# The Fundamental Difference in Interpretations of Quantum Mechanics - Comments

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#### A. Neumaier

So whatever is keeping us from making deterministic predictions about the results of quantum experiments, it isn't chaos due to nonlinear dynamics of the quantum state.
However, it is chaos in the (classical) part of the quantum state that is accessible to measurement devices.

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#### bhobba

Mentor
Phisolsophy need not be speculation. Neither Bohr's nor Einstein's nor Heisenberg's nor Feyman's philosophy was wild speculation.
Einstein and Feynman IMHO are good - they are clear - that is the key - for Bohr that wasn't always the case such as his explanation of EPR. Modern scholars, as I have posted elsewhere think his explanation, supposedly definitive, wasn't quite that. BTW Einstein, while clear was far from always right, not by a long shot. His math was particularly bad - his early papers required a lot of comments explaining the errors when collected and published - how they got through referees reports beats me - he wasn't famous then so it simply wasn't - well it's Einstein so who are we to criticize.

Thanks
Bill

#### bhobba

Mentor
I will post my thoughts now you have clarified (at least to me) what you mean we can get to the heart of the issue.
OK we have the principle of general invariance - the laws of physics should be expressed in coordinate free form.

This is an actual physical statement because it makes a statement about physical things - laws of physics.

We have the Principle of Least Action about the paths of actual particles - same as the above.

What I don't understand is why you don't think the same of the statement observations are the eigenvalues of an operator. That seems to be exactly the same as the above - it talks about something physical - an observation.

Thanks
Bill

#### A. Neumaier

Einstein and Feynman IMHO are good - they are clear - that is the key - for Bohr that wasn't always the case
There is a big difference between not being clear (which is in philosophy never completely the case) and being wild speculation. Speculation has nothing to do with philosophy but is just unfounded reasoning.

#### bhobba

Mentor
There is a big difference between not being clear (which is in philosophy never completely the case) and being wild speculation. Speculation has nothing to do with philosophy but is just unfounded reasoning.
Good point - they are different. But I have to say there is a tendancy to call something philosophical BS if it not quite clear - I think I fall for that one often. You shouldn't - but I find it hard not to.

Tanks
Bill

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#### A. Neumaier

there is a tendency to call something philosophical if it not quite clear
Philosophy = discussing the possible meanings, definitions, delineations, etc. of concepts, the arguments for or against the various uses, and associated fallacies.

This can be done (like anything else) with different degrees of clarity.

#### microsansfil

Philosophy = discussing the possible meanings, definitions, delineations, etc. of concepts, and the arguments for the various uses.
May be the misunderstanding about philosophy is that "The value of philosophy is, in fact, to be sought largely in its very uncertainty"

Bertrand Russell said:
http://skepdic.com/russell.html

The value of philosophy is, in fact, to be sought largely in its very uncertainty. The man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sense, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the co-operation or consent of his deliberate reason. To such a man the world tends to become definite, finite, obvious; common objects rouse no questions, and unfamiliar possibilities are contemptuously rejected. As soon as we begin to philosophize, on the contrary, we find, as we saw in our opening chapters, that even the most everyday things lead to problems to which only very incomplete answers can be given. Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what they may be; it removes the somewhat arrogant dogmatism of those who have never travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect.
Best regards
Patrick

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#### atyy

That depends on what you mean by orthodox. If you mean the formalism then you have to explain MW. The answer of course is its principles, axioms, whatever you want to call it doesn't have it.
Them you would say that Bell's theorem does not show that quantum mechanics is inconsistent with local realism.

#### bhobba

Mentor
Them you would say that Bell's theorem does not show that quantum mechanics is inconsistent with local realism.
Your reasoning for that statement beats me - how about spelling it out.

I have given Ballentine's axioms - collapse appears nowhere in there. Continuity allows you to show after an observation the state has changed, if it has not destroyed what was being observed. That is undeniably true - and if that is your idea of collapse beyond doubt. But collapse is usually thought as more than that - the state discontinuously changes on observation - its that discontinuity that is the issue:
https://en.wikipedia.org/wiki/Copenhagen_interpretation
There have been many objections to the Copenhagen interpretation over the years. These include: discontinuous jumps when there is an observation, the probabilistic element introduced upon observation, the subjectiveness of requiring an observer, the difficulty of defining a measuring device, and to the necessity of invoking classical physics to describe the "laboratory" in which the results are measured.

In MW its explained by decoherence not happening discontinuously - very fast - but not immediately. In Ensemble it's simply another preparation procedure so by the definition of a preparation procedure of course the state changes - but again not discontinuously.

Thanks
Bill

#### stevendaryl

Staff Emeritus
Just for reference the more convetional terminology for the various kinds of inferences here are, deductive vs inductive inference.

"hard contradictions" are typically what you get in deductive logic, as this deals with propositions that are true or false.
"soft contradictions" are more of the probabilistic kind, where you have various degrees of beliefs or support in certain propositions.
The issue I was talking about when I coined "soft contradiction" wasn't really inductive versus deductive. It was really about how we reason with huge numbers (or very tiny numbers). Let me give a toy example: Suppose I say that
1. A cat is completely described by Newton's laws.
2. A cat always lands on its feet
These two together might very well be contradictory. For some initial condition of a cat, maybe Newton's laws imply that the cat wouldn't land on its feet. But it might be completely infeasible to actually derive a contradiction. It certainly is not feasible to check every possible initial condition of a cat and apply Newton's laws to all the atoms making up the cat's body to find out if it would land on its back. Maybe there is some advanced mathematics that can be used to get the contradiction, using topology or whatever, but in the naive way that people might apply Newton's laws, chances are that a contradiction will never be derived.

Or imagine a mathematical statement $S$ such that the shortest proof (using standard mathematical axioms, anyway) takes $10^{100}$ steps. Then if I add $\neg S$ to my axioms, then the resulting system is inconsistent. However, it's unlikely that any contradiction will ever be discovered.

I feel that the rules of thumb for using QM may be a similar type contradiction. That recipe consists of
1. A rule for how microscopic systems evolve (Schrodinger's equation)
2. A rule for how measurements produce outcomes (Born's rule)
They work very well. However, since measurement devices are themselves quantum systems (even if very complex) and measurements are just ordinary interactions between measurement devices and the systems being measured, these two rules may very well be contradictory. But a detailed analysis of the measuring process as a quantum interaction may infeasible, so actually deriving a contradiction (that everyone would agree was a contradiction) may never happen.

There is actually an approach to making systems of reasoning with soft contradictions of the type I'm worried about into consistent systems. That is, instead of thinking of the rules as axioms in a mathematical sense, you organize them this way:
1. Split the possible situations that you might be in where you need to reason about something into "domains".
2. Within each domain, you have rules for reasoning within that domain.
3. If something is in the overlap of two domains, you come up with a "resolution domain" to reason about the overlap.
I think that's ugly, but I think it's doable. I think it's something like the way that we deal with the world in our everyday life. If you're trying to figure out how to get your girlfriend to stop being mad at you, you don't try to deduce anything using quantum field theory, you stick to the "relationship domain". Of course, there could be some overlap with other domains, because maybe the problem is that she suffers from headaches that make her irritable, and they might be due to a medical condition. So maybe you need to bring in the "medical domain". And maybe that condition could be treated by some kind of nanotechnology, which might involve physics, after all.

#### atyy

Your reasoning for that statement beats me - how about spelling it out.
MWI does not meet the conditions for Bell's theorem. Bell's theorem cannot be used to say that MWI is incompatible with local realism.

#### bhobba

Mentor
MWI does not meet the conditions for Bell's theorem. Bell's theorem cannot be used to say that MWI is incompatible with local realism.
Come again - you better give the detail of that one.

All interpretations, every single one, has the formalism of QM so Bells follows.

Thanks
Bill

#### atyy

Come again - you better give the detail of that one.

All interpretations, every single one, has the formalism of QM so Bells follows.
No, because all outcomes occur in MWI.

#### stevendaryl

Staff Emeritus
Good point - they are different. But I have to say there is a tendancy to call something philosophical BS if it not quite clear - I think I fall for that one often. You shouldn't - but I find it hard not to.
As someone who has dabbled in philosophy and has friends who are professional philosophers, I feel like that is the opposite of the truth. To me, philosophy is about careful reasoning--spelling out what it is that you are assuming, what are the principles of reasoning you are using, what sorts of categories of things you are talking about (material objects versus subjective knowledge versus laws of physics versus mathematical objects, etc.). So when people reject philosophy as useless, it seems to me that they are really saying: I don't need to be careful about my reasoning.

Sometimes, they're right. Physicists, especially the good ones, have an intuitive notion of what constitutes good physics and what constitutes rigorous reasoning, and maybe they think that it's a waste of time and energy to second-guess those intuitions. They could be right.

I guess there is a connection between the careful reasoning aspect of philosophy and the wild speculation caricature that so many people attach to it, and it's this: Most people have common-sensical beliefs about the world, and intuitions about what is likely to be true and what's likely nonsensical fantasy. So hypotheses that are too wild are rejected out of hand without even putting any thought into it. That's probably a good way to be, because why waste time on fantasy when there are real-world things to work on? However, a philosopher who wants to be careful about his reasoning won't be satisfied with the fact that his gut feeling tells him that something is nonsense. He wants to understand that gut feeling, and understand how reliable it is. So a philosopher might very well explore a possibility that your average man on the street would immediately reject as nonsense.

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#### PeterDonis

Mentor
it is chaos in the (classical) part of the quantum state that is accessible to measurement devices.
Can you elaborate?

#### Fra

The issue I was talking about when I coined "soft contradiction" wasn't really inductive versus deductive. It was really about how we reason with huge numbers (or very tiny numbers). Let me give a toy example: Suppose I say that
...
I feel that the rules of thumb for using QM may be a similar type contradiction. That recipe consists of
1. A rule for how microscopic systems evolve (Schrodinger's equation)
2. A rule for how measurements produce outcomes (Born's rule)
They work very well. However, since measurement devices are themselves quantum systems (even if very complex) and measurements are just ordinary interactions between measurement devices and the systems being measured, these two rules may very well be contradictory. But a detailed analysis of the measuring process as a quantum interaction may infeasible, so actually deriving a contradiction (that everyone would agree was a contradiction) may never happen.
So by "soft contradiction" you mean a contradiction that occur only during certain - possible, but improbable - conditions.
Thus the softly flawed inference is justified?

If so, i would still think that relates to the discussion of general inference. I see your case as a possible kind of rational inference of a deductive rule but in an subjectively probabilistic inductive way, and it´s also something that can be generalized.

A possible driving force for a rational agent to abduct an approximative deductive rule, to base expectations and thus action on, is that of limited resources.

A deductive rule that are right "most of the time", can increase the evolutionary advantage of the agent in competition. As the agent can not store all information, it has not choice but to choose, what to store and how, and what to discard.

This is perfectly rational, but it also brings deep doubts on the timeless and observer invariant character of physical law.

I have also considered that this might even be modelled as an evolving system of axioms, where evolution selects for the consistent systems. An agent is associated with its axioms or assumptions. And different systems of axioms can thus be selected among, in terms of effiency of keeping their host agent in business. Meaning, efficient coding structurs for producing expectations of their environment.

This is also a way to see how deductive systems are emergent, and there is then always an evolutionary argument for WHY these axioms etc. Ie. while axioms in principle are CHOICES, the choices are not coincidental. This would then assume a one-2-one mapping between the axioms in the abstraction, and the physical postualtes which are unavoidably part in the mud of reality. In this view, the axioms are thus simply things that "seem to be true so far" but arent be proved, and they serve the purposes of a efficient betting system, but they can be destroyed/deleted whenever inconsistent evidence arrives.

These ideas gives a new perspecive into the "effectiveness of mathematics". Like Smolin also stated in this papers and talks, the deductive systems are effective precisely because they are limited. But to really appreciate this, you must also understand how and why deductive systems are emergent.

/Fredrik

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#### rubi

There is nothing contradictory about having two types of time evolution (unitary evolution, collapse). In fact, this happens in classical Newtonian physics as well and we fully understand it. Whenever we have a stochastic description of some perfectly classical system, we have a probability distribution at $t=0$, which is then evolved by a probability conserving time evolution, then collapsed upon measurement, then evolved again, etc. The standard example is Brownian motion, which arises from completely classical equations like $F=ma$. In fact, this scheme applies to all classical probabilistic theories with time evolution, so it would actually be more mysterious if time evolution didn't work analogously in quantum mechanics, which too is probabilistic after all. In classical probability theory, the collapse too isn't an emergent phenomenon that just needs to be derived from a better theory. Instead, it's an elementary ingredient in the theory of stochastic processes, which can't be removed from the theory. And since classical probability theory is a special case of quantum theory (when all observables commute), there must be something within quantum theory that reduces to classical collapse if only commuting observables are considered.

Moreover, the notion of measurement in quantum theory is no less well-defined than in classical probability theory. A measurement in classical probability theory has occured, when the experimenter somehow has learned the measurement result. It's up to the experimenter to decide when this happened. However, the mathematical formulation is perfectly rigorous and if the experimenter knows the time of measurement and the measurement precision very well, then the theory will produce numbers that match the measured data very well.

Also, collapse is not in conflict with relativity. One can also have classical probabilitic theories of classical relativistic systems and of course they too will include collapse.

The only misconception about collapse is that it is often considered to be a type of time evolution. In fact, it's not a type of time evolution. It's just a necessary mathematical ingredient if you want to compute the probability distribution on the space of paths of a stochastic process. So by analogy, it's unlikely a type of time evolution in quantum theory either, because again, in the case of commuting observables, quantum theory reduces to classical probabilty theory.

The real quation about quantum theory is: Why does it make sense to have non-commuting observables in the first place?

#### Stephen Tashi

In classical probability theory, the collapse too isn't an emergent phenomenon that just needs to be derived from a better theory. Instead, it's an elementary ingredient in the theory of stochastic processes, which can't be removed from the theory.
A measurement in classical probability theory has occured, when the experimenter somehow has learned the measurement result.
I make the mild objection that "collapse" in the sense of a "realization" of some event in a probability space is not a topic treated by probability theory. It is a topic arising in interpretations of probability theory when it is applied to specific situations. What you are calling "classical probablity theory" is, more precisely, "the classical interpretations used when applying probability theory".

I agree that applications of probability theory to model macroscopic events like coin tosses involves the somewhat mysterious assumption that an event can have a probability of 1/2 of being "possible" and then not happen. (If it didn't happen, why can we assert it was possible?).

It would be interesting to hear opinions about whether there are problems in interpreting the "collapse" of the wave function that are distinct from the elementary metaphysical dilemma of applying probability theory to coin tosses.

One can also have classical probabilistic theories of classical relativistic systems and of course they too will include collapse.
What's an example of that?

#### rubi

I make the mild objection that "collapse" in the sense of a "realization" of some event in a probability space is not a topic treated by probability theory. It is a topic arising in interpretations of probability theory when it is applied to specific situations. What you are calling "classical probablity theory" is, more precisely, "the classical interpretations used when applying probability theory".
No, I really mean the rigorous measure theoretical formulation of probability theory and collapse is just the projection of the probability distribution. Of course, nobody in probability theory calls it "collapse". I don't like the word either, because it suggests that it is a physical process, but I just used it in order to stick with the terminology of the thread. Mathematically, it refers to the insertion of the projectors in the construction of probability measures on the space of paths of a stochastic process, i.e. the fact that these probability distributions have the form $UPUPUP \rho_0$, when evaluated on cylindrical sets. ($U$ denotes time evolution, $P$ denotes projection.)

I agree that applications of probability theory to model macroscopic events like coin tosses involves the somewhat mysterious assumption that an event can have a probability of 1/2 of being "possible" and then not happen. (If it didn't happen, why can we assert it was possible?).
I don't really understand how that relates to my post.

What's an example of that?
For example, you could study the Brownian motion of relativistic particles instead of Newtonian particles.

#### RUTA

These two options are generally called “psi-epistemic” and “psi-ontic,” respectively, in the foundations community. Psi-epistemic interpretations do not necessarily entail that QM is incomplete, see http://www.ijqf.org/wps/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf for example. I didn’t have time to read all 8 pp of this thread, so my apologies if something along these lines was already posted.

#### Stephen Tashi

No, I really mean the rigorous measure theoretical formulation of probability theory and collapse is just the projection of the probability distribution.
Projection of which probability distribution upon what?

For example, you could study the Brownian motion of relativistic particles instead of Newtonian particles.
I can imagine that as a topic in special relativity.

#### rubi

Projection of which probability distribution upon what?
When you have a distribution $\rho(x)$ at time $t$, then if you have gotten to know that $x\in A$, you multiply $\rho(x)$ by the characteristic function $\chi_A(x)$. The projection is $\rho(x)\rightarrow \chi_A(x)\rho(x)$. It's the same thing that happens to the quantum state $\psi(x)$ if you have learned the result of a measurement of the position operator $\hat x$. In quantum theory you have the additional complication that observables might not commute. If you have an observable in a different basis, you have to perform this multiplication in that basis, so for instance a measurement of the momentum $\hat p$ results in a multiplication of the fourier transformed state $\tilde \psi(p)$ by the characteristic function $\chi_A(p)$. Every projector $\hat P$ in quantum theory is a multiplication operator by some characteristic function in the eigenbasis of the corresponding observable, so for the special case of commuting observables, the mathematics of projections is exactly the same as in classical probability theory.

I can imagine that as a topic in special relativity.
I probabily don't have time for a long discussion about this, but this seems to be a good overview article: https://arxiv.org/abs/0812.1996

#### vanhees71

Gold Member
Philosophy need not be speculation. Neither Bohr's nor Einstein's nor Heisenberg's nor Feynman's philosophy was wild speculation.
Well, Einstein was at least understandable in his very clear criticism against QT. As is clear since Bell's work and the confirmation of the violation of the Bell inequality he was wrong, and QT came out right. Bohr has his merits in clearly stating the idea of complementarity and that QT is about what can be prepared and measured in a atomistic world. Unfortunately he was not very clear in his own writings but had to be translated by others into understandable statements. I'm not too keen about Heisenberg. E.g., he didn't get his own finding of the uncertainty principle right and was corrected by Bohr. Also his version of QT, matrix mechanics, had to be clarified in the "Dreimännerarbeit" by him, Bohr, and Jordan.

#### A. Neumaier

So whatever is keeping us from making deterministic predictions about the results of quantum experiments, it isn't chaos due to nonlinear dynamics of the quantum state.
However, it is chaos in the (classical) part of the quantum state that is accessible to measurement devices.
Can you elaborate?
What we directly observe in a measurement device are only macroscopic (what I called ''classical'') observables, namely the expectation values of certain smeared field operators. These form a vast minority of all conceivable observables in the conventional QM sense. For example, hydromechanics is derived in this way from quantum field theory. It is well-known that hydromechanics is highly chaotic in spite of the underlying linearity of the Schroedinger equation defining (nonrelativistic) quantum field theory from which hydromechanics is derived. Thus linearity in a very vast Hilbert space is not incompatible with chaos in a much smaller accessible manifold of measurable observables.

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#### A. Neumaier

I'm not too keen about Heisenberg.
His philosophy (what you called ''wild speculations'') lead him in 1925 to the discovery of the canonical commutation relations.

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