Seasons

To all:

Is anyone other than Psimagus and I interested in these QM posts? I don't want to take up huge amount of Seasons space if it's not of general interest. I've seen responses from other people in the past, so I've assumed that there is boader interest, but don't hesitate to say so if you feel crowded out.

I find them interesting.

Psimagus (3991):

[Classical Electromagnetic Theory is] Not wrong, just incomplete.

No, wrong. Max Planck invented his eponymous constant because Classical Electromagnetic Theory gave the wrong predictions for blackbody radiation. CET also said that electrons orbiting the nucleus of an atom should constantly radiate energy, and hence fall into the nucleus. CET gave the wrong predictions for the Photoelectric Effect. CET implies that all energy in the electromagnetic field would eventually drift into the high frequencies. Any example of tunnelling is a refutation of CET.

Prob123:

I actually know one guy who uses the term, "testosterone poisoning." But only one. He might use it to explain why, for example, so many more young men die in car crashes than young women.
I'm sorry if my remark contributed to some negative stereotype of females. I didn't intend it to, but that's no excuse.

Irina, I think anyone who doesn't want to read up on the QM stuff will just learn to read around. It's a perfectly legitimate topic for Seasons. I do find it interesting even if I can only follow about half of it. My Physics studies stopped at the end of Year 11 when I decided Literature was more my thing.

Thanks, Prob123. Please do not hesitate to ask questions, make comments, etc.. I want to learn how to express myself clearly.

Thanks, Corvin. Perhaps I can express myself in a more accessible way. That's what I'm trying to do when I compare Psi to ocean waves, operatic soprano sounds, and the like.

Irina,

In everyday speech, a ‘wave’ tends to be an entity with a single crest, like a single ocean wave.

Indeed, this is mere colloquial usage, and no physics, classical or otherwise.

A surfer can only surf on one ‘wave’ at a time. But in Physics, a wave (or wave function) can have multiple crests.

MUST have multiple crests, and troughs.

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.’

If it were all a single wave, that might be the case. But it is, in fact, a lot of different waves interfering with each other. There is, I would suggest, no feasible model that can regard the surface of even a relatively small area of the ocean as a single wave - there are currents and tides pulling in different directions all the time. The surf simultaneously breaks in diametrically opposed directions on either side of an island, after all.

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.

I had assumed that was what we were doing, since these are the proper terms.
Or at least that we were calling a wave a "wave" and a crest a "crest", in accordance with the accepted scientific terminology.

Irina,

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.

I hesitate to flatly contradict you, but I have to say that my understanding of Maxwell's e^i(kx-wt) has always been that it in fact describes propagating waves that do inevitably have an amplitude of zero at the points between each crest and trough, and trough and crest. A sinewave's amplitude cannot pass from a positive "crest" value to a negative "trough" value without passing through zero. Or are you proposing some sort of sawtooth wave? That would be a novelty!

I fear you are mixing this up with Psi again - Psi has a non-zero amplitude everywhere, precisely because it has no troughs (and thus has only fluctuations of positive values,) and is continuous. (And is only debatably a wave at all.)
If you have been dabbling with Hawking Radiation (I'm second guessing the source of confusion here - please ignore this if you haven't,) the zero-value is merely delayed by the acceleration exerted on the infalling particle by the black hole. It's effectively stuck with a crest that's stretching as fast as the particle is falling, until the black hole eventually evaporates in a few trillion years. Then the next trough will appear, the wave having been redshifted to within a gnat's crotchet of its life. But it's still a wave, and still with a trough to come, necessitating a point of zero amplitude at the transition from crest to trough. Just as there had been between the previous trough and the crest that stretched. This is the only scenario I have ever come across where a photon experiences an extended period of non-zero amplitude, but it is not non-zero "everywhere".

I confess - I don't know where to even begin with "being somewhere where it wasn’t a little while ago" so I won't, if you don't mind.
Propagation is propagation - it is not a massively complex concept (alright, it has some potentially abstruse ramifications, but the basic principle is unproblematic.)

There's a handy set of animations @ http://id.mind.net/~zona/mstm/physics/waves/propagation/huygens1.html and a good overview of the principles @ http://www.fas.org/man/dod-101/navy/docs/es310/propagat/Propagat.htm that I would recommend.

And (I hesitate to mention, lest the multicoloured, 3-dimensional undulations should overexcite you, but it's too good a toy to keep to myself,) a most entertaining java applet @
http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=35
which demonstrates the electric and magnetic components of the wave excellently.

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”.

Oh God - please Irina, not a third form of propagation! This is still a sinewave, propagating in classical fashion. It is just propagation, not propagation-n.
The soundwave has peaks (oh alright, crests then,) and troughs - if it's ringing A-440, then there are 880 instances of zero amplitude per second, between each peak and each trough, and then that trough and the next peak. At a lower frequency, you'd hear them, but that's way above the auditory flicker fusion threshold.

There is no "region" of non-zero amplitude floating in the room like some cloud of noise, surrounded by zero-amplitude calm. The zero and non-zero amplitudes combined are the noise.

Irina,

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

No. Psi is already defined, continuously across the universe for all the quanta which are currently contained in the flashlight (as well as for every other quantum that exists in the universe.) Some of these quanta, currently in the flashlight, will be excited into a high enough energy state to burst out of the bulb's filament when an electric current is applied to it, but they are still there, being probability-mapped continuously even before they do so. Psi never has an amplitude of zero, since there is always a possibility that it might suddenly turn up at the other end of the universe if we collapse the waveform by looking for it. It is just that the probability is ridiculously low (and always positive.) It is a genuinely "non-zero amplitude" phenomenon (and as such, nothing like the em-wave.)

(for sound, amplitude is loudness; for light, amplitude is brightness,

That is rather an oversimplification. Amplitude is the height of one peak + the depth of one trough. It can vary if modulated, and you can take any average you like to describe it, or specify a point and measure the point-instant value (+ive if it happens to be in a peak, -ive if in a trough.) But the loudness and brightness are not constant - they just appear to be because our brains cannot resolve that many fluctuations a second. Very low frequency noises are resolvable, which is why they discernably pulsate - you can hear the loud peaks and troughs, and also the quiet ~zero-amplitude crossover points.

for Psi, it is just “amplitude”). No scintillae appear on the screen.

It is the electromagnetic wave (and I don't mind if you describe it with Maxwell's e^i(kx-wt) or deBroglie's http:/www.be9.net/QUANTUM.JPG Fig.1,) NOT Psi that has the amplitude, is fired at the target, does the diffracting, and hits the detector causing a scintillum.
I can only repeat - Psi is merely a mathematical function that gives us a probability for every other location in the universe that, on collapsing the waveform, that particular quantum will be found there.

Every quantum in the universe can be described with its own Psi "map", which always covers the whole universe as a constant matrix of probabilities. It doesn't take a million years to "reach" a point a million light years away. In principle the (absurdly low) probability of it resolving to that point when we collapse the waveform can be calculated any time we like. That's what I mean when I say it's constant. If it propagated that probability value would have to shoot off at light-speed and take a million years to get there, just like an em-wave.

Any notion of amplitude we might ascribe to Psi is a very different one from any "proper" wave, since it has no troughs and doesn't propagate - the values are better described as eigenstates, I think.

Now we turn on the flashlight; Psi now propagates-3 from the bulb of the flashlight, to the barrier, through the slits, and

No, it is the electromagnetic wave that propagates, not Psi.

(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.

Yes. And Psi doesn't travel at all - it's already everywhere. And fluctuates instantaneously, for example, when the flashlight is turned on and a whole load of quanta get energised enough to form a stream of photons. Each one's Psi value for the point a million light years off changes instantly. It suddenly gets a tiny bit more likely they'll turn up there if the waveform's collapsed, since they have been energised (it is still VERY unlikely though!) Unless you're seriously going to propose faster-than-light propagation, the accepted continuous distribution model seems like a much smaller can of worms.

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?

Because it is the electromagnetic wave that propagates, not Psi.

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?

Because it is the electromagnetic wave that goes through the slits, not Psi.

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.

of the electromagnetic wave, not Psi.

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 electromagnetic wave is going from the flashlight to the screen, not Psi.
    
the diffraction and interference happen on the side of the barrier opposite to the flashlight. Light diffracts when it passes through a slit.

Yes, light does. Sound does. Water does. But probability doesn't any more than happiness or bad luck.

Well, perhaps you or Penrose will come up with an entirely different explanation of the interference patterns;

No need to - it is the standard model, and needs no explaining if you distinguish the electromagnetic wave from the probability. Please Irina, give me a single reference to support the wave diffraction of Psi from anywhere. An example of how hard such a thing is to find - I've just spent an hour searching google, and I'm sorry to say that not even the flat-earthers or perpetual motion enthusiasts seem to entertain the notion:

<-1>Your search - "diffraction of Psi" - did not match any documents.
Your search - "Psi diffracts" - did not match any documents.
Your search - "Psi diffracting" - did not match any documents.
Your search - "Psi is diffracted" - did not match any documents.
Your search - "Psi was diffracted" - did not match any documents.
Your search - "Psi will diffract" - did not match any documents.
Your search - "Psi will be diffracted" - did not match any documents.
Your search - "Psi had been diffracted" - did not match any documents.
Your search - "Psi would be diffracted" - did not match any documents.
Your search - "Psi would have been diffracted" - did not match any documents.
Your search - "Psi diffraction"... bingo! 13 matches! Unfortunately in some, "Psi" stands for "porous silicon", and has nothing whatsoever to do with probability, and in all the others refers to "tilt angle"s and "lattice parameters" in crystallography (they also use most of the rest of the Greek alphabet,) and nothing at all to do with probability.
"Psi diffracted" Another 2 Matches! ... ditto unrelated to probabilities.

All the above repeated with a single "f", eg: "difract" - no further matches.

All the above, replacing "psi" with the greek letter that won't paste in here - 7 more matches for "/Psi/ diffraction" - all, on closer examination, referring to crystallography.<0>

Google's not the Word of God, I know, but I find the deafening silence out there on this topic rather telling.


You have a wonderfully creative mind, and an elegant, almost poetic model of the universe. I just don't think it's this universe

Ok, another QM question..found this..is it true?

Now, if two quantum states are "entangled" then if you change one of those states, then by definition, you must also change the state in the other system it is entangled with. For example, atomic particles like electrons have a mysterious property called "spin" (it doesn't literally mean they are spinning). It is possible to entangle the spin of one electron with the spin of a different electron. In an electron, spin has only two possible states that we call "up" and "down" (again don't take that literally). So when two electrons are entangled like this we know that when one has "spin up", the other will always have "spin down" and vice versa.

This is interesting in itself. But it becomes even more interesting when we realise that the wavefunction doesn't imply any limitation of distance or velocity. So in theory, if one of our electrons is here, and the other entangled one is on the opposite side of the universe, then if we change the spin of the one here, the spin of the one there should also change instantaneously!