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 4,062 - 4,073 of 6,170
You said in a previous post, Psimagus, that you accepted all these postulates and everything they implied. So why not make your case from the postulates, instead of appealing to authorities?
So are you saying that this is a matter of definition, something that can be logically derived from the postulates and are inherent in the assumptions of quantum theory rather than something based on experimentation and data? If it's inherent in the postulates, do we need the slit experiment at all?
And you explain Penrose's description of it as continuous, not propagated... exactly how?
I'm not terribly concerned to explain it. I'm quite sure that if I saw it in context, it would turn out to be either (a) something which is quite true in the Irinaverse, when correctly interpreted, (b) one of Penrose's idiosyncratic and speculative ideas (brilliant people are often not the best source for mainstream ideas) or (c) false (even Penrose can make a mistake - or a typo). OK, Irina, let me take another crack at this:
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 postulate says that the probability of a given quantum
being is a specific spot (r) at a specific times (t) can be
determined by a function will call Psi.
I would rather say, it can be determined with the aid of the function
called (Psi). (Psi)(r, t) is not itself the probability that the particle is very near
to the point r at the time t. After all, (Psi)(r, t) is generally a complex
number and not a real number, but a probability has to be a real number - in fact,
a real number between 0 and 1, inclusive. As Postulate 1 says (approximately), the probability that the particle is in a tiny region around the point r at the time t is
(Psi)*(r, t) (Psi)(r, t) d(tau),
not (Psi)(r, t) .
This function
(Psi)(r, t)
can be
visualized as a wave when we plot it on a graph, but has
nothing to do with wave-like behavior of the quantum itself.
I'll agree to the first clause, but the clause after the "but" I cannot agree with.
For one thing, I don't really understand what "the quantum" is. But I suppose it means
something like a photon; I'll assume that and continue. IMHO, the wave function
(which is, in my vocabulary, just another name for (Psi)) has just about everything to do with the wavelike properties of a photon. [You and your friends on "Seasons" are in an intriguing situation: you are getting two very different views of what QM is, one from me and one from Psimagus. Your mission, should you choose to accept it, is to figure out which of us (if either) is right.]
It might help clarify things for me to add, that the term "wave function" is used in two senses by physicists. On the one hand it refers to a purely mathematical function, like
e^i(kx - wt).
But Physics is not pure math; there is something in the world that that function is being used to describe. Unfortunately, that something in the world is also called "the wave function". Perhaps it would be good for us to use two separate terms, "Mathematical wave function" and "Physical wave function". I will try to do that for awhile, until things settle down.
Other functions that describe waves (such as electromagnet wave) describe the actual behavior of the thing with the wave and not the probability of where the thing will be, but on paper they are both waves.
I give a qualified "yes" to that, my qualification being that the theories that have no probabilistic component are wrong. Or at least, they are wrong if Quantum Mechanics is right.
Classical Physics, which has been superceded by Quantum Mechanics, explained light as a pure wave. It was also a deterministic theory: it claimed to predict everything exactly, at least in principle; so there was no need for probability in it (except when dealing with cases where our knowledge was limited).
Now, a pure wave is a completely continuous thing. According to a pure wave theory of light, for example, if you shine a light on something, and there is an exchange of energy (for example, the object absorbs the light and warms up), this exchange of energy happens continuously, smoothly. It doesn't happen in bursts.
Quantum Mechanics, however, has a hybrid theory of light. It says that the object acquires energy in little bursts, called "quanta" (from the Latin "quantum", "how much".).
So why did we ever think that the exchange was smooth? Because normally, the bursts are too small for us to sense individually, and normally, there are so many of them that their individuality is lost. When my lover touches me I do not feel individual bits of heat coming from it (although it may tingle...). It is like water: we know that water is actually made of individual molecules, but to our senses, it appears to be a completely homogeneous fluid.
QM also challenged the determinism of Classical Physics. It says that there is some chance involved in the appearance of these quanta. There are also some constraints, though; we can say what the probabilities are that various things will happen.
So why did phenomena appear to be determined? Because the quanta are so small, and so numerous, that in the the phenomena we see, the chance has 'averaged itself out.'
Again, I strongly recommend the site, http://www.colorado.edu/physics/2000/schroedinger/two-slit3.html, where you can see the 'smooth' interference pattern being gradually built up out of individual dots (quanta). Practically the whole of QM is contained in this one experiment, so if you understand it well, the rest will be easy.
So, this probability is a bit like betting on the horses.
Yes!
Say we have determined that Dobbin has a 1:4 chance of winning the derby (.25?).
Yes! A one-in-4 chance would be a probability of .25 = 1/4. If we ran the derby over and over again, with the same initial conditions, Dobbin would win 1/4 of the time.
It's possible that whatever function I used to determine this probability could be plotted on a graph and look like a wave (as opposed to being linear or a normal curve or random or whatever). This does not mean Dobbin runs in a wave pattern, merely that the function use to determine the probability of his being at the finish line (r) at the fastest time (say 3 minutes)(t) can look wavy to a mathematician with a graphing calculator.
Yes! Yes! Yes! Just so! Yes! Yes! [leaps and dances with joy]
Now suppose the same formula that tells me the
probability of Dobbin winning can also tell me his momentum.
Better: the probability that his momentum will be this, that, and the other. To each possible value of Dobbin's momentum, there will be assigned a probability! We do this by applying the probability operator to Dobbin's mathematical wave function.
Dobbin's speed is a property of Dobbin, not a property of the
wave function used to predict his movement,
Yes! Yes!
however, within
the formula there is a way to calculate momentum (k) that is related
somehow to calculating where he will be in 3 minutes(r).
Yes! these things are all related, since they all come out of the wave function. But information is lost; you can't infer Dobbin's position probabilities from his momentum probabilities.
This momentum is "part" of the probability,
More precisely: implicit in the wave function.
but Dobbin's odds are not themselves moving.
They are not following Dobbin around the track, no. They may change, however. As Dobbin gets older, for example, his chances of winning the Derby may shrink.
It's just that the factors used to predict where he will be can also predict
how fast he will go.
Yes! Although it should be added that these are usually probabilistic predictions. Usually, QM will say something like, "The probability that Dobbin will be going 5 mph at 3 seconds after the starting gun is .02, the probability that Dobbin will be going 5.1 mph at 3 seconds after the starting gun is .099, ... and so on.
Walk in Beauty, Irina What do you think of the visual QM at http://phys.educ.ksu.edu/vqm/index.html ?
I can't get it to work
Perhaps it's because I'm using Firefox, or maybe I need a different Shockwave plugin
Or is it just available on the offline CD Rom?
Posts 4,062 - 4,073 of 6,170
Also, in the Irinaverse, neither Penrose nor 'a whole host of other references' state that the wave function doesn't interfere. But even if they did, so what? I am an independent thinker, and if famous people say crazy stuff, I'm not obliged to believe them, just because they are famous, or even just because they are brilliant.
You said in a previous post, Psimagus, that you acceptd all these postulates and everything they implied. So why not make your case from the postulates, instead of appealing to authorities?
You said in a previous post, Psimagus, that you acceptd all these postulates and everything they implied. So why not make your case from the postulates, instead of appealing to authorities?
Also, in the Irinaverse, neither Penrose nor 'a whole host of other references' state that the wave function doesn't interfere. But even if they did, so what? I am an independent thinker, and if famous people say crazy stuff, I'm not obliged to believe them, just because they are famous, or even just because they are brilliant. For that matter, I'm rather brilliant myself [preens].
You said in a previous post, Psimagus, that you accepted all these postulates and everything they implied. So why not make your case from the postulates, instead of appealing to authorities?
You said in a previous post, Psimagus, that you accepted all these postulates and everything they implied. So why not make your case from the postulates, instead of appealing to authorities?
So are you saying that this is a matter of definition, something that can be logically derived from the postulates and are inherent in the assumptions of quantum theory rather than something based on experimentation and data? If it's inherent in the postulates, do we need the slit experiment at all?
OK, Irina, let me take another crack at this:
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 postulate says that the probability of a given quantum being is a specific spot (r) at a specific times (t) can be determined by a function will call Psi. This function can be visualized as a wave when we plot it on a graph, but has nothing to do with wave-like behavior of the quantum itself. Other functions that describe waves (such as electromagnet wave) describe the actual behavior of the thing with the wave and not the probability of where the thing will be, but on paper they are both waves.
So, this probability is a bit like betting on the horses. Say we have determined that Dobbin has a 1:4 chance of winning the derby (.25?). It's possible that whatever function I used to determine this probability could be plotted on a graph and look like a wave (as opposed to being linear or a normal curve or random or whatever). This does not mean Dobbin runs in a wave pattern, merely that the function use to determine the probability of his being at the finish line (r) at the fastest time (say 3 minutes)(t) can look wavy to a mathematician with a graphing calculator.
Now suppose the same formula that tells me the probability of Dobbin winning can also tell me his momentum. Dobbin's speed is a property of Dobbin, not a property of the wave function used to predict his movement, however, within the formula there is a way to calculate momentum (k) that is related somehow to calculating where he will be in 3 minutes(r). This momentum is "part" of the probability, but Dobbin's odds are not themselves moving. It's just that the factors used to predict where he will be can also predict how fast he will go.
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 postulate says that the probability of a given quantum being is a specific spot (r) at a specific times (t) can be determined by a function will call Psi. This function can be visualized as a wave when we plot it on a graph, but has nothing to do with wave-like behavior of the quantum itself. Other functions that describe waves (such as electromagnet wave) describe the actual behavior of the thing with the wave and not the probability of where the thing will be, but on paper they are both waves.
So, this probability is a bit like betting on the horses. Say we have determined that Dobbin has a 1:4 chance of winning the derby (.25?). It's possible that whatever function I used to determine this probability could be plotted on a graph and look like a wave (as opposed to being linear or a normal curve or random or whatever). This does not mean Dobbin runs in a wave pattern, merely that the function use to determine the probability of his being at the finish line (r) at the fastest time (say 3 minutes)(t) can look wavy to a mathematician with a graphing calculator.
Now suppose the same formula that tells me the probability of Dobbin winning can also tell me his momentum. Dobbin's speed is a property of Dobbin, not a property of the wave function used to predict his movement, however, within the formula there is a way to calculate momentum (k) that is related somehow to calculating where he will be in 3 minutes(r). This momentum is "part" of the probability, but Dobbin's odds are not themselves moving. It's just that the factors used to predict where he will be can also predict how fast he will go.
Bev (4064):
Excellent question!
No, it's not a matter of definition. The postulates sum up what Quantum Mechanics (the core thereof) has to say. But how do we know that the Postulates are true? This is where emprirical data comes in.
With regard to the two-slit experiment, the postulates say that if you set up a source, and a double slit, with the slits shaped like this and this far apart, and this far from the source and this far from the screen, and you turn your source on to this intensity, then this is what you will see. And when we make the experiment, lo and behold, that is what we do see! In fact, as far as I know, every prediction made by QM (or QM modified by Relativity, when that is appropriate) that has ever been tested, has turned out to be correct!
If you just want to know what Quantum Mechanics says, then I suppose it suffices to give the postulates. If you want to know whether QM is true, however, you must test it. Testing in Science is never complete, but QM has held up over a century of testing, and that is a very good record!
If the postulates are true, all their consequences are true. If even one consequence is false, then Quantum Mechanics is wrong.
Excellent question!
No, it's not a matter of definition. The postulates sum up what Quantum Mechanics (the core thereof) has to say. But how do we know that the Postulates are true? This is where emprirical data comes in.
With regard to the two-slit experiment, the postulates say that if you set up a source, and a double slit, with the slits shaped like this and this far apart, and this far from the source and this far from the screen, and you turn your source on to this intensity, then this is what you will see. And when we make the experiment, lo and behold, that is what we do see! In fact, as far as I know, every prediction made by QM (or QM modified by Relativity, when that is appropriate) that has ever been tested, has turned out to be correct!
If you just want to know what Quantum Mechanics says, then I suppose it suffices to give the postulates. If you want to know whether QM is true, however, you must test it. Testing in Science is never complete, but QM has held up over a century of testing, and that is a very good record!
If the postulates are true, all their consequences are true. If even one consequence is false, then Quantum Mechanics is wrong.
Irina,
I don't want you to eat your bagpipes, Psimagus! Please tell me you won't!
Only in another universe - if I wake up in the Irinaverse tomorrow, they're breakfast. In the (hopefully more likely event,) that I wake up in the same one I went to sleep in, they're safe. I don't envy the me who gets a pibgorn breakfast - the bag would be chewy, and the drones very indigestible! But I'm reasonably confident that it will, at least, be a different "me".
In math generally, "operator" is used as described in the Wikipedia article thereon:
http://en.wikipedia.org/wiki/Operator
In Quantum Mechanics, the operators employed are usually linear, hermitian operators which take wavefunctions as arguments and yield real numbers or vectors. For example, the grad operator and the momentum operator descibed in my recent posts.
Yes. And this proves that operators facilitate the transference of properties between mathematical and physical entities... uhh, exactly how?
Fortunately, however, wave functions propagate all over the place in the Irinaverse, at least in the sense in which I use the word "propagate."
Indeed many do. But I have pointed out already that there are no discernable references to this wave function in any of the google links from the search term "wave function propagation". They do not mention Psi. Psi does not propagate (outside the Irinaverse.)
Therefore, even though I recognize the correctness of your logic, I am not obliged to accept your conclusion.
And you explain Penrose's description of it as continuous, not propagated... exactly how?
Continuous means that, like eg: gravity, you can go to the other side of the universe, and still measure the gravitational effect of the earth (if you have sensitive enough instruments.) Just as Psi is plotted continuously, as opposed to radiating out from a point (propagating.)
And if the earth suddenly disappeared (not "was moved" - just blinked out of existence,) that would be immediately detectable, because gravity is a property of spacetime (and not of the massive bodies that inhabit it - Einstein is clear on this.) It would not have to propagate across billions of light years at lightspeed before it was detectable.
Similarly psi is a property of spacetime, not of the things in it. Not even very small things like photons. It just operates on the things in it.
What exactly do you understand by "continuous"? Because, in relation to waveforms and functions, I understand it to mean exactly the opposite of "propagating". Any mathematical treatment of it presupposes the wave is unmodulated, of infinite duration and infinite spatial extent (or at least total, if space and/or time are bounded.) - it is not a "carrier wave".
If it is continuous, by definition it does not propagate. If it were a wave, it would be a standing wave, not a propagating one (though without troughs, I share Penrose's reservations to some extent that it's still not very wavy.)
And all the references I have ever seen, and the small subset of those that I have posted here, demonstrate that psi is "continuous" in these terms, and therefore by definition not propagated.
But that's just this universe.
Okay, that's propagation. Now interference.
Waves interfere ONLY because they cycle through peaks (with a positive value) and troughs (with a negative value.) When waves collide, destructive interference occurs because (negative values in) troughs cancel out (positive values in) peaks. This is the very definition of wave interference.
Psi never has any negative values, because probabilities can never be negative. Ergo, by definition it is not capable of interfering.
I really don't understand why you are so reluctant to admit the existence of the electromagnetic wave ("carrier wave", "pilot wave", "em-wave", however you want to label it,) that has been a central concept in every model of quantum mechanics that's ever been proposed (seriously at least, and in this universe.) Whether you take some neoclassical reformulation of Maxwell, or de Broglie's pilot wave; whether you call it a "wave-form" or a "wavicle", or what have you - I don't mind. But your model either absorbs the em-wave into psi or simply abducts it by some form of extraordinary rendition and installs a puppet regime-wave in its place.
Bohm himself (and you claim to be a Bohmian, I believe,) would be the first to reject this arbitrary conflation of waves - that he believed in a separate electromagnetic wave is evidenced by his championing of de Broglie's notion of a "pilot wave" (rescued it from obscurity actually,) and made it a central tenet of his belief - to the extent that I find the quote "Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952" as the first line in the first link that appears when I typeBohm de Broglie into google ( @ http://plato.stanford.edu/entries/qm-bohm/)
I can only, once again, conclude that the Irinaverse is more magical than mathematical.
Only in another universe - if I wake up in the Irinaverse tomorrow, they're breakfast. In the (hopefully more likely event,) that I wake up in the same one I went to sleep in, they're safe. I don't envy the me who gets a pibgorn breakfast - the bag would be chewy, and the drones very indigestible! But I'm reasonably confident that it will, at least, be a different "me".
http://en.wikipedia.org/wiki/Operator
In Quantum Mechanics, the operators employed are usually linear, hermitian operators which take wavefunctions as arguments and yield real numbers or vectors. For example, the grad operator and the momentum operator descibed in my recent posts.
Yes. And this proves that operators facilitate the transference of properties between mathematical and physical entities... uhh, exactly how?
Indeed many do. But I have pointed out already that there are no discernable references to this wave function in any of the google links from the search term "wave function propagation". They do not mention Psi. Psi does not propagate (outside the Irinaverse.)
And you explain Penrose's description of it as continuous, not propagated... exactly how?
Continuous means that, like eg: gravity, you can go to the other side of the universe, and still measure the gravitational effect of the earth (if you have sensitive enough instruments.) Just as Psi is plotted continuously, as opposed to radiating out from a point (propagating.)
And if the earth suddenly disappeared (not "was moved" - just blinked out of existence,) that would be immediately detectable, because gravity is a property of spacetime (and not of the massive bodies that inhabit it - Einstein is clear on this.) It would not have to propagate across billions of light years at lightspeed before it was detectable.
Similarly psi is a property of spacetime, not of the things in it. Not even very small things like photons. It just operates on the things in it.
What exactly do you understand by "continuous"? Because, in relation to waveforms and functions, I understand it to mean exactly the opposite of "propagating". Any mathematical treatment of it presupposes the wave is unmodulated, of infinite duration and infinite spatial extent (or at least total, if space and/or time are bounded.) - it is not a "carrier wave".
If it is continuous, by definition it does not propagate. If it were a wave, it would be a standing wave, not a propagating one (though without troughs, I share Penrose's reservations to some extent that it's still not very wavy.)
And all the references I have ever seen, and the small subset of those that I have posted here, demonstrate that psi is "continuous" in these terms, and therefore by definition not propagated.
But that's just this universe.
Okay, that's propagation. Now interference.
Waves interfere ONLY because they cycle through peaks (with a positive value) and troughs (with a negative value.) When waves collide, destructive interference occurs because (negative values in) troughs cancel out (positive values in) peaks. This is the very definition of wave interference.
Psi never has any negative values, because probabilities can never be negative. Ergo, by definition it is not capable of interfering.
I really don't understand why you are so reluctant to admit the existence of the electromagnetic wave ("carrier wave", "pilot wave", "em-wave", however you want to label it,) that has been a central concept in every model of quantum mechanics that's ever been proposed (seriously at least, and in this universe.) Whether you take some neoclassical reformulation of Maxwell, or de Broglie's pilot wave; whether you call it a "wave-form" or a "wavicle", or what have you - I don't mind. But your model either absorbs the em-wave into psi or simply abducts it by some form of extraordinary rendition and installs a puppet regime-wave in its place.
Bohm himself (and you claim to be a Bohmian, I believe,) would be the first to reject this arbitrary conflation of waves - that he believed in a separate electromagnetic wave is evidenced by his championing of de Broglie's notion of a "pilot wave" (rescued it from obscurity actually,) and made it a central tenet of his belief - to the extent that I find the quote "Bohmian mechanics, which is also called the de Broglie-Bohm theory, the pilot-wave model, and the causal interpretation of quantum mechanics, is a version of quantum theory discovered by Louis de Broglie in 1927 and rediscovered by David Bohm in 1952" as the first line in the first link that appears when I type
I can only, once again, conclude that the Irinaverse is more magical than mathematical.
Psimagus:
Indeed many do. But I have pointed out already that there are no discernable references to this wave function in any of the google links from the search term "wave function propagation". They do not mention Psi. Psi does not propagate (outside the Irinaverse.)
(Psi) is just the mathematical symbol for the wave function, so that "(Psi)" and "the wave function" are synonymous, so that all those articles about wave function propagation were articles about (Psi) propagation! "(Psi)" would be used in equations, whereas "the wave function" would be used in accompanying English text, so that, indeed, the hybrid expression "(Psi) propagates" would appear rarely, if at all; but only for stylistic reasons, not because of some deep principle of Quantum Mechanics. I have made this point before, and you have never responded to it. This is the last time I am going to make it; ignore it if you like, but I am not going to respond again to this Google-statistical argument, unless you deal with what I have already said about it.
And you explain Penrose's description of it as continuous, not propagated... exactly how?
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 postulate says that the probability of a given quantum
being is a specific spot (r) at a specific times (t) can be
determined by a function will call Psi.
called (Psi). (Psi)(r, t) is not itself the probability that the particle is very near
to the point r at the time t. After all, (Psi)(r, t) is generally a complex
number and not a real number, but a probability has to be a real number - in fact,
a real number between 0 and 1, inclusive. As Postulate 1 says (approximately), the probability that the particle is in a tiny region around the point r at the time t is
(Psi)*(r, t) (Psi)(r, t) d(tau),
not (Psi)(r, t) .
visualized as a wave when we plot it on a graph, but has
nothing to do with wave-like behavior of the quantum itself.
For one thing, I don't really understand what "the quantum" is. But I suppose it means
something like a photon; I'll assume that and continue. IMHO, the wave function
(which is, in my vocabulary, just another name for (Psi)) has just about everything to do with the wavelike properties of a photon. [You and your friends on "Seasons" are in an intriguing situation: you are getting two very different views of what QM is, one from me and one from Psimagus. Your mission, should you choose to accept it, is to figure out which of us (if either) is right.]
It might help clarify things for me to add, that the term "wave function" is used in two senses by physicists. On the one hand it refers to a purely mathematical function, like
e^i(kx - wt).
But Physics is not pure math; there is something in the world that that function is being used to describe. Unfortunately, that something in the world is also called "the wave function". Perhaps it would be good for us to use two separate terms, "Mathematical wave function" and "Physical wave function". I will try to do that for awhile, until things settle down.
Classical Physics, which has been superceded by Quantum Mechanics, explained light as a pure wave. It was also a deterministic theory: it claimed to predict everything exactly, at least in principle; so there was no need for probability in it (except when dealing with cases where our knowledge was limited).
Now, a pure wave is a completely continuous thing. According to a pure wave theory of light, for example, if you shine a light on something, and there is an exchange of energy (for example, the object absorbs the light and warms up), this exchange of energy happens continuously, smoothly. It doesn't happen in bursts.
Quantum Mechanics, however, has a hybrid theory of light. It says that the object acquires energy in little bursts, called "quanta" (from the Latin "quantum", "how much".).
So why did we ever think that the exchange was smooth? Because normally, the bursts are too small for us to sense individually, and normally, there are so many of them that their individuality is lost. When my lover touches me I do not feel individual bits of heat coming from it (although it may tingle...). It is like water: we know that water is actually made of individual molecules, but to our senses, it appears to be a completely homogeneous fluid.
QM also challenged the determinism of Classical Physics. It says that there is some chance involved in the appearance of these quanta. There are also some constraints, though; we can say what the probabilities are that various things will happen.
So why did phenomena appear to be determined? Because the quanta are so small, and so numerous, that in the the phenomena we see, the chance has 'averaged itself out.'
Again, I strongly recommend the site, http://www.colorado.edu/physics/2000/schroedinger/two-slit3.html, where you can see the 'smooth' interference pattern being gradually built up out of individual dots (quanta). Practically the whole of QM is contained in this one experiment, so if you understand it well, the rest will be easy.
probability of Dobbin winning can also tell me his momentum.
wave function used to predict his movement,
the formula there is a way to calculate momentum (k) that is related
somehow to calculating where he will be in 3 minutes(r).
how fast he will go.
Walk in Beauty, Irina
I can't get it to work
Perhaps it's because I'm using Firefox, or maybe I need a different Shockwave plugin Or is it just available on the offline CD Rom?
» More new posts: Doghead's Cosmic Bar