What kind of imperative can force quantum randomness?

I thank you sincerely for your responses.

Unfortunately, I did not explain my question well enough. And it is a subtle point. I used the word "decision" without being precise on my meaning. I wish to propose the idea that "decision-enforcement" is a separate process from decision-choice. My suggestion is that decision-enforcement constitutes a constraint on the quantity of information a quantum system can hold. The quantum system then must discard information if it is to comply with the constraint. Which of the system's information is discarded, is not determined. My question is not about decision-choice. My question is: What information does a quantum experiment impose that makes decision-enforcement imperative?

Thanks, Steve.

Bastijan Pauly

What kind of imperative can force such a decision?

The imperative of possibility.

Does such a decision resist the imperative?

No, it conforms to it.

Thank you Björn,

I agree the wording of my question is not ideal. I tried to improve my question by adding my answer above. (about the fourth down from the top).

Are you saying you think that the quantum world is deterministic?

My work takes the view that there is quantum randomness. It is from that premise I ask my question. I am very much hoping please, for responses that address my question and not my premise.

Best wishes.

If your work takes that view it is a game changer for sure. But if you search for the imperative you might consider going a level down to the deterministic world of coherence. Like we do

\psi = S \psi_0

where S is the evolution operator. Nothing random

John Sowa

This thread gets into a huge number of scientific, philosophical, psychological, and practical issues that have been debated for nearly a century. We're not going to solve them in this thread. But I'd like to make some observations about them.

I agree that the mathematics of wave functions is purely deterministic. But the uncertainty principle implies that any attempt to determine a precise value for one variable of a complementary pair will increase the uncertainly in any observation about the complementary variable.

David Bohm was trying to develop a theory of hidden variables that is consistent with the mathematics of wave functions. It might enable physicists to explain the source of uncertainty, but it won't remove the uncertainty. It cannot help us observe both variables in a complementary pair with arbitrarily precision.

Therefore, Bohm's theories (or any theories along the lines he pioneered) won't eliminate the randomness in practice. The only difference would be to change the kind of randomness. Instead of a randomness in nature itself, it would be a randomness in what we can know about nature. Whatever the source, it won't make a difference in practice.

Thank you sincerely John for your response,

I think I must ask this question again using tighter language. It is difficult to ask a question like this without setting off side issues and quarrels. I was hoping for a discussion about what agency might prompt decision.

Compare with the old story about the donkey who starved to death after being placed equidistant between two bails of hay. The idea is that a decision is impossible because no choice is preferred -- unless the decision is purely random. The kind of answers I was expecting would relate to symmetry breaking of the complimentary variable.

Thanks.

Taner Edis

I address some of these questions in a paper I wrote with Maarten Boudry, "Beyond Physics? On the Prospects of Finding a Meaningful Oracle." My view is that randomness in physics—quantum mechanics in particular—is fundamental, and not all that surprising.

Article Beyond Physics? On the Prospects of Finding a Meaningful Oracle

Dear Ramon,

Thank you for your very helpful, informative and kind response. From my studies, in the past few weeks, I have come to believe that quantum collapse is a mechanism something like the donkey situation. I have some very loose ideas of how the mechanism might work, but nothing yet specific. But I do suspect that there is such a mechanism, through which an experiment leaves the 'quantum-donkey' with no option but to take action.

Considering the example of a quantum measurement with two equally probable outcomes, the kind of mechanism I imagine is one entailing perfect symmetry prior to measurement. At measurement, the experimental apparatus imparts logically dependent information in the complimentary (variable) symmetry, which forces decision from the symmetry under measurement, but not the decision-choice.

With thanks, Steve.

Mihai Prunescu

Steve,

You wrote: """If the decision between two choices is to be made, but neither choice is preferred over the other, because there is perfect symmetry between the two, then no information separates the choices and the only decision that can be made is a random one."""

I believe that this situation cannot be found anywhere in nature, and also cannot be modelled in vitro. There will always be some unsymmetric factor around - more matter on the left side in the neighboring universe, or more light from one direction, or whatever. I would also dare to formulate a principle: "NATURE HAS HORROR OF SYMMETRY" In particular there will be no perfectly random phaenomena, even at quantum scale...

[of course nature has also horror of vacuum, and different degrees of partial vacuum exist - and the whole nature is a kind of game between vacuum and existence; the whole philosophy seems to work also if we substitute the word "vacuum" with the word "symmetry" in the lines above]

I think genuine ontological randomness is logically inescapable given what we know about the world so far. I can't see how QM can be made to work without it and still be compatible with the EPR experiment, for example. Bell's inequalities also shows very clearly that any theory relying on hidden variables must be wrong.

Bell inequalities compare two results obtained for the cases of probabilities (hidden variables, randomness) and amplitudes of probabilities (coherence). So far coherence wins over randomness,

Uncertainty principles is often formulated as impossibility to measure two variables with arbitrary precision. It is not so. It is deeper. One cannot construct such wave function. Not measure, but even imagine.

Igor, I agree regarding what you say about the uncertainty principles. But I don't get what you mean regarding the Bell inequalities. The standard view is that Bell showed that (local) hidden variables can't exist. And it's just a small step from realising that true randomness exists.

Igor, wave functions on phase space exist, they are well-known and often used in quantum optics. A standard representation of the canonical commutation relations.

And Bell's inequality is also no argument against classical probability. It is a conflict with Einstein causality. If one goes back to the Lorentz interpretion, where we have a hidden preferred frame, where causal influences can act with arbitrary high speed, no conflict arises. And existing hidden variable theories like de Broglie-Bohm theory have no problem with giving a model where classical probability - combined with classical causality in a preferred frame - predicts violations of Bell's inequality.

Bell inequalities are formulated for the hypothesized case of hidden variables. They are certain correlations shown to be bounded if the unknown hidden variables are distributed randomly with the probability p(\lambda). On the other hand, if the system is described with the coherent wave function \psi normalized as the amplitude of probability then the correlations may go beyond the limit. The Bell inequalities are then violated. That's what experiments show. I don't see how one can infer randomness of this.

Of cause, working with the wave functions we know procedures for calculating probabilities. But a half of the world is lost then. Amplitude of probability has more information.

I know very little about Bohm interpretation apart from it being a hybrid system which keeps wave function coherence and adds some additional classical variables. Well, if the coherence is kept...

Igor, hidden variable theories exist, you can study them if you like, de Broglie-Bohm theory is, in particular, quite well studied - and Bell was, by the way, one of its most rigorous proponents. The phase is not lost, but gets an interpretation, or as describing the velocity (like in deterministic dBB theory) or as the probability flow (in other interpretations like Nelsonian stochastics).

Again, the violation of Bell's inequality is not a problem at all, but a simple consequence of the definition of the effective wave function of a subsystem - one has to put the actual value (the not so hidden hidden variable) into the wave function to obtain the effective wave function for the remaining part. This is clearly a nonlocal influence and makes dBB theory and other hidden variable theories which use the same reduction formula non-Einstein-local.

You might like to read what physicists think about randomness:

Title: A Snapshot of Foundational Attitudes Toward Quantum Mechanics

Web: http://arxiv.org/abs/1301.1069

Igor, I think randomness can be inferred not from Bell but from a combination of the EPR experiment and relativity. Please see the first paragraph at page 66 in my paper. The idea is very simple.

Ilja, the main problem with hidden variable theories like Bohms pilot wave theory is that to make them work they need to be very explicitly non-local. So it's hard to get them to work together with the rest of established physics.

Steve, a poll. You are not serious. I will tell you a joke from my youth. I was studying calculus then. And was told that one French mathematician was trying to explain a theorem to a French noble to no avail. The noble could not understand. Then the mathematician exclaimed in desperation 'I swear it is so'. The noble said 'What is the problem? I am a gentleman, you are a gentleman. I will take your word for it.' This was so funny. I am not a noble.

But I see equations. And I know the procedure. I know how to obtain that randomness you are talking about from the deterministic wave function. I know also that this is not necessary if you assume that the world in quantum mechanical in its essence. This is an ontological question.

I don' know what an event is. That's difficult. I don't know what the mind is. Especially since my native language does not have that notion. I am thinking on.

Nick, no, this is not problematic at all. Yes, it is nonlocal and it has to be nonlocal, because quantum theory is nonlocal. But to incorporate established theories is not a problem, the first example of a relativistic field theory is part of Bohm's original paper, today there are proposals for all the standard fields.

What is violated is only relativistic ideology. That means, that a preferred frame is not only undetectable by observation, but is not allowed to exist. Thus, positivistic ideology - unobservables cannot exist. But, of course, those who are interested in hidden variables do not buy this ideology - it would forbid hidden variables anyway, without any impossibility theorems or so. And if hidden variables are not rejected consequently, out of positivistic ideology, why should one object against a hidden preferred frame?

Ilja, OK but in the process the theories just gets uglier and uglier. And as Dirac and others have pointed out if it's ugly it can't be true. ;-) But seriously, if you really believe in hidden variables at all costs for some reason you should of course pursue these solutions. I'm more into simply accept what nature tells us, and I think QM + relativity clearly tells us that ontological randomness do exist.

I'm actually writing an article about a new hidden variable theory, which seems much better than the existing ones. Essentially, quantum movement is classical Hamiltonian movement combined with a simple random process, which enforces the uncertainty relations - surprisingly, it can be made really that simple.

Great, I really look forward to see a simple hidden variable theory! Please let me know when your article is published or when you have a draft I can read. To me these theories as well as all the many world theories are just desperate attempts to restore determinism at the core of all physical theories. Why this urge among many physicists is so strong I don't know. This is despite that fact that determinism always has had well known philosophical problems of its own that are not solved by these theories by any means. So even if a really simple deterministic interpretation of QM is developed some day all the philosophical problems with determinism in itself remains.

Ilja, I'm curious. If you do the poll Steve sent a link to what will your answers be? (Mine are 1d, 2c, 3b, 4c, 5c, 6d, 7b, 8d, 9b, 10b, 11c, 12l, 13a, 14a, 15a, 16d.)

My answers to http://arxiv.org/pdf/1301.1069v1.pdf

1 randomness: whatever the actual theory says, the next more fundamental theory can give a different answer. My theory will contain a classical random process, but such a thing can easily transformed into a deterministic chaos by a more fundamental theory.

2: They have "their properties" defined - but this may not be the observable values. "Measurement" results depend also on the state of the "measurement devices", different to what their name suggests.

3: Partially correct (incompleteness) partially wrong (fundamental theory will not be Einstein-causal).

4: b Bohr is wrong

5. c Measurement problem is solved in another way (reduction to effective wave function using the actual trajectory of the measurement device).

6. abcd

7.a

8. no answer, tend to e, never, but in some limited scope something useful can come out of this.

9. a epistemic. But this is yet research program, ontic is simpler (the stochastic process which I need is simple if the full wave function can be used to define it)

10. a b

11 b

12 from the named candidates c dBB theory, but I of course will prefer my own ;-), so l.

13 c (minimal-> dBB -> Nelson -> Caticha -> my own)

14 b, in my case a little, because the philosophical ideas it is based on I refuse to name "prejudices" because I have considered (and rejected) alternatives based on arguments. A little bit prejudice will, of course, always remain - and influence which arguments I will consider decisive.

15 a - but only in principle

16 c who knows

Dear Steve,

Nature abhors a true degeneracy! In chemical physics we have the Jahn Teller theorem that provides the imperative.

However there is a much more serious problem lurking in the dark, namely when you are unable to choose because of an innate contradiction, cf. the liars paradox or whether the Gödel sentence can be proved.

You do not have to force any randomness. Quantum theory is inherently random

even at a one particle level. It just give different possible answers, with different

probabilities.

No Juan,

QM is not inherently random – it comes with important subtle constraints. Furthermore QM provides a remarkable agreement between theoretical predictions and the most accurate experiments including sophisticated advanced instrumentation.

Quantum theory is not deterministic like classical mechanics.

It deals with probabilities. There is no classical trajectory

Thats what I mean by random.

sure there are constraints, schrodinger plus boundary conditions.

I do not dispute its success.

Hello.

There are people who believe randomness is irreducible, others who don't. You may like to refer to these publications. The first is experimental evidence of randomness having mathematical origins as opposed to physical. The second is a survey of what physicists believe.

This question I ask is not intended to prolong debate about whether or not. My interest is in conceptualising a mechanism for randomness.

Article Logical independence and quantum randomness

Article A Snapshot of Foundational Attitudes Toward Quantum Mechanics

Steve,

It seems to me that randomness in connection with quantum mechanics is a very confusing concept as it is intimately connected with the interpretative questions of QM as well as depends on what question is asked and what measurement one intends to do. Randomness associated with e.g. equilibrium in statistical mechanics seems to be an entirely different concept. Some people even question the meaning of randomness.

Thanks for the references offered! Zeilinger, a devout Bohrian, is able to devise the most ingenious experiments of teleportation, being a clear thinker and advocate of QM. What I miss in his general outlook is a relevant extension of QM to incorporate propositions that are subject to Gödel's theorem(s).

Thank you Erkki,

I agree about incorporation of Gödel into physics. You might like the paper attached. It shows there is logical independence in arithmetic, using Soundness and Completeness Theorems. It is logical independence that is relevant to quantum theory. It could be logical independence that is precisely the same as mathematical undecidability whose existence Gödel proves, But it seems impossible to confirm that it is.

Article The logical machinery of arithmetic: Elementary algebra as a...

Thanks Steve,

I will look at it, but I to me logical independence is not commensurate with Gödel.

Best

erkki

Erkki, the attached link is to a thread addressing exactly your last comment.

https://www.researchgate.net/post/Is_logical_independence_of_the_square_root_of_minus_one_a_consequence_of_arithmetics_incompleteness

There is some sort of analogy, undecidable statements in arithmetic, meaning

incompletness, and perhaps einsteins feeling that qm is an incomplete theory.

But that is where it stops. People think they undersand what integers mean,

but electrons and photons are basically unknown entities.

Juan,

Undecidability extends into the arithmetic of rational numbers. Physical theory is based on that arithmetic. In that arithmetic, rationals exist by theorem. Complex numbers exist by consistency. Note that all measurements are rational -- non-witnessable, Inferred entities are complex.

Article Undecidability Everywhere?

Some Sankar Bhattacharya

Dynamics (Schrodinger) in operational quantum theory is deterministic. The phenomena of randomness or in-determinism in operational quantum theory arises when an act of measurement is considered and operationally it is unavoidable in a Bell-type scenario [http://link.springer.com/article/10.1007%2Fs10701-012-9669-1].

To understand the source of randomness in quantum theory, one can ask whether this randomness or in-determinism is "irreducible" or not. This is to say whether one can do away with this 'quantum randomness' by constructing a finer theory (ontological model) which assigns deterministic probabilities(0 or 1) to all measurement outcomes and reproduces quantum predictions on the operational level.

While answering this question there exist two prominent approaches in literature. One is due to Colbeck and Renner, who have shown that under a free-choice assumption (criticized by Ghirardi and Romano) one can show that quantum randomness is irreducible.

On the other hand there exist an approach through ontological models (formulated by Harrigan and Spekkens) which without any auxiliary assumptions leads to a few interesting (although not conclusive) results. We have recently worked out one such result [http://arxiv.org/abs/1508.02234] which shows that if the ontological model obeys 'preparation-measurement reciprocity'(obeyed by operational quantum theory), it is bound to be in-deterministic, whereas if the reciprocity condition is removed one can still construct a deterministic ontological model consistent with quantum theory.

From another perspective I would like to point out that one may think 'true-randomness' is in conflict with causality, since two different outcomes must have been caused by two different physical states of the 'cause'. But I think this is not the case. One can also define causality as the existence of a 'unique' pre-image (or cause) of the effect. In that way, even if one can completely specify the physical state of the 'cause', the only imperative it has on the theory is that the outcome sets of different causes must be disjoint.