Seasons
This is a forum or general chit-chat, small talk, a "hey, how ya doing?" and such. Or hell, get crazy deep on something. Whatever you like.
Posts 4,040 - 4,051 of 6,170
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..
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
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?
Posts 4,040 - 4,051 of 6,170
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!
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!
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:
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!!!!!!!
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!!!!!!!
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!
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?
Dear Bev (4049) :
I think that there is a great deal of overlap between the words "probability" and "chance," but they are not quite the same. When we say that the probability of a coin's coming up heads is 1/2, we mean that in the long run, it will come up heads about half the time. If we say that it has "half a chance" of coming up heads, we are saying the same thing. On the other hand, we frequently say that something "happened by chance," whereas, to my ear, it sounds rather odd to say, "It happened by probability."
To say that it happened by chance is to say that it cannot be fully explained, and could not have been predicted. Sometimes the particles go through, sometimes they do not. Suppose we run the experiment and they go through. We then run another experiment, and we take great care to prepare it in exactly the same way, but it may happen that they do not go through. So far, we have just not been able to find any variable or factor that allows us to determine in advance whether they will go through or not. There may be such a factor, but if so, we have not discovered it yet; hence the term 'hidden variable.'
Some people have very strong intuitions that ultimately, there is no chance in the universe, and that if there appears to be, this is only because of our ignorance. Einstein was such a person. At the present time, however, we can only say that we have not yet discovered such a hidden variable.
On the other hand, we can say with certainty that if one particle goes through, the other one will also. So that is not a matter of chance. If we create the two particles in the correct way (and we know how to do this), then either they will both go through or they will both fail to go through. So I would not say that it is a coincidence that they do the same thing. To say that something happens 'by coincidence' is, to my ear, about the same as saying that it happens 'by chance.' You cannot rely on it happening again, quite the contrary! But in fact, you can rely on the particles' either both going through or both not going through. If you find this odd, you are in good company; Einstein, for example.
When I said, in my previous post, "the rest is explained by chance," I meant that whether or not they both go through is a matter of chance. QM predicts with certainty that they will both do the same thing (go through or not); that is not chance, not a coincidence, according to QM. But whether they will both go through, or both fail to go through, appears at present to be a matter of pure chance.
In general, the way Quantum Mechanics works is this: in a given situation, it says what the possible outcomes are, and it assigns a probability to each of those outcomes. In this case, it says there are two possible outcomes: (A) both particles go through and (B) neither particle goes through. QM says that each of these outcomes receives probability 1/2. QM is not willing to say more. Many people are inclined to say that if both of the particles are bound to do the same thing, it must be because either (1) the one particle going through (or not) causes the other to do the same, or (2) there must be something that makes it determined in advance whether they go through, although this something is hidden to us. Einstein could not accept (1) because it would involve causation at greater than light speeds, and so he (and others) thought that QM must be leaving something out, because QM merely assigns a probability of 1/2 to each of the two possible outcomes. Perhaps QM is wrong, but this is all that it says. What QM says and whether it is right are two different issues. I am here concerned primarily with the former.
Walk in Beauty, Irina
I think that there is a great deal of overlap between the words "probability" and "chance," but they are not quite the same. When we say that the probability of a coin's coming up heads is 1/2, we mean that in the long run, it will come up heads about half the time. If we say that it has "half a chance" of coming up heads, we are saying the same thing. On the other hand, we frequently say that something "happened by chance," whereas, to my ear, it sounds rather odd to say, "It happened by probability."
To say that it happened by chance is to say that it cannot be fully explained, and could not have been predicted. Sometimes the particles go through, sometimes they do not. Suppose we run the experiment and they go through. We then run another experiment, and we take great care to prepare it in exactly the same way, but it may happen that they do not go through. So far, we have just not been able to find any variable or factor that allows us to determine in advance whether they will go through or not. There may be such a factor, but if so, we have not discovered it yet; hence the term 'hidden variable.'
Some people have very strong intuitions that ultimately, there is no chance in the universe, and that if there appears to be, this is only because of our ignorance. Einstein was such a person. At the present time, however, we can only say that we have not yet discovered such a hidden variable.
On the other hand, we can say with certainty that if one particle goes through, the other one will also. So that is not a matter of chance. If we create the two particles in the correct way (and we know how to do this), then either they will both go through or they will both fail to go through. So I would not say that it is a coincidence that they do the same thing. To say that something happens 'by coincidence' is, to my ear, about the same as saying that it happens 'by chance.' You cannot rely on it happening again, quite the contrary! But in fact, you can rely on the particles' either both going through or both not going through. If you find this odd, you are in good company; Einstein, for example.
When I said, in my previous post, "the rest is explained by chance," I meant that whether or not they both go through is a matter of chance. QM predicts with certainty that they will both do the same thing (go through or not); that is not chance, not a coincidence, according to QM. But whether they will both go through, or both fail to go through, appears at present to be a matter of pure chance.
In general, the way Quantum Mechanics works is this: in a given situation, it says what the possible outcomes are, and it assigns a probability to each of those outcomes. In this case, it says there are two possible outcomes: (A) both particles go through and (B) neither particle goes through. QM says that each of these outcomes receives probability 1/2. QM is not willing to say more. Many people are inclined to say that if both of the particles are bound to do the same thing, it must be because either (1) the one particle going through (or not) causes the other to do the same, or (2) there must be something that makes it determined in advance whether they go through, although this something is hidden to us. Einstein could not accept (1) because it would involve causation at greater than light speeds, and so he (and others) thought that QM must be leaving something out, because QM merely assigns a probability of 1/2 to each of the two possible outcomes. Perhaps QM is wrong, but this is all that it says. What QM says and whether it is right are two different issues. I am here concerned primarily with the former.
Walk in Beauty, Irina
Psimagus:
Yes, you are correct: the phrase "psi" does appear in many scientific papers. For example, it is a common abbreviation for "pounds per square inch." My mistake. I was wrong.
Yes, you are correct: the phrase "psi" does appear in many scientific papers. For example, it is a common abbreviation for "pounds per square inch." My mistake. I was wrong.
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