# I A skeptic's view on Bohmian Mechanics

#### Demystifier

2018 Award
To me, it's superdeterminism if the explanation for why something happened can potential involve fine-tuning the initial conditions of the entire universe.
Exactly! But the problem is to give a precise definition of "fine".

Getting back on-topic: There should be a definitive answer, one way or the other, about whether BM requires superdeterminism of the conspiracy kind. I don't see that it does.
Neither do I. But some think that quantum equilibrium is a conspiracy. Unfortunately, it's impossible to give a rigorous proof that it isn't, because there is no precise definition of conspiracy.

#### rubi

The general idea is that only "soft" superdeterminism is admissible, i.e. superdeterminism which does not involve some kind of conspiracy in initial conditions. But what exactly is conspiracy? Unfortunately, there is no precise definition. Is thermal equilibrium a conspiracy? Is quantum equilibrium a conspiracy? Is 't Hooft's theory of local hidden variables a conspiracy? As you may guess, opinions differ.
This guy claims to have a superdeterministic local hidden variables model for the EPRB correlations that retains more free will (in a quantifiable way) than non-local models. I didn't study it in depth, but it seems like if we allow superdeterminism at all, then you can get along with soft superdeterminism in local hidden variable models as well.

As you say, this is contextuality in the CH framework. But in the framework of hidden variable theories, contextuality is interpreted in a slightly different way.
You can certainly interpret it in many ways, but the no-go theorem says that you can't form statements of the form $S_x=+1\wedge S_y=-1$ without somehow including a reference to the context. Bohmian mechanics can't circumvent this necessity.

Note also the following. In BM, particle at a given instant of time has both position and momentum (velocity times mass). And yet, in the FAPP sense, it makes the same predictions as standard QM. If you think it's impossible, note again that I said FAPP. The FAPP acronym was devised by Bell, and one always needs to have the FAPP caveat in mind when thinking about BM. Without the FAPP caveat, BM looks impossible, wrong, inconsistent, or in contradiction with experiments. One must learn the FAPP way of thinking to understand BM.
I don't know how this works exactly in BM, but you can also make such FAPP statements in CH by taking coarse grained families of histories or maybe computing Wigner quasidistributions and cutting off the negative parts and so on.

Well, if $\lambda$ depends on $\alpha$ and $\beta$, and $A$ depends on $\lambda$, then indirectly, $A$ depends on $\alpha$ and $\beta$.
Well, I was asking about $P(\lambda|\alpha,\beta)$ in order to compare it to Bell's formula, because I wasn't sure whether I understood your example.

If something is not deterministic, then it surely is not superdeterministic, either. The point is to show that having $\lambda$ depend on $\alpha$ and $\beta$ does not imply superdeterminism.
But the situation is different in BM. Not $\alpha$ or $\beta$ determine $\lambda$, but $\lambda$ determines $\alpha$ and $\beta$. The initial conditions must be such that the detector settings attain the values that produce the correct correlations and this is the case if and only if they have been tuned to be distributed according to $\left|\Psi\right|^2$. A wrong initial distribution of the hidden variables will produce deviations from the QM predictions.

#### Demystifier

2018 Award
You can certainly interpret it in many ways, but the no-go theorem says that you can't form statements of the form $S_x=+1\wedge S_y=-1$ without somehow including a reference to the context. Bohmian mechanics can't circumvent this necessity.
Sure, you must somehow include a reference to the context. Copenhagen does it in one way, CH in another way, and BM in a third way.

#### stevendaryl

Staff Emeritus
But the situation is different in BM. Not $\alpha$ or $\beta$ determine $\lambda$, but $\lambda$ determines $\alpha$ and $\beta$. The initial conditions must be such that the detector settings attain the values that produce the correct correlations and this is the case if and only if they have been tuned to be distributed according to $\left|\Psi\right|^2$. A wrong initial distribution of the hidden variables will produce deviations from the QM predictions.
Ah. I see what you mean now. The $\lambda$ for Bohm is basically the positions of everything in the universe, which of course determines Alice's and Bob's settings. On the other hand, the reasons for rejecting superdeterminism, which is the feeling of things happening by conspiracy, don't seem to apply. So I think that it shows that our definition of superdeterminism of the bad kind needs to be refined.

I'll have to think about it.

#### Demystifier

2018 Award
or maybe computing Wigner quasidistributions and cutting off the negative parts and so on.
Wigner quasidistribution is an interesting quantity for comparison with BM. For a Wigner quasidistribution $W(x,p)$ we have
$$\int dp W(x,p)=|\psi(x)|^2$$
$$\int dx W(x,p)=|\tilde{\psi}(p)|^2$$
In BM there is a true (positive definite) distribution $\rho(x,p)$ which, in general, satisfies
$$\int dp \rho(x,p)=|\psi(x)|^2$$
$$\int dx \rho(x,p) \neq |\tilde{\psi}(p)|^2$$
At first sight, the last inequality (compatible with the KS theorem) looks like a serious problem. Nevertheless, it is not a true problem because $\rho(x,p)$ depends on the context, and in the context in which $p$ is measured one has
$$\int dx \rho(x,p) \simeq |\tilde{\psi}(p)|^2$$
where $\simeq$ is an equality in the FAPP sense.

#### DejanK

My point is that EPR realism can be dropped in many different ways. Solipsism is one way, but there are also others. What is the "right" way?

As one possible meaning, let me copy-paste from my presentation at a conference:

1.2 Making sense of local non-reality

- One interpretation of Bell theorem: local non-reality
- Physics is local, but there is no reality.

- Does it mean that nothing really exists?
- That would be a nonsense!

Here is what it should really mean:

- Physics is not a theory of everything.
- Something of course exists, but that’s not the subject of physics.
- Physics is not about reality of nature,
- In physics we should only talk about measurable stuff.
- It’s important to talk also about non-measurable stuff,
but just because it’s important is not a reason to call it physics.

Bell theorem ⇒ reality is non-local
- logically correct, but that is not physics

QM ⇒ signal locality
- that is measurable, so that is physics

In short, “local non-reality” should mean:
- Reality is non-local.
- Physics is about the measurable, which is local.

- In that form, local non-reality does not necessarily
need to be accepted, but at least can be reasonably debated.
I believe that whole QM and related discussions became way too complex, likely because of use of so many abstract terms which everybody interprets in many different ways.
For example - what is meant by 'non-reality' is very abstract and confusing. One might wonder if it means material reality, for which some aspect of matter/energy occupies finite physical space, or it also includes an abstract reality as some material creature like us might create an abstract picture in ones mind as part of its reality.
Does reality includes abstraction in form of laws of physics describing part of nature as it is, etc.... one might be quite confused with possible spectrum of meanings, so no wonder people are confused.
Such state of confusion will likely be quite difficult to resolve...
In my humble opinion, I believe that science requires very solid 'bedrock' of axiomatic principles which are simple, understandable and agreeable on which basis all should be built on.
Other than that we should have theories which clearly state on which basis such proposals are made and which can clearly delineate between what is proven in physics, what is proposed etc.
Unfortunately, formal mechanisms of mathematical abstraction does not include tools which would allow for clear delineation between what is proven, what is postulated, and what is pure fairy tales. Until we have something like that, we will keep depending on fairly wishy-washy interpretations from each individual perspective, driven by all that makes each of us - not so perfect individuals, point in time, personal traits and levels of knowledge, including quality of chalk used on a whiteboard and how well professor slept the night before lecture...
Also, in this culture of 'winners' and perpetual need to be correct and the best, it is quite unusual to hear statement 'I don't know'. Recognizing the gaps of lack of understanding might be first step towards trying to think about alternatives that might be still open questions... Only correct and sincere questions that might be outstanding for resolution, will eventually takes us somewhere...but in a zoo of informal and non structured expressions it is not going to be easy...

#### DrChinese

Gold Member
1. I believe that whole QM and related discussions became way too complex, likely because of use of so many abstract terms which everybody interprets in many different ways.

2. For example - what is meant by 'non-reality' is very abstract and confusing. One might wonder if it means material reality, for which some aspect of matter/energy occupies finite physical space, or it also includes an abstract reality as some material creature like us might create an abstract picture in ones mind as part of its reality.
Does reality includes abstraction in form of laws of physics describing part of nature as it is, etc.... one might be quite confused with possible spectrum of meanings, so no wonder people are confused.
1. The differences in interpretations of QM may be as you say ("abstract terms"), but application of QM generally does not. You can look at advanced textbooks on the subject, and see that the theory is well-developed, matches experiment nicely, and generally of high predictive value.

2. In the EPR/Bell sense, "reality" (and therefore "non-reality") has a much more specific meaning. That is: do quantum observables (such as position, momentum, spin) have well-defined values at all times? EPR held that since any of these could be predicted with 100% certainty without disturbing a particle, there must be an element of reality to their existence. Bell showed otherwise if certain "reasonable" assumptions were made.

None of this, in other words, really relates to the kinds of "reality" you refer to - which are more philosophical concepts than physical ones.

#### DejanK

1. The differences in interpretations of QM may be as you say ("abstract terms"), but application of QM generally does not. You can look at advanced textbooks on the subject, and see that the theory is well-developed, matches experiment nicely, and generally of high predictive value.

2. In the EPR/Bell sense, "reality" (and therefore "non-reality") has a much more specific meaning. That is: do quantum observables (such as position, momentum, spin) have well-defined values at all times? EPR held that since any of these could be predicted with 100% certainty without disturbing a particle, there must be an element of reality to their existence. Bell showed otherwise if certain "reasonable" assumptions were made.

None of this, in other words, really relates to the kinds of "reality" you refer to - which are more philosophical concepts than physical ones.
I do not believe that we are on the same page regarding point 1, as we might be writing about two mutually different things. Application of quantum mechanics is absolutely not in question as theory is well developed and it fully matches experiment nicely. That is absolutely so.
However, my point is, in order for us to be in position to advance from that point on, we will have to postulate and explore reality of nature further, in order to eventually reach better understanding of underlying processes which must be supported by experimental data. Negating possibility to be able to eventually do so is not in spirit of science nor in alignment with lessons learned and with historically accumulated experience of mankind (ie. not long ago many believed that it would be impossible to travel by car 100km/h as driver would loose air for breathing). Therefore, we must give ourselves a chance to imagine that it is possible and to explore what really might make sense.
Example: analog thermometer constructed with liquid mercury, together with instruction manual, confirms instruction manual for its use each time temperature measurement is performed (assuming that instructions are followed correctly). Each such measurement would represent yet another confirmation of experimentally validated fact which scientists previously studied in order to correlate experimental data of liquid mercury volume expansion or contraction with temperature change.
Knowing that thermometer works correctly, as per scientifically backed instruction manual, hopefully should not prevent someone to wonder why mercury expands or contracts to start with. Our science could have stopped at that point, but it did not, as people realized and learned much deeper structure related to that specific metal and learned why it actually behaves so. We went much further than that.

Therefore, to say that QM simply works and that we do not need to worry about it is simply not good enough for the ones that will eventually, like we always did, learn and experimentally prove yet another layer of the same reality that we keep re-discovering with deeper understanding.

In case that such perspective is considered philosophy, I believe that is perfectly fine, as science does not exist in isolation from people that think and wonder. Also, our ability to question and obtain new perspectives and knowledge, was proven to be the key factor for our evolutionary success, differentiating ourself from the species taking their environment for granted, and because of that, I do not see any reason why we should stop now.

#### DrChinese

Gold Member
...In case that such perspective is considered philosophy, I believe that is perfectly fine, as science does not exist in isolation from people that think and wonder. Also, our ability to question and obtain new perspectives and knowledge, was proven to be the key factor for our evolutionary success, differentiating ourself from the species taking their environment for granted, and because of that, I do not see any reason why we should stop now.
Well, this is not the philosophy forum for one thing. And I don't think that pondering (or not) whether Bohmian Mechanics is (or is not) the best interpretation will boost evolution of the species. And debating the best way to advance science is a separate topic, and certainly one with room for many different opinions.

At any rate, it would make more sense for this thread if we discussed "realism" within the realm of Bohmian theory. That is why I included point 2 in my post.

#### DejanK

Well, this is not the philosophy forum for one thing. And I don't think that pondering (or not) whether Bohmian Mechanics is (or is not) the best interpretation will boost evolution of the species. And debating the best way to advance science is a separate topic, and certainly one with room for many different opinions.

At any rate, it would make more sense for this thread if we discussed "realism" within the realm of Bohmian theory. That is why I included point 2 in my post.
Just a reminder that Dr. Bohm himself thought that segregation of science and topics from one larger 'wholistic' attempt to understand nature, represents problem on its own, which I agree with, so I feel that my opinion is in that context relevant for this room.

Regarding point 2 regarding realism within realm of Bohmian theory, I have question regarding interpretation of 'realism' - maybe somebody knows- is realism meant as:
a) very specific local values in case that somebody can measure them
b) very specific local values without anybody ever measuring

By b) is meant that for instance laws of physics were in existence before we evolved to the point to be in position to even think of measurement.

#### eloheim

In quick before the padlock comes down on this one...
But anyway, I would find it more interesting to restrict the discussion to whether Bohmian mechanics is superdeterministic or not, since this can be analyzed mathematically, while adopting CH is a matter of taste.
This has probably been covered and resolved already, but isn't Bohm's theory saved from a need for superdeterminism by the existence of non-local influences? It sounds like you're wanting to think about local quantum theories, rubi, (and whether they would need to be superdeterministic), but just as far as the issue of Bohmian Mechs and superdeterminism, doesn't the non-local guiding pilot wave adequately answer that charge? And honestly I am asking non-rhetorically, because I'm not at all familiar with the intricacies of Bohmian foundations study. (Sorry!)

I just wanted to say to the participants above (especially Arnold Neumaier, demystifier, rubi) that I very much enjoyed reading the back and forth. Although I doubt many minds were changed, the scope and intensity of the debate was very enlightening to me.
Also, while I'm here, I whole-heartedly second DrChinese's sentiments here. Even if it's not pretty, this thread testifies to the broad range of opinions educated people can hold on these topics, despite the seemingly endless discussion. I'm not so impressed that people ARE arguing these issues after so long, but by the quality of the workmanship, and the effort expended by all sides throughout! Cheers!!

"A skeptic's view on Bohmian Mechanics"

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