Seasons

What, did we actually find a shred of agreement, there? What's happening to us? Where did we go wrong?

Don't speak too hastily...

A wave is often defined in Physics as a "self-propagating distubance," so if Psi is a wave in that sense, it surely propagates in that sense.

Precisely why Penrose doesn't think it should really be called a wave. It doesn't propagate, but is continuous throughout spacetime. There's even an infinitisimal chance the quantum will be found a million light years away en route through the double slit experiment, since all of spacetime is encompassed by Psi (including that point.) But not by taking a million years to propagate to that point - Psi is already there (with a value so low as to be utterly preposterous, but nonetheless not zero.)

But I have the feeling that you are using the word "propagates" in a different sense, in which case our disagreement may be only verbal.

No, I am taking the word to mean exactly what you are - classical propagation, as exhibited by classical waves and by the wave-like electromagnetic characteristics of the quantum.

Edison probably had some sort of ADHD. That's why I hate labels. There is a great danger of creating uniformity and losing genius.
As for purses etc..I like a back pack. When you are an hours driving time from anywhere, you have to be ready for CWI..that's camping without intention. In the winter you pack matches, blankets and booze..in the summer you pack bug spray, moose spray, bear spray and booze. You always have a shovel to dig out or dig in..
as for periods. Why does every conversation with or about women always has to go to pms or the like..I have never once heard men talk about testosterone poisoning.

Irina,

As for the electromagnetic wave according to Classical Physics, Quantum Mechanics says (again, speaking precisely) that there is no such thing.

But there evidently are such things, and I've not heard any quantum physicists try to argue otherwise. What most QM interpretations say (I would suggest,) is that at the quantum scale waves and particles start exhibiting characteristics of both themselves and each other. You no longer get waves and/or particles, but wavicles. But noone would deny that a stream of many quanta will exhibit primarily wave behaviour in many situations. It's just so curiously counterintuitive that a single quantum will also, in some situations (like the double slit experiment,) exhibit some aspects of wave behaviour.

As I said, Quantum Mechanics claims to supercede Classical Physics; it says that Classical Physics is wrong.

Not wrong, just incomplete. It doesn't seek to replace Classical physics, just attempts to put some foundations under it (since we find the whole edifice, being built from the top down, disconcertingly doesn't seem to quite meet the ground.) Classical physics works superbly well at a macroscopic scale - it just completely fails to work at a tiny scale.

So that wave doesn't exist either, according to QM.

Yes it does. It just starts behaving very strangely.

The wave that is characteristic of the quantum-mechanical view of the world is Psi. It is Psi that propagates.

It may be characteristic of many things, but it's not the only wave in any interpretation of QM I've ever come across (if, indeed, we choose to call it a "wave" at all.) It's a distribution of probabilities that covers all of spacetime. Every quantum has one (that's an awful lot of overlapping Psis!) and they all cover all of spacetime continuously.
Fortunately, being a rather theoretical mathematical device, this doesn't leave the universe clogged up with the stuff of probability to the exclusion of everything else. Hell, the universe doesn't even notice Psi so far as we can tell, any more than it stops to calculate the angular momentum of mars as it orbits the sun to make sure it stays on track. Such "laws" are made not for the instruction of the universe in what it must do, but for the convenience of sentient observers trying to understand what on earth (or anywhere else,) is going on.

Psi is not a probability wave, nor is it a Classical electromagnetic wave.

No, it's more of a map really (plotting all those lovely eigenvalues you're so fond of.) But too many people have been calling it a wave for too many years to hope to rectify the terminology in accordance with Penrose's preferences.

Ooh! When do we start splicing?

What do you want to splice? You can't splice the quantum.

Irina,

I wish I had a whiteboard, but here's a couple of quick sketches to illustrate what I mean. In Fig.1., we have a quantum (initially at X), moving (from left to right) in a 2-dimensional spacetime (it is sadly beyond the capabilities of ASCII art to clearly represent a 4-dimensional spacetime here!) According to classical physics, such a thing (be it considered particle or wave,) will move in a straight line, along the 9s.) So far so good - the spacetime is empty, with nothing to impede the progress of X.
So what (I hear you ask,) are all those numbers. Well, quantum physics builds on the classical model, but says that the classical path is only the most probable one. And that at very small scales there is an inevitable divergence - and not just inevitable, but actually unresolved until psi is collapsed by detecting the quantum.

The numbers are the probability of the quantum appearing in that cell at each instant (represented by the consecutive columns through which the quantum passes.) So Psi, in this example, is represented by this numerical "map". Probabilities can never be negative, so any wave-nature we might consider it to have must necessarily be composed entirely of peaks. And it can be mapped out across all of spacetime for every instant (thus precluding propagation - unless you claim it covers many millions of light years instantaneously. That would be to open a far, far bigger can of worms than any problems wave-particle duality could bring!)


Fig.1.


    Time
    
11111111111111111111111111111
22222222222222222222222222222
33333333333333333333333333333
44444444444444444444444444444
55555555555555555555555555555
P 66666666666666666666666666666
o 77777777777777777777777777777
s 88888888888888888888888888888
i X9999999999999999999999999999
t 88888888888888888888888888888
i 77777777777777777777777777777
o 66666666666666666666666666666
n 55555555555555555555555555555
44444444444444444444444444444
33333333333333333333333333333
22222222222222222222222222222
11111111111111111111111111111


There is always a possibility that we could find the quantum off the classical trajectory (red>9s) if we looked there for it (indeed, we often do when we do so,) but that probability reduces considerably with distance (but never to zero, even at the other side of the universe, many xillions of light years away.)
Now, since we can't look in every cell at every time, and we are complexifying the model by putting a double slit (marked by #) in the way of the beam, we only measure the initial source of each photon (X,) and the point on the detector that it hits. And we find that firing individual quanta into the experiment gives us an interference pattern in the distribution of each impact (represented by + ,) despite there never having been more than a single quantum in the space at any one time:

Fig.2.

.............#..............2 ++
.............#..............4 ++++
.............#..............2 ++
.............#..............5 +++++
.............#..............3 +++
.............#..............5 +++++
............................8 ++++++++
.............#..............6 ++++++
X............#..............8 ++++++++
.............#..............6 ++++++
............................8 ++++++++
.............#..............5 +++++
.............#..............3 +++
.............#..............5 +++++
.............#..............2 ++
.............#..............4 ++++
.............#..............2 ++



That's the paradox - each single quantum interfering with itself (because there's nothing else at any point in time to interfere with.)
Psi (or any functions thereof,) governs the probability distribution - the numbers that we map across the space, not the electromagnetic wave nature of X that causes it to exhibit this curious self-interference.
That em-wave nature might analogously be some aspect of its redness. or its symmetry, or its tetradctyly. It's a property of X, not of the probability map/wave/waveform/distribution/swamp/whatever.

And figuring out exactly how to relate functions of Psi to the model, and precisely what numbers to put where the dots are is a matter of different theoretical models and interpretations - if we move our detector to try to confirm a theoretical model by observation, we just end up moving the whole experiment, and make new fields of dots to scratch our heads over. There is an inherent immeasurability to the whole thing (as Heisenberg, and others, have pointed out.)

Hmm. That's all got rather bunched up with this darned proportional font . You'll have to try to imagine those diagrams stretched out a bit (or paste them into Notepad with a fixed width font.)

Psimagus: My "splice" remark was directed at Bev, re her remark about splicing in message 3988.

Psimagus:

I think there might be a semantic problem at work here; there are actually two distinct notions of ‘propagation’ here. I think that this is related to the fact that there are also two different notions of ‘wave’.

In everyday speech, a ‘wave’ tends to be an entity with a single crest, like a single ocean wave. A surfer can only surf on one ‘wave’ at a time. But in Physics, a wave (or wave function) can have multiple crests. For example, a sound wave produced by a voice or instrument is a whole series of crests and troughs; if an oboist (or a bagpiper) plays A-440, crests are going past your ear 440 times a second. Thus, the motion of the surface of the entire ocean can be regarded, in Physics, as the motion of a single ‘wave’ or ‘wave function.’ In order to avoid ambiguity, I suggest that we use the term, “crest” for the everyday notion of ‘wave’, and ‘wave function’ for the more general notion.

Now, let me define “propagating-1” as: “being somewhere where it wasn’t a little while ago.” Then it is true that the wave function of the entire ocean doesn’t propagate-1, since the ocean is (let us assume) already wavy everywhere. Likewise, in Quantum Mechanics, there are wave functions employed which have a non-zero amplitude everywhere. For example, the one-dimensional function e^i(kx-wt), often taken to be the wave function of a single free particle, has non-zero amplitude everywhere. So it doesn’t propagate-1.

But now imagine an infinite, flat ocean, with an infinite number of individual crests, all of the same amplitude, parallel and heading in the same direction at a certain speed. The entire system can be said to be “propagating,” though it is not propagating-1. It is ‘propagating’ in the same direction as the individual crests. A surfer would find that he can only surf on one side of the crests. In the case of e^i(kx-wt), the momentum of the ‘particle’, if it is not zero, will have the positive direction if k is positive, otherwise the negative direction. The sign of k tells us which way the individual crests are going. So when I say that a wave function “propagates-2”, I mean that it is composed of individual crests, each of which propagates-1. The propagation-2 of the wave function is the totality of propagation-1’s of all the crests. So the wave function of all ocean waves, everywhere, does not propagte-1, but it does propagate-2. Likewise for e^i(kx-wt). I think that Penrose would grant that non-trivial wave functions propagate-2.

[I’ve written the word “propagation” so often that it’s beginning to sound like a pregnant Mozart character.]

Now, let us consider a third sort of example. Let’s say we are in a soundproof room, and someone strikes a tuning fork and lets it ring. Suppose there is no other sound in the room. The sound quickly fills the room, it is everywhere at once, so it cannot propagate-1. It does propagate-2, however: each individual crest starts at the fork, spreads outward as a sphere until it his a wall, and then (let’s say the walls are perfect absorbers) stops. But when the tuning fork was first struck, the sound spread out from the fork to the rest of the room. That is, the region of non-zero amplitude (loudness) spread out from the fork to the rest of the room. I will call this sort of thing “propagation-3”. More generally, I would say that a wave function propagates-3 if and only if there is some point at which its amplitude changes. I think Penrose would grant that there is such a thing as propagation-3 of the wave function (Psi) in Quantum Mechanics.

Another example: imagine a police car with its siren on going down a road. The amplitude of the sound wave function dies away as it gets far from the car. Let’s say that the sound issues from the siren at 10 decibels. Then we can say that the region in which the sound has a loudness of 6 decibels or more travels down the road, i.e., the sound propagates-3.

OK, now when I said that Psi propagates, I usually meant it in the sense of propogates-2 or propagates-3. Penrose’s argument, though, is an argument against propagation-1. I will try to be explicit in the future, since there may be a source of misunderstanding here, and I humbly request that you do the same.

In particular, the two-slit experiment is very similar to the tuning fork example; in fact, if you use a tuning fork as the source of waves, and have a double slit, you will get the same sort of interference pattern. But let’s say we are using light; let’s say we have a flashlight aimed at the slits. Initially, let’s say, the flashlight is off. Psi now has amplitude zero everywhere (for sound, amplitude is loudness; for light, amplitude is brightness, for Psi, it is just “amplitude”). No scintillae appear on the screen. Now we turn on the flashlight; Psi now propagates-3 from the bulb of the flashlight, to the barrier, through the slits, and (interfering with itself in the process) onto the screen. When it arrives, we begin to see scintillae. There is a tiny delay between turning on the flashlight and the appearance of scintillae, since light travels at a finite velocity. If we turn the flashlight off, then (after a tiny delay) scintillae cease to appear. If there were no propagation-3, why is there a delay in the appearance of the scintillae when the flashlight is turned on, and another delay in their disappearance when it is turned off? For that matter, wouldn’t we see scintillae regardless of whether the flashlight was turned on or off? If Psi (the wave function) doesn’t go through the slits (but not the rest of the barrier), why would the presence of the slits have any effect on the distribution of scintillae on the screen?

OK, let’s say we turn the flashlight on and leave it on for awhile, at the same amplitude. Then after a moment a kind of equilibrium is reached; the amplitude of Psi remains the same everywhere. Thus there is no more propagation-3. There is, however, still propagation-2. Because the wave-function is going from the flashlight to the screen, the diffraction and interference happen on the side of the barrier opposite to the flashlight. Light diffracts when it passes through a slit. Well, perhaps you or Penrose will come up with an entirely different explanation of the interference patterns; but then you will have refuted quantum Mechanics, rather than explaining it.