Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?
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Although Bell did defend pilot wave theory--which is taught in every introductory QM course and covered in every introductory QM text--he himself did not see it as anything more than an inspiration for a more complete interpretation, which would necessarily be non-local in accordance with the theorem that bears his name.
My own belief is that pilot waves cannot account for quantum statistics, and therefore cannot account for the heat capacity of solids: http://www.tjradcliffe.com/?p=470 There is a claim that pilot wave theory somehow deals with this, but the argument is focused on the decay of radioactive particles rather than thermodynamics, which seems to be odd, because the thermodynamic argument is the fundamental one: the heat capacity of solids is an unequivocal way of counting available states, and if hidden variables (such as the "true" positions and momenta of the piloted particles) exist then they break the symmetry under exchange that gives rise to the statistics we observe, and create additional states that would... hmmm...
OK, having thought about it for a bit I'm no longer entirely convinced it's impossible that pilot waves might preserve the symmetry while also preserving identity. It would require that exchanging the labels on the pilot waves precisely compensate for the labels on the particles. Would that be enough? I'm going to have to think more about this before forming a more firmly held opinion on it.
Then there are irrational probabilities :)
Now we observe that after the photon passes through the slit, we can decompose the function as |P(t)> = sqrt(0.94)|Q(t)> + sqrt(0.06)|R(t)> where Q and R are independent, each individually evolving according to the laws of quantum mechanics. This is already derived rather than fundamental, but the phenomenon is real, because the causality relation is real. Our neurons under Q (and of course a "neuron" isn't really fundamental, it's an interpretation of a particular group of particles behaving in a particular way, i.e. of particular aspects of the wavefunction) have no effect on our neurons in R and vice versa.
All that is physically real; the only remaining question is what we should expect to subjectively experience. Since our neurons in Q have no effect on our neurons in R and vice versa, it seems like we'd experience either being in Q or being in R. With what probability? Well, whatever it is it had better be conserved; it makes no sense to say that we'd experience R with 4% probability in 5 minutes and then 8% probability in 10 minutes. If we send another photon through in Q, splitting the wavefunction further into |S(t)> + |T(t)> + |R(t)> where Q = S + T, then our subjective probabilities should be such that the probability we find ourselves in S or T = the probability that we found ourselves in Q before sending the second photon.
What's the probability-like quantity that's conserved by quantum evolution of a system? Why, it's the norm, ||P>|^2. I guess that's what we'd expect to be the subjective probability then.
It uses the (uncollapsed) wave function to have a mass density on physical space. There are many realities, if you like, implied, but they all move about in a self-consistent way. The analogy is that it is as if two tv channels were overlying each other. You can follow each separately if you watch the evolution, but at any one time it would look a bit like a mess.
The problem with just having the wavefunction and nothing else is that it is not at all clear what the probabilities would be about. You need something that the theory describes that makes contact with our 3 dimensional experience.
The interpretation I subscribe to is that measurement is a situation of entanglement. In the electron slit experiment, when you observe the electron traveling through lets say the right slit, subsequent behavior of the electron and the "memory" in the person will be correlated.
I don't know how memory and the brain really work here. I think that is the real question - the mechanics of the brain and an observation.
Regarding Occam's razor, to me this seems like a much simpler explanation of observation than having the wavefunction of the entire universe collapsing when a random human is in the loop.
Having assisted in teaching intro QM courses, I can say this is very incorrect -- unless you replace "every" with "many" and "taught/covered" with "mentioned off hand".
I just pulled the very popular "introduction to quantum mechanics" by Griffiths off my shelf. It contains nothing about pilot waves except for a single footnote in an appendix used as an example of "a number of hidden variable theories [proposed over the years]".
I shall now walk away mumbling about the degenerate state of today's youth...
For spin, one has to realize that it is modeled well by wave functions that take on vectors as values. When moving to multiple particles with spin, we tensor (kind of multiply) those vectors together. But the key point is that we tensor based on the spatial location. So instead of tensoring over particle 1 and particle 2, we tensor over their positions. This gives us complicated vector bundles. It opens a lot more possibilities, but when you look at general quantum dynamics, the only stable ones in 3D are the bosons and fermions.
Thus, not only can Bohmian mechanics account for it, it actually provides a very natural explanation. It is completely rooted in considering what the configuration space is. Where Bohmian mechanics shines is that what the configuration space is comes from what the theory itself is concerned with, namely particles with definite positions.
And just as a side note, the standard formalism of quantum mechanics emerges in a mathematically rigorous way from Bohmian mechanics. Everything in non-relativistic quantum mechanics is completely accounted for and you get a clear foundation for extending it to other spaces and more general questions.
As for relativity and quantum field theory, that is still a work in progress, but the main stumbling block is actually having a well-defined evolution of the wave function in interacting cases. If we had that, then the Bohmian additions are easily handled for the most part. Research has been done and is being done.
A simple (layperson) reference for this is sadly lacking, but you can try either http://arxiv.org/pdf/quant-ph/0506173.pdf or my thesis (chapter 5) at http://jostylr.com/thesis.pdf Hopefully they are somewhat accessible to this audience.
Thanks for the references, I'll see if I can understand them!
One question - What aether/field do the pilot waves travel in? E? B? something else?
There are fascinating lab experiments related to black holes [1]. Researchers have figured out how to build things in the lab that obey some laws that are mathematically very similar to those that we think that black holes obey. These black hole analogues end up doing similar things to what we expect real black holes to do.
Nonetheless, no one seems to see those experiments and conclude that "Wow! Our universe must contain black holes that emit Hawking radiation!".
These oil droplet experiments do something quite similar. They create an environment that is reasonably well described by the same equations as pilot waves, and, since those equations are known to make the same predictions as quantum mechanics, the oil droplets do the things that we would imagine quantum particles to do.
This may be beautiful, but just as the existence of black hole analogues in the laboratory does not imply that black holes are real, the existence of pilot-wave-following oil droplets does not imply that pilot waves are better than quantum mechanics.
[1] http://www.nature.com/nphys/journal/v10/n11/full/nphys3104.h...
IANAP.
physical system -> theoretical description -> physical system
physical system -> theoretical description
It's not surprising that when you set out to simulate a black hole you end up with a black hole! The main reason I could accept them being useful for is when some emergent aspect of the theory is very expensive to simulate.
If the Copenhagen model and the pilot-wave model make the same predictions, which I believe they do since I believe they're mathematically equivalent, then you can't say one is better than the other on the basis of their predictions alone. But there are other evaluation criteria.
The pilot-wave model has a (ideally, complete) simple physical analogue that can act as an aid to intuition; the Copenhagen model, IIUC, asserts that there can be no analogue---all you have is the wave function. In which case, the pilot wave model has an advantage.
Further, if it were possible to experimentally separate the particle from the pilot-wave, the two models would not be equivalent. But you would never look for that kind of experimental evidence if you are only using the Copenhagen model.
On the other hand, from the article:
"Quantum physicists tend to consider the findings less significant. After all, the fluid research does not provide direct evidence that pilot waves propel particles at the quantum scale. And a surprising analogy between electrons and oil droplets does not yield new and better calculations. “Personally, I think it has little to do with quantum mechanics,” said Gerard ’t Hooft, a Nobel Prize-winning particle physicist at Utrecht University in the Netherlands. He believes quantum theory is incomplete but dislikes pilot-wave theory."
I'm thinking he is saying the same thing you are.
"Yet an experimental test of droplet entanglement remains a distant goal."
And it will remain a distant goal forever. Per Bell's theorem, entanglement is inherently non-local. Bohmian pilot waves are also non-local, so they can reproduce all the results of QM, but no purely classical model can.
The original idea—that the wave function is the whole deal—works just fine if you accept that we can be in superposition too. If you simply accept that the entire classical concept might be an illusion, and work up from the wave function, there's no reason to shoehorn in an idea like Collapse or Pilot-Wave.
Yes, Copenhagen is wrong. Yes, Collapse is patently absurd. Yes, assuming that there is exactly one, stochastic, probabilistic reality makes no sense. But that doesn't mean we need to add something complicated like an underlying superfluid that supports all of spacetime. This smells like Aether.
Why does no one talk about Many-Worlds?
It's like dynamic programming. It's just one way to look at the problem. It doesn't really exclude any of the other solutions.
The strong objection to Many Worlds is not that macroscopic objects cannot be in superposition. There are many objections [2], but the principal one is the difficulty of deriving the Born Rule.
This is a deep objection. The Born rule predicts of the result of quantum measurements in QM, and it's not clear how to get those results out of MWI. The Born Rule in MWI is inserted ad-hoc afterwards, or arises via some weird "world-counting" formalism that doesn't naturally connect to probabilities. So MWI has more the flavor of a visualization, not a theory that aims at making predictions.
When you say "collapse is wrong," it depends on what is being collapsed. Sure, inserting some special "wavefunction collapse dynamics" separate from ordinary evolution is a pretty rough approach. But when the wavefunction is understood as encoding probabilities, then it's not something physical, and its collapse is no more mysterious than the probability of the Giants winning the World Series "collapsing" to 100% once the final game was played.
[1]: http://arxiv.org/abs/1301.1069 [2]: http://www.mat.univie.ac.at/~neum/physfaq/topics/manyworlds has some [3]: http://arxiv.org/abs/gr-qc/9703089
No, from my understanding this is not correct - what you say would be true if we lived in a classical world.
The problem with this approach - that is, interpreting the wave function as encoding probabilities of different states of the world that merely reflect our ignorance of the true state - is that it doesn't explain how we can get interference effects between those different potential states of the world.
The wavefunction definitely encodes probabilities - that's the Born rule, and it's a key result of QM. But probabilities of what? Not of the probability of the system being in different states, for there is only one state, which is described by the wavefunction. Instead it encodes the probability of the results of measurements.
For example, in the double-slit experiment, the wavefunction tells us, if we were to deploy a measuring device at the left slit, or right slit, or at various points on the screen, what the probability of measuring an electron would be. It does not tell us the probability that the electron went through the left or right slit. That would prohibit quantum interference, as you say!
A key point (of non-Bohmian interpretations) is there is no underlying "true state," i.e. predetermined values of observables. The uncertainty principle drives that home.
> we can get interference effects between those different potential states of the world
If these possibilities were classical, that would be impossible, as you say. But they are quantum possibilities, and quantum possibilities can interfere. AFAIK this has to be made a postulate of the theory. But once you've done that, and specified the mapping from quantum probabilities to classical measurements (i.e. the Born rule), you can show how classical measurements reflect the interference.
The key idea is that an electron's wavefunction is "made of" probabilities or numbers, not electron-stuff or matter or anything physical. Then "wavefunction collapse" is just a change in subjective knowledge, not a physical process.
A further objection is aimed ad the claim that "we can be in a superposition" and it is: "If we can be in a superposition, why aren't we aware of it?"
This is a general question that any interpretation of QM must answer, and none does, which comes down to: "Why is there a classical world at all?"
There is a sense in which every interpretation of QM is an attempt to answer this question, but none do.
Decoherence, for example, simply asserts that we cannot be aware of quantum effects except via interference phenomena. Why not? Why can't we be directly conscious of the various incoherent components of the wavefunction in the same sense of directly that I am directly conscious of my cat sitting beside me? [1] I don't have to do any fancy interferometry or statistical inference to be aware of the cat, so why do I have to mess about with statistics and interferometry to be aware of the wavefunction, given I myself am described by one?
The fact that my multiple incoherent states do not interfere with each other is irrelevant unless you have some reason to believe that it is only via coherent interactions (interferecne patterns) that the wavefunction manifests itself to consciousness, and why would that be?
When I measure a gamma decay why am I aware of an event at a moment in time rather than a continuous probability wave? Likewise, why can't I be conscious of the wholistic universe that Many Worlds implies?
I've focused on consciousness here because there is no doubt we are directly aware of the classical world but are only indirectly aware of the quantum world, but there is very little reason to believe there is anything particularly special about consciousness in this regard. More likely, the brain, body, planet, etc, all "partake in" classical physics, none of which makes any sense from a quantum perspective.
That is: if all you knew about was quantum mechanics, you would never come up with Born's Rule or anything like it because you would never have any reason to talk about the results of classical measurement. You would not be aware than anything like classical measurement could exist.
So if we believe that QM is somehow foundational or fundamental to the classical world (and who doesn't?) then the fact that it gives no indication that the classical world even exists is something of a problem.
[1] To belabour the point: I do not mean "direct" in any Cartesian sense, but simply that there is a perfectly ordinary causal relationship between my cat and my awareness of my cat, which is quite different from my awareness of wavefunctions, which can only be via indirect means. We might have any number of additional senses, but all of them would be direct in this sense: none of them would allow me the immediate, simultaneous perception of a photon travelling through both slits at once. As Feynman said: this is the fundamental mystery.
Sounds rather like the fish being unaware of water. What would not being in a superposition feel like?
> Decoherence, for example, simply asserts that we cannot be aware of quantum effects except via interference phenomena. Why not? Why can't we be directly conscious of the various incoherent components of the wavefunction in the same sense of directly that I am directly conscious of my cat sitting beside me? [1] I don't have to do any fancy interferometry or statistical inference to be aware of the cat, so why do I have to mess about with statistics and interferometry to be aware of the wavefunction, given I myself am described by one?
So "you" is a quantum computer or something behaving like one, right? For you to "be aware of" a wavefunction, you'd have to causally interact with it. And that's very hard because of e.g. the no-cloning theorem; all you can do is entangle a qbit in your head with the qbit you're trying to measure, but what does that actually get you? What does that subjectively feel like? What operation would you expect to be able to perform that you can't?
You do though, you're just not consciously aware of it.
Because it is metaphysics: it generates no predictions that are not generated by some other interpretation of quantum mechanics.
(Anything that produces different predictions is something more than, or at least other than, an interpretation of QM.)
A) Accept that the quantum reality is real and the classical one is not, and adjust our preconceptions, OR
B) Look for a deeper physics.
Of course this could be complicated by a mechanism at the source that ensures a single pair to be emitted. Imagine a mechanism that ensures that only one pair is produced, but it is produced eventually, like a for-loop with a break statement. And maybe the only way to conduct the Bell's Inequality experiment meaningfully is with such a throttling mechanism, which would mask the answer to the question above. Though there might be hints in the amount of time required to generate that singular pair, as if the for-loop had to run more iterations before it was produced, detected only with sensitive timing instruments like with side-channel timing attacks in cryptographic black boxes.
One of the sad things about physics these days is that it has become more like religion in a bad way. I first heard about Bohmenian mechanics, which this article is about, 8 years ago. I never believed in it, and always thought it was silly. I say "believe" because at this point it really is a question of faith.
It was amusing to me to read this article, it makes all the same points I used to argue against but in a very clever and well written way. What the Bohmeanian mechanics people used to say was the only reason they couldn't respond to this or that problem with the theory was "not enough people were working on it".
From the article:
"Some researchers said that [Bohmean Mechanics] has trouble dealing with identical particles, and that it becomes unwieldy when describing multiparticle interactions. They also claimed that it combines less elegantly with special relativity. But other specialists in quantum mechanics disagreed or said the approach is simply under-researched."
Science. We're doing it wrong.
Show me the scientist who has replicated every experiment in the scientific texts and journals they read. They don't exist.
At some point, you have to trust the system, trust other scientists, trust what you're reading, and believe that the system works. Sure, in principle you might be able to verify any experiment (given enough time and resources, which no one has), but in practice you can't even get close.
It sounds convincing but I'm having trouble figuring out what it would actually mean....
So instead of breaking c, we assume things with non-locality that particles 'spookily know'/are affected by things that may possibly be on the other side of the universe. This causes a myriad of problems in the actual physical interpretations.
I remember thinking as well, hey why don't we just accept non-locality, but, actually doing physics with it you end run into myriad headscratchers that even make the broken Copenhagen look attractive! One that I did for my MSc was for the case of an single electron in a (harmonic was it?) potential well and solving for a stationary state. By dealing with the Bohmian waveguide model you end up getting that electron is experiencing no overall force - therefore it is literally stationary (serious problems there!) or moving at a constant speed, and could be ANYWHERE in space (non-locality). So your could have 'bound electrons' that are over in Mars or... aren't moving? I'll put up a work through of that if anyone wants to check! Just one example, but my professor (a very thoughtful guy) thought it was cute, had its uses in some applications, but sadly probably not the right story.
Would love to see that worked through in more detail!
The key is that we distinguish between theories that have experimental evidence and proven predictive power and ones that don't yet have that distinction. Until last year the theoretical framework for the existence of the Higgs Boson could reasonably have been described as 'under-researched'.
I do of course completely agree that those fluid dynamics experiments don't count as experimental evidence.
http://plato.stanford.edu/entries/qm-bohm/#o
It's true that Bohmian mechanics has never been extended to a full QFT. But considering how little time has been spent on it, isn't it possible this is a result of observed bias against it, and not because it's fundamentally intractable?
For comparison, other theories that have ended up in more intractable places (such as string theory) seem to be considered mainstream.
But the main point of why Bohmian mechanics over standard quantum mechanics is that the standard one is ill-defined. "Collapse happens when a measurement occurs, but not before." What is a measurement? Trying to make this precise is a problem. Collapse too early and you get the wrong results while collapse too late and you get into the cat paradox. Bohr, I believe, understood this which is why he advocated for a split between classical and quantum with a statement not to worry about the split.
There are other ways of dealing with this problem, but Bohmian mechanics is the simplest in my opinion. Instead of something that is sometimes wave-like and sometimes particle-like, we have two things: a wave and a set of particles. The evolution of the particles is governed by the wave. Everything in standard quantum mechanics can be deduced by this picture.
For example, while the path of a piece of paper as it drops to the ground can be modeled exactly based on several parameters such as gravity, air currents (and its parameters), etc. the number of parameters are so large and their interactions so complex, that the only useful approach is to model it statistically. The same goes for the weather. Or the economy. Or the stock market.
It appears that the current quantum mechanical view of the world is simply an acknowledgement of this complexity and the associated unknowns. While it presents a statistical "model" that works for our purposes, it must be acknowledged as a model and not confused with reality. The push for figuring out what drives the statistics needs to continue beyond the building of a model.
This is not a accurate representation of quantum mechanics.
If you were to write down a classical description of the state of all the particles in a piece of paper and the state of all the particles that they might interact with over the course of a few seconds, and you solved the equations for what happens, you would get an exact description of the result. This description would be wrong if you look closely enough because classical mechanism doesn't correctly describe the universe we live in.
If you did the same thing with a quantum description of the initial state of the paper, you would also get an exact description of the result. That description would be very strange -- if try to deduce what you would see if you looked at the piece of paper (remember, you're just a bunch more particles interacting with that paper), you learn the bizarre answer that you would seem to have some chance of seeing the paper in one configuration and some chance of seeing the paper in a different configuration.
But there's no respect in which quantum mechanics is an acknowledgement of some kind of complexity that is beyond our computational ability to describe exactly. To the contrary, quantum mechanics is our attempt to describe things exactly, and it works amazingly well.
It's certainly true that a full quantum description of all but the smallest systems is far beyond our ability to compute directly. That's when we switch to statistical mechanics or similar techniques to try to deal with the complexity in a manageable way.
To the pedants: if you're trying to model a piece of paper with quantum mechanics, then you'll have to approximate the very small-scale high-energy bits, because we don't know the laws of physics at those scales. But there is so far no compelling reason to believe that those laws will not fit perfectly in the framework of quantum mechanics once we figure them out.
And so why couldn't there be an underlying parameter that determines that chance of which configuration you will see the paper in?
> But there's no respect in which quantum mechanics is an acknowledgement of some kind of complexity that is beyond our computational ability to describe exactly.
I certainly didn't mean that we are limited by our computational ability. What I meant (if it wasn't clear) was that we currently lack the understanding of these unknown parameters and their interactions
See also http://en.wikipedia.org/wiki/Loopholes_in_Bell_test_experime.... Many of these are practical matters and have been overcome in one experiment or another, but some issues (like the possibility of superdeterminism) are more fundamental.
And the article explicitly mentions how pilot waves through superfluids could give rise to nonlocal yet deterministic effects.
Very controversial statement.
http://en.wikipedia.org/wiki/Hidden_variable_theory#Bohm.27s...
Global hidden variables are no different than modelling quantum mechanics on a computer (using traditional quantum field theory) and saying that the seed you use for your random number generator value is a global hidden variable. There's nothing deep in that.
This seems like a bit of an insult based on a misconception. There are many things that could lead to a more fundamental understanding of reality, and many different people working on different options. There is no real reason for people to jump on this one, especially since it isn't clear what insight it could actually give.
I was a big fan of exploring the alternative ideas in quantum mechanics, and I tried to like Bohmian pilot waves. They are very philosophically appealing. Then I saw some results in quantum optics which pretty much convinced me it was a silly idea. Walther's ideas on Surrealistic Bohm trajectories should have been enough. I'd be curious if these oil droplets exhibit the surrealistic trajectory behavior. It would be neat if they did, but I doubt it.
While the fluid mechanical experiments are pretty damn neat, the modern revival of Bohmian mechanics is a symptom of the disease that afflicts today's physics community: there are many people who call themselves physicists who insist on working on things which have no physical consequences. If you can't do an experiment, you're a philosopher, armed with math. People who claim they might be able to make an experiment in 20-40 years (after they have tenure and have retired) are arguably worse: yes, I am looking at you, entire field of quantum information snake oil salesman: build something or shut up. All this is a sign of decadence and decay, and it is extremely sad to see so many clever people being so stupid.
FWIIW, I was exposed to Bohm mechanics in my junior year QM course; it's not like nobody has heard of it. It is actually quite ubiquitous in certain kinds of gutter popular literature; the kinds of popular QM books people who believe in psychic powers read. I've met strippers in gothic nightclubs who knew who David Bohm is. As in, more than one.
I have a general question for those who are expert in physics, or who have a hobbyist interest: have you read Louis de Broglie's "Ondes et mouvement" (1926)? it's only 133 pages in the original French edition. Or his 1924 PhD thesis? [2]
[1] http://www.physics.utoronto.ca/~colloq/Talk2011_Couder/Coude...
an article about this gets published about once a year. here's the first one i encountered: http://physicsworld.com/cws/article/news/2012/jul/09/bouncin...
Any debate about the interpretation of quantum mechanics refers to to this question of what really happens, not to any details of what QM actually predicts will happen. That is, until/unless experiments are devised to separate these philosophical explanations, but nothing much has happened on this front for decades.
It's like making Newtonian mechanical predictions based on F=ma vs. energy arguments, or analysing computation using a Turing machine vs. lambda calculus. The theory can't fundamentally change but you can use a different conceptual framework to get the same results (and some may be much easier to work with / more intuitive than others).
Mathematically it makes sense, experimentally it makes sense, it is as proven as classical physics are proven yet the two contradict each other.
Perhaps it is as the old zen-buddhist saying go. Wisdom lies in paradox.
P = 1/Sqrt[2] (Yes + No).