So it's been said that the wavefunction has no physical meaning except to predict the presence of a particle at a particular space and time. Yet quanta seem to exhibit wave-like properties even in isolation (single-electron interference, for example). Further, quanta _NEVER_ exhibit particle-like behavior in the absence of an interaction (i.e. you can't see which slit the electron came through unless you interact with it while it's still close to the slit). Doesn't the wave-particle duality mean simply that "particles" are nothing more than the result of two quanta (waves) interacting? And if so, is it really so peculiar? Isn't it possible that there is no such thing as a single free particle at all?
Yes, I agree that that's what the "wave-particle duality" would mean if there was such a thing. It doesn't seem to be a very popular concept among physicists, where the particle is king. And yet over the course of time, many phenomena which were once held forth as the prime examples of things you couldn't explain without particles (light particles in particular), such as the stability of the hydrogen atom, the photo-electric effect, and the Compton effect, were easily explained as wave interactions, just as you suggested. All that was needed was for a correct wave equation of matter to be developed. The absorption and emission of radiation in specific quanta could then be understood as following from the properties of atoms. The more difficult question is whether we can understand the charge of an electron as arising from a wave function. I don't think anybody has an idea of how to do this. Matter absorbs and emits light energy in specific quantities, and that follows purely from wave interactions. But matter also absorbs and emits CHARGE ("electrons") in specific quantities. If you could show that this somehow followed from a wave equation interacting with continuously distrubuted charge density, then you wouldn't need particles at all. Of course, no one has any idea how to do this kind of thing. But that doesn't mean they never will. Marty
You might want to start with reading the FAQ in the General Physics forum and see if you still think there is such a thing as a 'duality'. Zz.
It really doesn't matter, because there aren't any "duality" in the description of any quantum particles, massive or not. It is extremely important to see how things are done in practice. You'll never find such "duality"in QM where we have to switch formulation from a 'wave' to a 'particle', and vice versa, simply because one picture no longer works. Zz.
Well, the "duality" comes into play only when one of the following happens: - Two quanta interact - A quanta is observed - A wavefunction "collapses" IMO those are all the same thing. Until then, sure, the Schroedinger equation adequately and accurately predicts the location of the quanta. But when an interaction occurs, there's suddenly particle-like behavior such as - - Cannot be in two places at once - Cannot share space with another particle - Conservation of momentum, etc. The question I pose is whether the latter properties ever appear in the absence of an interaction, and, if not, then if we can really say there is such a thing as a free particle at all, or if everything is waves, and the particle-like behavior can be described by the interaction of two waves, as Monish discussed.
You are forgetting that ALL of these are described by the SAME thing - the Schrodinger equation. You should think of what we mean by "duality". Classical mechanics has different, completely different, way of describing "particles" and "waves". So if you have a system, and in one phenomena you had to use the wave description, and for other phenomena, you have to switch gears and use the particle description, then yes, that system has a 'duality', because no one description can account for all behavior. Now, did you have to switch the QM formulation when describing ALL of the phenomena of a quantum system, before and after measurement? Can you point to me where you have to do this? Zz.
How do you explain any delayed choice two-slit experiment, then, if not by switching the formalism depending on the choice of measurement? Why is it that the emergence of an interference pattern depends on whether which-path information is obtainable? [Edit] Also, how does the Schroedinger equation predict that the particle cannot be in two places at once? As Einstein once said, how do the atoms in the detector that did not get hit by the electron "know" that they didn't get hit if, at an infinitessimally small period of time before the detection, the electron's probability density was distributed across the entire detector? Either an FTL action propoagated across the entire universe promulgating the collapse of the wavefunction, or the formalism must change for the act of collision. No?
You should look at the formalism used to describe such an experiment. Did they have to "switch" from a "particle" to a "wave" formalism, or is the same general starting point remain the same? Look at this paper on single-photon sources: B. Lounis and M. Orrit, Rep. Prog. Phys. v. 68, p.1129 (2005) Can you tell me where they had to change gears in the formulation of all the observed phenomena, including your which-way experiment? Zz.
Perhaps what I should be talking about is _interpreting_ the results rather than describing the experimental predictions. Granted the QM equations accurately predict all the results. But I don't see how you can interpret the results' physical meaning without the duality concept. You have to admit that it's the different interpretations of QM that leave the most to be desired at this point.
Interpretation is a matter of tastes. Nowhere in physics does interpretation dictates the formulation. It is always the other way around first. Still, if only ONE formulation can describe ALL of the observed phenomena, what possible reason do you have to still want to insist that there is "duality". I mean, do you still insist on the electric and magnetic fields to be "different" even after it has been unified by Maxwell Equations? After all, before that, people thought they were of different beasts. Rational people would conclude that after a single set of formulations unify those two, all talk about them being different from each other would stop. It is the same thing here. Look at QM, and there's one single, consistent formulation for "wavelike" and "particlelike" behavior. Yet, you still want to insist that there are still "duality". This "duality" only exists when we try to force our classical picture onto a quantum system, or when physicists talk to a general audience. We seldom even consider such a thing among ourselves. Zz.
How does the Schroedinger equation, or any mathematical formalism (other than, perhaps, MWI) describe the collapse of the wavefunction?
Look at the postulates of QM! Besides, what does a "collapse" have anything to do with being a "particle" or a "wave"? If the system is a sum of its eigenstates, all you get after a measurement is still one of its eigenstate, which can still be a "wavefunction". What does this have anything to do with "particle" or "wave"? I think you have missed or didn't understand what I meant by the "formulation". It isn't just ONE equation. It is the whole theoretical concept behind the description. You can set up the Schrodinger equation, or you can set up the Hamiltonian, typically via 2nd Quantization. It doesn't matter. You still get only one consistent formulation. I don't particular care about "interpretation", and if we go by Feynman, neither did he. Unless you first understand the exact formulation, then it is useless to argue about interpretation, because what exactly is it that you're trying to interpret? That's like a blind man trying to interpret a painting. Zz.
Ok, I'm probably not using the terms right but what you said about eigenstates helps me formulate the argument (hopefully) slightly better. What I mean by "particle-like" behavior is precisely the removal of eigenstates of the particle (and its entangled cousins) after a measurement. So, for the photon in a double slit before measurement, the wavefunction is .5|slitA>+.5|slitB>. Once you see it at slitA, the wavefunction is just 1*|slitA>, or vice-versa. (I could be using the wrong notation; I'm just an admitted hack). The former I'd call "wave-like", the latter I'd call "particle-like." Does that help frame the discussion better? Well, I'm not gonna be able to get a physics PhD anytime soon. :) I still hope I'll be able to comprehend this a little better though!
No, it doesn't. The fact that one can actually write such a wavefunction and describe ALL observed phenomena is my argument that it is just ONE single description. It is the observable (or the operators) that determine what you get upon measurement. If you put a detector at one of the slit, then you've removed the superposition of path that the system have and the problem setup now gives you one or the other eigenstate. This came from the same, consistent premise. The fact that you are still using the eigenstates means that the mathematics is the same. Now compare that to the drastic change you have to make in classical physics when you go from "particle" description to "wave" description. It is not even close. Do you get a particle if you simply select one harmonic out of the superposition of many within the classical wave description? Zz.
You're right. The collapse of the wave function is a direct result of interpreting physics in terms of particles. I would say that particle descriptions are the basic source of all the paradoxes and strange things that baffle people about quantum mechanics. I wouldn't worry too much about what ZapperZ is saying. He's misinterpreting the whole concept of duality. Duality doesn't mean you use waves to explain some things and switch to particles to explain other things. It means there are two entire, consistent ways of describing the universe: either you do it with particles or with waves. The mathematical results come out the same in either case. It's just the interpretations that are different. People have done a lot of work on building up the particle interpretation and have basically got it working. The cost, which they're willing to pay, is that you get all these philosophical issues of causality and probability. Along the way, they've come up with quite a few half-baked "proofs" to the effect that it's impossible to explain such-and-such using waves. The most famous of these so-called proofs have been effectively rebutted over the course of time, but people keep repeating them and coming up with new ones. It's an open question as to whether duality, in the sense I've explained it, actually describes the universe. As I said before, it's not a popular concept among physicists. What some of them seem to forget is that there's a difference between the following statements: 1. "I don't know how to explain such-and-such using waves". 2. "It's impossible to expalin such-and-such using waves". People often say #2 when they're only entitled to say #1. Marty
Fine. Look at a 2-spin system. [tex]|\Psi> = a_1|up> + a_2|down>[/tex] Can you tell me where is this "wave"? If I make a measurement of the spin state, and get, say [itex]|down>[/itex], can you explain where in here is there a "particle"? Was this particle there before? Why? In the Delft/Stony Brook experiment where there is a superposition of the supercurrent that has been equated to the Schrodinger Cat-state, they make a measurement of the coherence energy gap. Can you please show me where the "wave" and/or "particle" in those systems before and after such measurement? At some point, you have to consider that you are getting stuck and paying way too much emphasis on words without understanding the formulation, which should have been the other way around. I also haven't seen anyone disputing the fact that in most physics papers, the issue of "wave" or "particle" have very seldom cropped up. It is obvious that this is a non-issue for most physicists. Why is it such a big deal here? Have you run out of things to puzzle on? I can give you plenty if you need some. Zz.
Oh, it's more than that. It seems QM transcends spacetime all together. How about Wheeler's example where the paths of two entangled photons bent around a black hole that eventually arrive on Earth are determined by how they're measured on Earth light years away and years after they're sent? Only way that works is if the "collapse" is non-local, non-deterministic, and non-temporal. And no formalism I'm aware of can reconcile that with relativity. You either have to believe in time travel (Cramer), stick your head in the sand (Copenhagen), or smoke something (MWI) to explain it. ;) (no offense to MWI believers - I just tend to be flippant now and then).
You're not seriously telling us that you think the non-local collapse of the wavefunction is not a big deal are you? I think that's the $64,000 quesiton of the 21st century, personally. Wave models can explain it, but as monish said, fail for other reasons. And particle models cannot. I think that's a big deal. That said, I do not deny that I have much too much time on my hands.
But your ability to actually say "non-local collapse" came out of current formulation of QM which didn't switch from one formulation to another! Don't you see that? You are being mired by needing to "explain" why such-and-such occurs, and you're confusing that by thinking you can explain it by going back and forth between "particles" and "waves". And I haven't even started to question you on how you think "waves" would explain such "non-local collapse", considering that in QM, there's no physical anything that connects those remote properties. Your "wave" nor "particle" does nothing to explain such entanglement or have they been detected. I still want you to explain how the collapse of the example of my spin states somehow implied something went from a wave to a particle. You are going off on using more complex example of quantum entanglement, yet ignoring a simple example that I've given. Unless you can illustrate it using something we know very, very well already and on a very simple scale, then what hope do you have that your "model" will work with something that has an added layer of complexity such as entanglement? Zz.