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.
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Well, I feel obliged to announce that my ideas on Quantum Mechanics have reached a bit of a crisis.
I take it the quantum computing book has arrived then?
It's a shame though - I was really looking forward to a wave-based qubit model
***OK, skip this if you aren't into the jargon: a set of values, one for each of the eigenvalues of all the operators in some complete commuting set of observables, or, otherwise put,***
But how do you view the eigenvalues? Are they anything more than a mathematical device to explain what we observe, or do you see them as describing something that is causally "real"?
what is actually going on, whether we know it or not. For example, Schroedinger's cat is always either alive or dead, it can't be half-and-half, although the probability that it is alive may be only 1/2, relative to certain initial conditions.
Agreed. Not least because cats are a) conscious observers in their own right, and b) far too large to exhibit such quantum behaviour (at survivable temperatures anyway.) The trouble with all analogies is that they're apt to be taken overliterally.
On the other hand, as you know, I have recently argued that quantum particles need not exist in between "source" and "target".
But, as the wave function propagates, it always gives probabilities for position of the particle. ***The position operator is always defined for it.***
It is psi that gives the probability, and this is never a negative value, thus cannot act in true "wave" fashion to exhibit destructive interference. Nor does it propagate. The em-wave nature of the quantum does propagate and interfere.
Since the equations for these two "waves" (note common parlance in the case of the pseudo-wavefunction psi,) are not amenable to typing in plain ASCII here, I've uploaded a copy I copy+pasted from the windows character map tohttp://www.be9.net/QUANTUM.JPG - I still have to insist that they are separate phenomena.
So my realist requirement forces me to maintain that the particle has a definite position at each moment.
That would be to go further than I would
I think it only need be definite when we "catch one out" and make it show us the location. Like by putting a couple of slits in the path of the beam. Or a cloud chamber.
Since my realism is more important to me than whatever motivated me to deny the existence of the particle in-between, I will accept the existence of the particle in-between. My position is now close to, or perhaps identical with, that of David Bohm.
Progress
I still do not feel obliged to accept that the particle travels along an unbroken path, however. In fact, I still think that the phenomenon of quantum tunneling shows that this cannot be so.
That certainly depends how we define "unbroken". I agree it evidently can't travel in a classical trajectory like a billiard ball along a 1-dimensional line. Any such model forcibly applied, would be necessarily broken all over the place.
It seems we have to allow our definition of "trajectory" (and any continuity it may possess,) to include a rather "fatter" structure - a tube, or somesuch, with a cross-sectional area defined by psi, and length calibrated by (in this case,) the fixed velocity c at which the quantum passes down it. And until we take a peek, the location is anywhere and/or everywhere in the cross-section corresponding to the time the quantum passes through it. So it's not even like a pea in a hose (that would be to take the anology over-literally, I fear,) - if that cross-sectional area happens to straddle a barrier, there's a chance we can catch the quantum on the wrong side of it (even though we know it cannot have passed through it.) The whole thing is strange and counterintuitive sorcery, but I don't think we have any fundamental disagreement over "trajectory" or "unbroken" (and I'm happy to dispense with the words if you prefer.)
Unless you have any radical disagreement with either "anywhere" or "everywhere" (or "and/or")
Posts 3,928 - 3,939 of 6,170
I guess beer will do that to you too, but it's not as classy, and much more gassy..as the old poem goes.
Ernest Dowson
Poet (1867- 1900)
"Absinthe makes the Tart grow fonder"
Ernest Hemingway
Author (1899-1961)
"Got tight last night on absinthe. Did knife tricks."
Paul Marie Verlaine
Poet (1844-1896)
"[In] Paris where the beer is awful, it was upon absinthe that I threw myself, absinthe day and night".
Emile Zola
Novelist and critic (1840-1902)
"Boche had known a joiner who had stripped himself stark naked in the Rue Saint-Martin and died doing the polka - he was an absinthe drinker".
Oscar Wilde
Playwright, writer, and bon viveur (1854-1900)
"A glass of absinthe is as poetical as anything in the world. What difference is there between a glass of absinthe and a sunset?"
Ernest Dowson
Poet (1867- 1900)
"Absinthe makes the Tart grow fonder"
Ernest Hemingway
Author (1899-1961)
"Got tight last night on absinthe. Did knife tricks."
Paul Marie Verlaine
Poet (1844-1896)
"[In] Paris where the beer is awful, it was upon absinthe that I threw myself, absinthe day and night".
Emile Zola
Novelist and critic (1840-1902)
"Boche had known a joiner who had stripped himself stark naked in the Rue Saint-Martin and died doing the polka - he was an absinthe drinker".
Oscar Wilde
Playwright, writer, and bon viveur (1854-1900)
"A glass of absinthe is as poetical as anything in the world. What difference is there between a glass of absinthe and a sunset?"
Well, I feel obliged to announce that my ideas on Quantum Mechanics have reached a bit of a crisis. On the one hand, my realist proclivities urge me to say that in addition to a quantum state, which gives probabilities of various outcomes, a quantum system also has, at any time during which it exists, a quantum status, consisting of
***OK, skip this if you aren't into the jargon: a set of values, one for each of the eigenvalues of all the operators in some complete commuting set of observables, or, otherwise put,***
what is actually going on, whether we know it or not. For example, Schroedinger's cat is always either alive or dead, it can't be half-and-half, although the probability that it is alive may be only 1/2, relative to certain initial conditions.
On the other hand, as you know, I have recently argued that quantum particles need not exist in between "source" and "target".
But, as the wave function propagates, it always gives probabilities for position of the particle. ***The position operator is always defined for it.*** So my realist requirement forces me to maintain that the particle has a definite position at each moment.
Since my realism is more important to me than whatever motivated me to deny the existence of the particle in-between, I will accept the existence of the particle in-between. My position is now close to, or perhaps identical with, that of David Bohm.
I still do not feel obliged to accept that the particle travels along an unbroken path, however. In fact, I still think that the phenomenon of quantum tunneling shows that this cannot be so.
Walk in Beauty, Irina
***OK, skip this if you aren't into the jargon: a set of values, one for each of the eigenvalues of all the operators in some complete commuting set of observables, or, otherwise put,***
what is actually going on, whether we know it or not. For example, Schroedinger's cat is always either alive or dead, it can't be half-and-half, although the probability that it is alive may be only 1/2, relative to certain initial conditions.
On the other hand, as you know, I have recently argued that quantum particles need not exist in between "source" and "target".
But, as the wave function propagates, it always gives probabilities for position of the particle. ***The position operator is always defined for it.*** So my realist requirement forces me to maintain that the particle has a definite position at each moment.
Since my realism is more important to me than whatever motivated me to deny the existence of the particle in-between, I will accept the existence of the particle in-between. My position is now close to, or perhaps identical with, that of David Bohm.
I still do not feel obliged to accept that the particle travels along an unbroken path, however. In fact, I still think that the phenomenon of quantum tunneling shows that this cannot be so.
Walk in Beauty, Irina
I take it the quantum computing book has arrived then?
It's a shame though - I was really looking forward to a wave-based qubit model
But how do you view the eigenvalues? Are they anything more than a mathematical device to explain what we observe, or do you see them as describing something that is causally "real"?
Agreed. Not least because cats are a) conscious observers in their own right, and b) far too large to exhibit such quantum behaviour (at survivable temperatures anyway.) The trouble with all analogies is that they're apt to be taken overliterally.
But, as the wave function propagates, it always gives probabilities for position of the particle. ***The position operator is always defined for it.***
It is psi that gives the probability, and this is never a negative value, thus cannot act in true "wave" fashion to exhibit destructive interference. Nor does it propagate. The em-wave nature of the quantum does propagate and interfere.
Since the equations for these two "waves" (note common parlance in the case of the pseudo-wavefunction psi,) are not amenable to typing in plain ASCII here, I've uploaded a copy I copy+pasted from the windows character map to
That would be to go further than I would
I think it only need be definite when we "catch one out" and make it show us the location. Like by putting a couple of slits in the path of the beam. Or a cloud chamber.Progress
That certainly depends how we define "unbroken". I agree it evidently can't travel in a classical trajectory like a billiard ball along a 1-dimensional line. Any such model forcibly applied, would be necessarily broken all over the place.
It seems we have to allow our definition of "trajectory" (and any continuity it may possess,) to include a rather "fatter" structure - a tube, or somesuch, with a cross-sectional area defined by psi, and length calibrated by (in this case,) the fixed velocity c at which the quantum passes down it. And until we take a peek, the location is anywhere and/or everywhere in the cross-section corresponding to the time the quantum passes through it. So it's not even like a pea in a hose (that would be to take the anology over-literally, I fear,) - if that cross-sectional area happens to straddle a barrier, there's a chance we can catch the quantum on the wrong side of it (even though we know it cannot have passed through it.) The whole thing is strange and counterintuitive sorcery, but I don't think we have any fundamental disagreement over "trajectory" or "unbroken" (and I'm happy to dispense with the words if you prefer.)
Unless you have any radical disagreement with either "anywhere" or "everywhere" (or "and/or"
)
Dear Psimagus:
you write:
It is psi that gives the probability, and this is never a negative value, thus cannot act in true "wave" fashion to exhibit destructive interference.
Psi gives the probability, but it isn't itself the probability. One gets the probability of (e.g.) the particle's being in a given spatial region by integrating Psi*Psi, the square of the modulus of (normalized) Psi, over the region [Psi* being the complex conjugate of Psi (yes, Bev, I am a great fan of complex conjugation)]. This gives a positive real number betweeen zero and one, as desired for a probability. Psi itself, however, is not so restricted. In fact, Psi typically takes on complex values. Therefore, there is no problem with Psi exhibiting characteristically wavish phenomena such as diffraction and interference.
you write:
I have been trying to understand a tiny bit of what you are talking about..I looked up QM for dummies and ran into this
To take the two-slit example, we never see electrons dematerialize, or rippling through something, we just find it necessary to think that they do to explain the pattern that we see on the screen. If we deliberately try to observe where the electrons go, we see them as particles somewhere else, but the interference pattern disappears. In effect, the problem is that we cannot say what the particles look like only when they cannot be seen.
Now this is an uncomfortable thought, because all our instincts tell us that particles must be somewhere, even when we cannot see them. But if quantum mechanics can accurately describe all the information we can ever obtain about the outside world, perhaps we are simply being greedy to ask for anything more. The headline "Physics Fails to Describe Events That Cannot Be Observed" is, again, rather lacking in impact.
So ..where is the somewhere else?
To take the two-slit example, we never see electrons dematerialize, or rippling through something, we just find it necessary to think that they do to explain the pattern that we see on the screen. If we deliberately try to observe where the electrons go,
Now this is an uncomfortable thought, because all our instincts tell us that particles must be somewhere, even when we cannot see them. But if quantum mechanics can accurately describe all the information we can ever obtain about the outside world, perhaps we are simply being greedy to ask for anything more. The headline "Physics Fails to Describe Events That Cannot Be Observed" is, again, rather lacking in impact.
So ..where is the somewhere else?
Actually, there is another option I could take, which as far as I can see is not inconsistent. I could have it both ways - be a realist and still claim that particles have no trajectories at all. But I would have to treat position values different from the others, and this would seem to be rather ad hoc. Or maybe not - I'm thinking now that I should retreat (for the time being) to agnosticism on this point until I have investigated in more detail the advantages and disadvantages of various options.
If I had to take a stand this moment, though, I would say that being a realist doesn't force me to believe that there is always a fact of the matter concerning the eigenvalues of some complete commuting set of observables.
So, I must be dragged, kicking and screaming, back to that quasi-orgasmic (according to Bev, message 3917) state of working on a problem. Ah, the sacrifices I make!
If I had to take a stand this moment, though, I would say that being a realist doesn't force me to believe that there is always a fact of the matter concerning the eigenvalues of some complete commuting set of observables.
So, I must be dragged, kicking and screaming, back to that quasi-orgasmic (according to Bev, message 3917) state of working on a problem. Ah, the sacrifices I make!
In fact, here's another problem: the eigenvalues of which complete commuting set of observables constitute the status? It seems that any selection must be arbitrary. Yes, I must clearly take lots of time to think this through.
Wait, no, the realist doesn't have to say which set, just that there is one! And it needn't include position! [whimpers]
A realist doesn't have to deny that our knowledge is limited. In particular, our ability to predict is limited by the probabilistic nature of Quantum Phenomena. [moans]
Oh, Prob123! You've come to join me!
Well, I haven't seen that particular discussion, but often in discussion of the two-slit experiment, the author says, "OK, now what happens if we close one slit? then we'll know that the electron went through the open slit, so we'll know exactly where it was at that moment."
Let me back up for a moment. If the electron were a classical or commonsense particle, it would travel in a straight line, and so what you would expect to see on the screen would be two little rectangles, one from particles that went through slit A, and one for particles that went through slit B. [Shudders with pleasure.] If we saw a single scintillum, it would be easy to tell which slit the particle that made it had gone through. [sighs]
But instead, we get a complicated pattern that looks just like a wave interference pattern, so if we think of classical or common-sense particles, tiny and traveling in straight lines, it seems that most of them must have been radically deflected somehow.
Well, I haven't seen that particular discussion, but often in discussion of the two-slit experiment, the author says, "OK, now what happens if we close one slit? then we'll know that the electron went through the open slit, so we'll know exactly where it was at that moment."
Let me back up for a moment. If the electron were a classical or commonsense particle, it would travel in a straight line, and so what you would expect to see on the screen would be two little rectangles, one from particles that went through slit A, and one for particles that went through slit B. [Shudders with pleasure.] If we saw a single scintillum, it would be easy to tell which slit the particle that made it had gone through. [sighs]
But instead, we get a complicated pattern that looks just like a wave interference pattern, so if we think of classical or common-sense particles, tiny and traveling in straight lines, it seems that most of them must have been radically deflected somehow.
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