Seasons

Dear Prob123:
Re yur message 4013:
Sorry to take so long getting back to you. You wrote:
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!
I think it is not quite right to say that "if you change one of those states, then by definition, you must also change the state in the other system it is entangled with." I think I see why the author said that, however.
The simple, archetypal entanglement scenario is something like this: two particles (let's say they are photons) are simultaneously created, with opposite spins (you don't have to know what spin is, just that it has two values, traditionally called "spin up" and "spin down."). They fly off in opposite directions. Then each one comes to a diffraction grating, which is a device sensitive to spin. They arrive at precisely the same time. It either allows the particle to pass, or allows the particle to go through. The gratings are, in fact, set so that each particle will have 1/2 a chance of going through. And, when the experiment is repeated, this is exactly what happens: in the long run, each grating permits about half the particles that come to it to go through. But QM cannot predict, in any specific case, whether they will go through or not; it only says that the probability is 1/2.
What is odd is this: in each simultaneously created pair, the one goes through if and only if the other goes through. It never happens that the one goes through and the other does not.
Imagine that two people each take a coin from a common source, go off at some distance to each other, and flip their coins simultaneously. The coins are presumably fair, so each one has 1/2 a chance of getting heads. And, sure enough, they do, but it also happens that whenever one gets 'heads', the other does as well. That would suggest that the two coins were connected in some way (hence the term 'entanglement'). There are two ways that this might occur: (1) somehow, one coin's coming up heads (or not) would cause the other coin to come up heads (or not), and (2) each pair of coins might have been set to go through (or not) in advance. Analogously, there are two ways one might explain the coincidence in the case of the two particles: (1) somehow, one particle's going through the grating (or not) would cause the other particle to go through the grating (or not), and (2) each pair of coins might have been set to go through (or not) in advance.
Einstein had, however, convinced everyone that no causal influence could travel faster than light. Since the two events at the gratings occur simultaneously, and some distance apart, neither one could cause the other. So (1) is not an option. That leaves (2), which is plausible since the two particles have a common origin (you can't just take any two particles and do this).
Einstein thought that this showed that Quantum Mechanics was incomplete. To abbreviate his reasoning somewhat: there must have been something about the two particles that determined in advance whether they would go through or not. Otherwise, why would they always do the same? But QM cannot predict whether a specific particle would go through or not. It only says that there is a chance of 1/2 that they will. Therefore, Einstein (and others) concluded, there is something about the particles that QM is unable to account for, and QM is, therefore, incomplete.
From the conclusion that the particles always do the same thing, I think someone leapt to the conclusion that if you somehow forced the one particle to go through, then the other particle would also. At least, that is what the statement, "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." But I don't think the two particles are that intimately connected, according to QM. If they were, they would genuinely break Einstein's prohibition on faster-than-light communication. You could send a message to me instantaneously by forcing the particle at your end to go through (or not), thus forcing the other one to do the same. I would observe the other one, thus receiving the message.
Does this make sense? Does it answer your question? Do you have more questions?

Walk in Beauty, Irina

Dear Bev:
Thanks for your note!
You wrote:
Thanks Psimagus and Irina. Irina I promise to do more reading and check the sites. It's not that they aren't good sites, it's just that I don't always stop to follow up on them, and then the discussion moves on.

I did know what Ø was in terms of it being a Greek letter*, but it's good that you explained it because there are probably others reading who don't ask as many questions as I do. My background is Psychology (BS), law (JD but in another sense, also BS) and a Masters in Teaching (MAT but also BS in the same way as the JD**). As you can see, I'm rather well versed in BS without much in the way of "hard science" and only the required math (which tends to be statistics). It doesn't matter though, because we have all ranges of people who read these posts, so if you explain some basics that I happen to know, I am sure someone will be happy you did.

I found Psimagus' checkerboard analogy to be helpful. I also think in understand the dual slit experiment. If I understand the central issue here we are trying to determine the best way to predict the movement of quanta over spacetime. We are talking about a model which works for large number of quanta in a "best fit" sort of way, but which does not necessarily apply to one specific quantum. Your man Schroedinger wrote an equation about this while I was out looking for chocolate bunnies.

It may be there is some level of equivocation going on in the debate, so I am glad I asked you to define the terms.


I agree about the equivocation. Psimagus seems to use several words in quite a different sense from mine. This makes it difficult to see when there is really disagreement. As my attempts to forge a common vocabulary with Psimagus have failed, I have decided to simply describe everything in my own language, and express my own opinions, and leave Psimagus to do the same for himself. I believe that my language is the same as physicists normally use, but as you know he disagrees. Feel free to ask me for definitions at any time.


It seems that Irina and Psimagus disagree as to how Ø should be used as it applies to Schreodinger's equation and quantum physics. Also, Irina says that predicting quantum movement can be done based on standard wave function (propagation). Is that it?


Roughly, yes. I'm afraid that I believe that many things that Psimagus has said are false, or expressed in non-standard terminology, or both. I don't think there is any point in my arguing with him about it, however, for this has led nowhere in the past. I leave it to each of you to decide for him/herself who (if either) is right.

* I was once in an honorary fraternity called ØX but we never discussed quantum physics. Also, to me Ä means defendant more often than it means change and ð stands for plaintiff, not 3.14.

** When you think of my background, think of Mel Brooks' History of the World, specifically the scene withe the Roman unemployment office. "Oh, you area BS artist. Have you BSed today? Did you try to BS today?"

Bev: Oops, some of your Greek letters got mysteriously shifted.

What I would like to do nowis go through the six postulates of Quantum Mechanics and try to explain them in non-mathematical terms, or at least less-mathematical terms.

OK, let's see what happens to the notation when I try to paste postulate 1 in here. Hmm, yes, I don't know how to get all those special symbols into a Forge chat box, so I will have to paraphrase. You can see what I am doing by comparing with the original. I represent the Greek letter Psi (which looks sort of like a trident) by "(Psi)", and the Greek letter tau, which looks sort of like a flattened "t") by "(tau)". I have omitted the footnotes.

Here begins the excerpt:

Postulates of Quantum Mechanics

In this section, we will present six postulates of quantum mechanics. Again, we follow the presentation of McQuarrie [1], with the exception of postulate 6, which McQuarrie does not include. A few of the postulates have already been discussed in section 3.

Postulate 1. The state of a quantum mechanical system is completely specified by a function (Psi)(r,t) that depends on the coordinates of the particle(s) and on time. This function, called the wave function or state function, has the important property that
(Psi)*(r,t)(Psi)(r,t) is the probability that the particle lies in the volume element located at at time (Psi)*(r,t)(Psi)(r,t)d(tau) .
The wavefunction must satisfy certain mathematical conditions because of this probabilistic interpretation. For the case of a single particle, the probability of finding it somewhere is 1, so that we have the normalization condition


(110) [Integrate from negative infinity to infinity](Psi)*(r,t)(Psi)(r,t)d(tau)(Psi)*(r,t)(Psi)(r,t)d(tau)


It is customary to also normalize many-particle wavefunctions to 1.

The wavefunction must also be single-valued, continuous, and finite.

(end of paraphrase)

OK, that should give you the idea of my notation. In the next posting I will go through the postulate step by step, trying to explain it in less technical terms. Something will of course be lost in such a translation. I urge - no, I beg - you to ask questions!

But I don't think the two particles are that intimately connected, according to QM. Ok, not faster than light, but they are connected some how aren't they? or technologies relying on quantum entanglement that are now being developed would be impossible, and a waste of time. Isn't there research being done on quantum cryptography, using entangled particles to transmit signals that cannot be eavesdropped and the work on quantum computation..

RATS! I just realized that there's an error in my paraphrase, and it's too late to edit - hold on, I will redo it. But first:

Prob123 (4043):

Yes, you are absolutely right that the sort of phenomenon I just described has actually been verified, and that people hope to use it in cryptography. For although you can't control whether the particles go through, you can observe whether they go through or not, and you know that your confederate at the other end is seeing the same thing. So if you have a prior agreement on how to use a binary number as a key, you can send a message with that as key. Now, if you had sent him a key over a phone line or whatever, there would always be a possibility that someone would tap the line and get it. But here there is no line to tap - no message is being sent, since it would have to be faster than light.
Now, if you agree with Einstein that there must be something about the particles that determines in advance whether they go through or not, then you are what is known as a 'hidden variables' theorist. The idea is that there is some variable x whose value is (say) 0 or 1, and if x is 1 the particle will go through, and that if x is 0 it will not. But this variable is not taken into account in Quantum Mechanics.

Some people have developed 'hidden variable' theories, notably David Bohm, but they have not been able to predict whether the particle goes through or not. so their theories are not really any stronger than QM. They say, "Yes, there is a hidden variable," but they do not tell us how to measure it in practice. So their theories are not really any stronger than QM. Furthermore, certain recent theoretical results (Google on "Bell's Theorem") suggest that 'hidden variables' theories would have to pay a very steep price - that they would have other bizarre qualities, at least as bizarre as entanglement. So there is no great rush to abandon QM.

OK, now I'm going to cross into IMHO territory. IMHO, what QM says is that after the two particles have been created, but before they strike the gratings, the quantum state of the system is an equal superposition of two states: a state in which they both go through, and a state in which neither goes through. Saying that it is an "equal superposition" of the two means, that each of them has an equal chance of happening, and that nothing else has any chance at all of happening. Well, it's like a coin which has a 1/2 chance of landing heads, and a 1/2 chance of landing tails: it's going to do one or the other.

As you may recall, I wrote (message 3048) of two alternatives to explain why the particles always do the same thing: (1) one particle's going through causes the other to go through (superluminal message), and (2) whether the particle goes through or not is determined before it hits the grating (hidden variables). But the situation I just described is, IMHO, a third possibility. QM says: "Either (a) they both go through or (b) they both don't. Each one has .5 probability. The rest is up to chance." Then chance decides which. There is no faster-than-light message, as in (1), but whether the particles go through is not determined in advance, as in (2). We don't need superluminal messages or hidden variables.

Is this clear? Do you have any questions?


Walk in Beauty, Irina

OK, I will now correct message 4042:

OK, let's see what happens to the notation when I try to paste postulate 1 in here. Hmm, yes, I don't know how to get all those special symbols into a Forge chat box, so I will have to paraphrase. You can see what I am doing by comparing with the original. I represent the Greek letter Psi (which looks sort of like a trident) by "(Psi)", and the Greek letter tau, which looks sort of like a flattened "t") by "(tau)". I have omitted the footnotes.

Here begins the excerpt:

Postulates of Quantum Mechanics

In this section, we will present six postulates of quantum mechanics. Again, we follow the presentation of McQuarrie [1], with the exception of postulate 6, which McQuarrie does not include. A few of the postulates have already been discussed in section 3.

Postulate 1. The state of a quantum mechanical system is completely specified by a function (Psi)(r,t) that depends on the coordinates of the particle(s) and on time. This function, called the wave function or state function, has the important property that
(Psi)*(r,t)(Psi)(r,t) is the probability that the particle lies in the volume element d(tau) located at r at time t.

The wavefunction must satisfy certain mathematical conditions because of this probabilistic interpretation. For the case of a single particle, the probability of finding it somewhere is 1, so that we have the normalization condition


(110) [Integrate from negative infinity to infinity](Psi)*(r,t)(Psi)(r,t)d(tau)(Psi)*(r,t)(Psi)(r,t)d(tau)


It is customary to also normalize many-particle wavefunctions to 1.

The wavefunction must also be single-valued, continuous, and finite.

(end of paraphrase)

OK, that should give you the idea of my notation. In a posting to come soon I will go through the postulate step by step, trying to explain it in less technical terms. Something will of course be lost in such a translation. I urge - no, I beg - you to ask questions!

Unfortunately, something has come up, and I won't be able to get to my detailed commentary for several hours. I do,however, have time for the following:

Dear Bev:

I'm sorry if my remark about splicing was out of line. But you can't blame me for being intrigued by someone whose name is the standard abbreviation for BILLION ELECTRON VOLTS!!!!!!!

Bev: Oops, some of your Greek letters got mysteriously shifted.

There should be a paradigm shift joke in there somewhere, but very few people would get it anyway.

Freaky weird. I tell you, Schroedinger's chocolate bunny lives in the PF forums and plays with the posts!

But the situation I just described is, IMHO, a third possibility. QM says: "Either (a) they both go through or (b) they both don't. Each one has .5 probability. The rest is up to chance." Then chance decides which. There is no faster-than-light message, as in (1), but whether the particles go through is not determined in advance, as in (2). We don't need superluminal messages or hidden variables.

Is this clear? Do you have any questions?
Yes, what is the difference between probability and chance? If there is a .5 probability, is there also a .5 chance? When you say "the rest is explained by chance," you lost me. Do you mean it's a coincidences that we see a spooky effect?