# The use of probability in QM

1. May 26, 2012

### juzzy

I watched this video http://www.youtube.com/watch?v=aJ0FVez0FSc&list=UU_fHG6JygMd7oIvQ5S_cSIg&index=7&feature=plcp and the guy says that we don't know wether probability is a fundamental description of the particle or wether it is because of our lack of knowledge of the underlying system (ie as in measuring temperature).

Would it be correct to say that we don't know? Doesn't the delayed choice quantum eraser prove that at it's most fundamental, nature is probabilistic.

2. May 26, 2012

### Maui

Well, that would be interpretation dependent, but with propability being a fundamental part of quantum reality, you get a visual picture of how a 'particle' moves(i.e. through successive measurements). Extrapolate that to bigger systems - atoms and molecules and you'd get a picture how atoms and molecules move. I have no idea how a wavefunction moves in the BI(the implied ftl signaling makes it even more awkward). I guess the whole plethora of interpretations are there because some people need a crutch for the ERH(external reality hypothesis), hence they'd want to convince you of there being hidden variables at play, hidden realities, other worlds and other tricks. There has been a rather long debate between Einstein and Bohr about the probability in qm and it's generally accepted that Einstein lost the debate(certain tests of realism have since confirmed the notion as well, the uncertainty principle upholds the notion too). Those who like to stay out of metaphysics will likely claim that only results of measurements are meaningful and leave the deeper issues to philosophers.

Last edited: May 26, 2012
3. May 26, 2012

### Mark M

Different interpretations can vary on the issue of determinism. For example, Many-Worlds and de Broglie-Bohm are deterministic. However, the textbook interpretation of quantum mechanics, the Copenhagen Interpretation, holds that the results of a quantum event are fundamentally probabilistic.

4. May 26, 2012

### juzzy

Thanks for the replies so far,
Maui, I'm not sure it's wise to leave the deeper issues to philosophers lol. I'm just wondering you see, if the actual 3 dimensional structure of an atom (carbon for instance) is described by a probability function, and cannot be described at all classically, isn't this evidence strong enough to prove that probability is fundamental. If you add to that the result you see in the double slit experiment, and in particular the delayed choice version of the experiment, then I don't really see how that isn't conclusive proof. In other words how would you build a deterministic picture from the results of that experiment, because even the many-worlds interpretation isn't deterministic in my opinion, it just says that all 'probabilities' exist in some way or another??? Or am I misinterperating the theory?

5. May 26, 2012

### Maui

It is sort of classically described, as a collection of measurements done with electron tunneling microscope(the 3D 'images' you've seen of atoms). Otherwise, the wavefunction of an atom is a probability function(confirmed by the experiments with buckyball molecules).

With a healthy dose of imagination and assumptions(even unwarranted), you could picture anything. That's why the operational interpretation is a minimalist one - that which is measured/observed is meaningful for the theory, not the underlying mechanics which does not behave classically. Quantum theory doesn't have problems, people do. As i said it gets philosphical when you ask who has false beliefs about the world?

Last edited: May 26, 2012
6. May 26, 2012

### juzzy

I didn't mean images of atoms as such. I mean the mathematical description of the atom in QM, which leads to a probability distribution for the electron(s) and hence describes it's geometry intuitively as a 3d object, which is in accordance with observation of the 3d structure of molecules etc. However, in the classical description the atom would just collapse in on itself.

I'm not sure this has anything to do with philosophy really, it just seems obvious from these kind of results in QM, that probability is the most fundamental thing because only after the observation is made can we say anything deterministic about the result. The initial result of the measurement is random as far as I can tell

It's just that the guy in the video said we don't know, but I wonder how many physicists would agree that we don't know or would most say we do?

7. May 26, 2012

### Maui

As i said earlier, the mathematical description for the electron(s) around the nucleus is a probability wave(this is the standard interpretation, there are others though).

I agree with that, but the best thing one can learn here(beside the facts) is getting to know where physics ends and philosophy begins. Your topic covers both physics and philosophy - there are more ways than one of dealing with the quantum weirdness.

I'd say that most accept that nature is fundamentally indeterministic at the quantum level, but a minority would disagree.

8. May 26, 2012

### StevieTNZ

Bohm Mechanics has the particle go through one slit (pre-determined), yet an interference pattern emerges if we do the double-slit experiment. This is because of the guiding wave of the particle - that goes through both slits.

9. May 27, 2012

### the_pulp

Im part of that minority. I think, similar but not equal to Ballentine, that an experiment tipically can be modelled by correlating:

1) an instrument state which has an eingenvector related to the indicator state (lets say "ind") and an eingenvector related to the state of the millons and millons of macroscopically uncontrolled particles that conform the instrument (lets say "m")
2) a system state (lets say "r")

and letting time goes by (that is to say, applying the evolution operator to the correlated state). Mathematically:

U(r$\otimes$ind$\otimes$m)

If r is an experiment eigenvector then the final state eigenvector should be ind(r) (the value of the indicator related to the system state "r"):

U(r$\otimes$ind$\otimes$m)=U(r$\otimes$ind(r)$\otimes$m')

m' is another state of the uncontrolled variables that they can take due to the interaction with the system.

If r is not an eigenstate, then the experiment makes the system go to an experiment eigenstate ("r(i)"):

U(r$\otimes$ind$\otimes$m)=U(r(i)$\otimes$ind(r(i))$\otimes$m'')

With probability calculated from the Born Rule.

However, the evolution, as it is implicit in the last equation, is purely deterministic. The probability arrives due to the macroscopic ignorance of the "m" state. And, due to some theorems (see saunders "Derivation of the Born Rule From Operational Assumptions"), the only possible way that this probability can depend on only the initial state "r" (otherwise the experiment would not be considered an experiment but merely an interaction whose result depends on some controlled parameters) is that it is calculated with the Born Rule.

So, to me, the probabilities are something aparent to us, humans, who are not able to know every component of the instrument, but in reality evolution is deterministic (as Schrodinger equation or every equation that describes the evolution of a system).

Im not a profesional so I could be totally wrong!

10. May 27, 2012

### Staff: Mentor

Well really we don't know because it is not known, nor in principle can it be, what future research will discover.

What we do know is, as far as we can tell today, that at the most fundamental level nature obeys the superposition principle. Now there seems to be only two possibilities - such states are deterministic or we can only predict probabilities. The first is actually contained in the second - but the probabilities are 0 or 1. Now there is a very important theorem that is not as well known as it should be - that the only way to define probabilities if the superposition principle holds (ie the states are a vector space) is the standard way it is done in QM - it is called Gleasons Theorem. Not only that but assuming only 0 or 1 can be assigned to such a space leads to a contradiction ie nature at it fundamental level is probabilistic. Its really unavoidable if the superposition principle holds. There are a number of outs such as introducing assumptions of contextuality but really to me they all seem a bit contrived.

Why the principle of superposition? Check out:

Thanks
Bill

Last edited by a moderator: May 6, 2017
11. May 27, 2012

### Jano L.

Juzzy, here is what I think:

Physics is essentially part of philosophy, so one important work of the physicist _is_ to think about deep issues and explanation of the things. If he denies this, than he is giving up the possibilities.

It is difficult to prove that classical theory cannot handle this or that. Classical theory is not some rigid structure that can be disproved by disproving one or two old ideas. Flogiston, ether were dismissed, molecules were accepted, and the classical theory get to a better shape. It is possible the same will happen in future. It may require further revisions and improvements, but these will not bring down all classical physics.

Some concept can be fundamental within a theory (like probability in quantum theory), but the physical theory itself cannot possibly be fundamental as a The Correct Theory of Nature. There never was such a thing in science and the physicists themselves prefer to have more humble goals.

Niel Bohr put it himself perfectly:

'There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about Nature.'

— Niels Bohr
http://todayinsci.com/B/Bohr_Niels/BohrNiels-Quotations.htm

Furthermore, there are scientists who argue that probability is more a matter of logic than that of physical laws. In their view, the probability is just a subjective measure and is not fundamental even on the level of physical theory. They have very convincing arguments - see, for example,

E. T. Jaynes, G. Larry Bretthorst, Probability theory - the logic of science 2003.

12. May 27, 2012

### juzzy

Thanks for all the replies so far, I've read them with interest. I will take it that the guy in the video therefore made a legitimate statement. And also I should say I hope I didn't offend any philosophers in my earlier post, my comments were in jest I assure you.

Ok then, I still have to disagree with any deterministic picture. In a simple zach-mender interferometer, the particle would be detected at both detectors with a probability of 1/2 if the particle was behaving deterministically. The fact we only see a build up at one detector can only be if the particle went both ways and interfered with itself, which seems deterministic in the sense that you know it will always go both ways, but actually follows probalistic laws. By that I mean it has an equal chance of going both ways and so does , as opposed to going one way or the other.

Yes I guess I am slipping into philosophy it's almost impossible to avoid with this subject

13. May 27, 2012

### lugita15

How does Bohmian mechanics get around what you're saying?

Last edited by a moderator: May 6, 2017
14. May 27, 2012

### krd

Well maybe that's a cop out. Probability does not actually explain anything.

Also Bohr's statement leaves the possibility open for mathematical fictions - where the maths agrees with results, but theory is either wrong or absent. His idea may be based on flawed idea that all the world can be accurately expressed through maths - which is true, but at the same time flawed. You can describe a mountain in terms of polygons - but you're still just left with a bunch of polygons.

He could be dead right. But when you ditch the real world for abstract models, you run the risk of missing something.

He could be dead wrong. What appears random, could be deterministic - just the mechanism is well hidden. The actual mechanisms could be a lot stranger than current ideas.

It could be a bit like listening to a radio of station. If you didn't know how they playlist the music, you might assume the music just plays at random - you might be able to calculate the probabilities of certain songs being played. But your assumption of randomness would be wrong.

There is no DJ. There is only an abstract quantum physical description of a DJ.

15. May 27, 2012

### Staff: Mentor

Bohmian Mechanics is explicitly contextual - ie it attacks the assumption of non-contextuality which is the hidden assumption in Gleasons theorem ie the probability associated with a projection operator does not depend on the other elements of a resolution of the identity it is part of.

You will find discussions on this issue scatterd about the place eg:
http://physics.stackexchange.com/qu...-to-obtain-born-rule-in-many-worlds-interpret
'I note that Gleason's theorem has played a small role in the reception accorded to a completely different interpretation, Bohmian mechanics. Gleason's theorem was at one time taken as a proof of the impossibility of hidden variables, but John Bell pointed out that it's only inconsistent with noncontextual hidden-variable theories, in which all observables simultaneously have sharp values. Bohmian mechanics is a contextual theory in which position has a preferred status, and in which other observables take on their measured values because of the measurement interaction. This runs against the belief in ontological equality of all observables; but perhaps reflecting on the status of Gleason's theorem within the Bohmian ontology will tell us something about its meaning for the real world.'

It is an out but like I said strikes me as rather contrived and against symmetry/invariance which lies at the heart of much of physics.

Thanks
Bill

16. May 27, 2012

### lugita15

But is there not some basis in ascribing a reality to position that other observables do not have, since presumably it is the only directly observable quantity in nature? Isn't everything else indirectly observed via an appropriate pointer basis?

17. May 27, 2012

### Staff: Mentor

Why do you think it is the only directly observable quantity (it isn't - energy is for example is directly observable - but curios why you think so)?

And even if true - so? That does not change the fact that Bohmian Mechanics is rather contrived - you have this pilot wave you can not in principle observe all for the express purpose of having nature behave how you would like it to behave. 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.

Thanks
Bill

18. May 28, 2012

### lugita15

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.

19. May 28, 2012

### Staff: Mentor

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.

Thanks
Bill

20. May 28, 2012

### krd

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.