Seasons

I said that the wave interacts with the detector in a punctiliar fashion

Well, assuming you mean punctiliar to imply some sort of teleportation effect (because, truth to tell, I've only ever heard the word used linguistically to describe verbal aspect, so I'm not totally sure of its intended application here,) - whereby the photon moves from A to C without passing through B, the problem remains that interference generated by the passage of this quantum through both the slits at B occurs. If it had bypassed this altogether, I cannot see that the recorded interference could occur. Or am I missing something?

Now, as to the photoelectric effect:

My claim is that Einstein's explanation of the photoelectric effect requires only that the energy gained by the electrons be quantized in accord with the Planck-Einstein relations, which in turn follow from the appropriate form of the Schroedinger Equation (postulate 5, which I should also have mentioned in connection with the two-slit experiment, since it is the wave equation - my bad!), with a little help from some of the othe postulates. The problem was, that the ability of light to free electrons seemed to depend on frequency, which Classical Physics claimed to be irrelevant. Einstein's solution was, that according to Planck's hypothesis, E=hf (Energy of a packet = Planck's constant times frequency) , packets of low-frequency light didn't have the energy to free an electron. This is, however, entirely a matter of what goes on at the electrode itself - it says nothing about how the photons get there. In this case the electrons are playing the role of (photon) detectors.

So we have a local, punctiliar interaction - perfectly compatible with my interpretation.

Well, I still don't understand what you mean by punctiliar. The Concise OED doesn't give it at all (it's clearly not related to "punctate" = 'Biol. studded with points' or "punctilio/punctilious" = 'attentive to formality or etiquette',) and I sadly don't have my full OED available (lost the dongle ) And when I type "define punctiliar" into google, I just get lots about the Greek Aorist tense, and indications that it's some sort of synonym for "momentary", or possibly even "instantaneous". My own conception of its linguistic meaning would be more like "timeless" (or "unfixed in time", or something.) Since the speed of light is neither infinite nor varied by the presence of slitted obstacles in the photon's path, I doubt you mean any of these meanings. Could you elucidate?

Actually, IMCO, the strongest evidence for trajectories comes from scattering, e.g., Compton Scattering.

The strongest evidence against trajectories, IMCO, comes from quantum tunneling. We have a producer of photons, completely surrounded by an unbroken region in which it is impossible for a photon to exist. Outside this barrier, there is a photon detector. There turns out to be a small but non-zero probability that a photon will appear at the detector. How can this be reconciled with the claim that the photon travels in a continuous trajectory?

The term "tunneling" is actually a little misleading, since it suggests that the photon made a hole in the barrier. But this is not so. In quantum tunneling, the barrier remains intact.

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!