Seasons

I: Look, a wave!
P: No, it's a particle!

Except that I don't say it's a particle, I have repeatedly said it is a thing with both wave-like and particle-like properties, ie: a wavicle. But you do claim it's a wave, not a particle, and apply a classical model of wave diffraction that can't be made to consistently fit the observed results.

Again, you make all kinds of claims without relating them to the postulates of QM.

I totally accept the six postulates you have referenced. They are absolutely 100% relevant to the behaviour of the quantum, and the mechanics of quantum interaction. But they are not, I think, actually very relevant to its nature. This whole argument began, as I recall, because we started discussing (rather speculatively,) the behaviour of the quantum, without first ensuring that we agreed on its nature. And it doesn't look as if we're going to make much progress on what a quantum does until we can agree on what a quantum is. I think it wise to learn to walk in step, before we attempt to run a Schroedinger marathon!

What I would say is relevant to the nature of the quantum is the fundamental notion of wave-particle duality. If you don't accept that, then I'm far from surprised that you find the whole industry consisting of finding the most bizarre possible interpretations of Quantum Mechanics [Message: 3745] an affront to common sense. In fact I still can't figure out how any interpretation could make sense without WPD.

If the probability that a coin will come up heads is 60%, this does not mean that we can expect it to come up 60% heads and 40% tails, whatever that might mean, on a single throw. It means that in the long run, it will come up heads 60% of the time.

Yes. Because the probability is not part of the coin, but merely governs its behaviour. That is my point precisely.

Likewise, if the probability that a scintillum will appear in a certain region is 60%, this doesn't mean that we will get only 60% of a scintillum there, it means that we will get a scintillum 60% of the time, in the long run.

Precisely. Because the probability affects the location of the scintilla, and not any degree of their 'apparition'.

And that's precisely the 'indivisible nature of the quantum' in this case - you either get a scintillum or you don't.

That appears to be a complete non sequitur. The location of impact on the detector can surely have no special relevance to the composition of the impacting object, be it wave, particle, wavicle, snark or boojum!

You have said yourself that psi is a continuous function. It may be defined by the wave-like properties of the quantum, but it cannot be bound up compositionally in the quantum. It is a comprehensive wave function, not merely the wave-like properties of a wavicle.

I have decided to learn more about quantum computing, and have ordered a book for this purpose.

If you want to read up on it while you're waiting for the book to arrive, you might find
http://www.quantiki.org/wiki/index.php/Basic_concepts_in_quantum_computation
worth a look (I'd be fascinated to know how you would explain the workings of an entirely wave-based quantum computer! )

In fact the whole http://www.quantiki.org/wiki/ site is pretty good.

Psimagus:

Once again, I don't have a wave-only theory. My view is that it's the wave, psi, which propagates. That's why you get diffraction and interference and other wave effects. But the amplitude of the wave measures the probability that certain discrete (quantized) events will occur. These discrete events are not waves.

Analogy: you have an operatic soprano, and a rack of small, delicate wine glasses. When the soprano sings, some of the wine glasses break. There are two schools of thought on how this happens. One school of thought says that she emits tiny particles, called spit bullets, which fly from her mouth to the glasses. If a spit bullet (of sufficient energy) hits a glass, the glass breaks. The other school of thought says that there's a wave that travels from her mouth to the glasses.

To test this, they make the following experiment: they set up a bank of very tiny glasses, so that they can measure very precisely what the pattern of breakage is. They also place a soundproof, bulletproof barrier between the soprano and the glasses; but they make a small hole in the barrier. Bothe the soprano and the glasses are at some distance from the barrier. They reason follows: if the damage is done by spit bullets, then a glass will break only if there is a straight line from the soprano's mouth through the hole to the glass, except perhaps for a few bullets that ricochet off the edges of the hole. So the glasses will break primarily in a circular region. On the other hand, if it is a wave that does the damage, it will diffract, producing a pattern known as an Airy Pattern, which is a series of concentric rings; in some rings there will be a lot of damage, in others less damage or even none. They make the experiment, and behold, they get an Airy pattern!

But, not to rush to judgment, they try another experiment: the double-slit experiment. They set up the barrier, but instead of a single circular hole, they cut two vertical rectangular slits next to each other. If the soprano is sending off spit bullets, then we would expect the glasses to break mainly in two vertical rectangles, since there has to be a straight line from the soprano's mouth to the target through one of the slits (again, there will be a few strays that ricochet off the edge of the slits, but these will be rare and fairly random in where they end up.
On the other hand, if a wave propagates from the soprano's mouth, then it will diffract from the slits, and there will be two waves emerging on the other side of the slits. They will spread out (as you said above, it will be like ocean waves passing through two narrow gaps in a seawall; the waves on the other side will spread out), and so they overlap with each other, and (being waves) interfere with each other, producing a complex pattern. Where they reinforce each other, the amplitude of the resulting wave will be very high; where the high point of one meets the low point of the other, they will cancel each other out. So the result will be a very complicated pattern of parallel lines (parallel to the slits). In some of these lines there will be lots of damage, in others less. They make the experiment, and behold, they get the interference pattern!

But, not to rush to judgment, they try another experiment: they enclose the soprano entirely in a barrier that is impervious to projectiles, but not to sound (although it does tend to dampen the sound). She sings, and a few glasses break. The barrier is examined very carefully to make sure there are no holes in it, and there aren't any. It is completely intact.

Well, at this point, the wave theory looks pretty good! However, there is one thing that is a little mysterious. When the soprano sings very softly, the glasses break one by one. But, curiously enough, occasionally it happens that a glass will break in a region where the amplitdue of the wave is relatively small (i.e., the sound of her voice is not loud), while the glasses in a region where the amplitude is high remain unbroken (for the time being). Observation over a long period of time shows that the probability of a glass breaking is higher where the amplitude of her voice is greater; in the long run, then, there will be more damage in the regions of greater amplitude, but from time to time, something improbable can happen, namely a glass breaking in a quiet area.
So they conclude that there is a wave, but the actual damage done is not done inevitably by the wave (else all the glasses in areas where the wave is strong would break if even one glass broke in the quieter areas), but rather that the amplitude of the wave in the neighborhood of a glass gives the probability that the glass will break.
When the soprano sings louder, so many glasses break in a short time that the amount of damage in a region clearly reflects the probability of breakage in that region, so that diffraction and interference patterns become immediately visible. But the same thing happens over the long run; if the soprano sings softly, but sings over a long period of time, these patterns eventually emerge, 'by the law of averages.'

Now, all by itself, the fact that a glass will break while other glasses in areas of equal or greater intensity do not would seem to support the spit-bullet theory: the effect is local because a spit bullet is small. "If it were a wave," argue the spit-bullet proponents, "it would spread out, and wherever the amplitude was sufficiently high, all the glasses would break at once." However, the proponents of the probability wave theory have an answer to this (see my previous post), and besides, the spit bullet theory can't explain diffraction, interference, and tunneling.
So we conclude with a theory has is in some ways a wave theory and in some ways a particle theory. It is a wave theory in that causation propagates as a wave, but it is particle-like in that its effects are highly local.
Also, the source of the wave is local, or, to use that delicious word, punctiliar (like or occurring at a point).

So I am not a wave-only theorist; I might however be called a propagation-by-wave-only theorist. I see no need for a particle that traces a unique, continuous path from source to target; but then, neither do you, Psimagus, since you say that the particle in the two-slit experiment goes through two slits at once. If you want to say, with David Bohm, that punctiliar particles ride on the wave, tending to the high points, I don't know of any contradiction you will get into; but since the wave alone is sufficient to explain everything, except at source and target, Occam's Razor would tend to shave them off.

Wait! Irinia says there is a particle like energy which travels in waves and has characteristics of both, and Psimagus says there is a wavicle, which is a partile-wave thing that shows characteristics of both. What exactly is the difference?

As for quantum computers, they would have to be largely based on wave behaviour, since, as I understand it, they mustn't decohere until the computation is finished. The computation is done with waves, the I/O is punctiliar.