most consistent, if the dielectric differentiated between or sorted excitons indiscriminately, with regard to whether those were coupled with a left-handed or a right-handed photon.


 

Birefringence is easily explained through classical wave-mechanics, but my best attempt to describe it at the single-photon level would be like this:

The ordinary and extraordinary beams correspond to excitons, that are differentiated along axes of anisotropy of the dielectric. Each type of exciton does propagate at a slightly different velocity, but should still be coupled with either a left-handed or a right-handed photon, provided that randomly-polarized, or plane-polarized light entered the dielectric.

Therefore, after a phase-shift has been introduced between these two polaritons, and each exits the dielectric, it could still give off either type of photon. But the photons that would theoretically spin oppositely to the direction of the phase-shift, would see their wave-functions cancel out. They would arrive at the axis of their counterparts phase-shifted 180⁰.

OTOH, Photons that spin in the same direction as the phase-shift, should arrive at the axis of their counterparts in-phase.

Now, if the light was circularly-polarized before entering the birefringent dielectric, then a situation has been set up which I do not see described in the public literature. I interpret this to mean that the wave-function is out-of-phase as the photons cross the boundary in. I also interpret this to mean, that the exciton along each axis of the dielectric can only be coupled with one direction of photon, not with either.

Out of these two interpretations, given visible wavelengths of light, one would require much more precision to guide into a predictable difference in behavior, than the other…


 

(Edit 05/06/2017 : ) One concept which my paraphrasing, of the QM description of polarization and refraction, has totally skipped so far, is the QM concept of ‘superposition of states’.

If I simply state that as the photon enters the dielectric medium, its direction of polarization – i.e. its direction of spin – is not known, but remembered by the polariton it forms, because the photon is still a fundamental particle while the polariton is not, then I am also saying, ‘Its direction of polarization is superposed.’ There is only one, but its direction is ambivalent.

My gut feeling is, that this affects how circularly-polarized light travels through a dielectric, which is lossy when polarized along one axis. Here we are saying, ‘The direction of the photon is no longer superposed, but the direction of the exciton is.’ So, again the photon does not need to be grouped with more than one exciton, in order for the excitons facing along the wrong axis to be absorbed – gradually, until all the polaritons have vanished. That one exciton simply needs to be ambivalent, about which direction it is polarized in.

So another possible experimental conclusion that would not irk me, could be that when circularly-polarized light enters a linear polarizer, it could gradually just be absorbed to 0%.

 

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