Are observables like position emergent properties?

  • #1

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Title basically says it all. I'm a physics undergrad trying to wrap my head around quantum physics, and I was hoping people here could help. My question comes from something in one of my textbooks. It tries to explain particle-wave duality through a piece of string, which I'll quickly go over as best I can. If the string is flat everywhere except one place where it suddenly spikes upwards, the string's "location" can be thought of as the spike. If one asked for the string's wavelength, you'd look at them like they're nuts since it doesn't have one. But if the string is in a sine wave pattern then you have something you can call a wavelength, but since it's periodic you don't have anything to call its position. A particle's wavefunction is supposed to be like the piece of string, especially in one dimension where the wavefunction is drawn exactly like a piece of string.

This tempts me to think that a lone particle is its wavefunction, and that observables are just emergent properties of whatever the wavefunction's shape happens to be at a given moment. A given particle wouldn't have a position, just a wavefunction so incredibly scrunched up that it may as well have a position. Is this right at all? And if not, what have I misunderstood? Thank you in advance, and I look forward to reading what you have to say.
 

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  • #2
phinds
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Title basically says it all. I'm a physics undergrad trying to wrap my head around quantum physics, and I was hoping people here could help. My question comes from something in one of my textbooks. It tries to explain particle-wave duality through a piece of string, which I'll quickly go over as best I can. If the string is flat everywhere except one place where it suddenly spikes upwards, the string's "location" can be thought of as the spike. If one asked for the string's wavelength, you'd look at them like they're nuts since it doesn't have one. But if the string is in a sine wave pattern then you have something you can call a wavelength, but since it's periodic you don't have anything to call its position. A particle's wavefunction is supposed to be like the piece of string, especially in one dimension where the wavefunction is drawn exactly like a piece of string.

This tempts me to think that a lone particle is its wavefunction, and that observables are just emergent properties of whatever the wavefunction's shape happens to be at a given moment. A given particle wouldn't have a position, just a wavefunction so incredibly scrunched up that it may as well have a position. Is this right at all? And if not, what have I misunderstood? Thank you in advance, and I look forward to reading what you have to say.
As is discussed on probably hundreds of threads on this forum, "wave particle duality" is a concept that is dead and was buried some 80 years ago except that for some reason it has hung on in beginner's texts and in pop-sci in the mistaken belief that it helps explain things. The objects of which it was once said there was a "wave particle duality" are have long been called "quantum objects". They are not waves at all and they are not particles at all. They exhibit some of the characteristics of each of these classical concepts, depending on what you measure, but they are not either one.
 
  • #3
bapowell
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Title basically says it all. I'm a physics undergrad trying to wrap my head around quantum physics, and I was hoping people here could help. My question comes from something in one of my textbooks. It tries to explain particle-wave duality through a piece of string, which I'll quickly go over as best I can. If the string is flat everywhere except one place where it suddenly spikes upwards, the string's "location" can be thought of as the spike. If one asked for the string's wavelength, you'd look at them like they're nuts since it doesn't have one. But if the string is in a sine wave pattern then you have something you can call a wavelength, but since it's periodic you don't have anything to call its position. A particle's wavefunction is supposed to be like the piece of string, especially in one dimension where the wavefunction is drawn exactly like a piece of string.
Identify wavelength with momentum and you've supplied the intuition behind the Heisenberg Uncertainty Principle.
 
  • #4
As is discussed on probably hundreds of threads on this forum, "wave particle duality" is a concept that is dead and was buried some 80 years ago except that for some reason it has hung on in beginner's texts and in pop-sci in the mistaken belief that it helps explain things. The objects of which it was once said there was a "wave particle duality" are have long been called "quantum objects". They are not waves at all and they are not particles at all. They exhibit some of the characteristics of each of these classical concepts, depending on what you measure, but they are not either one.
Thank you for the valuable information (I didn't know particle-wave duality was dead). But my question isn't about particle-wave duality. I only brought up how my textbook explained it so I could trace back my line of thought and make it easier for people to point out where I went wrong. What you said seems to me to agree with my understanding: a "quantum object" isn't a wave or a particle, but if it's scrunched up then it may as well be a particle since it behaves almost exactly like one. And if it's shaped like neither, then it behaves like neither. Wave-like and particle-like shapes are just common and easy for physicists to work with, and they wouldn't be unique by any means. So is my understanding right? And if not, what's wrong with it?
 
  • #5
bapowell
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The world is made of particles; their wavelike nature arises from the quantum behavior exhibited in their wavefunctions.
 
  • #6
phinds
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The world is made of particles; their wavelike nature arises from the quantum behavior exhibited in their wavefunctions.
So I'm wrong in saying that electrons, for example, are NOT particles but quantum objects that sometimes exhibit particle-like behavior?
 
  • #7
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So I'm wrong in saying that electrons, for example, are NOT particles but quantum objects that sometimes exhibit particle-like behavior?
That is correct.

By particles Bapowell meant quantum particles. They are in fact excitations of quantum fields.

Thanks
Bill
 
  • #8
WannabeNewton
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"Particle" has a very precise definition in QFT. There is an entire chapter devoted to the rigorous definition of a particle in Weinberg Vol1 (c.f. chapter 2), specifically through representations of the little group of the Lorentz group. An electron is a particle as bapowell stated. When one says "particle" in QFT they do not mean particle in the classical sense. And as bapowell stated, the wave-like behavior of particles is simply due to their states evolving under the time evolution equation ##H|\psi \rangle = i\partial_t |\psi \rangle## in both QFT and in QM.
 
  • #9
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but if it's scrunched up then it may as well be a particle since it behaves almost exactly like one.
Scruched up? Don't know what you mean. QM is a theory about observations that appear here in an assumed common-sense classical world. What it's doing, being, etc etc is anyone's guess.

And if it's shaped like neither, then it behaves like neither. Wave-like and particle-like shapes are just common and easy for physicists to work with, and they wouldn't be unique by any means. So is my understanding right? And if not, what's wrong with it?
The theory is silent about shape, etc etc when not observed.

If you want to see what IMHO is the essence of QM check out:
http://www.scottaaronson.com/democritus/lec9.html

Thanks
Bill
 
  • #10
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"Particle" has a very precise definition in QFT. There is an entire chapter devoted to the rigorous definition of a particle in Weinberg Vol1 (c.f. chapter 2), specifically through representations of the little group of the Lorentz group.
Just a note to those reading this. Wienberg's text, IMHO (and I have a copy of all the volumes) is THE book on QFT - but it's quite advanced.

If you want investigate QFT the following is a much better place to start:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Its also considerably cheaper :D:D:D:D:D:D

Thanks
Bill
 
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  • #11
phinds
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"Particle" has a very precise definition in QFT. There is an entire chapter devoted to the rigorous definition of a particle in Weinberg Vol1 (c.f. chapter 2), specifically through representations of the little group of the Lorentz group. An electron is a particle as bapowell stated. When one says "particle" in QFT they do not mean particle in the classical sense. And as bapowell stated, the wave-like behavior of particles is simply due to their states evolving under the time evolution equation ##H|\psi \rangle = i\partial_t |\psi \rangle## in both QFT and in QM.
Thanks. The bolded part clears up my confusion.

So I should say "quantum particle" rather than the "quantum object" that I have been using, yes?
 
  • #12
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So I should say "quantum particle" rather than the "quantum object" that I have been using, yes?
There's no one right way... It depends on the audience. WbN may be right that there is a rigorous definition of "particle", but someone who is not aware of that definition will not apply it when they hear "quantum particle". "Quantum object" or "quantum system" may not be formally correct, but at least it keeps the little-tiny-bullet misconception at bay long enough to explain that "particle" doesn't mean what it sounds like.
 
  • #13
Scruched up? Don't know what you mean. QM is a theory about observations that appear here in an assumed common-sense classical world. What it's doing, being, etc etc is anyone's guess.
Sorry, I think I might need to be less sloppy with my words. When I think of a wavefunction, I think of it as a graphed function like this: http://en.wikipedia.org/wiki/Wave_packet#mediaviewer/File:Wave_function_of_a_Gaussian_state_moving_at_constant_momentum.gif .Which I guess might not be the best way to think of it. When I said it was scrunched up, I meant that the wavefunction, if graphed, would make a narrow and "scrunched up" bump. I think using the way of thinking about it in your link, it would mean that if n was always a real number and |n> was the nth location there is in space (even though that's a bit silly since space is continuous, so each |n> would have an infinitely small amplitude I think), then the by far biggest amplitudes would all be very close to some mth point in space. That should mean that on observation of any (quantum) particle with such a wavefunction, your particle-detecting thingy practically always gives you a reading really close to the mth point in space, and near where the wavefunction graph has a narrow peak. My question is if this particle-detecting thingy is reading an emergent property or a fundamental one. A shirt might have a color, but that's not a fundamental property of the shirt. The shirt has its color because of how electrons are absorbing and emitting light. It makes no sense to ask for a neutrino's color, since the property doesn't really emerge in neutrinos. Well it might, but I don't think it does. Is asking to simultaneously know a particle's exact position and momentum the same as asking for a neutrino's color, or is it nonsense and/or unanswerable for a different reason? And would it be alright to say that in the strictest sense a particle doesn't ever have a position, but it always does have a concrete something (a wavefunction), and the something often makes it behave almost exactly like it did have a position to the point that it may as well have one?

The theory is silent about shape, etc etc when not observed.

If you want to see what IMHO is the essence of QM check out:
http://www.scottaaronson.com/democritus/lec9.html

Thanks
Bill
Again, I meant to refer to the wavefunction's shape if you plot it on a piece of paper. Which assumes you know the particle's wavefunction ahead of time, and that it has a wavefunction. Even when a particle isn't being interacted with, (I think) you can ascribe a "correct" wavefunction to it. The wavefunction might just be useless since you're not trying to use it to predict an interaction.
 
  • #14
Demystifier
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As is discussed on probably hundreds of threads on this forum, "wave particle duality" is a concept that is dead and was buried some 80 years ago except that for some reason it has hung on in beginner's texts and in pop-sci in the mistaken belief that it helps explain things.
Wave-particle duality is still alive, as demonstrated by a recent paper published in Nature Communications
http://lanl.arxiv.org/abs/1403.4687
However, the modern meaning of the expression "wave-particle duality" differs significantly from that in beginner's texts and pop-sci. Perhaps a better name for this modern meaning of "wave-particle duality" would be interference-path complementarity.
 
  • #15
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Just a note to those reading this. Wienberg's text, IMHO (and I have a copy of all the volumes) is THE book on QFT - but it's quite advanced.

If you want investigate QFT the following is a much better place to start:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Its also considerably cheaper :D:D:D:D:D:D
It cannot be cheaper, except if they give money for taking it ;) because Weinberg you can find for free in the net.
 
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  • #16
DrDu
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The problem with QFT is that it is not a closed theory in the mathematical sense but some rather ill defined kind of perturbation theory. While it is relatively easy to define non-interacting particles, it is not clear at all how to precisely define interacting (quantum) particles or their wavefunction. Most of the, up to now, not too successful attempts to set up a well defined quantum field theory regard the algebra of the observables as the underlying object, with the wavefunctions forming rather a representation of this algebra. Anyhow the observables seem to have a primate over the wavefunctions or particles conceptually.
 
  • #17
Demystifier
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because Weinberg you can find for free in the net.
Only a Russian can say that in public without a hesitation. ;)
(Which I meant as a compliment.)
 
  • #18
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My question is if this particle-detecting thingy is reading an emergent property or a fundamental one.
We don't know - the theory is silent about such things.

Thanks
Bill
 
  • #19
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However, the modern meaning of the expression "wave-particle duality" differs significantly from that in beginner's texts and pop-sci. Perhaps a better name for this modern meaning of "wave-particle duality" would be interference-path complementarity.
That's correct.

I have read papers that give it a precise definition - but its a long way from what beginner texts say.

Thanks
Bill
 
  • #21
phinds
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Wave-particle duality is still alive, as demonstrated by a recent paper published in Nature Communications
http://lanl.arxiv.org/abs/1403.4687
However, the modern meaning of the expression "wave-particle duality" differs significantly from that in beginner's texts and pop-sci. Perhaps a better name for this modern meaning of "wave-particle duality" would be interference-path complementarity.
Be that as it may, I think what I said is appropriate for a first discussion with laymen whereas yours will just lead to confusion. Dropping the duality is supported by numerous discussions on this forum. Examples:

bhobba in this post https://www.physicsforums.com/threads/bells-inequality.791592/page-3#post-4975280
says "You need to forget this wave particle duality stuff - it was overthrown in 1926 by Dirac"

And in the forum FAQ here https://www.physicsforums.com/threads/is-light-a-wave-or-a-particle.511178/ it says "So there is no duality – at least not within quantum mechanics. We still use the “duality” description of light when we try to describe light to laymen because wave and particle are behavior most people are familiar with. However, it doesn’t mean that in physics, or in the working of physicists, such a duality has any significance."
 
  • #22
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Be that as it may, I think what I said is appropriate for a first discussion with laymen whereas yours will just lead to confusion. Dropping the duality is supported by numerous discussions on this forum
Mate its the context thing. The context of those precise definitions is entirely different to what's said in beginning tests.

Don't worry about it,

Added later:
Check oiut the following:
http://en.wikipedia.org/wiki/Englert–Greenberger_duality_relation

Rather than calling it wave particle duality or complementarity distinguishably would be a better term, and it is not what is meant in beginner texts.

Thanks
Bill
 
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  • #23
phinds
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Mate its the context thing.
Exactly. That was the point of my response to demystifier
 
  • #24
My question is if this particle-detecting thingy is reading an emergent property or a fundamental one.
We don't know - the theory is silent about such things.

Thanks
Bill
I think that's the answer to my question, and I'm taking it as the "right" answer unless anyone has any objections. Thank you all for your time, and for giving me some valuable info beyond what I asked for or expected.
 
  • #25
phinds
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... Thank you ... for giving me some valuable info beyond what I asked for or expected.
Hey, we always overthink things here on PF :D
 

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