Seasons

You have to remember that if the photon is in several places at once, the "trajectory" is not going to be a neat straight line - it's going to be a probability cone (or cylinder? hmm, I'm not sure,) I certainly don't claim that it moves like a billiard ball along a classical path (obviously if it did, it couldn't be in two places at once,) but it must nonetheless move (I hope we can agree on that!) And it does so at a constant fixed velocity, so that the time taken is exactly proportional to the distance between the two points we locate it. You seem to be implying some sort of arbitrary teleportation/"hopping" from point to point? That would be hard to square with a fixed speed of light, surely?

In quantum tunneling, it can appear on the wrong side of a boundary precisely because the barrier is thin enough to be straddled by the probability cone(/cylinder.) So sometimes you're bound to see the electron on the wrong side of it.

BTW, I want to state that I rather like you, Psimagus, and that I think you are one of the most intelligent people I ever met; I would not be at all surprised to learn that you are in the 99.9 percentile.

Aww! *blush*

Likewise, and you're a pleasure to argue with (I love a good argument - you'd probably noticed )
I'm sure we're arguing the same position (because I believe that everyone fundamentally is,) but a little dharma combat over the viewpoint is always fun.
Alas, I must away to work now (but I'll come back to the QM tomorrow

OK, let me try to deal with this message now:
(you write)
My apologies, I must have misinterpreted your position. But you did say
"A wave goes through two slits and is diffracted."
And since

A) the integral premise of quantum theory is that stuff comes in indivisible units (quanta), and since

B) photons are such units,

I can't see how you can argue that this unitary "thing" (be it wave, particle, or anything else,) does not pass in its entirety through both slits simultaneously. How else can the interference possibly occur? Or do you disagree with (A) or (B)?
(end of your message)

Actually, let me take that bit by bit:

maroonA) the integral premise of quantum theory is that stuff comes in indivisible units (quanta),

As compared to classical physics, QM des indeed tend to see things as occurring in discrete forms.
But even when a phenomenon is discrete, probabilities concerning that phenomenon can be continuous. For example, let's say that a coin can only come up heads or tails (discrete). Nevertheless, the probability that it comes up heads can be any real number between 0 and 1, depending on how badly biased it is. Now the wave, psi, expresses the probability that some event will happen, so even though the event may have only a finite or denumerable number of values (these are the eigenvalues mentioned in Postulate 3), the probability that a particular value will be the actual one can vary continuously. So Psi is almost invariably a continuous distribution in space and time.

Man, I just can't do that color thing, can I?

OK, now let me discuss

B) photons are such units,

Yes, and that is why when you turn down the intensity, you see individual dots. But I hesitate to conclude that because I see a dot on the screen, there must have been a little particle that flew from the source to the screen. It is rather that the wave carries the probability of there being a dot on the screen. This way I save myself the trouble of having to figure out why a particle can diffract and interfere withitself.
In all fairness, I must add that there are at least two interpretations which bite the bullet on this one, without getting in trouble as far as I can see. In David Bohm's interpretation, the particles ride on the wave rather as surfers ride on ocean waves. They tend to congregate where the wave is high. The waves diffract and interfere, and the surfers follow them until they crash into the screen (=beach?).
The Feynamann interpretation is harder to explain. I think you will like it, Psimagus (perhaps you already know and relish it). The idea is that a particle going from A to B follows every possible path - or, if you prefer, there are an infinity of ghostly particles for each real one, and the ghostly particles follow every possible path. Each particle has a little clock in it. Sometimes it happens that all the particles in a given region will have their clocks in agreement, or very close to it. The more this is so, the more probable it is that the real particle will be found there. In the 2-slit experiment, some ghost particles will go through one slit and some through the other.

But even when a phenomenon is discrete, probabilities concerning that phenomenon can be continuous.

Yes, but when you toss a coin, it's not the continuous probability that comes up heads or tails - it's the coin. Likewise, it's not the continuous probability that passes through the slits, it's the discrete photon. Are you not confusing the waveform with the wavicle?

Now I really must go to work!

Irina,

Man, I just can't do that color thing, can I?

There is the option to edit posts - the "Email" link (under "Mark" and "Flag") is replaced by "Edit" for 10 minutes or so after you post, so you can go back and change it (invaluable sometimes when you miss a pointy bracket or cock up an AIScript example, I find!)


Yes, and that is why when you turn down the intensity, you see individual dots. But I hesitate to conclude that because I see a dot on the screen, there must have been a little particle that flew from the source to the screen. It is rather that the wave carries the probability of there being a dot on the screen.

Well, if you object to "particle", let us call it a "quantum packet" then. The experiment can be set up demonstrably to release these one-by-one, and they are indivisible. There is no duality of "carrier" and "load" (or "wave" and "surfer" - see below.)
And if you replace the screen with a cloud chamber, you get a well-defined track instead of a dot (it is, in fact, demonstrably a trajectory, much as the notion seems to offend you.) I can't see how a wave ("coupled" in some undefined manner to a probability or not,) can do this. And even so, I still think you're over-objectifying the probability. Would you say that the coin carries the probability of coming up heads? Perhaps so if you intend the verb in a purely figurative sense (as perhaps Bohm would intend, see below,) but I find it implies that you might expect to toss a coin and get it to land 40% heads, 60% tails.

This way I save myself the trouble of having to figure out why a particle can diffract and interfere withitself.

But give yourself (what looks to me like,) the far greater trouble of reconciling the indivisibility of the quantum with the notion that it contains two separate and distinct components. And of explaining where the momentum (p=h/l after all,) and mass (m=(h/l)/v [where p=momentum, h=Planck's Constant, l=wavelength & v=velocity],) of the packet come from (the wave, or the probability? It must be one or the other, since these are all you admit the packet to contain.) You would have to radically reformulate the nature of waves and/or probability in all classical and quantum models to make this remotely consistent, wouldn't you?

In all fairness, I must add that there are at least two interpretations which bite the bullet on this one, without getting in trouble as far as I can see. In David Bohm's interpretation, the particles ride on the wave rather as surfers ride on ocean waves. They tend to congregate where the wave is high. The waves diffract and interfere, and the surfers follow them until they crash into the screen (=beach?).

I am sure that if we were to dig Bohm up and ask him, he would nonetheless agree that the packet is truly indivisible, but I have always found this description thoroughly unsatisfactory, since it clearly implies that there are two distinct components - the surfer and the wave. And that if we were only cunning or industrious enough, we might contrive to separate the "surfer" from the "wave". I would prefer to say that the "photon is its own medium" - this may not be as striking and simple an analogy, but I think it avoids the risk of misinterpretation (and I'm sorry to say that your position appears to me to be precisely such a misinterpretation.)

The Feynamann interpretation is harder to explain. I think you will like it, Psimagus (perhaps you already know and relish it).

I do, and I do. And I agree with it more than most. Though I would rather avoid the description of particles as "ghostly" - it seems to imply that they are somehow less "real" than the "real" one. From my readings of Feynman, I don't see that this was at all his intended interpretation. I would rather find a more neutral term - "instantiations" for example.

The idea is that a particle going from A to B follows every possible path - or, if you prefer, there are an infinity of ghostly particles for each real one, and the ghostly particles follow every possible path.

I think they all have to be equally real (I do not say "how real" that is though. Indeed, I wonder how meaningful the description would be anyway.) They all carry the same energy, possess identical spin (magnetic moment and angular momentum,) travel the same distance at a fixed velocity (c), insofar as these can be determined. I tend to view them as leaking in from adjacent "many worlds" time lines (David Deutsch suggests this, I think,) where there may be some "seepage" before they have diverged beyond the Planck limit from other branches. They would be the same particle that they were before they diverged, but somewhat "dislocated" (dimensionally, rather than spatially.) But these are just words (and a considerably more extended can of worms than mere WP duality.)

Each particle has a little clock in it. Sometimes it happens that all the particles in a given region will have their clocks in agreement, or very close to it. The more this is so, the more probable it is that the real particle will be found there. In the 2-slit experiment, some ghost particles will go through one slit and some through the other.

I would rather say that one instantiation of the particle go through one slit and one through the other.
I think the prerequisites for such descriptions are scientific accuracy and linguistic clarity - sadly many scientists are noticeably far better at the former than the latter.

Well, one way of looking at it is that three things happen:

1. The source of the photon loses a discrete amount of energy and momentum.
2. A wave propagates from the source to the detector screen; in so doing it passes through the two slits, diffracts, and interferes, so that a spot is more likely to appear in certain regions of the screen than in others.
3. An electron on the screen receives exactly as much energy and momentum as was lost by the source, thus satisfying the conservation laws. [This triggers a chemical reaction, resulting in a visible scintilla.]

What is the analogue of the coin? It seems to me that it is the screen. Just as the coin will either fall heads or tails, so the screen will either display a spark here or here or here or here or ...

And in general (see Postulate 3, http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html ), what happens is that one possible eigenvalue is picked out of a set of possible eigenvalues (this can happen simultaneously with several different parameters, provided the corresponding operators commute).

Actually, a wonderfully irenic possibility occurred to me: We could agree to refer to the entire threefold process as the "photon". Then I could agree with you, for example, that the photon goes through both slits. It does it while it is a wave, and there's no problem with a wave going through two slits simultaneously.

To all:

Oh, dear, I feel like a notorious gunslinger walking into a bar; everyone falls silent.

Here, I'm checking my colt 45's at the door, see? Just because I am talking about Quantum Mechanics or whatever doesn't mean you have to. Just because I'm talking in a deadly serious tone doesn't mean you have to. And I promise not to shoot the piano player!

Walk in Beauty, Irina

Meh. If we don't talk about QP, what else are we gonna do?

Did you see that quantum computer thingy? I can get a link if you want it.

What the hey, here's the URL: http://www.dwavesys.com/

Irina,

There are two distinct problems here - the composition or nature of the quantum, and the indivisibility of the quantum.

1. The source of the photon loses a discrete amount of energy and momentum.

Yes. It also loses a little mass. The source of the photon loses one photon. This photon carries away some energy, momentum and mass at a calculable frequency and wavelength and (sorry, but it's true), along a measurable trajectory (but not strictly a 2-dimensional one like a billiard ball, I allow.) Its nature is that of a quantum packet that displays fixed wave-like and particle-like characteristics at all times and in all situations.
This wavicle passes through both slits, without dividing, and makes one spot on the screen.

Classically, waves do not have mass, or momentum. Energy yes. Wavelength yes. Frequency yes.
Particles do have mass and momentum, and energy. But they do not have wavelength or frequency.
The wavicle has all these things. All the time. It cannot be solely wave or particle, either constantly or alternately.

2. A wave propagates from the source to the detector screen; in so doing it passes through the two slits, diffracts, and interferes, so that a spot is more likely to appear in certain regions of the screen than in others.

An indivisible quantum can only pass through two slits simultaneously by being in 2 different places at once (since the slits are necessarily in 2 different places.) It appears to me that you are confusing this with the (comfortable, macro-scale) analogy of a water wave washing against 2 slits, because you envisage that such an experiment produces an interference pattern. But you have failed to take into account, I would suggest, that a wave of water is eminently dividable, by virtue of being made up of a large mass of water molecules - some may flow through one slit, and some through the other, but the whole point of a photon/wavicle/quantum packet is that it is not so divisible. In the same way that a single molecule of water cannot constitute a wave that washes through slits (and is too big to exhibit the quantum effect of being in two places at once - it is not a wavicle.) Logic surely dictates that, in maintaining this position, you must either:

A) deny the indivisibility of the quantum, or

B) demonstrate that the photon in the 2-slit experiment is not, by its nature, such a quantum.

3. An electron on the screen receives exactly as much energy and momentum as was lost by the source, thus satisfying the conservation laws. [This triggers a chemical reaction, resulting in a visible scintilla.]

Yes, it satisfies the conservation laws - so could a host of otherwise spurious explanations involving star-trek-style teleportation, orgone radionics, pixies, or the bat-bogey hex from the Harry Potter books. But it provides no valid mechanism (ie: one that is consistent with what we understand of the physical laws of this universe,) to explain how (and not merely that) the energy and momentum actually get from the source to the screen. This is a matter of the nature of the quantum. Only a quantum with both wave-like and particle-like qualities can do the job (actually teleportation might be possible, but that's a whole other kettle of eels!)

What is the analogue of the coin? It seems to me that it is the screen. Just as the coin will either fall heads or tails, so the screen will either display a spark here or here or here or here or ...

Well, you seemed to be trying to preserve a semblance of duality by claiming the quantum to be a combination of wave and probability (itself a wave. I don't know why you take so against particles, but you seem to.) If this were the case, I would expect to get a scintillum that was, say, only 40%, or 60% present. Instead, we see that the scintilla themselves can only measurably differ in continuous variations of energy/frequency/momentum/etc. Not in probability. The scattering of the scintilla, and the location of each point, is affected by probability of course, (just as is the way up that the coin lands,) but that's a very different matter - it's still either present or not. Heads or tails. Probability is no more a part of the photon than it is a part of the coin. psi is not lamda!
Since we have no indication that probability of itself can possess mass or momentum, isn't wave-particle duality a more sensible model for quanta than the wave-probability model you seemed to be (perhaps accidentally,) advocating?

And in general (see Postulate 3, http://vergil.chemistry.gatech.edu/notes/quantrev/node20.html ), what happens is that one possible eigenvalue is picked out of a set of possible eigenvalues (this can happen simultaneously with several different parameters, provided the corresponding operators commute).

Yes, but the eigenvalue relates to the position of the wavicle, not its nature. You are conflating waves again, I fear. The probability wave has nothing to do with the nature of a photon (its composition or any innate wavelike properties,) - it has everything to do with its behaviour (in this case particularly where it is, and where it's going.)

Actually, a wonderfully irenic possibility occurred to me: We could agree to refer to the entire threefold process as the "photon". Then I could agree with you, for example, that the photon goes through both slits. It does it while it is a wave, and there's no problem with a wave going through two slits simultaneously.

Well, it's an accommodation of language a politician would be proud of, and the words will fit, but I do worry that this attachment to waves still indicates that you are clinging to an inapplicably classical model (of large waves washing through 2 slits,) and attempting to apply it to the quantum situation in order to make it more common-sensical. There is (as Thoreau observed,) no sense so common as men asleep, which they express by snoring (not entirely relevant, but any excuse for a favourite quote.) What would be the point of a universe that made sense anyway, common or otherwise? It would have to be smaller than we were, and really rather dull.


Oh, dear, I feel like a notorious gunslinger walking into a bar; everyone falls silent.

I don't think it fell silent - it's just an incidentally quiet time. There hadn't been many posts here for weeks before the QM started up, and no-one's posted in Doghd's for well over a week.

Oh yes, nearly forgot to mention - this week's New Scientist has a very interesting interview with Marvin Minsky on AI and emotions (he's got a new book out apparently.) If you're not a regular reader, I can highly recommend it! (the preceding article on causal set theory is pretty fascinating stuff too.)

http://www.dwavesys.com/

Excellent! I want one