Careful, there… They are circularly polarized. Spin along direction of travel is exactly equivalent to circular polarization.
Yes, measuring the helicity of a photon is equivalent to making a measurement of a polarization. I suppose I didn’t phrase that well.
Of course anything I suggest will have an interpretation for photons, since photons do behave “like particles”. There’s an extent to which saying that you “see a particle” versus “seeing a wave” is meaningless. It’s neither a wave nor a particle, but something else that behaves in a manner similarly to both. It’s a solution to a differential equation which looks much like that of a wave, but which admits relatively stable solutions with almost-compact support, or with almost-compact support in the Fourier transform.
How do you explain that the wave side is exactly on a par with the particle side? Come to think of it, all the standard examples used by popularizers are “particles with wavelike attributes” rather than “waves with particlelike attributes”.
The crucial bit of information that made me understand (well, sort of) how light can be both a wave and a particle is that all objects with momentum have a wavelength, called the de Broglie wavelength. (See here for an equation.) Since the de Broglie wavelength depends on Planck’s constant, which is very small, large objects (i.e. objects with a lot of momentum, which depends on mass) have very small de Broglie wavelengths. A baseball, a bullet, and the Earth in orbit all have a de Broglie wavelength, but it’s negligible compared to the other factors influencing their motion. On the other hand, photons have substantial de Broglie wavelengths, which is why light behaves as a wave in certain experiments.
The Wikipedia article on wave-particle duality explains this well. I’ll leave the rest to philosophy-of-physics people.
It is possible to demonstrate that a single photon interferes with itself.
I’m low on blood sugar, it is waaaay after a reasonable dinner time here, but I’ll try not to make any mistakes. Measuring position is measuring something that is intrinsically particle-like. It is easier to answer where a billard ball is, than were a sound wave is.
Let’s just stick to quantum mechanics and ignore quantum field theory, and look at the Shrodinger equation. That equation closely resembles a wave equation, so much so that it’s solution is called a wave function. The wave function can not be shown, or at least couldn’t when I was in school, to be “real”. The wave function for an electron contains the probability that the electron is at some position. (The wave function also contains the probability of other properties, such as its spin.) It is tempting to think of the wave function as the electron, but that is a leap that may not be valid. (Consider a photon sent by a distant quasar. The nonzero part of the wave function might be light years across, but a CCD finds the photon in just one spot. Did a photon light years across suddenly coalasce into a small locale, thus appearing to violate relativity? Or is the wave function merely the most complete possible mathematical description of the photon’s position?
Since we speak of wave functions, and not particle functions, I could argue that “waviness” is more fundemental than “particleness”, but that would be as wrong as your converse statement. The wave function describes probabilities. It takes a large number of measurements to experimentally determine a probability distribution.
Whether it is rigorously accurate or not (I have a BS in Physics so, while having some quantum, never got to the really detailed stuff) what has helped me the most is, instead of thinking of a photon existing simultaneously everywhere until it is observed, is to think of a statistical probability range that describes the probability that a photon can interact with a detection device or object at a certain moment in time. One inherently interferes with the probability space by physically attempting to observe the photon, and any further measurements on that particular photon are corrupted.
For example, my dog exists in a probability space of my house and yard, with certain likelihoods of existing in certain places (some more likely than others). However, when I open my refrigerator door, I force my dog’s wave function to collapse and have him appear right beside me. Any future determinisms of my dog’s behavior based on his original wave function description are rendered impossible.
That’s fine so long as it is indeed a dog, and not another common household pet, and your real name isn’t Schroedinger. Otherwise, I think a call to the ASPCA might be in order.
The level of this discussion is already way over my head, and I apologise for taking it down a few hundred notches, but I gotta know:
I’ve read and re-read Feyman’s QED with interest, and one thing aways kind of stumped me: his picture of a particle with a little imaginary dial that tells us what phase it’s in suggests rather explicitly that the particle has, along its path, a property that oscillates. Rather like a wave. But it’s not a wave, it’s a particle. But it’s got a “phase”.
Obviously, photons don’t have little spinning dials in them that point in a particular direction after they’ve taken their path from A to B, whatever that happened to be. That’s an abstraction. But an abstraction of what? What’s oscillating? If it were a wave, I could make some sense of it, but, as Feynman says, it’s not a wave. It goes ping! from over here and pong! over there in one discrete lump. Yet that lump has a phase.
To me, this is one of the hardest wave-particle-duality conundrums I’ve tried to understand, and I just can’t. I used to understand wave-particle duality as a kind of artifact of the types of experiments we did. But even when you do experiments that fully allow quantum entities to manifest as particles, and explain away all the wave-like interferences of paths by saying the cancel out, you get to the point that this cancellation is due, in simple terms, the the way that little spinning arrow is pointing. That oscillating property of this “particle”, this dimensionless packet of energy.
My mind just boggles.
I believe the “spinning dial” is meant to represent a complex number to a lay audience, and the particle going in every direction at once corresponds to the wave. But other than that I don’t know.
The reason that you’re getting confused about it not being a wave is that it is a wave, at least in a sense. You can’t give a complete description of quantum behaviour by talking exclusively about classical particles, nor by talking about classical waves. Arguably, you can give a complete description in terms of things that are absolutely particles, but they’re quantum particles, not classical particles, which means that they have some wavelike properties. Likewise, you could arguably talk in terms of things that are absolutely waves, but with some particulate properties. Given this, I personally prefer to consider them to not be absolutely either, but in some sense both. But if you find it easier to use some other mental model, go right ahead.
Well, that’s just it. It’s a quantum particle, which looks like a “wavicle” or something, depending on how one observes it.
Makes me wonder if there’s anything to that “pilot wave” stuff.
Okay, I read this thread, with the heavy use of google as a brain enhancer. I dropped out of college after a year and a half… so… math and physics aren’t my strong point.
But, I have one question:
Burried in the above thread, is a mention that locality is out of favor. Some googling tells me locality has to do with speed of light limits. So, scientiest have declared the speed of light is not a limit, and faster than light travel is possible, and I learn about it in a Doper’s thread? Way to go CNN!
No. Perhaps the biggest restriction on local phenomena is the inability to transfer useful information faster than light. Quantum weirdness does nothing to violate this restriction. The reason you can’t send messages using the apparent non-locality of certain quantum phenomena is that the state of entangled entities is completely unknown and undetermined until they are measured, according to the Copenhagen Interpretation, which so far has never been shown to be in violation of the math. So, if somebody on Earth measures the polarity of a photon, and somebody in the Andromeda Galaxy makes the same measurement on this photon’s entangled partner, they both could compare notes and agree that when the Earth observer made the measurement, the photon in Andromeda instantaneously assumed a complimentary state. However, it will take the two observers millions of years to share this information, so there’s no violation of Special Relativity here. So far, no one can deny that quantum entaglement appears to render changes in state that are instantaneous, no matter what the separation in time and space, of entagled partners, once a measurement is made. It is tempting to assume that entagled partners somehow act on one another in this instantaneous manner, which, prima fascia, seems to violate SR. But on closer analysis, since there’s nothing that can be done with this “spooky action at a distance” to send information of any kind, SR is in no way contradicted.
So, you’re putting this in the same category as shadow moving faster than the speed of light?
No, it’s in a catagory all it’s own, I’m afraid. Richard Feynman, who may have grasped these things as well as anyone, instructed people, essentially, to give up thinking about it. “Shut up and calculate!” was his recommendation. Quantum entanglement takes any common-sense analogy and throws it out the window. Things in the sub-microscopic world, simply do not behave in any way that our brains are evolved to cope with on a conceptual level. It is not an exaggeration to say that quantum mechanics suggests that nothing exists until you look at it. And looking at it changes it. So you can never know what it was doing before you looked at it, or even if it was really there. Those kinds of common-sense questions are no longer relevant. You’re forced to just forget about them.
What you know is, when I look in this box here, I see something. And that something can be connected somehow to something else in another box way the hell over there. Their states depend on one another, clearly. But how do they “know” what the other is doing? That is a complete mystery. It may make more sense to look at entagled particles as really flip sides of the same thing. They’re not “separate entities”, though our perception of them makes them appear to be so. They’re one. And they’re not. If Feynman is right, it’s hopeless to try to figure it out.
I once jokingly said that because there was an infinite distance in any direction from any point in the universe, all points were really the same point. Maybe that’s not so much a joke anymore 
There’s really a question of what it means to be a point. Usually physicists tend to regard the spacetime manifold as an ur-object (philosophically), but there are models coming out which think it might be an emergent concept. Existance “really is” something completely other, a certain aspect of which behaves like a smooth 4-manifold.
One way to visualize entanglement is that the members of an entangled set of particles can talk to each other instantaneously, but there’s no way whatsoever to tell them what to say. Or, rather, if you do tell them what to say, the entanglement is broken, and they don’t talk to each other any more. Is this the “correct” interpretation? The question is meaningless. But it’s a self-consistent way to describe the phenomenon.
I still say the easiest ontological interpretation (keeping spacetime as an ontological primitive) of entanglement is that there are no “separate” particles. There’s one photon field. An EPR pair is a disturbance of the field which is nonnegligible in two spacelike-separated compact regions. From this standpoint it’s perfectly natural that observvations are correlated: there’s only one object to observe in the first place.
Can one find in this model a connection that goes beyond entaglement? After all, if I understand any part of QM (and I don’t understand much, I’m afraid), the mere act of observing one member of an EPR pair not only appears to cause it to go from an undetermined state to a determined one, it causes the other member to do the same. After that, they are no longer entagled, except through some intermediary which cannot violate locality. Hence, they now look like separate particles in every respect. Yet if, on some level, they are not separate, they still “know” about the other particle, even if they don’t pay any more attention. Or do they? If spacelike dimensions are somewhat illusory in their “extendedness”, or if there are other dimensions which can link spacelike-separated regions, potentially every particle is connected to every other. Instantaneously. Now, does this give us a Machian interconnectedness that might provide some explanation for inertia and radiation resistance? Einstein seems to have given up on Mach’s principle; but did he simply not understand space-time topology well enough? And does the definition of “entaglement” need to be expanded?
Remember that in this model there are no “two particles”. An observation of the photon field affects it: the whole field.
And after the observation the disturbance is expressible as a combination of two disturbances, each localized to a compact region.
Not after the observation is made. Even the EPR setup agrees with this.
There are debates as to how well Einstein grokked differential geometry and topology. This is as maybe, though: Mach’s principle is worse than abandoned in GR. GR invalidates the very assumptions implicit in the statement of the more general versions of Mach’s principle. General covariance means that every coordinate system is exactly as valid as every other as far as physics is concerned. There are no “inertial” or “non-inertial” frames. The whole classical notion of inertia is put on relatively shaky ground.
The notion of entanglement has a very rigorous definition. Assume two quantum systems have state spaces V[sub]1[/sub] and V[sub]2[/sub]. The combined system’s state space is the tensor product of these two vector spaces. Some states of the combined system are expressible as the tensor product of a state in V[sub]1[/sub] with one from V[sub]2[/sub], but most cannot. Those which cannot are “entangled” while those which can are “unentangled”.