Seasons

Because the photon is in two places at once. Just as it is when it passes through both slits in the diffraction grating. Doesn't this prove my point?

Ah, I'm sorry about "punctiliar" - it means, "having the form of (or like) a point." (Latin punctum, point) That was poor communication on my part! [Punishes self by swearing off sex for 2 hours.]

It applies to QM in this way: If you have a bright (intense) beam of 'particles', and you pass it through (e.g.) two slits, then the screen behind the slits shows an interference pattern, which is a continuous pattern of varying brightness. This would suggest that you are simply dealing with a wave. BUT if you turn the intensity down, then you see, not just the same pattern at lower intensity, but individual points (as if the screen were being hit by minute particles). However, the individual points appear more often in the areas which were brighter when the beam was high. Otherwise, they appear to be randomly distributed: we cannot predict where the next one is going to be. This gives rise to the following model (postulate 1) : the intensity of the wave at a point on the detector is proportional to the probability of the appearance of a dot. The pattern appears to be continuous at high intensity only because there are so many dots, coming so fast, that we don't see the individual dots.
Because the wave 'carries' the probability, it is often called the 'probability amplitude wave.' Since it is a wave, it diffracts and inteferes.

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. If I didn't think you were smart, I wouldn't bother to argue with you. I am also awed by your generous spirit, as manifested by all the help you give to people on the Forge, including me. Please do no misinterpret my opposition to certain of your opinions as an opposition to you personally!!!!!!!!

Ah, I'm sorry about "punctiliar" - it means, "having the form of (or like) a point." (Latin punctum, point) That was poor communication on my part! [Punishes self by swearing off sex for 2 hours.]

It applies to QM in this way: If you have a bright (intense) beam of 'particles', and you pass it through (e.g.) two slits, then the screen behind the slits shows an interference pattern, which is a continuous pattern of varying brightness. This would suggest that you are simply dealing with a wave. BUT if you turn the intensity down, then you see, not just the same pattern at lower intensity, but individual points (as if the screen were being hit by minute particles). However, the individual points appear more often in the areas which were brighter when the beam was high. Otherwise, they appear to be randomly distributed: we cannot predict where the next one is going to be. This gives rise to the following model (postulate 1) : the intensity of the wave at a point on the detector is proportional to the probability of the appearance of a dot. The pattern appears to be continuous at high intensity only because there are so many dots, coming so fast, that we don't see the individual dots.
Because the wave 'carries' the probability, it is often called the 'probability amplitude wave.' Since it is a wave, it diffracts and inteferes.

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. If I didn't think you were smart, I wouldn't bother to argue with you. I am also awed by your generous spirit, as manifested by all the help you give to people on the Forge, including me. Please do no misinterpret my opposition to certain of your opinions as an opposition to you personally!!!!!!!!

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.