Looking for a hard determinism type of QM interpretation

[trendal]

Hi all! I am wondering if there is an interpretation of QM where the future is "set in stone" (for lack of a better phrase). It can be unknowable (the future)...but it shouldn't be random in any way.

Edit: basically I'm looking for a hard determinism type of QM interpretation.

 

[StevieTNZ]

I don't believe so.

The closest I've encountered is Bohm Mechanics.

 

[jedishrfu]

http://www.bohmian-mechanics.net/

 

[trendal]

Found this: http://www.wired.com/2014/06/the-new-quantum-reality/

Pretty neat! A replication of the double-slit experiment using droplets bouncing on a liquid...something I haven't seen before! Lends more evidence to support the pilot wave theory.

 

[StevieTNZ]

Found this: http://www.wired.com/2014/06/the-new-quantum-reality/

Pretty neat! A replication of the double-slit experiment using droplets bouncing on a liquid...something I haven't seen before! Lends more evidence to support the pilot wave theory.

Not necessarily. There is some question surrounding whether its evidence for Bohm Mechanics or not.

 

[bhobba]

Hi all! I am wondering if there is an interpretation of QM where the future is "set in stone" (for lack of a better phrase).

Sure eg as another poster said BM and its probably not the only one.

The real issue with QM is not this or that issue such as being probabilistic, non local or whatever. Its that we have all these different interpretations that fixes up any issue that may annoy you such as lack of determinism, but we don't have one that fixes them all.

The issue with BM is its explicitly non local (that personally doesn't worry me - but others find such quite troubling) and you have this unobservable pilot wave - which does. Its far too much like the aether hypothesis in SR for my liking. One of the lessons of modern physics is to not introduce ad hoc hypothesis whose only purpose is to have the world conform to a pre-conceived bias in how it operates - which was Einstein's issue that caused Bohr to comment - Einstein - Stop telling God to do. The joke is on both of them though because it turns out they were both wrong - but that is another story. Do a post about it if you are interested - its way off topic in answering this so doesn't belong in this thread, but is an interesting issue.

But if you discuss the aether hypothesis with genuine physicists that believe in it (not kooks - which leaves only a few - it really is a backwater idea these days) you find they have a slightly different take - ie we live in a world of broken symmetries and this breaks symmetry at a very fundamental level.

No right or wrong here.

Thanks
Bill

 

[Nugatory]

Hi all! I am wondering if there is an interpretation of QM where the future is "set in stone" (for lack of a better phrase). It can be unknowable (the future)...but it shouldn't be random in any way.

Edit: basically I'm looking for a hard determinism type of QM interpretation.

Google for "superdeterminism" and "block universe". They won't be exactly what you're looking for, but they'll give you a pretty good sense of what it might mean to set the the future "in stone". Be aware that neither one can be refuted by experiment, so although they're interesting to contemplate there's not a lot of solid physics content here.

 

[kurros]

Technically the wavefunction evolution is deterministic in Many Worlds, so this is kind of like the future being "set in stone". This doesn't help us know our own subjective future, though, since we never know what branch of the wavefunction we are in/will experience.

 

[StevieTNZ]

You can say any interpretation of QM is deterministic in the sense that it follows the fundamental Schrodinger equation, which only deterministically predicts probabilities for certain events to occur.

 

[kurros]

You can say any interpretation of QM is deterministic in the sense that it follows the fundamental Schrodinger equation, which only deterministically predicts probabilities for certain events to occur.

Well not really. If wavefunction collapse "really happens" in a non-deterministic way, then that is a fundamentally non-deterministic part of the evolution of the universe. This never happens in many-worlds; there is only schrodinger, and no other kind of evolution. From the initial conditions of the multiverse you can predict the full history of the full multiverse. You can't do that if there is a fundamentally non-deterministic step somewhere. You can instead only predict the full possibility-space. But in many-worlds, those are not just possibilities, they are reality.

 

[StevieTNZ]

If there was actually collapse of the wave function, then QM would need modification to allow that.

 

[kurros]

If there was actually collapse of the wave function, then QM would need modification to allow that.

Why? It already has projection operators.

 

[bhobba]

If there was actually collapse of the wave function, then QM would need modification to allow that.

No it wouldn't. You simply postulate that's what happens. Any theory has unexplained things.

Why? It already has projection operators.

Exactly. Its interpreting it that's the issue. There are all sorts of ways of doing that. A modern one is consistent histories. A history is a sequence of projection operators. In that interpretation QM is the stochastic theory of histories - there isn't collapse. Some say its MW without the worlds.

Thanks
Bill

 

[StevieTNZ]

Well not really. If wavefunction collapse "really happens" in a non-deterministic way, then that is a fundamentally non-deterministic part of the evolution of the universe. This never happens in many-worlds; there is only schrodinger, and no other kind of evolution. From the initial conditions of the multiverse you can predict the full history of the full multiverse. You can't do that if there is a fundamentally non-deterministic step somewhere. You can instead only predict the full possibility-space. But in many-worlds, those are not just possibilities, they are reality.

According to QM there is only the Schrodinger equation evolution, correct?

 

[atyy]

Hi all! I am wondering if there is an interpretation of QM where the future is "set in stone" (for lack of a better phrase). It can be unknowable (the future)...but it shouldn't be random in any way.

Edit: basically I'm looking for a hard determinism type of QM interpretation.

The question that diffrrent QM interpretations try to answer is not determinism versus randomnes. The question is whether a realistic theory can underlie QM, in contrast to the operational viewpoint of Copenhagen in which a measurement device is a fundamental object required in defining the theory.

 

[atyy]

Found this: http://www.wired.com/2014/06/the-new-quantum-reality/

Pretty neat! A replication of the double-slit experiment using droplets bouncing on a liquid...something I haven't seen before! Lends more evidence to support the pilot wave theory.

Wolchover's article is misleading. The analogy between the fluid experiments and quantum mechanics is so weak that the fluid experiments are not able to lend support to the pilot wave theory. Also, the pilot wave theory needs no support from such experiments. It is already a leading approach, and consensus acknowledges it as a correct solution to the measurement problem for non-relativistic quantum mechanics.

 

[Matterwave]

According to QM there is only the Schrodinger equation evolution, correct?

Usually that the wave function evolves according to the Schrodinger equation is only one of the postulates of QM. The other postulates include that the observables are represented by Hermitean operators and that measurements of such observables yield eigenvalues of such operators in statistical accordance with the probabilities described by the wave function (the Born rule). It is this latter postulate that I think Bhobba was referring to in his previous post.

 

[RUTA]

Hi all! I am wondering if there is an interpretation of QM where the future is "set in stone" (for lack of a better phrase). It can be unknowable (the future)...but it shouldn't be random in any way.

Edit: basically I'm looking for a hard determinism type of QM interpretation.

Time-symmetric QM might be relevant http://jamesowenweatherall.com/SCPPRG/AharonovPopescuTollaksen2010PhysToday_TimeSymQM.pdf

 

[bhobba]

According to QM there is only the Schrodinger equation evolution, correct?

No.

Here is the basic axiom:

An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

One then applies Gleason's theorem to prove a formula for that probability known as the Born rule, which is there exists a positive operator P of unit trace such that the probability of Ei is Trace (PEi). By definition P is called the state of the system.

This has recently been discussed in a thread where I posted my proof of this important result (claiming no credit - I came up with it by picking the eyes out of a number of different proofs):
https://www.physicsforums.com/showthread.php?t=758125

These are the two axioms of QM the development of which you will find in Ballentine. But because of the beautiful Gleason's theorem its only one key axiom.

Schrodinger's equation is simply a requirement from symmetry - again the detail can be found in Chapter 3 of Ballentine.

Indeed, in both Classical Mechanics and Quantum Mechanics, and even Quantum Field theory, the dynamics is determined by symmetry. This is the amazing change in paradigm that came about when the great mathematician Emily Noether proved her profound and beautiful theorem:
http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html

To understand it better I actually suggest a book on Classical Mechanics - Mechanics by Lev Landau:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Whenever I link to that I can't resist posting the following:
'If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages.'

'The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophisitication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.'

But back to the original question - no that is not what QM says - that the outcomes are probabilistic is built right into its foundations. Schroedinger's equation, rather than being at odds with it, depends on it.

Thanks
Bill

 

[bhobba]

Usually that the wave function evolves according to the Schrodinger equation is only one of the postulates of QM. The other postulates include that the observables are represented by Hermitean operators and that measurements of such observables yield eigenvalues of such operators in statistical accordance with the probabilities described by the wave function (the Born rule). It is this latter postulate that I think Bhobba was referring to in his previous post.

Schroedinger's equation actually follows from symmetry so in a sense its not really a separate axiom but rather a requirement of the Principle Of Relativity (POR). Of course you have simply replaced one axiom with another, but most consider the POR to be more fundamental than things you can derive from it like Schroedinger's equation because its applicable to many different areas of physics. The POR is actually a meta law - a law about laws. Schroedinger's equation is simply an instance of that law. The strange, and very beautiful thing, is that meta law often implies the law in particular instances eg here Schroedinger's equation is implied by QM's foundational axioms (or in my case axiom) and the POR - specifically that the probabilities are frame independent. Its crazy when you think about it - but in science fact is often stranger than fiction.

What I am trying to get across is that the FORMALISM of QM doesn't have collapse as part of its foundations. Its simply assigning a probability to the outcome of an observation that has been mapped to the mathematical objects of the theory - in my treatment POVM's. The state is simply a mathematical requirement from that mapping. Its not usually presented that way except in highly mathematical treatments such as Geometry of Quantum Theory by Varadarajan:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

But its still true.

Thanks
Bill

 

[bhobba]

The question that diffrrent QM interpretations try to answer is not determinism versus randomnes. The question is whether a realistic theory can underlie QM, in contrast to the operational viewpoint of Copenhagen in which a measurement device is a fundamental object required in defining the theory.

Hmmmm.

I agree with your basic thrust, but I think the motivation for differing interpretations lies in deep held foundational beliefs of their various advocates.

Thanks
Bill

 

[atyy]

Hmmmm.

I agree with your basic thrust, but I think the motivation for differing interpretations lies in deep held foundational beliefs of their various advocates.

Thanks
Bill

What I'm trying to say is that Bohmian mechanics and the many-worlds approach are trying to solve the same problem - the need for a classical/quantum split in Copenhagen or the ensemble approach - which is purely instrumental.

For the sake of argument, let me assume many-worlds works. Then scientifically one has no preference between BM and MWI - that should be decided by experiment. Then the only preference one has is the belief that one should be able not to have a purely instrumental theory.

 

[bhobba]

What I'm trying to say is that Bohmian mechanics and the many-worlds approach are trying to solve the same problem - the need for a classical/quantum split in Copenhagen or the ensemble approach - which is purely instrumental.

Stated that way - I agree.

Thanks
Bill

 

[RUTA]

I agree with atyy, foundations is (ostensibly) about finding a fundamental ontology accommodating both quantum and classical physics. Since theory underdetermines ontology, I find most physicists working in foundations aren't interested in the ontology per se, but in new ideas for theory and experiment that radical ontologies can help motivate.

 

[strangerep]

To understand it better I actually suggest a book on Classical Mechanics - Mechanics by Lev Landau:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Whenever I link to that I can't resist posting the following:

If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages.

[...] Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. [...]

[...]

Do you know precisely where L+L derive that result as stated by Bosco Ho? Afaict, L+L get something equivalent to F=ma in their (eq(5.3) on p5. But that's just from putting in a position-dependent potential energy U into the Lagrangian by hand. The only (non)uniqueness argument I see there involves the fact that one can add a constant to U -- since the equations of motion are not affected by adding a total derivative to the Lagrangian. But this is not the same as what that Amazon reviewer said.

[Apologies if this is tangential to the main topic.]

 

[bhobba]

Do you know precisely where L+L derive that result as stated by Bosco Ho?

I think he is referring to the top of page 4 (when referring to the Euler-Lagrange equations at the bottom of page 3):

'Mathematically, the equations constitute a set of s second order equations for s unknown functions qi(t). The general solution contains 2s arbitrary constants. To determine these constants and thereby to define uniquely the motion of the system, it is necessary to know the initial conditions which specify the state of the system at some given instance, for example the initial value of all the coordinate and velocities.'

Thanks
Bill

 

[Matterwave]

Schroedinger's equation actually follows from symmetry so in a sense its not really a separate axiom but rather a requirement of the Principle Of Relativity (POR). Of course you have simply replaced one axiom with another, but most consider the POR to be more fundamental than things you can derive from it like Schroedinger's equation because its applicable to many different areas of physics. The POR is actually a meta law - a law about laws. Schroedinger's equation is simply an instance of that law. The strange, and very beautiful thing, is that meta law often implies the law in particular instances eg here Schroedinger's equation is implied by QM's foundational axioms (or in my case axiom) and the POR - specifically that the probabilities are frame independent. Its crazy when you think about it - but in science fact is often stranger than fiction.

What I am trying to get across is that the FORMALISM of QM doesn't have collapse as part of its foundations. Its simply assigning a probability to the outcome of an observation that has been mapped to the mathematical objects of the theory - in my treatment POVM's. The state is simply a mathematical requirement from that mapping. Its not usually presented that way except in highly mathematical treatments such as Geometry of Quantum Theory by Varadarajan:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

But its still true.

Thanks
Bill

Replacing the Schroedinger equation assumption with the principle of relativity is not without disadvantages. For a first thing, you have to take a rather convoluted road to obtaining the equation of motion. First you have to figure out all the operators and their commutation relations, then you have to modify the Hamiltonian to be the dynamical time evolution operator, then you have to figure out the position space representations, etc.

Instead, I could merely postulate the Born rule and:
$$-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}\Psi(x,t)+V(x)\Psi(x,t)=i\hbar\frac{\partial}{\partial t}\Psi(x,t)$$

And I would have a basically working theory with testable predictions.

Secondly, it is aesthetically displeasing for me to postulate a set of assumptions that are explicitly counter to the actual principle of relativity. After all, to obtain Schroedinger's equation, we must postulate Galilean relativity not Einsteinian relativity. Of course the SE is not Lorentz invariant, but at least if I postulate it, I don't explicitly show off this fact. This is just a matter of taste.

 

[vanhees71]

The symmetry principles are of that much importance that at one point one should teach quantum theory from the point of view of the analysis of the underlying symmetries of the model. However, this you can do only when the students already have some previous acquaintance with quantum theory. That's why one usually uses a heuristic approach to quantum theory.

Traditionally, there are (at least) two ways to do so. One is using the idea of "wave-particle dualism" from the old quantum theory and develops wave mechanics along the line of its historical development. In my opinion the disadvantage of this approach is that students get the impression that wave-particle dualism is at the heart of quantum theory although it's only a heuristical idea which is mostly overcome by the advent of modern quantum theory. The advantage is that you are quite quickly at a point where you have the Schrödinger equation at hand to use it for a lot of applications in atomic, molecular and even very modern "nano" physics.

Another approach is to use Hamiltonian mechanics in the Poisson-bracket formulation and translate it to commutation relations on the operator algebra of observables on a Hilbert space. The disadvantage of this way is that you introduce the Hilbert space ad hoc without much motivation. The advantage is that you keep the old-fashioned heuristics of old quantum theory to a minimum.

I'd use a mixture of the two approaches in a "QM 1" lecture (in Germany usually we have a theoretical physics course, where quantum mechanics 1 is taught in the 4th semester to BSc students and another lecture quantum mechanics 2, which is taught to MSc students). I'd start with wave mechanics and then motivate the Hilbert-space formulation from it. In the exercise sessions you can do a lot of practical applications of the Schrödinger equation while in the lecture you develop the Hilbert-space formalism further.

The approach via symmetries is of course the most appealing, but I'd spare this for the QM2 lecture. I've taught this, and the students liked the approach, although it's (particularly for the Galileo group) not so simple, because you need a lot of subtle group/Lie-algebra representation theory, because the Galileo group representation used in non-relativistic QM is necessarily a true central extension with the mass as a non-trivial central charge. The Poincare group's ray representations are all induced by unitary transformations and the mass (squared) is a Casimir operator. Here, the problem is of course, that you don't get physically sensible one-particle models (except for the free particle) and you have to do many-body theory right from the beginning.

 

[Matterwave]

I would imagine using the Poisson bracket to commutator approach is greatly hindered by the fact that Poisson brackets themselves are not usually taught in a undergraduate level classical mechanics course, but introduced much later as the fourth or fifth retelling of the classical mechanics story. It also has its roots deep in the geometrical/symplectic structure of phase space, which is probably not even mentioned at the undergraduate level. Add to that the difficulties with geometric quantization, and the fact that the classical picture is the one which should arise as a limit from the quantum picture, and I have some deep doubts about the utility of this approach in an introductory quantum mechanics course.

 

[bhobba]

Replacing the Schroedinger equation assumption with the principle of relativity is not without disadvantages.

Very true. Which is why only advanced treatments do it.

The symmetry principles are of that much importance that at one point one should teach quantum theory from the point of view of the analysis of the underlying symmetries of the model. However, this you can do only when the students already have some previous acquaintance with quantum theory. That's why one usually uses a heuristic approach to quantum theory.

Again very true.

Personally the way I would do it to start with is simply axiomatically - its what this guy does:
https://www.amazon.com/dp/0071765638/?tag=pfamazon01-20

Then mention the axioms can be presented much more transparently and elegantly, but requires more advanced math that's best left until later.

The point of mentioning it here though is to understand the actual basis of Schrodinger's equation in regard to:

According to QM there is only the Schrodinger equation evolution, correct?

Its really the other way around - the basic principles of QM, and a very important general principle of physics, the POR, actually implies the Schroedinger equation - basically there is only the two axioms as found in Ballintine.

The fact it requires an advanced treatment doesn't change what's really going on.

Thanks
Bill

 

[bhobba]

and I have some deep doubts about the utility of this approach in an introductory quantum mechanics course.

You would have to have rocks in your head to try this in an introductory course, and even in advanced courses unless the audience has sufficient math background.

But that's not the point I am trying to make here. Its the principles that underlie what QM is about.

Thanks
Bill

 

[Matterwave]

You would have to have rocks in your head to try this in an introductory course, and even in advanced courses unless the audience has sufficient math background.

But that's not the point I am trying to make here. Its the principles that underlie what QM is about.

Thanks
Bill

I was actually referring to Vanhees's statement that he taught a Poisson bracket to commutator relations approach to QM in a quantum 1 course. Rereading his post, I see that Quantum 1 is actually taught to upper level undergrads who I guess *might* understand this approach (maybe German classical mech is taught differently as well?). I thought Quantum 1 was taught to entering undergrads, which I thought was way too early to have anything to do with Poisson brackets.

 

[atyy]

But is it true that QM cannot exist if POR were to fail?

If QM can still exist (say using Sakurai and Napolitano's axioms) in the absence of POR, then POR is not a principle of QM. Rather, POR is a principle that can be consistent with QM.

For example, does QM not work in curved spacetime, where POR does fail?

 

[PhilDSP]

I thought Quantum 1 was taught to entering undergrads, which I thought was way too early to have anything to do with Poisson brackets.

It seems a great shame that things like Poisson brackets and Phase Space aren't introduced early, even in high school. There's obviously no need to go into high technical detail. But a hand-wavy "this is what PB's look like and this is why we use them" type of approach might go a long way towards generating interest, curiosity and familiarity (rather than fright or aversion) early on IMO. Then it is fair to tell students that they will not be tested on those subjects and the situation becomes one of "learning by inspiration".

 

[rubi]

But is it true that QM cannot exist if POR were to fail?

If QM can still exist (say using Sakurai and Napolitano's axioms) in the absence of POR, then POR is not a principle of QM. Rather, POR is a principle that can be consistent with QM.

For example, does QM not work in curved spacetime, where POR does fail?

The Schrödinger equation is actually more fundamental, because it still works in situations that aren't symmetric under time translations. This is the case for time-dependent Hamiltonians for example, which appear in many practical applications. Of course, if the system has a time-translation symmetry, one can typically derive the Schrödinger equation from it.