Drawing the line between the Pilotwave and Stochastic Interpretations

[Risk]

Greetings…

I requested some books that deals with the different interpretations of QM almost a year ago and I read lots of them. My favourite was Laloe's (so whoever recommended it, extra thanks for you).

I noticed something interesting in the Bohmian mechanism, a common misconception if I may say: De Broglie-Bohm interpretation is not always rigidly deterministic, by that I mean not all of the laws are dynamic (one-valued), there is some statistical (probabilistic) laws [e.g. Quantum Equilibrium]. And these statistical laws exist objectively (not merely our ignorance as Laplace proposed). This was made clear in Bohm's book Causality and Modern Physics as well as in Vigier's work.

Now, the stochastic interpretation proposed by Edward Nelson (with Fényes and de La Peña-Auerbach) is becoming indistinguishable from De Broglie-Bohm-Vigier's, at least to me. The concepts are almost the same (Hidden Variables, Statistical Nature, No "real" wave collapse, etc...) so it would be really helpful if someone helps me out distinguish at least the main conceptual differences between the two interpretations.

Thanks in advance.

Note: I am a medical student who is interested in philosophy (in this case, the philosophy of science). So if the question seems very naïve then excuse me, it is not my "speciality".

 

[Demystifier]

My favourite was Laloe's (so whoever recommended it, extra thanks for you).

I often recommend Laloe, so it could have been me.

I noticed something interesting in the Bohmian mechanism, a common misconception if I may say: De Broglie-Bohm interpretation is not always rigidly deterministic, by that I mean not all of the laws are dynamic (one-valued), there is some statistical (probabilistic) laws [e.g. Quantum Equilibrium]. And these statistical laws exist objectively (not merely our ignorance as Laplace proposed). This was made clear in Bohm's book Causality and Modern Physics as well as in Vigier's work.

I would say that "statistical" and "probabilistic" are not the same. The statistical content of quantum equilibrium is objective, but its probabilistic content is a matter of ignorance. Since you are a medical student, let me use a medical analogy. When you say that 10% of population dies from cancer, it's an objective statistical claim. But when someone infers from that that there is 10% chance that you will die from cancer, it's a probabilistic statement that stems from ignorance. With additional information about you (e.g. about your genes and current health problems) one might conclude that your own chances are significantly different.

Now, the stochastic interpretation proposed by Edward Nelson (with Fényes) is becoming indistinguishable from De Broglie-Bohm-Vigier's. The concepts are almost the same (Hidden Variables, Statistical Nature, No "real" wave collapse, etc...) so it would be really helpful if someone helps me out distinguish at least the main conceptual differences between the two interpretations.

In De Broglie-Bohm theory, the probability just stems from ignorance. In Nelson theory, the probability is objective.

 

[Risk]

I often recommend Laloe, so it could have been me.

Well, I just checked that old thread and a mentor called "DrClaude" recommended it, you then approved his recommendation, so thanks both of you!

When you say that 10% of population dies from cancer, it's an objective statistical claim. But when someone infers from that that there is 10% chance that you will die from cancer, it's a probabilistic statement that stems from ignorance

I actually do not see any difference between the two examples; 10% of the population dies from cancer every year, I am an individual from the population, therefore there is 10% chance I'll die from cancer. Now of course there are some conditions predisposing to cancer in the particular, but that doesn't change the fact in the universal. For example, if I flipped a coin, and the result is tails, no one in his sane mind would think that there was no cause/conditions that favoured the tails over the heads in that particular instant. But if we flipped the coin 100 000 times and the coin was symmetrical, the both possibilities would be realized with almost identical necessity i.e. it will approach 50-50. In this instant the statistical law (50-50) emerged from the dynamical law of each toss. On the contrary, dynamical laws can emerge from statistical ones, such as the statistical nature of the gas molecules and the dynamical state of the gas as a whole (an this is the example that Bohm discussed in his book).

In De Broglie-Bohm theory, the probability just stems from ignorance. In Nelson theory, the probability is objective.

What about Bohm and Vigier's works on Quantum Equilibrium for example? Bohm was Marxist by then (whereas Vigier died a Marxist), and dialectical materialism does state that chance events (and therefore statistical laws) are objective, not a mere reflection of our ignorance (as Laplace claimed).

Thanks again.

 

[Demystifier]

Well, I just checked that old thread and a mentor called "DrClaude" recommended it, you then approved his recommendation, so thanks both of you!

You are welcome.

I actually do not see any difference between the two examples; 10% of the population dies from cancer every year, I am an individual from the population, therefore there is 10% chance I'll die from cancer. Now of course there are some conditions predisposing to cancer in the particular, but that doesn't change the fact in the universal.

But you are not the universal, precisely because of your predisposing conditions. For instance, if right now you are in the plane with a malfunction on both engines at 10.000 km, the probability that you will die from cancer is almost 0%.

By the way, it is well known that medical students have problems with understanding probability, especially when false positives and false negatives are involved. See e.g. https://brownmath.com/stat/falsepos.htm

What about Bohm and Vigier's works on Quantum Equilibrium for example? Bohm was Marxist by then (whereas Vigier died a Marxist), and dialectical materialism does state that chance events (and therefore statistical laws) are objective, not a mere reflection of our ignorance (as Laplace claimed).

Marxism and dialectical materialism are irrelevant here. One particular paper of Bohm and Vigier adds a stochastic element to the De Broglie-Bohm theory, which is more similar to the Nelson theory than to the standard De Broglie-Bohm theory.

 

[Risk]

But you are not the universal, precisely because of your predisposing conditions. For instance, if right now you are in the plane with a malfunction on both engines at 10.000 km, the probability that you will die from cancer is almost 0%.

True, I am not the universal, but when a scientific research says that "10% of the population dies from cancer every year" it takes into the account the conditions that the population lives within. The same as saying that "there is 50% of coin tosses will yield heads", it takes into account the conditions such as the symmetry of the coin. Yes, there are particular conditions that favored the heads in a given toss like the strength of the hand, but I wouldn't say that the statistical law (the 50%) was a reflection of my ignorance, on the contrary, statistical laws are a mode of manifestation as the dynamical ones. And I gave two example where the statistical and the dynamical laws were once a part and a whole.

By the way, it is well known that medical students have problems with understanding probability

LOL! very true! I had to read some of the history of statistics to grasp the different views on the topic (and I barely do :S). Anyways, what I stated (the objectivity of chance events and statistical laws) was also held by Cournot, the French philosopher and mathematician.

Marxism and dialectical materialism are irrelevant here.

True. I mentioned them just to contrast between their philosophical and scientific beliefs. I really rule out the inconsistency in their views.

One particular paper of Bohm and Vigier introduces a stochastic element to the De Broglie-Bohm theory, which is more similar to the Nelson theory than to the standard De Broglie-Bohm theory.

It is more than just one paper, Bohm's Causality and Chance in Modern Physics dealt with the "dialectic" of statistical and dynamical laws. I really recommend you reading it, it's a small book.

which is more similar to the Nelson theory than to the standard De Broglie-Bohm theory

So the modified version is stochastic also? Weird. The concepts are becoming harder to grasp. I will wait for any explanation from other members.

And for the millionth time, thanks Demystifier!

 

[stevendaryl]

I actually do not see any difference between the two examples; 10% of the population dies from cancer every year, I am an individual from the population, therefore there is 10% chance I'll die from cancer.

Suppose that 10% of the population has blue eyes. Does that mean that there is a 10% chance that you will have blue eyes? If I know nothing else about you, then I might assign that probability. But if I knew that your parents were Chinese, I would assign a much lower probability that you have blue eyes.

So the statistic that 10% of the population has blue eyes is an objective fact that we can establish by counting. My estimate that you have 10% chance of having blue eyes is based on my ignorance about you.

 

[stevendaryl]

Suppose that 10% of the population has blue eyes. Does that mean that there is a 10% chance that you will have blue eyes? If I know nothing else about you, then I might assign that probability. But if I knew that your parents were Chinese, I would assign a much lower probability that you have blue eyes.

So the statistic that 10% of the population has blue eyes is an objective fact that we can establish by counting. My estimate that you have 10% chance of having blue eyes is based on my ignorance about you.

This is actually why health statistics are so frustrating. If they report that people who drink lemonade are more likely to have diabetes, or whatever, that doesn't actually tell me whether I will be more likely to get diabetes if I drink lemonade, or whether I will be less likely to get diabetes if I give up my lemonade. The statistics don't actually say anything about me (or they may not).

 

[Risk]

The thing with your example Steven is its simplicity. The statistics of the eye colour is descriptive, there is no relation, whether causal or not, between veriables of any kind. Compare and contrast your example with the cancer in a population suffering from risk factors or the result of a toss of a coin. In the latter instances you can see a causal link being investigated, that stable relation what marks a “law”! Something that your example doesn't satisfy.

Anyways, it will be better to stick to the main problem I'm suffering from. In his book, Bohm clearly developed his ideas on determinism and chance. The gist is:
1. There is no absolute (Laplacean/Mechanistic) necessity.
2. Necesity and chance are complementary in nature.
3. Statistical laws, as the dynamical ones, reflect an objective reality, are mode of manifestation, and aren't merely a projection of human ignorance.

The forward was written by de Broglie himself, which is filled with praise. Allow me to quote from it:

Professor Bohm has thought that the moment had come to take up again in his researches the critical examination of the nature of physical theories and of interpretations which are susceptible to explaining natural phenomena as fast as science progresses. He has compared the development of classical physics, where in succession the viewpoint of universal mechanism, and then of the general theory of fields, and then of statistical theories have appeared, one after the other, with the introduction by quantum physics of its own new conceptions. He has shrewdly and carefully analysed the idea of chance and has shown that it comes in at each stage in the progress of our knowledge, when we are not aware that we are at the brink of a deeper level of reality, which still eludes us. Convinced that theoretical physics has always led, and will always lead, to the discovery of deeper and deeper levels of the physical world, and that this process will continue without any limit, he has concluded that quantum physics has no right to consider its present concepts definitive, and that it cannot stop researchers imagining deeper domains of reality than those which it has already explored.
I cannot give here a complete account of the thorough and fascinating study which Professor Bohm has made. The reader will find a very elegant and suggestive analysis which will instruct him and make him think. No one is better qualified than Professor Bohm to write such a book, and it comes exactly at the right time.

De Broglie also mentioned his protégé, Jean-Pierre Vigier, and the collaboration with Bohm in certain experiments. So it appears to me that three of them adopted a “modified” version of the pilotwave. One that doesn't eliminate chance but encompasses it. One that I have a problem strictly distinguishing it from the stochastic interpretation.

 

[stevendaryl]

The thing with your example Steven is its simplicity. The statistics of the eye colour is descriptive, there is no relation, whether causal or not, between veriables of any kind. Compare and contrast your example with the cancer in a population suffering from risk factors or the result of a toss of a coin. In the latter instances you can see a causal link being investigated, that stable relation what marks a “law”! Something that your example doesn't satisfy.

That's exactly the point: There is a difference between a probabilistic model and a statistical model. The mere existence of a statistical correlation between two variables doesn't imply that they are causally related. With health studies showing that x% of people who do y develop disease z, the researchers are HOPING to get at some causal relationship, but the mere fact of the statistical correlation doesn't prove there is a causal relationship.