The use of probability in QM


by juzzy
Tags: probability
bhobba
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May28-12, 03:00 AM
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Quote Quote by lugita15 View Post
How is energy or any other quantity directly observable except through the use of position? In order to measure anything don't we need a detector of some kind, and isn't reading (say) the position of an indicator or dial the only way to get information from a detector? How do acquire any information about the world at all except from position?
Actually, I think the pilot wave is just the imaginary part of the wave function, so that's not the contrived part. Rather, I think the unobservable thing that is just postulated for philosophical reasons is the hidden variable, namely the position of each particle.
I think there's another connection between Bohmian mechanics and aether: I vaguely recall someone saying that the nonlocality somehow leads to there being a preferred frame, so that Bohmians are effectively believers in the Lorentz aether theory without the physical aether.
Energy changes in an atom are measurable for example by a spectrograph and can be displayed in a digital readout or recorded into computer memory to avoid any connection to position such as some kind of pointer.

The pilot wave is entirely contrived so as to guide the particle - can't quite recall exactly if and/or how it relates to the imaginary part of the wavefuntion - you can check that out for yourself. It however has a real existence in that theory but is not directly measurable:
http://en.wikipedia.org/wiki/Pilot_wave
'According to pilot wave theory, the point particle and the matter wave are both real and distinct physical entities. (Unlike standard quantum mechanics, where particles and waves are considered to be the same entities, connected by wave-particle duality). The pilot wave guides the motion of the point particles as described by the guidance equation. Ordinary quantum mechanics and pilot wave theory are based on the same partial differential equation. The main difference is that in ordinary quantum mechanics, the Schrödinger-equation is connected to reality by the Born postulate, which states that the probability density of the particle's position is given by. Pilot wave theory considers the guidance equation to be the fundamental law, and sees the Born rule as a derived concept.'

I am no expert in Bohmian Mechanics so I will/can not really comment any more than what I said above. If you want to discuss it I suggest a separate thread where experts in it can comment. And yes it is related to the existence of an aether.

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Bill
krd
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May28-12, 08:52 AM
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Quote Quote by bhobba View Post
'According to pilot wave theory, the point particle and the matter wave are both real and distinct physical entities. (Unlike standard quantum mechanics, where particles and waves are considered to be the same entities, connected by wave-particle duality).

The pilot wave guides the motion of the point particles as described by the guidance equation.
Does it explain the double slits experiment done with a single electron? In that experiment the electron passes through both slits. If it's a point, it should only go through one slit. If you're doing the Young slits with a flood of photons, then the pilot wave idea might look okay.

I've heard one description of this - that the point goes through one slit, but then travels back and goes through the other slit - then it covers every possible path, and then collapses. To be honest that sounds stupid. It's like there's a particle fairy being helpful and convenient.
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May28-12, 10:49 AM
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Quote Quote by krd View Post
Does it explain the double slits experiment done with a single electron? In that experiment the electron passes through both slits. If it's a point, it should only go through one slit. If you're doing the Young slits with a flood of photons, then the pilot wave idea might look okay.
With the de-Brogle-Bohm interpretation, the electron passes through one slit only, while the pilot wave passes through both and guides the particle to some position on the screen (with the usual interference pattern as limit for many particles).

While this interpretation needs some specific frame to perform calculations, the resulting physics is the same in all frames afterwards.
Ken G
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May28-12, 12:36 PM
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Quote Quote by bhobba View Post
It reminds me of the aether of LET - yea its a valid theory but you have to ask - why bother? Of course the answer is philosophical - I however prefer the simpler answer of no pilot wave and no aether - but everyone is different - to each his/her own.
I agree with you that interpretations are fundamentally personal and subjective, and anyone that can get the answer right is not making any kind of mistake even if they use an approach that we might view as unsavory in some way. But I think in the case of interpretations of quantum mechanics, there is more going on than just a search for personal cognitive resonance. Underneath it is all is very much the question of what is physics trying to be. This question has been resolved age by age throughout history, and is constantly changing, and ultimately is controlled by whatever works, moreso than whatever we would like to work. But until we know whatever will work in the case of the next theory after quantum mechanics, we can still recognize that the different interpretations are asking us to think differently about what physics is.

I feel the issue comes down to what I see are three separate possibilities here, aligned with the three main ways to think about what physics is: rationalist, empiricist, or realist.

The rationalist approach says that physics is a search for the laws that the universe actually follows, and tends to frame the universe as a mathematical structure (we often hear words to the effect that "God is a mathematician" in this school of thought). But this is more than just a philosophical framework from which to regard physics, it makes genuine claims about what the process of doing physics should be trying to do (to wit, it should be searching for "the laws", or "the theory of everything".) I believe that approach not only colors what we think physics is, it actually changes what we think physics is. The many-worlds approach to quantum mechanics is often aligned with this style of thinking.

The empiricist approach says that physics is a set of observations that we are trying to understand, but the physics is the behavior, not the postulates we invent to approximate, idealize, and understand the behavior. Bohr was the consummate example of this approach, as he said "there is no quantum world" (anti-realist) and "physics is what we can say about nature" (with emphasis on "we", it is anti-rationalist). Again this is more than just a philosophical bent, it changes how we teach and perform physics, it changes what physics is trying to be.

The realist approach says that physics is trying to use a marriage of mathematical and empirical techniques to determine what reality is "really like". It says there is a reality out there, and physics is trying to find out what it is, more or less at face value. Einstein was a realist, indeed he was so radical of a realist that he didn't even like the realist approaches of de Broglie and Bohm because they embraced some unreal elements (the pilot wave) as the price of admittance to the sphere of being able to talk about the "real" positions and trajectories of particles. Einstein's approach has largely earned him disfavor, as he was considered to have lost the Einstein/Bohr debates, and his EPR paradox is no longer viewed as a paradox. But de Broglie's realism has generally been viewed as fully consistent with quantum mechanics, as you say. My point is that if we adopt the deBroglie-Bohm approach, we are not just choosing a philosophical favorite, we are again taking a stand on what we think physics should actually be.

So I agree with you that we don't at present know what physics should actually be, and the interpretations of QM all work, so we are at the moment left with a purely subjective and personal choice about how we like to frame it. I'm just saying that underneath that choice, there is a real struggle happening, like water piling up behind a dam and we don't yet know which path that water will take when it reaches its breaking point (which here will be some new observation that is not described by quantum mechanics). But what we should expect is that ultimately this issue will be far from moot-- it will determine the future direction of what physics becomes, be it a primarily rationalist, empiricist, or realist endeavor. I think it's exciting that we can't foresee which path future physics will take, but I think the "all three, you choose" approach cannot last forever!
krd
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May28-12, 04:44 PM
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Quote Quote by mfb View Post
With the de-Brogle-Bohm interpretation, the electron passes through one slit only, while the pilot wave passes through both and guides the particle to some position on the screen (with the usual interference pattern as limit for many particles).

While this interpretation needs some specific frame to perform calculations, the resulting physics is the same in all frames afterwards.
In a way, or in a few ways, it sounds like a terrible idea. Not that I have a better idea - I'm only tinkering with quantum physics as a hobby - and it will take a few years for me to get up on the maths.

I don't have an interpretation to proffer - but I think the actual explanation could be uglier and neater at the same time. It could be really weird - it could be the waves are an emergent property of classical space time - just we can't see what's doing it. Not that it would make them absolutely deterministic. A resolution of spooky action at a distance may be, there is no distance.

It's a real headache - strictly speaking, the wave never becomes a particle. The detectors only detect the occurrence of another kind of wave.
krd
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May28-12, 04:53 PM
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Quote Quote by Ken G View Post
So I agree with you that we don't at present know what physics should actually be, and the interpretations of QM all work, so we are at the moment left with a purely subjective and personal choice about how we like to frame it.!
In parts of the ancient world, the theory that a giant scarab beetle, made the sun rise and set, "worked".

There's a danger in theory becoming religious dogma - maths is just maths, anyone who puts it on a pedestal is up to something religious.
Ken G
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May28-12, 09:48 PM
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Quote Quote by krd View Post
There's a danger in theory becoming religious dogma - maths is just maths, anyone who puts it on a pedestal is up to something religious.
And yet maths should be on some kind of pedastol in physics, that much is clear-- the issue is how high? I don't object to putting it on a pedastol, the problem is putting it in a monolithic tower! In short, the problem is in expecting it to be the truth, an error that every generation seems to make over and over without ever learning the lesson until the next revolution in thought comes along.
bhobba
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May29-12, 12:47 AM
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Quote Quote by krd View Post
There's a danger in theory becoming religious dogma - maths is just maths, anyone who puts it on a pedestal is up to something religious.
Sorry to burst your bubble but maths is more than maths - it is the language of physics and so should be on a pedestal. Why that is is a very very deep mystery - but nonetheless true.

Whenever I see remarks like that I get the sneaky suspicion the person writing it doesn't quite understand modern physical theories. For example Noethers Theorem is just maths but it has shocking physical implications ie statements like energy conservation are nothing more than tautological statements about a systems symmetry (in the case of energy time symmetry) - without the math it would have remained hidden. Indeed at it's deepest level physics to a large extent is about symmetry - this is a profound truth about nature - but it took math to reveal it.

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Bill
bhobba
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May29-12, 12:50 AM
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Quote Quote by Ken G View Post
And yet maths should be on some kind of pedastol in physics, that much is clear-- the issue is how high? I don't object to putting it on a pedastol, the problem is putting it in a monolithic tower! In short, the problem is in expecting it to be the truth, an error that every generation seems to make over and over without ever learning the lesson until the next revolution in thought comes along.
True - no very true. Math is the language of physics and of course because of that should be on a pedestal - however it is not physics. It helps reveal profound truths like the importance of symmetry but the truths thus revealed is physics - not math.

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Bill
krd
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May29-12, 08:44 AM
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Quote Quote by Ken G View Post
And yet maths should be on some kind of pedastol in physics, that much is clear-- the issue is how high? I don't object to putting it on a pedastol, the problem is putting it in a monolithic tower! In short, the problem is in expecting it to be the truth, an error that every generation seems to make over and over without ever learning the lesson until the next revolution in thought comes along.
I've been racking my brain trying to remember precisely where the idea originated - I think from some of the Greek mathematicians. An idea that everything in reality can be represented through mathematics. Which is true - but what is very important not to forget, is that mathematical representations are just representations. They are not to be confused with the underlying reality itself.

"The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell."

-- Saint Augustine


I'm not saying the mathematicians are in league with the devil. It's just they may get carried away with themselves.
krd
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May29-12, 09:12 AM
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Quote Quote by bhobba View Post
Sorry to burst your bubble but maths is more than maths - it is the language of physics and so should be on a pedestal. Why that is is a very very deep mystery - but nonetheless true.
Maths is not a deep mystery. It's a system of representation.

It's hard to shake the idea, that there is something magical in it. Isaac Newton spent most of his time investigating magic, and trying to turn base metals into gold, than he did on the work he's remembered for. John Dee, the English mathematician is worth looking into too.

The peculiar mystical ideas in regard to maths, have a history. And it's the same with astronomy. In that in the past astrologers and astronomers were one and the same thing.

The marvel in a mobile phone working, is that it works, not the maths that describes its working.
Hurkyl
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May29-12, 10:00 AM
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The biggest issue with realism is that the word is often used not to describe the philosophical notion of realism, but instead a class of hidden variable theories.

e.g. orthodox quantum mechanics would use a wave-function to describe a particle.

But for some strange reason, someone who insists that the state space has properties "position" and "momentum" would call himself a realist, despite those ideas appearing nowhere in the scientific description of "what is".
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May29-12, 10:10 AM
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Quote Quote by Hurkyl View Post
The biggest issue with realism is that the word is often used not to describe the philosophical notion of realism, but instead a class of hidden variable theories.

e.g. orthodox quantum mechanics would use a wave-function to describe a particle.

But for some strange reason, someone who insists that the state space has properties "position" and "momentum" would call himself a realist, despite those ideas appearing nowhere in the scientific description of "what is".
To me the use of the word realism is perfectly consistent. It is the belief that the observable properties of the particle are real.
Ken G
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May29-12, 10:33 AM
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Quote Quote by krd
Maths is not a deep mystery. It's a system of representation.
The issue was insightfully explored by Wigner: http://www.dartmouth.edu/~matc/MathD...ng/Wigner.html
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May29-12, 10:45 AM
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Quote Quote by Hurkyl View Post
But for some strange reason, someone who insists that the state space has properties "position" and "momentum" would call himself a realist, despite those ideas appearing nowhere in the scientific description of "what is".
Quote Quote by lugita15
To me the use of the word realism is perfectly consistent. It is the belief that the observable properties of the particle are real.
I think this debate raises a very important weakness in the concept of "realism": what is it anyway? If we take the approach that realism means the things we observe are real, it's not clear we are making any kind of claim other than we observe consistencies. We can all agree that when we observe something, we are really observing it, but most people want "realism" to mean more than that-- they want it to mean the existence of something independent of our observing it. But the language quickly becomes incoherent when we start trying to talk about things that are independent of our observations, given that our observations are all we have to build our language.

Yet, we can easily see the need for some kind of realism if we consider this example: my daughter asks me if unicorns are real, I tell her that her love for unicorns is real but unicorns themselves are not. So what is the difference? She observes her love for unicorns, and she observes drawings of unicorns, but she does not observe real unicorns. So we need a word like "real" to navigate those distinctions. But when we talk about our theoretical constructs, does the word still apply?

Personally, I view realism as an element of a physical theory as an essentially empty concept-- if the language is used carefully, there is no need for any concept like realism in physical theories. Indeed, I would argue that realism is what leads every generation to make the same mistake, of thinking that their own world view is "what is actually happening", whereas everyone before them was laboring under some misconception or other! But when we see the historically obvious point that science is always provisional on what we know and what tools we have, then we see realism in science for what it is: a crutch that came become, if not used carefully, a lie.
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May29-12, 10:56 AM
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Quote Quote by Hurkyl View Post
The biggest issue with realism is that the word is often used not to describe the philosophical notion of realism, but instead a class of hidden variable theories.
I completely agree. Indeed, this is by beef with the PBR theorem-- the authors claim you need to be some kind of radical anti-realist if you are not willing to accept the concept that "properties" are real and therefore must be what actually determines behavior (which sounds to me closer to hidden variables, just as you say, because even if we are able to observe the properties, it is still "hidden" how these are supposed to determine the behavior).

To me, a property is more like the opposite of what is real-- a property is how we think about something, how we make sense of it, how we organize our perceptions around it. It's not even a pure perception, and even if it was, it still has us embedded deeply in it. Yet to be a "realist", we need to ignore our role in the concept of properties, and pretend, quite completely independent from any evidence, that we have nothing to do with properties. And that makes us a realist!?? Instead, I would offer a more sensible definition of realism as simply the imagining of a gap between, on one hand, our perceptions and logic and abilities, and on the other hand, what is "out there" independent from us. The act of recognizing how wide that gap is is exactly what I would call realism, and yet that is exactly what other people call anti-realism!
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May29-12, 11:14 AM
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Quote Quote by krd View Post
An idea that everything in reality can be represented through mathematics. Which is true - but what is very important not to forget, is that mathematical representations are just representations. They are not to be confused with the underlying reality itself.
This makes sense to me. An arguably anologous mistake (in my opinion) is made in the cognitive sciences as Searle points out:
The same mistake is repeated by computational accounts of consciousness. Just as behavior by itself is not sufficient for consciousness, so computational models of consciousness are not sufficient by themselves for consciousness. The computational model of consciousness stands to consciousness in the same way the computational model of anything stands to the domain being modelled. Nobody supposes that the computational model of rainstorms in London will leave us all wet. But they make the mistake of supposing that the computational model of consciousness is somehow conscious. It is the same mistake in both cases.
http://users.ecs.soton.ac.uk/harnad/...arle.prob.html

Unfortunately, unlike some mental stuff where we have intrinsic "access" to it (so that we can see that mathematics is not enough), the same cannot be said with respect to stuff described by physics. Some argue that the underlying "reality" will forever remain from our grasp, so that:
the propositions of physics are equations, equations that contain numbers, terms that refer without describing, many other mathematical symbols, and nothing else; and that these equations, being what they are, can only tell us about the abstract or mathematically characterizable structure of matter or the physical world without telling us anything else about the nature of the thing that exemplifies the structure. Even in the case of spacetime, as opposed to matter or force—to the doubtful extent that these three things can be separated—it’s unclear whether we have any knowledge of its intrinsic nature beyond its abstract or mathematically representable structure.
http://mitpress.mit.edu/books/chapte...13102pref2.pdf

Maybe that's why many physicists believe that physics has to 'free itself' from ‘intuitive pictures’ and give up the hope of ‘visualizing the world'? Steven Weinberg traces the realistic significance of physics to its mathematical formulations:
we have all been making abstract mathematical models of the universe to which at least the physicists give a higher degree of reality than they accord the ordinary world of sensations' ( e.g. so-called 'Galilean Style').
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May29-12, 12:51 PM
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Quote Quote by lugita15 View Post
To me the use of the word realism is perfectly consistent. It is the belief that the observable properties of the particle are real.
It's inconsistent, because that's not in orthodox QM's description of "what is". Momentum is not an observable property of a particle. The closest you can get is the facts
  • For most states, one 'can' perform a "momentum measuring experiment" and get a number
  • Most states yield a probability distribution over the outcomes of such an experiment
  • That probability distribution describes the distribution of results of repeated identical tests
But the idea that a particle has a particular numeric value for momentum? It simply isn't present in the scientific theory, and so the belief that it does is not realism. Instead, you are asserting a hidden variable theory, and presumably applying realism to the hidden variable theory instead of to orthodox QM.


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