It is known that light is a wave of propagating electric and magnetic fields (that does not require any medium, so please do not throw in any luminferous aether into this discussion) Like all waves when light waves interfere destructively, they (the resultant electric and magnetic fields) cancel out at the region, but continue to propagate and pass through each other as if nothing happen Similarly for water waves (let's ignore the non linear ones such as deep ocean waves for the purpose of this discussion) and waves on the string, where at region of destructive interference, the displacement of the water molecules and string molecules are zero. The waves (periodic disturbance of the displacement of the molecules that carry it, not sure if this is a good way to phrase it) propagate through each other as if nothing happened Now my question is Assume: 1. Two electrons (thus not particle A or B in our previous discussion in a previous thread, hence no such issue of the wavefunctions residing in different Hibert Space hence they cannot interfere) So we knew that if we mod square the wavefunction, we obtained the probability of finding the particle represented by the wavefunction From the Davisson-Germer experiment, we learnt that electrons have wave like properties and form interference pattern like light waves. Doing the maths, if we mod square the wavefunction at the region of destructive interference, ideally we expect there is zero probability of finding an electron My question is, as far as the current tread of mainstream physics, what is actually interfering that can result in a change of probability of finding the electron? Or more concisely, light waves (and all waves in general interfere) because the two waves have differing phases so (my understanding) 1. Light waves (the differing in phase is caused by the difference in oscillation of electric and magnetic fields, where one light wave might be leading the other) 2. Mechanical waves such as water waves, waves on string, 'Mexican Wave' (the differing in phase is caused by the difference in the periodic disturbance in a sequence of particles (in the general sense) that form the wave, again one might be leading the other) BUT 3. Matter waves/De Brogile waves: (The differing in phase is caused by the difference in oscillation of ???, which is shown mathematically in the wvafunction. But what exactly is this ??? that is not even a physical entity like an electric field) Please supplement more info if I have left out something by accident thanks! P.S. From this rather recent journal article http://physics.aps.org/articles/v6/58 The wavefunction (actually the probability distribution) of hydrogen is imaged Thus the wavefunction is really there, but what is the physical meaning of the phase of a matter wave? which so far the only thing observable from it is how when two wavefunctions in the same Hibert Space (i.e. particles with sufficiently identical properties) interfere with each other, result in a probability distribution that differs from the two wavefunction alone?
That's a good question Secret. I'm no expert, but I think that the electromagnetic field consists of "virtual photons". Perhaps those matter waves are "virtual electrons"?
Must admit I'd always contented myself with imagining that the sign of the wavefunction in a region of space didn't matter because the wavefunction was simply a sort of wave of "square root of the probability", in that region (OK, I know that strictly one multiplies by the complex conjugate, but just for simplicity in thinking of it). For example an atomic p orbital has one lobe of +ve phase and one of -ve phase, but the electron spends equal time in both and the sign can thus be ignored except when the symmetry of interactions is important e.g. an electronic transition, or whether a pair of neighbouring p orbitals combine to form either a bonding or an antibonding molecular orbital. But I'm only a chemist, so maybe I've just been ducking the issue all these years.
As far as I know they call this particle precognition with an action at a distance. I don't think anyone has been able to explain this phenomena, and it is called this because the particles can pick up information about the future trajectories of the waves and then choose not to travel in directions where their waves would then "cancel" each other out. So then if the waves would be forced into a situation where they would cancel then the particles then choose to go a different direction before they even get to the point where they would be canceled. Then the particle or wave cannot be detected at these locations. I think it is because they travel close to the speed of light, but then again I think everything in modern physics happens because they travel close to the speed of light...
Yes indeed. Atkins, in Molecular Quantum Mechanics, has an intriguing image in which he maintains that the wavefunction will always interfere destructively along all paths except that of Least Action - and that it is as if it explores all possible paths before the electron actually arrives (??!!) and only the path of least action is left with non-zero probability. Creepy action at a distance, perhaps, but I suspect those familiar with Hamilton's and Lagrange's formulations of mechanics may find it less so. (I am not one of those, by the way.)
Your problem is that you keep using terminology like and then this In QFT everything is irreducibly field like, it is a theory of fields which have a wave like picture. However, the real world of quantum mechanics only involves particles, irreducible quanta of measurement. The "field like" or "wave like" picture only arises when one takes a statistically relevant number of measurements of particles. So you can have a wave like description , but only when you've collected a statistically relevant set. You're asking questions like This ??? is a probability amplitude function, if you absolutely need to describe it. Don't get bogged down worrying about the wave-like characteristics of quanta, it only appears when you add up many quanta. In the end, if you do all the interpretational digging in physics, you'll come to the same conclusion that I have come to, the quanta is an amount of information. It has no such "real physical existence" like a field or a wave or a particle or or mass or energy or whatever all else. It is analytic truth value to the propositions which may state its description in the representation of your choice. That is what ??? is.
Al, I'd go along with most of what you say here, except the bit I quote above. I thought it was now established that particles passing one by one through a pair of interference slits dot the detector in a way that builds up a wavelike interference pattern. Even though the pattern is - just as you say - only apparent after a statistically relevant set of measurements, surely the implication is that the wavefunction of each individual particle is interfering with itself. Which suggests there is a "something" wavelike, at the level of individual particles. Or, would I be right in thinking that the way you see it is that the waves are there all right, behind the scenes as it were, but can only be DETECTED in a quantised manner, i.e. either a whole particle is detected or nothing?
Yes, it does explore all possible paths before the electron actually arrives, and then takes a direction where the wavelengths wouldn't "cancel" if reflected. This is why it is said to be an action at a distance. Then by it changing its course then it is said to be precognition at an action at a distance. It is as if it knows of possible paths before it gets their and then chooses a different direction to travel in.
This reminds me of the single photon interference experiment I have done in my 2nd year physics labs just 2 months ago. Even if the source of light is sufficiently dim that it is practically counting photons one by one, there is still an interference pattern produced as the variations in the number of photons per unit time Yes I agree, the interference pattern is apparent only when you have measuring a pile up of particles at each location when applying the statistics (not sure if this is a good way to paraphase it), but at the level of individual photons, how can an interference pattern still be possible Unfortunately the time interval for the photon count cannot be made small enough due to limitation in the 2nd year lab instrument precision etc. But would we still get an interference pattern made of photon counts if we made the time interval sufficiently small (e.g. in femtoseconds?) As for the "explore all possible path before arriving", I have heard briefly about that before, but how can this prevent violation of general relativity (that nothing with non zero mass can travel at the speed of light?) Some nice fruit for thoughts indeed, still a lot more to learn
I think al is referring to the fact that a pattern is only apparent after many measurements. Light can be thought of as Maxwellian EM waves or Born probability waves. We use Born probability waves in the case of electrons, I think Secret is asking if there's any other "counterpart" to this. Will "virtual electrons" cut it, or I am just embarrassing myself? Please Register or Log in to view the hidden image!
Exchemist, you're quote This does not fit in with my picture of what a particle is. Remember what I said earlier, The "particle" as you call it is nothing more than truth value to proposition, it is its description, and that's all it is. There is no such "particle" which has a wave like property that "interferes with itself". See Zeilinger 99' : A foundational principle of quantum mechanics
Thanks Al, I dont know Zellinger - and am unfamiliar with the philosophical language: "truth value to proposition", etc. Evidently I'll have to do some more reading - there's always more to learnPlease Register or Log in to view the hidden image!.
My major question is what's the physical nature of the phase of a wavefunction of a matter wave Since even in waves that require no medium like light waves, we can still give a physical picture on what is actually doing the oscillation (electric and magnetic fields) However as far I know, there is no attempt to explain what is actually oscillating in a matter wave, other than it is referred as a probability amplitude (which is kinda hard to picture since probability is always positive and bound between 0 and 1) As Al, Layman and Exchemist have pointed out, the interference pattern can be slowly built up and predict by statistics, and that there's an interpretation mentioned in atkins that the wavefunction will always interfere destructively along all paths except that of Least Action - and that it is as if it explores all possible paths before the electron actually arrives. (Pilot wave model) But all of these does not really shed light on the nature of the phase of a matter wave. More stuff related to wave particle duality here http://en.wikipedia.org/wiki/Wave–particle_duality A particle has an wavelike nature as evidenced by many experiments such as the davidson germer electron diffraction experiment, GP Thompson, neutron scattering etc. I am not sure whether virtual particles can account for the oscillation since virtual particles exist so briefly to produce any observable physical effect other than the casmir effect Just recently 2012-2013 things gets weirder as another interference experiment showed that light can act like particles and/or waves, or anything in between http://www.nature.com/nphoton/journal/v6/n9/full/nphoton.2012.179.html http://www.livescience.com/24509-light-wave-particle-duality-experiment.html http://www.newscientist.com/article...um-shadows-the-mystery-of-matter-deepens.html (They all describe the same thing, as far I aware) But there's still nothing to explain what physical aspect does the phase of the wave portion of matter represent
Ah but that's why I was careful to say I think of the "wave" as the SQUARE ROOT of probability. That takes care of the sign of the phase. But of course the state function also contains a lot more information than just the probability distribution - that is just the most obvious property: when operated on with the appropriate QM operator, it yields other system properties as well, such as momentum, energy and so forth. I suppose it really has to be seen as the essence of matter which, rather poetically, or perhaps musically, just happens to have some wavelike characteristics. By the way - Atkins again - the Schroedinger equation in its full, time-dependent form is not in fact a true wave equation, because while it has 2nd derivatives of spatial coordinates, that of time is only a 1st derivative. It is a diffusion equation. Atkins then makes the enigmatic observation that one might think it appropriate that the fundamental equations of matter should be diffusion equations. I leave you to make of this what you will. Al Onestone can be a bit impenetrable but, when he speaks of a "truth value to proposition", I think this is a polite, philosophical way of saying: "That's how the world appears to behave, so just get used to it".
I think you would be just embarrassing yourself as usual. There either is an electron or their isn't an electron, there wouldn't be something that is like an electron but then doesn't have the correct mass in these locations. If there was some electron like particle that then went in all directions then it wouldn't be correct to say that the particle just didn't go in that direction and then choose another direction because of particle precognition at an action at a distance.
