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 4,023 - 4,034 of 6,170
Well, my universe's google doesn't have any problems - 13 and a half million matches for capital Psi:
{QUOTE}
Results 1 - 100 of about 13,500,000 forΨ. (0.19 seconds)
{/QUOTE}
where? is the Greek letter /psi/, pasted in from the Windoes character map.
There is apparently a shortcut ( U+03A8 ) according to the character map, but it's easier to just copy and paste.
You need to complain to the God of the Irinaverse, or your timeline's google admin or something I think....
Results 1 - 100 of about 13,500,000 for Ψ. (0.19 seconds)
Whooah!
ΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨ<0>
Well, that's an object lesson in making assumptions as to the limitations of the Forge's character set without testing it first, and no mistake!
Well, Psimagus, in my reality, The Greek letter Psi is just the letter that is used for the wave function in equations, and anyone who has read anything about QM other than popularizations knows that.
It is used ONLY for the probability wavefunction. Not a coulomb wavefunction, not an electromagnetic wavefunction, not a water, wind, sound, shock, or any other sort of wavefunction. And it does not propagate as part of the quantum.
Of course you won't find the three-letter English word, "Psi", in technical papers.
Oh really?
{QUOTE GOOGLE}
Results 1 - 100 of about 1,220,000 for Psi wave. (0.19 seconds)
Results 1 - 100 of about 206,000 for Psi wavefunction. (0.31 seconds)
{/QUOTE GOOGLE}
Posts 4,023 - 4,034 of 6,170
Well, Psimagus, in my reality, The Greek letter Psi is just the letter that is used for the wave function in equations, and anyone who has read anything about QM other than popularizations knows that. It's the Greek letter that looks sort of like a trident or a sai. Apparently, Google does not search for the Greek letter psi when you write "psi", which is perfectly understandable. Because I don't know how to get a real Psi on the Forge chat system, I wrote it out as "Psi". Of course you won't find the three-letter English word, "Psi", in technical papers. They will use the Greek letter itself in equations, and in accompanying text they will call it the wave function, or something like that. To call attention to the absence of the English word "psi" would b (in my universe) a merely linguistic quibble and would have nothing to do with the content of QM. Similarly,
your attempt to get anything from Google for "Psi diffracts" would have been doomed to failure in my universe as well, for the same reason. Google is a very powerful tool, but if someone doesn't have a certain background knowledge in making a search, they will get strange results. In the Wikipedia article on the two-slit experiment (in my universe), it describes the two-slit experiment thus:
"A beam of light perpendicular to the X axis which propagates in the direction z encounters a screen S1 which presents a narrow (with respect to the wavelength of the ray) slit. After having passed through the slit, the wave function diffracts with an angular opening that causes it to encounter a second screen S2 which presents two slits. The successive propagation of the wave results in the formation of the interference figure on the final screen F."
[from http://en.wikipedia.org/wiki/Bohr-Einstein_debates]
Please notice that this passage ascribes both propagation and diffraction to the wave function. In fact, it describes the two-slit experiment in pretty much the same way I have been doing; but then, it is an article from my universe.
your attempt to get anything from Google for "Psi diffracts" would have been doomed to failure in my universe as well, for the same reason. Google is a very powerful tool, but if someone doesn't have a certain background knowledge in making a search, they will get strange results. In the Wikipedia article on the two-slit experiment (in my universe), it describes the two-slit experiment thus:
"A beam of light perpendicular to the X axis which propagates in the direction z encounters a screen S1 which presents a narrow (with respect to the wavelength of the ray) slit. After having passed through the slit, the wave function diffracts with an angular opening that causes it to encounter a second screen S2 which presents two slits. The successive propagation of the wave results in the formation of the interference figure on the final screen F."
[from http://en.wikipedia.org/wiki/Bohr-Einstein_debates]
Please notice that this passage ascribes both propagation and diffraction to the wave function. In fact, it describes the two-slit experiment in pretty much the same way I have been doing; but then, it is an article from my universe.
Bev,
No, it's a good question (and I wouldn't condemn you to trawl back through... good grief, it really is hundreds of posts with no forum search facility!)
What exactly is "psi" again? How does it relate to a probability amplitude wave? Sorry to make you go backwards, but when I think of the slits experiments, I keep thinking photons, and then it seems to jump to psi
I can't speak for the Irinaverse, but in my universe (which I'd like to think I'm not accidentally marooned alone in, Psi-less in Gaza,) psi is a measure of probability plotted across spacetime. It's colloquially called a "probability wave(form)", but it doesn't propagate like a regular wave.
Kee thinking about the photons - they're what's important in the functioning of the experiment, psi is only relevant in explaining the results.
Imagine the universe is a chessboard (it's a small universe.) There is a minimum unit of "stuff" (the quantum - this one's a photon, but there are others,) and a cellular structure to space time, so the quantum can only occupy a square on the chessboard. It can't straddle a line, because the squares are so small - the same size as the quantum in fact. Spacetime is digital. But quanta are tricky to pin down - in fact, until you look for them you can't tell where they are exactly. You might assume it's on B5 (because that's what the classical formulae tell you,) but it could turn out to be on B4, or B6, or C5 if you actually stuck a detector there. You get the idea. There's a lower probability that it might be more than one square away, even a very (VERY) low probability that it might turn up on G8 at the other end of the board - you don't know till you look. Psi can be calculated for every quantum's probability of being on any particular square (using Schroedinger's formula)
In this case, we've only got the one, so you could pencil in the probability values (between 0.0 and 1.0) on each square, the numbers reducing smoothly as the distance from the classically predicted point increases.
The "map" of those probabilities across the board is the "probability wave" (or "waveform", but lose the "amplitude".) It sort of looks wavy, in that the values form something like a ripple, but a) all the values are greater than 0 (so the wave has no troughs,) and b) it doesn't propagate. The values are all across the board, but the speed of light will only allow the quantum to move 1 square per time instant.
I'm going to descrine a 3-d model here - compare the difference with the 2-d model I posted before - if you can ever find it !
)
If our quantum, nominally on B5 moves into the board at a diagonal to B6 on another board behind it, representing the next time instant, all the Psi values across that board are adjusted instantly (with no need to wait for anything to travel to them at 1 square per instant.) The quantum is now nominally on B6, so it's less likely to turn up on B4 (now 2 squares away,) and more likely to turn up on B7 ( now only 1 square away from where the classical formulae tell us it must be.) Remember, these "nominal" values are where classical theory tells us they "ought" to be - it's just at a quantum scale they very often aren't. At the angle it's moving, classical physics would suggest a trajectory through a stack of boards, B5-B6-B7-B8, but the probability values on each square of each successive board would fluctuate.
Psi is just the map of these probabilities - a mathematical model. The fact that the value we've pencilled on G8 changes instantly when our quantum move a square at the other end of the board doesn't mean that there's any faster-than-light communication involved - we could only test G8 by going there. We could only communicate any discovery of our quantum there at no greater than lightspeed. But it does demonstrate that Psi can't propagate (unless it does so at greater than lightspeed,) because it's managed to adjust squares at the other end of the board in the time light travels from one square to an adjoining one.
Does that make any sense? Sorry, I haven't slept for quite a long time and my brain's not at its best to explain.
No, it's a good question (and I wouldn't condemn you to trawl back through... good grief, it really is hundreds of posts with no forum search facility!)
I can't speak for the Irinaverse, but in my universe (which I'd like to think I'm not accidentally marooned alone in, Psi-less in Gaza,) psi is a measure of probability plotted across spacetime. It's colloquially called a "probability wave(form)", but it doesn't propagate like a regular wave.
Kee thinking about the photons - they're what's important in the functioning of the experiment, psi is only relevant in explaining the results.
Imagine the universe is a chessboard (it's a small universe.) There is a minimum unit of "stuff" (the quantum - this one's a photon, but there are others,) and a cellular structure to space time, so the quantum can only occupy a square on the chessboard. It can't straddle a line, because the squares are so small - the same size as the quantum in fact. Spacetime is digital. But quanta are tricky to pin down - in fact, until you look for them you can't tell where they are exactly. You might assume it's on B5 (because that's what the classical formulae tell you,) but it could turn out to be on B4, or B6, or C5 if you actually stuck a detector there. You get the idea. There's a lower probability that it might be more than one square away, even a very (VERY) low probability that it might turn up on G8 at the other end of the board - you don't know till you look. Psi can be calculated for every quantum's probability of being on any particular square (using Schroedinger's formula)
In this case, we've only got the one, so you could pencil in the probability values (between 0.0 and 1.0) on each square, the numbers reducing smoothly as the distance from the classically predicted point increases.
The "map" of those probabilities across the board is the "probability wave" (or "waveform", but lose the "amplitude".) It sort of looks wavy, in that the values form something like a ripple, but a) all the values are greater than 0 (so the wave has no troughs,) and b) it doesn't propagate. The values are all across the board, but the speed of light will only allow the quantum to move 1 square per time instant.
I'm going to descrine a 3-d model here - compare the difference with the 2-d model I posted before - if you can ever find it !
)If our quantum, nominally on B5 moves into the board at a diagonal to B6 on another board behind it, representing the next time instant, all the Psi values across that board are adjusted instantly (with no need to wait for anything to travel to them at 1 square per instant.) The quantum is now nominally on B6, so it's less likely to turn up on B4 (now 2 squares away,) and more likely to turn up on B7 ( now only 1 square away from where the classical formulae tell us it must be.) Remember, these "nominal" values are where classical theory tells us they "ought" to be - it's just at a quantum scale they very often aren't. At the angle it's moving, classical physics would suggest a trajectory through a stack of boards, B5-B6-B7-B8, but the probability values on each square of each successive board would fluctuate.
Psi is just the map of these probabilities - a mathematical model. The fact that the value we've pencilled on G8 changes instantly when our quantum move a square at the other end of the board doesn't mean that there's any faster-than-light communication involved - we could only test G8 by going there. We could only communicate any discovery of our quantum there at no greater than lightspeed. But it does demonstrate that Psi can't propagate (unless it does so at greater than lightspeed,) because it's managed to adjust squares at the other end of the board in the time light travels from one square to an adjoining one.
Does that make any sense? Sorry, I haven't slept for quite a long time and my brain's not at its best to explain.
{QUOTE}
Results 1 - 100 of about 13,500,000 for
{/QUOTE}
where
There is apparently a shortcut ( U+03A8 ) according to the character map, but it's easier to just copy and paste.
You need to complain to the God of the Irinaverse, or your timeline's google admin or something I think....
Dear Bev:
What exactly is "psi" again? How does it relate to a probability amplitude wave? Sorry to make you go backwards, but when I think of the slits experiments, I keep thinking photons, and then it seems to jump to psi (probably because I am not really studying everything you both told me to look at). So right now, I'm the kid in the back of the class who sat through a whole hour before raising her hand to say, "I have a question....what are you talking about?"
Actually, Bev, I am really glad you wrote. You are not slowing anything down.
This is the way it is in my universe:
There is a Greek letter, which is sort of like a trident or a sai; since it is not in our alphabet, and since I don't know how to get Greek letters on Forge chat, I write "psi" instead. I am sorry if this has been confusing. You can see a "Psi" in the Schroedinger equation, the central equation of Quantum Mechanics, here:
http://scienceworld.wolfram.com/physics/SchroedingerEquation.html
In the first equation, just to the left of the equals sign, you see something that looks like a fraction, and at the right of the 'numerator' you see a letter that looks sort of like a pitchfork with the handle broken off, with a serif on the middle tine. That is an upper-case psi. But the important thing is not the letter, but what it stands for. In QM, the letter psi is the standard way to represent what is often called the "wave function' (a.k.a. wavefunction, wave vector, state vector, probability amplitude wave, etc.). I often wrote "psi" instead of "the wave function" for the sake of brevity. It's just a shorthand, like "t" for time.
Actually, Bev, I am really glad you wrote. You are not slowing anything down.
This is the way it is in my universe:
There is a Greek letter, which is sort of like a trident or a sai; since it is not in our alphabet, and since I don't know how to get Greek letters on Forge chat, I write "psi" instead. I am sorry if this has been confusing. You can see a "Psi" in the Schroedinger equation, the central equation of Quantum Mechanics, here:
http://scienceworld.wolfram.com/physics/SchroedingerEquation.html
In the first equation, just to the left of the equals sign, you see something that looks like a fraction, and at the right of the 'numerator' you see a letter that looks sort of like a pitchfork with the handle broken off, with a serif on the middle tine. That is an upper-case psi. But the important thing is not the letter, but what it stands for. In QM, the letter psi is the standard way to represent what is often called the "wave function' (a.k.a. wavefunction, wave vector, state vector, probability amplitude wave, etc.). I often wrote "psi" instead of "the wave function" for the sake of brevity. It's just a shorthand, like "t" for time.
Whooah!
ΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨΨ<0>
Well, that's an object lesson in making assumptions as to the limitations of the Forge's character set without testing it first, and no mistake!
It is used ONLY for the probability wavefunction. Not a coulomb wavefunction, not an electromagnetic wavefunction, not a water, wind, sound, shock, or any other sort of wavefunction. And it does not propagate as part of the quantum.
Oh really?
{QUOTE GOOGLE}
Results 1 - 100 of about 1,220,000 for Psi wave. (0.19 seconds)
Results 1 - 100 of about 206,000 for Psi wavefunction. (0.31 seconds)
{/QUOTE GOOGLE}
Dear Bev: (continued):
The wave function is also called the "probability amplitude wave" and sometimes the "probability wave," but these expressions are a bit imprecise.
The wave function (a.k.a. Psi) has to satisfy the Schoedinger equation, which is a form of the wave equation; hence it represents a wave, hence the term "wave function." The term "wave function" has a much more general meaning in Physics than it does in everyday language, however. It refers not only to nice regular, periodic phenomena like ocean waves, but to the result of adding together an infinite number of such waves. You can get isolated sharp spikes, for example.
The wave function is also called the "probability amplitude wave" and sometimes the "probability wave," but these expressions are a bit imprecise.
The wave function (a.k.a. Psi) has to satisfy the Schoedinger equation, which is a form of the wave equation; hence it represents a wave, hence the term "wave function." The term "wave function" has a much more general meaning in Physics than it does in everyday language, however. It refers not only to nice regular, periodic phenomena like ocean waves, but to the result of adding together an infinite number of such waves. You can get isolated sharp spikes, for example.
Dear Bev:
when I think of the slits experiments, I keep thinking photons, and then it seems to jump to psi (probably because I am not really studying everything you both told me to look at).
Well, this is what is called "wave-particle duality." Light is in some ways like a particle, in some ways like a wave. So in a complete explanation, one will sometimes be using language suggestive of waves, and at other times, language suggestive of particles. This can be confusing, since we are accustomed to thinking of these as very different sorts of things.
But before I drone on any further, let me check in with you: has what I have said so far made sense to you? What question would you ask now?
But before I drone on any further, let me check in with you: has what I have said so far made sense to you? What question would you ask now?
Dear Bev (continued):
probably because I am not really studying everything you both told me to look at
As a matter of fact, Bev, I think many of the sites I have mentioned are well worth looking at. For one thing, many of them have neat graphics, like this one:
http://www.colorado.edu/physics/2000/schroedinger/two-slit2.html
A picture is indeed often worth many, many words in this sort of thing, and this site has very good moving pictures. I am here limited to verbal descriptions, which can get quite tedious.
As a matter of fact, Bev, I think many of the sites I have mentioned are well worth looking at. For one thing, many of them have neat graphics, like this one:
http://www.colorado.edu/physics/2000/schroedinger/two-slit2.html
A picture is indeed often worth many, many words in this sort of thing, and this site has very good moving pictures. I am here limited to verbal descriptions, which can get quite tedious.
I also recommend the Wikipedia article on the two-slit experiment.
http://en.wikipedia.org/wiki/Double-slit_experiment
Actually, I don't know how much math and physics you have, so I'm not sure just what to say or to recommend. I don't wish to patronize you, but I don't wish to talk over your head, either.
http://en.wikipedia.org/wiki/Double-slit_experiment
Actually, I don't know how much math and physics you have, so I'm not sure just what to say or to recommend. I don't wish to patronize you, but I don't wish to talk over your head, either.
Irina,
anyone who has read anything about QM other than popularizations knows that.
Now I'm sure that that wasn't aimed at anyone in particular, but you might want to have a quick look at the reviews of Penrose's book:http://www.amazon.com/Road-Reality-Complete-Guide-Universe/dp/0679454438
And perhaps read a little about him, just in case you're tempted to write him off as a mere popularizer, whose opinions are not worthy of serious consideration.
http://en.wikipedia.org/wiki/Roger_Penrose
I'm no unquestioning admirer - there are things he says that I take issue with, particularly in the field of AI. But I wouldn't consider my own meagre understanding of quantum mechanics to be so far in excess of one of most acclaimed and awarded quantum physicists of his generation, that I would simply ignore his views. Especially if I couldn't find any relevant references to refute him in a matter like the propagation of Ψ.
Of course, there is one way to test the matter - take this discussion to the sci.physics newsgroup, or one of the quantum physics forums out on the net, and see what the professionals think. What do you think?
Now I'm sure that that wasn't aimed at anyone in particular, but you might want to have a quick look at the reviews of Penrose's book:
And perhaps read a little about him, just in case you're tempted to write him off as a mere popularizer, whose opinions are not worthy of serious consideration.
I'm no unquestioning admirer - there are things he says that I take issue with, particularly in the field of AI. But I wouldn't consider my own meagre understanding of quantum mechanics to be so far in excess of one of most acclaimed and awarded quantum physicists of his generation, that I would simply ignore his views. Especially if I couldn't find any relevant references to refute him in a matter like the propagation of Ψ.
Of course, there is one way to test the matter - take this discussion to the sci.physics newsgroup, or one of the quantum physics forums out on the net, and see what the professionals think. What do you think?
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