04
Aug
2015

## Bohmian Mechanics

How did I never hear about this until this week? Anyway, it kinda sorta uses the distinction I was getting at in the comments over at Steve Landsburg’s blog. Then it purports to explain subatomic events without resort to weird quantum stuff. And best of all, it’s got “Bohm” in the title–like Eugen von Bohm-Bawerk, you know?

Bob, you should know that there’s one downside to Bohmian mechanics – it’s a nonlocal theory. If you have a pair of entangled electrons and take them a trillion miles apart and measure their spins (along the same axis), one of them will be spin up and the other will be spin down no matter what. In the conventional quantum mechanics view (the Copenhagen interpretation), this is explained by saying that entangled electrons were in a superposition of states until their spins were measured, at which point the wave function collapses and they settle on definite spins. In Bohmian mechanics, on the other hand, the electrons communicate with each other instantaneously in order to coordinate their behavior. Most physicists prefer the wavefunction collapse explanation to the instantaneous communication explanation.

But there’s another interpretation of quantum mechanics that you may like even better. It’s called superdeterminism, and it says that rather than the electrons communicating instantaneously with each other when they’re far apart, they somehow know how in advance what experiments the experimenters are going to choose to perform in the future, and so they plan their behavior right from the start, thereby avoiding the need for long-distance communication. This is even more of a common-sense interpretation than Bohmian mechanics, but it suffers from one problem: it arguably denies the existence of free will. That is, if you define free will as the ability of humans to make choices that are unpredictable, than superdeterminism denies free will because the entangled electrons already know what you plan to do with them before you even decide.

Keshav, I assure that, true or false as it may be, the idea that electrons know in advance what I will do tomorrow is absolutely, positively as far from common sense as may be.

I just meant that it conforms to common sense except for the free will issus.

How?

Apart from the free-will issue, it’s more of a common-sense view than Bohmian mechanics, because it doesn’t involve the instantaneous faster-than-light communication between distant particles that Bohmian mechanics involves. It’s very hard to reconcile the idea of instantaneous communication with the special theory of relativity, which has a speed-of-light limit. That’s why adherents of Bohmian mechanics so often abandon the theory of relativity and adopt the Lorentz aether theory, which is experimentally indistinguishable from the theory of relativity but assumes the existence of an undetectable aether frame.

If anyone wants an explanation of Lorentz aether theory, please ask me. It’s an absolutely fascinating chapter in the history of physics.

“… and so they plan their behavior right from the start …”

That would require free will on the part of the electrons.

guest, I was just speaking metaphorically. If you want me to describe it more precisely, the behavior of the entangled electrons when they’re far apart is determined by a certain variable lambda that they both have. And the value of lambda is a function of what those electrons are going to encounter in the future. So no one’s talking about electrons literally making decisions.

How does lambda get input from the future?

I’m pretty sure this is not going to be a big deal. But since you brought up free will, I thought I’d say something.

Well, lambda doesn’t have to get input from the future. Since we’re assuming that the universe is completely deterministic (hence the name “superdeterminism”), that means that that the future is determined by the past, so lambda can depend on whatever initial conditions are ultimately going to be responsible for what the entangled electrons are going to encounter in the future.

“… lambda can depend on whatever initial conditions are ultimately going to be responsible for what the entangled electrons are going to encounter in the future.”

Compare with a scenario in which there is no lambda, and it can be said of each particle that its location could not have been anywhere other than it is, at any given point in time, given their first locations.

You’re saying more than this in the case of lambda, which requires that it have input about the initial location of each particle that it will come into contact with in the future.

Do depend on initial conditions, it must have input about those initial conditions.

How did it get that input?

Here is how lambda gets its input. Let’s call the group of particles that ultimately give rise to the pair of entangled electrons group A. And let’s call the group of particles that ultimately give rise to the particles that the two electrons interact with group B. Then it’s a theorem of special relativity that at some point in the past, group A and group B were.close enough that they had enough time to communicate with each other slower then the speed of light. (To be technical, their past light cones overlap.) So it is through group A’s interaction with group B that the information about what the entangled electrons are going to encounter is obtained, and that is ultimately what is used to set the value or the variable lambda.

If only lambda can do this, how did Group B’s particles come to contain the information about all of its future interactions with its other non-lambda group particles, such that it could pass that information on to lambda?

Perhaps I wasn’t clear enough. Group B is supposed to be the group of particles that completely determine what the two entangled electrons are going to face. So if other particles affect how a given particle is going to interact with one of the entangled electrons, then those other particles (or those particles’ “ancestors”) are also included in group B. In principle group B could consist of (the ancestors of) all the particles in the universe.

It seems, from the following comment:

“And let’s call the group of particles that ultimately give rise to the particles that the two electrons interact with group B.”

… that Group B are non-lambda particles from which the lambda particles are supposed to get input about the future states of non-lambda particles.

But how did the non-lambda particles come to contain the information upon which the lambda particles will react when experimented upon?

guest, the particles in group B have information about their current state, so that’s enough to predict all future states they have. (Again, group B could consist of all the particles in the universe.) And so when the particles in group A interact with the particles in group B, they’re able to acquire the current information about the particles in group B, and that’s enough to determine exactly what the two entangled electrons will encounter, and thus it’s enough to ultimately set the value of lambda.

“… the particles in group B have information about their current state, so that’s enough to predict all future states they have.”

It would be enough to begin the deductive process of prediction (which would require a mind and the free will to apply it), but a machine-of-sorts that you’re talking about, that merely reacts to prior causes, would need all of the in between information, as well.

Ultimately, such a lambda mechanism would need to base its actions on input about the 2nd-to-last cause (before the experiments), which would be based on the 3rd-to-last cause, and so on.

So, unless the lambda particles have the free will to go through the deductive process, then it will not be enough for them to have input about Group B’s initial state.

guest, we’re not assuming any conscious process of deduction. Since we’re assuming that the universe is deterministic, that means that the future state of a given set of particles is a mathematical function of the initial state. So lambda can be written in terms of that mathematical function. The particles aren’t sitting around calculating anything.

“So lambda can be written in terms of that mathematical function.”

But the in between variables must be known/set in order for lambda to react according to them.

Superdeterminism would require the lambda particles to contain logic circuits that controlled for all the physical and chemical reactions that could occur for each Group B particle.

Not that I believe that your lambda exists, but wouldn’t that be evidence of the free will of a designer?

“Superdeterminism would require the lambda particles to contain logic circuits that controlled for all the physical and chemical reactions that could occur for each Group B particle.” guest, for any computer program that that takes an input and spits out an output, there exists a mathematical function that gives the exact same result. So there doesn’t need to be an computers inside the particles, lambda is just automatically a certain mathematical function of the initial state of the particles in group B.

“Not that I believe that your lambda exists, but wouldn’t that be evidence of the free will of a designer?” Why would it be evidence of a designer? Regardless of whether lambda exists, there are tons of equations in physics where some variables are functions of other variables. There’s nothing at all unusual going on here as far as that’s concerned.

The variables in any function have to be known so that the operands can do calculations. Your lambda particle would have to have so many logic circuits to keep track of what the variables will turn out to be.

Also, computer programs are evidence of free will.

“The variables in any function have to be known so that the operands can do calculations. Your lambda particle would have to have so many logic circuits to keep track of what the variables will turn out to be.” guest, the only variables in the function are the initial states of the particles. What the particles in group B are going to do is not an actual input to the function. No computer programs are being run.

“… the only variables in the function are the initial states of the particles.”

The operands of functions do operand-y stuff with the variables.

For example: A(A+A).

The variables in the parentheses have to be operand-ed on, before the function can multiply the result by A.

guest, how much physics do you know? What you’re describing isn’t something unique to superdeterminism; mathematical functions far more complex than A(A +A) are part of all sorts of theories of physics, from Newtonian mechanics to Maxwell’s theory of electromagnetism to general relativity. All these theories, superdeterminism included, have the same basis property that the particles behave according to one or more differential equations, the solution of which is a potentially complicated mathematical function.

So superdeterminism doesn’t use “computer programs” any more than other theories of physics. Now if your point is that the fact that the laws of physics seem to be written in the language of mathematics signifies that there’s an intelligence at work in the operation of the Universe, I actually agree with you. I should add, though, that there are arguments against this view; Hartry Field wrote a book called “Science without Numbers” where he tried to reformulate Newtonian mechanics so that it involve little or no mathematics. Mathematics, in his view, was nothing but a useful fiction created by humans. But I’m a Mathematical Platonist (of the Frege-Russell brand of logicism); I think Mathematics is too consistent to be an arbitrary of the human mind. But for a contrary view, see Lakoff and Nunez’s book “Where Mathematics Comes From”, which argues that mathematics is an evolved feature of the human brain.

“For example: A(A+A).

The variables in the parentheses have to be operand-ed on, before the function can multiply the result by A.” Also, I think you’re operating on a misunderstanding; f(A) = A(A +A) is a single function; you don’t need to split it up into addition first and then multiplication. That’s just an srtifact of how we humans happen to write down the definition of the function.

“All these theories, superdeterminism included, have the same basis property that the particles behave according to one or more differential equations, the solution of which is a potentially complicated mathematical function.”

I’ve been trying to think of a way to express that equations should be understood independently from the nature of the particles, themselves, but all particles *will* react with each other in formulaic ways.

So, it’s difficult to make this distinction.

I believe that formulas are what humans impose on their observations.

Let me try a couple of things.

Different particles have different properties, so humans will impose differing formulas for each.

Or I like this better:

Imagine some particle with properties and a “behavior formula” that do not exist in this universe.

It can’t be said that the existing particles behave according to a formula which accounts for this particle, because it doesn’t exist.

But if such a particle were to be introduced to this universe, would the rest of the particles simply not have a reaction to it?

I think that they would, because of the nature of the particles.

“Now if your point is that the fact that the laws of physics seem to be written in the language of mathematics signifies that there’s an intelligence at work in the operation of the Universe, I actually agree with you.”

So, since a claim of superdeterminism is that a lambda particle would preclude free will, you either don’t believe in superdeterminism, or you believe that a lambda particle doesn’t preclude free will?

“Also, I think you’re operating on a misunderstanding; f(A) = A(A +A) is a single function; you don’t need to split it up into addition first and then multiplication.”

f(A) would be what we labeled the function, but the function that is called involves the split.

There’s different ways to repeat a variable in a single equation that would have different outputs for the same input..

“So, since a claim of superdeterminism is that a lambda particle would preclude free will, you either don’t believe in superdeterminism, or you believe that a lambda particle doesn’t preclude free will?” To be clear, people have concerns about superdeterminism denying free will for humans as to what experiments they choose to perform. But it has nothing to say on whether a higher power has free will in running the Universe. In any case, if you want to know my views on all this, I’m a Hindu. I think all things are determined by fate, but I don’t think that implies that we’re not morally responsible for our own actions. A villain in a movie does the same things every time you watch it, but that doesn’t mean he’s nit evil. Or better yet, a Hitler documentary plays the same way every time you watch it, but that doesn’t mean Hitler wasn’t morally responsible for his actions.

You could say that I believe in will, but not “free” will: I don’t think humans can change what is going to happen, but I think humans can play a role in bringing about what is going to happen. I’m a one-boxer in Needomb’s paradox, if that clarifies things. (Tell me if you don’t know about Newcomb’s paradox.)

“f(A) would be what we labeled the function, but the function that is called involves the split.

There’s different ways to repeat a variable in a single equation that would have different outputs for the same input..” I have nod idea what you’re talking about. We’re not calling any functions; this isn’t a computer program. The particles just behave in a accordance with a certain potentially complicated function f. There’s no computer program that’s run to calculate the value of f(x).

“You could say that I believe in will, but not “free” will:”

That’s close enough for me, with regard to superdeterminism.

“(Tell me if you don’t know about Newcomb’s paradox.)”

I didn’t, but I glanced at some stuff.

I guess I hold to a kind of one-boxer-ish view, technically, in that I believe God knows the future.

Apparently, the original paradox had a Predictor that could be fallible.

In that version, I’m a two-boxer.

“The particles just behave in a accordance with a certain potentially complicated function f.”

But that function would have to have nested functions the output of which would need to be known in order to be used by the nesting functions.

In order to do that there would have to be logic circuits.

“I guess I hold to a kind of one-boxer-ish view, technically, in that I believe God knows the future.

Apparently, the original paradox had a Predictor that could be fallible.

In that version, I’m a two-boxer.” OK, it’s good to hear that you’re alsp a one-boxer. (When people talk about one-boxers and two-boxers, they’re usually referring to the infallible predictor version.)

Note that this puts you at odds with many Austrians, who believe that being a one-boxer leads to a performative contradiction. Here’s a lecture by Roderick Long arguing that Newcomb’s paradox implies that you cannot self-consistently believe that your actions can be known in advance:

https://mises.org/library/3-free-will-two-paradoxes-choice

“But that function would have to have nested functions the output of which would need to be known in order to be used by the nesting functions.

In order to do that there would have to be logic circuits.” That’s a very strange view. So then do you believe that Newtonian mechanics and Maxwell’s classical electromagnetism also require logic circuits?

“That’s a very strange view. So then do you believe that Newtonian mechanics and Maxwell’s classical electromagnetism also require logic circuits?”

If those schools of thought have something comparable to a lambda particle, then they would have to.

guest, both those theories involve particles that behave according to functions that are far more complex than f(A) = A (A +A), so by your standard they would involve logic circuits.

In any case, do you reject Roderick Long’s praxeological argument?

Nice video! I always thought that in reality there can never be true randomness, but only randomness from ignorance, and that this a basic point in physics. And yet it seems quantum mechanics is based on the existence of true randomness.

It sounds like you’d sympathize with Steve Landsburg’s views on determinism:

http://www.thebigquestions.com/2012/07/23/late-night-thoughts-on-determinism/

He also believes that determinism in the sense of “things could not have occurred other than the way they actually occurred” is trivially true.

I need to clarify one thing. My comment only refers to dead things like particles, molecules, atoms, quarks etc. I don’t think it is good to throw thinking beings (who of course consist of said particles, molecules atoms etc) automatically into it.

Neither determinism nor true randomness can be the basis for free will. Free will is purposeful action depending on one’s values. So the question is, is there a third thing so called free will or not. I think it got nothing to do if there is true randomness in quarks or not. I mean my decisions aren’t automatically “true random” just because it is not possible to determine my next decision of either doing A or B even if you knew all physical conditions of all atoms etc within my brain and how they relate physically to each other at a certain point. They can just be purposeful.

I don’t know of course but I believe there is free will because: If there weren’t then it doesn’t seem possible or plausible to question one-self, to be self-aware, to have meaningful philosophical discussions. Why would you do that, why would a totally deterministic universe lead to us talking about the existence of free will, let alone one containing true randomness, all just coincidence?

“throw thinking beings (who of course consist of said particles, molecules atoms etc)”

If those things are what thinking beings consist of, and those things are absolutely deterministic, then there is no free will. So that must not be all thinking beings consist of.

Right I see the implications. For me it is a paradox, and I cannot reconcile it with my believe that we have free will, except with a possible existence of a soul -> god.

Your comment reminded me of this short interview with Alvin Plantinga.

https://www.youtube.com/watch?v=WOTn_wRwDE0

Levi,

Ok I see what you mean but in contrast to Mr Plantinga I don’t see how the mere thinkable possibility proves already what Mr Plantinga says it proves.

A possibility is finally defined as something that might be true or not true, else it would not be a possibility but a fact.

If you think that you think, then (maybe) you are only thinking that you think.

😉

“then there is no free will. So that must not be all thinking beings consist of.” Why do you pre-suppose free will? The other obvious solution is that there is no free will. I do not see any reason to favor the existence of free will over the existence of some mysterious third force of which we know nothing.

Interesting! This has huge philosophical implications. A friend once told me that Ayn Rand didn’t believe in quantum mechanics due to the violation of the law of contradiction. This seems to support her argument.

Wallace Thornhill, don’t get stupid over not knowing what’s going on in the field. Math is not god, it merely describes stuff, sort of, if applied correctly. No paradox here, just a 100 years old story that is dead wrong.

I still can’t get over Molyneux not getting timespace and in it time being concept only, despite his grinding of concept formation in his philosophy intro.

You might be interested in this article, that deals with the possibility that Quantum Computing could elucidate which of the QM interpretations is the true one:

http://www.pbs.org/wgbh/nova/blogs/physics/2015/06/can-quantum-computing-reveal-the-true-meaning-of-quantum-mechanics/

In case people are still reading this thread, here’s another way to think about Bohmian mechanics. The standard interpretation of quantum mechanics is the Copenhagen interpretation, where each particle has a wavefunction that’s in a constantly evolving superposition of states, and then when the particle is observed the wave function collapses and the particle randomly assumes a single state. The problem with this view has always been the following: what makes the observer so special? Why is it that the electron is in a superposition of states, whereas the experimentalist is apparently only in one state and is able to collapse the wave function?

One interpretation that solves this problem is the Many Worlds interpretation, which says that the sxperimentalist is also in a superposition of states, it’s just that the different versions of the person don’t interfere with each other much (due to something called decoherence). More generally, Many Worlds says that the entire Universe is always in a continuously evolving superposition of states, and that there’s nothing outside the Universe to collapse th Universe’s wave function. To take the example of Schrödinger’s cat, there’s one branch of the wave function which evolves as follows: first the radioactive particle decays, then the cat dies, then the experimentalist is sad. In another branch of the wave function, first the radioactive particle fails to decay, then the cat is happy, then the sxperimentalist is happy. But why is it that we don’t see these other “worlds” or branches of the Universe’s wave function? The explanation is that the different branches don’t interact much (again, because of decoherence).

Now what if you were to take just one of the branches of the wave function, and see how it evolves over time? What would you see? You would see something very much like the classical world that we humans think we inhabit, where each particle in the universe is only at one place at any given time, because it’s only in other branches of the wave function that the particle is in other places. So you could focus on a single particle and track how its position changes in a single branch of the wave function, and you’ll see that it moves quite smoothly. How would you describe this motion? Well, for large objects, it approximately obeys Newton’s laws, but for smaller objects there’s an extra term in the equation F = ma, and we can dub that the “quantum force”. That’s Bohmian mechanics in a nutshell.

So to sum up, Bohmian mechanics is what you get when you take the Many Worlds interpretation of quantum mechanics, pick one of the worlds and call it the “real” world, and then try to explain the motion of particles in that world without reference to the other worlds. It’s quite beautiful when you think about it.

“The standard interpretation of quantum mechanics is the Copenhagen interpretation, where each particle has a wavefunction that’s in a constantly evolving superposition of states, and then when the particle is observed the wave function collapses and the particle randomly assumes a single state.”

If I hold my hand behind my back and ask you how many fingers I am holding up, then I don’t suppose you are thinking that my hand is in a superposition of states that is constantly evolving (multiple states at the same time). It just means you just don’t know. The amount of fingers could change but still at each moment it would only be one definite amount. And the amount would not be random, it would only appear to you as random. So in my view Bohmian mechanics doesn’t pick any world and calls it the real one, no I think it looks at it as it really and only is.

I think Schrödingers cat is just a very complex way of saying that you don’t know the actual state of something as long as you don’t check it, and if you want to do calculations that include the cat that you have to account for the lack of this knowledge one way or another (doing two separate calculations or consider the cat “halfdead”).

PS: I think the main reason this thought experiment is so popular is because it has a cat in it. I mean seriously how many other physics thought experiments do people know? I only know this one. After checking other ones would include ladders, buckets, sprinklers, demons, cannonballs, even monkeys and astrochickens whatever that is!

“So in my view Bohmian mechanics doesn’t pick any world and calls it the real one, no I think it looks at it as it really and only is.” skylien, yeah, I’m not criticizing Bohmian mechanics. Certainly from the perspective of Bohmian mechanics, it’s describing what reality actually is. I was just explaining what Bohmian mechanics would look like from a Many Worlds point of view.

By the way, things are not as quite common-sensical in Bohmian mechanics as your “fingers behind your back” example would suggest. It’s certainly closer to common sense than the Copenhagen interpretation, but there’s still some quantum-mechanical weirdness that carries over. Let me give you an example.

If you send a photon through a polarizer, then regardless of how you orient the polarizer the photon has a 50% chance of going through the polarizer and a 50% chance of not going through the polarizer. And if you have a pair of entangled photons and you send them through two polarizers oriented at the same angle, then regardless of what that angle is, they’ll either both go through or they both won’t go through. They have a 50% chance of both going through, and a 50% chance of both not going through.

So how would you explain this? You’d say that the two photons have a common property which determines whether they’re going to go through or not go through at a given angle, right? But that explanation doesn’t work. See this web page for a good explanation why:

http://quantumtantra.com/bell2.html

Here’s the gist of it: let’s assume that the behavior of the two photons when they encounter a polarizer oriented at a given angle is determined by some common property. Let’s use that common property to define a function f(theta), which equals 1 if the photons are “planning” to go through polarizers oriented at angle theta, and which equals 0 if the photons are planning to not go through polarizers oriented at angle theta. Then if we take any three angles theta1, theta2, and theta3, then P(f(theta1) != f(theta3)) should be less than or equal to P(f(theta1) != f(theta2)) + P(f(theta2) != f(theta3)). (!= means does not equal, and P means probability.)

But it turns out experimentally that if you let theta 1 = -30, theta2 = 0, and theta3 = 30, then that inequality turns out to be false.

That’s why Bohmian mechanics relies on intantaneous faster-than-light communication, rather than the fingers-behind-your-back explanation you would assume.

I am sorry for the late reply. I wanted to look into this more closely to get a better understanding, because so far I am not understanding how this entanglement is prove really works, but I am just quite busy myself at the moment. And especially thinks like this need a bit time. However you are right it is not as simple as my hand example.

It is just so weird because obviously entanglement looks like it violates SRT, and only “strange” (in my view) explanations are currently able to reconcile this…

skylien, it may help if I write the proof in steps.

1. It is an experimental fact that if two entangled photons are sent through polarizers oriented at the same angle, then they always do the same thing, i.e. they’ll either both go through or both not go through.

2. Let us assume that for any given angle theta, the two photons have “agreed” in advance whether to go through or not. If they’ve agreed to go through if faced with a polarizer oriented at angle theta, let’s denote that as f(theta) = 1, and if they’ve agreed not to go through, let’s denote that by f(theta) = 0.

3. If f(0) ≠ f(60), then either f(0) ≠ f(30) or f(30) ≠ f(60).

4. Thus the probability that f(0) ≠ f(60) should be less than or equal to the probability that f(0) ≠ f(30) + the probability that f(30) ≠ f(60).

5. Experimentally, if two entangled photons are sent through polarizers oriented at angles 30 degrees apart, then the photons do different things (one going through and one not going through) 25% of the time, and if the polarizers are oriented at angles 60 degrees apart, then then they do different things 75% of the time.

6. Thus the probability that f(0) ≠ f(30) and the probability that f(30) ≠ f(60) are both equal to 25%, and the probability that f(0) ≠ f(60) is equal to 75%.

7. Step 6 contradicts step 4.

8. Therefore, the assumption made in step 2 must be false.

Please tell me the earliest step that you don’t understand. You can also read the link I gave in my previous comment.

The conclusion of the argument is that what a photon does “over here” seems to be somehow instantaneously affected by what kind of polarizer its twin encounters “over there”, and that any proposed explanation that suggests that there’s some “hidden” piece of information that merely makes it look like instantaneous action at a distance must fail.

Now there’s multiple ways you can react to this conclusion. You can choose to embrace instantaneous action at a distance, in which case you may forced to reject special relativity and accept the (experimentally equivalent) Lorentz Aether Theory. Or you can assume that the photons somehow knew what the experimenters were going to do in the future, in which case you may run into free will problems.

This is the homepage of the international research network on Bohmian Mechanics that was started in the 1980s by Prof.