How two subjects might be confused, that both have to do with polarized light.

There exists a concept, by which a single photon is visualized as having an electrostatic dipole-moment, which does not lie in a plane, but which performs a corkscrew, either left-handedly, or right-handedly, to start the phenomenon of electromagnetic radiation as based on circularly-polarized light, as opposed to being based primarily on plane-polarization. A quantity of photons could then still form plane-polarized light, not because they interact with each other, but because they coincide with each other in such a way, that their electrostatic fields cancel along one axis, but reinforce perpendicularly to the axis along which they cancel.

In reality, it’s dangerous to make such statements, about what exactly one photon does, because nobody has ever ‘seen’ a photon. We’re mainly able to make more-coarse measurements of what light does, when composed of swarms of photons, and must then deduce what the properties of one photon could be.

But there is the matter of how any of this agrees with the classical, electrodynamic explanation of ‘light’, which would say that it has a magnetic dipole-moment, that oscillates with the same set of frequencies, with which the electrostatic dipole-moment, oscillates, but perpendicularly to the electrostatic moment.

The question could be asked of, If the electrostatic moment was plotted against time, What its phase-position would be, relative to the magnetic moment. And what I claim to know, is that they’d be in-phase.

This subject has been confused at times, with the question of whether the electrostatic component along one plane of polarization, is in-phase or out-of-phase, with the electrostatic component, along the perpendicular plane of polarization. Those are out-of-phase, in the case of circularly-polarized light, as well as in the case of circularly-polarized photons.

(Edit 02/07/2018 : )

 

photon_3

Now, the question about plotting this could get sidetracked, by the question of whether it’s more correct, if where the electrostatic dipole moment, which I’ll say is denoted by the Green line above, is pointing ‘upwards’, the magnetic dipole moment, which I’ll say is denoted by the Red line above, should be pointing ‘towards the viewer’, or ‘away from the viewer’. The way I presently have it, at the left end of the plot, the red line is towards the viewer at that instant. Because magnetic dipole moments differentiate between North and South, while electrostatic dipole moments differentiate between Positive and Negative, these signs of polarity are independent. By convention, the magnetic North pole is denoted by positive numbers. If it was assumed that the Red line corresponds to North, as shown above, then the photon would need to be traveling from the left, to the right, which also corresponds to an increasing parameter (t), just in case anybody is interested in actually analyzing the Math I entered.

In that case it should also be noted, that ‘Wolfram Mathematica’ switches the (Y) and (Z) plotting axes, so that (Z) actually faces upwards, but needs to be given as the 3rd input of a parametric 3D plot, while (Y) faces away from the viewer, which is different from how some other 3D plots work. The way I tend to visualize World Coordinates these days, (Y) should be facing Up, and (Z) should be facing Towards the Viewer.

(Updated 02/08/2018 … )

This type of 3D plot represents a real-world phenomenon. This means, that it can be rotated 180⁰ round one axis, and still represent the same phenomenon, but as if viewed from a different direction. When we rotate a 3D model around one axis this way, we are actually reversing it along two axes – I.e., by rotating such a model 180⁰ around (Y), we are reversing it simultaneously along (X) and (Z), thereby reversing it left / right as well as towards-viewer / away-from-viewer.

If we were to take such a model and reverse it linearly along only one axis, in fact we’d be creating a new object.

But what this means is that If the ‘light’ was traveling from right to left instead, then the North magnetic dipole moments should be facing away from the viewer, when the electrostatic dipole moments are facing up.

 


 

But then again, I did write at length on this subject, In this posting.


About the WiKiPedia treatment of this subject:

The WiKiPedia article on photon polarization, spends several paragraphs, attributing all the known, wave-based properties of light, to the photon, as a superposition of its possible states. In theory, this might not be wrong, especially, since systems of Math can always be written, which define this. But then, buried deep in its text, is The subject of the angular momentum of the photon. The WiKi’s current statement of the subject is, and I quote, “Photons have only been observed to have spin angular momenta of ± ℏ. ” This statement is buried so deep in the article, that most casual readers would not find it. But if it should turn out to be true, it may be the most important statement in the entire article.

The reason for this is, the fact that if a photon was capable of a non-superposed state, in which it was plane-polarized, then that photon would eventually be detected as having a spin of zero. But according to the above quotation, the photons have only been observed – i.e., witnessed – as having two, non-zero spin-states.

What this seems to suggest, is that plane-polarized light can only exist, as a superposition of two states which the photon can finally have.

The WiKi tries to make a non-committal statement, about whether the wave-functions of individual photons, are in fact helical. In case they are generally so, plane-polarized light can follow as a superposition of these states. Otherwise, the strange state of affairs would seem to be, that an (X) and a (Y) axis form the intrinsic states, even though neither axis is special. Then of course, circularly-polarized light would seem to follow, as a superposition of plane-polarized states.

But, the concept of photon spin is still being researched, and one reason might be, ‘±ℏ‘ being a very small amount of angular momentum to measure accurately.


 

Simultaneously, the superposition of states in QM is mainly thought to take place, as long as the original state of some particles was not known. If the full quantity of particles was in one known (base-vector) state out of two they could have – for example, because they emerged from a circular polarizer – then after that point, a superposition of this base-vector, with the other, is no longer possible, purely as a QM-phenomenon. This is because originally, the superposition of states was about probabilities, which were treated as in some way equivalent to amplitudes, by Feynman’s theories.

A superposition of states can ultimately be “collapsed”, after which it does not resume.

If the photon was such, that even to be plane-polarized does not collapse its superposition of states, while being one of its base-vectors, then this would differ from some other examples in QM, of superposition of states, but who knows – Photons could be complex. This would mean that any one orientation of plane-polarized light would still, in a way, represent a superposition between two plane-polarized states, that have not been defined.


 

I think that one problem with plane-polarized photons would be, that they do not explain the demonstration of Bell’s Inequality, as shown in the video, which my earlier posting is linked to. In that case, photons should ‘remember’ perfectly-well from their passage through a first plane-polarizer, whether they will pass through the second plane-polarizer or the third with greater probability, when three plane-polarizers are positioned in a sequence and at angles.

I think another would be, that circularly-polarized light would be represented Mathematically, as a superposition between two plane-polarized base-vectors, in which one of the two has an imaginary element, to denote its 90⁰ phase-shift with respect to the other.

The problem I see here, is that plane-polarized light would then be represented by a superposition of states, in which both base-vectors have real-numbered elements. Having many possible state-operators, one with one imaginary element and one with only real elements, would actually tend to add to the permitted number of states, of one photon, beyond what could really be, for fundamental particles in general. It basically suggests that two types of photons coexist, one helical, and one planar.


 

  1. AFAIK, It’s possible in QM, to say that a fundamental particle has its intrinsic states A and B, but that C or D can arise out of their superposition.
  2. Likewise, it’s possible to say that the particle’s intrinsic states are C and D, but that A or B can arise out of their superposition.

But, it’s not possible to say about the same type of particle, that both (1) and (2) above describe it.

One element of awkwardness in explaining a photon as having 2, plane-polarized states as its intrinsic states, is the fact that our real world has more than 2 coordinates. There is little sense to say, that an arbitrary X-axis, or an arbitrary Y-axis, belong to the intrinsic states of the particle, traveling along the Z-axis, because even if the Z-axis is known, for example, the X-axis can be chosen arbitrarily, so that the corresponding Y-axis will follow.

OTOH, Whether a particle is intrinsically left-handed or right-handed, is definable, since the apparent Z-axis along which it is traveling, is definable. There are many examples where left-handed and right-handed, intrinsic states apply to other particles.


 

(Edit 02/08/2018 : )

How my Hypothesis relates to Quantum Computers:

It’s an established fact in Physics, that Scientists are able to create 3-qubit quantum computers, based on photons. This suggests that such quantum computers possess 3 state-vectors, in which each element could be real or complex, as well as a minimum set of ‘operators’, that makes these state-vectors available for the full set of computations which any computer should ultimately be able to perform.

What this also means, is that a state-vector will eventually be (1, 0) , or, (0, 1) , and yet, that the superposition does not collapse.

The reason for which I do not believe this contradicts the hypothesis I describe in this posting, is my assumption, that a quantum computer can still only continue to perform computations, as long as its states of superposition do not collapse. I.e., they’d need to start out superposed and stay that way for the duration of the computations. This also means, that once a quantum computer has output its data, the state of the photons will be known (‘witnessed’) , their superposition collapsed, and no further computations possible, using the same set of photons.

But then an implication would arise, if both my own hypothesis and the success of these experimental quantum computers were true, that Scientists must have been initializing their quantum computers using plane-polarized light, and not circularly-polarized light, where the state of the photons in plane-polarized light can be expressed as Mathematical state-vectors, but be superposed from the start.

At the same time, if a state-vector was to arise out of a quantum-computation, which can also define one of the non-superposed states of the photon, this would not necessarily collapse the superposition of states, because all it would mean in Human logic would be, ‘If the original state of the photon was … , then at this stage of the computation, its state would become … , but, the original state of the photon was not known, so that this outcome is not definite, at least, until we obtain output from the quantum computer.’

Also, an assumption which I make about how Scientists study quantum computers is, that their quantum computer may only involve 3 photons, and perhaps, consist of ‘a quantum-dot’. But then, because the amount of light output from one quantum-dot might be too weak to measure, they would still base their experiments on numerous quantum-dots, and therefore, on numerous quantum computers, being fed the same equation to compute. The combined light output from these quantum-dots, would then be stronger, and easier to measure.

Well that also suggests, that Scientists may be able to measure an output state-vector, that corresponds to plane-polarized light, only because output from numerous quantum computers was combined in practice, and not because this would be a non-superposed state of one photon.

I do know, that Quantum Computing depends heavily on Particle Entanglement. AFAIK, This is the case, because one set of superposed states, is supposed to lead to the next. These phenomena usually seem better-described, in terms of the wave-functions. It’s easy to visualize, that some sort of stimulus is being fed to a set of quantum computers, that acts as a kind of clock, and that causes this to happen once, but that is not described in a very prominent way, in the Scientific literature, which announces a newly-found, working, quantum computer. More-conventional phenomena certainly exist, which need to witness the state of ‘a provoking particle’ – which is therefore no longer superposed – before they have some sort of known effect. AFAIK, those do not generally depend on entanglement, and I do not consider them to belong, exclusively, to Quantum Mechanics.

Dirk

 

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