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JakeStan said:
You can go through the derivation by yourself, it is found in (almost) every intro textbook in QM.
What Are Some Common Misconceptions About Quantum Mechanics?
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You can go through the derivation by yourself, it is found in (almost) every intro textbook in QM.
nfelddav
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unseensoul said:That's confusing...
Isn't there a easier way to explain it without the use of mathematics?
Sorry... but no. as you've probably noticed by know, QM is basically a purely mathematical theory. The physical representation (if there is one) not part of the theory at all. The only way to explain it is in the mathematics, because that's really all there is.
malawi_glenn said:
But for this I have to go the other direction: You seem to be dismissing a physical representation which sounds very reasonable. As far as I know, many/most people think there must be some physical explanation for the mathematics of QM.
HUP is obtained by simply using the anticommutator of the position and momentum operator, but it is not unreasonable to assume that something physical makes it happen. I've seen the argument that the probe alters the system put forth a lot.
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nfelddav said:Sorry... but no. as you've probably noticed by know, QM is basically a purely mathematical theory. The physical representation (if there is one) not part of the theory at all. The only way to explain it is in the mathematics, because that's really all there is.
But for this I have to go the other direction: You seem to be dismissing a physical representation which sounds very reasonable. As far as I know, many/most people think there must be some physical explanation for the mathematics of QM.
HUP is obtained by simply using the anticommutator of the position and momentum operator, but it is not unreasonable to assume that something physical makes it happen. I've seen the argument that the probe alters the system put forth a lot.
So in the first section in your answer you stresses that QM theory is just math math math.. then you switch position?
You mean that the commutator itself has a 'physical' relation? And with "physical" here, you mean some kind of "collision"? Why is not the description of the commutator itself physical? Is it physical to talk about that an operatoration on the wavefunction with an operator makes the wavefunction collapse into one of its eigenstates to the operator? Further definitions of what "physical" means is required.
Tac-Tics
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QM seems strange because in every experiment, there are particles flying towards each other, a black box where "something magic happens", but you're not sure what, and then particles flying back out, whose properties we can predict with the theory.
It seems this is no different than any other physical theory. In mechanics, if you roll two billiard balls into each other, you know their incoming speeds and you know their outgoing speeds, but you don't know jack about the mechanism which cause their speeds to change. It isn't encompassed by the theory. (Something to do with electrons interacting or some nonsense). But no one seems confused by this!
Billiard balls collide and magically trade momenta. Electrons collide and trade spin. Same deal. The mechanism isn't well understood given the theory used to predict the correct and useful results.
The annoying part of QM, from what I can tell, seems to be that the black box in the experiment seems significant.
In the billiard ball example, we pretend that the world acts the same inside the box and outside, and that the ball it just made of quadrillions of smaller balls, all acting under the same physical rules.
With QM, inside the black box, we know that things obey a different set of rules. At least, according to our theory. Everything outside of the box is measured "classically" and everything inside is in a superposition of classical states. We of course realize that the box isn't really there at all, and the rules of physics should apply just as well to the outside. Why don't we see the billiard ball splitting into an infinity of balls when we strike it with a cue stick? Why do measurements seem to cause all those "ghost" balls to vanish, leaving only a single classical state?
The answer is, shut up and calculate. Physicists don't deal with questions that are impossible to measure, so they just stick to electrons and photons and slits and detectors and pretend it's all just magic, because no one quite understands the truth.
It seems this is no different than any other physical theory. In mechanics, if you roll two billiard balls into each other, you know their incoming speeds and you know their outgoing speeds, but you don't know jack about the mechanism which cause their speeds to change. It isn't encompassed by the theory. (Something to do with electrons interacting or some nonsense). But no one seems confused by this!
Billiard balls collide and magically trade momenta. Electrons collide and trade spin. Same deal. The mechanism isn't well understood given the theory used to predict the correct and useful results.
The annoying part of QM, from what I can tell, seems to be that the black box in the experiment seems significant.
In the billiard ball example, we pretend that the world acts the same inside the box and outside, and that the ball it just made of quadrillions of smaller balls, all acting under the same physical rules.
With QM, inside the black box, we know that things obey a different set of rules. At least, according to our theory. Everything outside of the box is measured "classically" and everything inside is in a superposition of classical states. We of course realize that the box isn't really there at all, and the rules of physics should apply just as well to the outside. Why don't we see the billiard ball splitting into an infinity of balls when we strike it with a cue stick? Why do measurements seem to cause all those "ghost" balls to vanish, leaving only a single classical state?
The answer is, shut up and calculate. Physicists don't deal with questions that are impossible to measure, so they just stick to electrons and photons and slits and detectors and pretend it's all just magic, because no one quite understands the truth.
nfelddav
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malawi_glenn said:
Yeah that's just about it...
I was stressing that if you want to understand anything about QM, you have to do the math, because as Tac-Tics says, we don't know what happens in that "black-box."
Then the second part was the observation that something does.
A collision would be an example of something physical, yes. Sorry, I hate imprecise language as well, but I'm having trouble on precise formulation. Physical as in not just the mathematical formulation: that which causes the system to behave in the way described by the operator.
Something which "has material existence" (dictionary definition).
unseensoul
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By the way, if the wave-behaviour of a particle is related to where the particle might be found (wavefunction) why do particles diffract as well (in this situation it seems to behave like a REAL wave)? I can't relate both concepts...
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nfelddav said:
And since we don't know what happens, we should not perhaps extrapolate what happens in the "classical" macroscopic world at all.
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unseensoul said:
why not? The math of wavefunctions is (almost) the same as for light waves. Just that the intepretation on what it is differs. In light, it is the density in electric field (and so on) and in QM it is the density of probability.
The probability DENSITY can be negative, and even complex valued! But the probability, which is the probability density modulus squared - is always positive.
newbee
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unseensoul
"if the wave-behaviour of a particle is related to where the particle might be found (wavefunction) why"
becomes
" ... if the theory of quantum mechanics predicts the probability of measuring a particle to be at a give position why ..."
Think about it for a while. Also:
Let me modify a phrase above to be more in line with the way physicists speak and see if it helps:unseensoul said:
"if the wave-behaviour of a particle is related to where the particle might be found (wavefunction) why"
becomes
" ... if the theory of quantum mechanics predicts the probability of measuring a particle to be at a give position why ..."
Think about it for a while. Also:
According to QM it ALWAYS behaves as a probability density wave.unseensoul said:
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Only when it's isolated from the environment.newbee said:
Phrak
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Fredrik said:
It strikes me that you can have such a device, Fredrik. One SG beam splitter. This feeds two SGs. One measures up; one measures down.
It seems that we have to specify, in the least, that the two non-commuting observables are measured in the same space-time region.
Interesting it itself, I suppose. But obvious in retrospect. When there is imposed temporal constraint one should beware of a lurking spatial constraint.
In addition, the regional constraint seems a necessary, but not completely sufficient condition.
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nfelddav
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I agree completely. Trying to extrapolate what we cannot measure is beyond physics. I merely argued that we should acknowledge that something does.malawi_glenn said:
triplemaya
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Hi. Much the best explantion I have found is given in Nick Herbert's book Quantum Reality, I will do my best to precis in brief.
Wave information can be packaged in different ways, and analog or digitgal are very different. If you want to describe a sine wave by far the simplest way to do so is with an analog formula, a simple wave equation defines it completely, while to describe this digitally takes a large number of samples. Coversely, if you want to describe spike data, very few digital samples are required, while to define it using only sine wave formulae would require a very large number of waves designed to cancel each other out by addition leaving only the spike. The two methods are complementary, or better conjugate, in that the easier it is to describe wave information in one way the harder it is in the other way. However, obviously, the two ways are describing the same information. The conjugate properties of a quantum, such as position and momentum, are like digital and analog, two different ways of defining the same data. Of course, to us position and momentum seem like wildly different things, so this does not make sense, but that is how the quantum works. The two things are mutually exclusive conjugate properties, which basically means that they are not so much different properties of the quantum, as they appear to us to be, but conjugate attributes of a single property, positionmomentum.
Making a measurement of position is the same thing as finding out the digital spike version of the information and making a measurement of momentum is the same thing as finding out the analog sine wave version of the information. You can do one or the other not both ( well, you can do both, but only partly, so that you have a partial measurement of position and a partial measurement of momentum. )
As Herbert states "the conjugate attributes correspond exactly to conjugate wave form families (eg sine wave and digital)" thus if you measure a quantum for position, digital measurement, you can have no information about momentum because you have no sine wave information, and vice versa. What Heisenberg is saying is that it is not a question of what we can measure, the quantum itself is of that nature, it's a thing which has conjugate properties, or more accurately properties which have conjugate forms, and if one is precisely defined the other is inherently undefined, thus embracing all possible values.
This can be seen as simple and direct evidence that physical reality *is* the wave function, and there is no underlying 'real physical stuff', it doesn't work like that! The real physical stuff is how the wave function appears to us at our macroscopic level.
HTH
Wave information can be packaged in different ways, and analog or digitgal are very different. If you want to describe a sine wave by far the simplest way to do so is with an analog formula, a simple wave equation defines it completely, while to describe this digitally takes a large number of samples. Coversely, if you want to describe spike data, very few digital samples are required, while to define it using only sine wave formulae would require a very large number of waves designed to cancel each other out by addition leaving only the spike. The two methods are complementary, or better conjugate, in that the easier it is to describe wave information in one way the harder it is in the other way. However, obviously, the two ways are describing the same information. The conjugate properties of a quantum, such as position and momentum, are like digital and analog, two different ways of defining the same data. Of course, to us position and momentum seem like wildly different things, so this does not make sense, but that is how the quantum works. The two things are mutually exclusive conjugate properties, which basically means that they are not so much different properties of the quantum, as they appear to us to be, but conjugate attributes of a single property, positionmomentum.
Making a measurement of position is the same thing as finding out the digital spike version of the information and making a measurement of momentum is the same thing as finding out the analog sine wave version of the information. You can do one or the other not both ( well, you can do both, but only partly, so that you have a partial measurement of position and a partial measurement of momentum. )
As Herbert states "the conjugate attributes correspond exactly to conjugate wave form families (eg sine wave and digital)" thus if you measure a quantum for position, digital measurement, you can have no information about momentum because you have no sine wave information, and vice versa. What Heisenberg is saying is that it is not a question of what we can measure, the quantum itself is of that nature, it's a thing which has conjugate properties, or more accurately properties which have conjugate forms, and if one is precisely defined the other is inherently undefined, thus embracing all possible values.
This can be seen as simple and direct evidence that physical reality *is* the wave function, and there is no underlying 'real physical stuff', it doesn't work like that! The real physical stuff is how the wave function appears to us at our macroscopic level.
HTH
Naty1
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If you are looking for introductory explanations try the following
Wikipedia, online
Warped Passages, Lisa Randall
The Fabric of the Cosmos, or The Elegant Universe, Brian Greene
The Trouble With Physics,or Three Roads to Quantum Gravity*, Lee Smolin
* The most detailed non mathematical discussion, about 200 pages
For a more mathematical approach: The Road to Reality, Roger Penrose
Wikipedia, online
Warped Passages, Lisa Randall
The Fabric of the Cosmos, or The Elegant Universe, Brian Greene
The Trouble With Physics,or Three Roads to Quantum Gravity*, Lee Smolin
* The most detailed non mathematical discussion, about 200 pages
For a more mathematical approach: The Road to Reality, Roger Penrose