# Why Quantum Mechanics as a non-fundamental effective theory?

My question: What (physical or mathematical) reasons (not philosophical) do some physicists ('t Hooft, Penrose, Smolin,...) argue/have in order to think that Quantum Mechanics could be substituted by another theory in the future? Namely...Why should it be an effective and non-fundamental (non-ultimate'') theory? 't Hooft has spent some years trying to "prove" that Quantum Mechanics can arise from a classical theory with information loss through some particular examples (cellular automata, beable theory,...). Penrose advocated long ago that gravity should have a role in the quantum wave function collapse (the so called objective reduction), Smolin wrote a paper titled , I believe, Can Quantum Mechanics be the approximation of another theory?. What I am asking for is WHY, if every observation and experiment is consistent (till now) with Quantum Mechanics/Quantum Field Theory, people are trying to go beyond traditional QM/QFT for mainly "philosophical?" reasons. Is it due to the collapse of wavefunctions? Is it due to the probabilistic interpretation? Maybe is it due to entanglement? The absence of quantum gravity? Giving up philosophical prejudices, I want to UNDERSTAND the reason/s behind those works...

Remark: Currently, there is no experiment against it! Quite to the contrary, entanglement, uncertainty relationships, QFT calculations and precision measurements and lots of "quantum effects" rest into the correction of Quantum Mechanics. From a pure positivist framework is quite crazy such an opposition!

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Although this is quite a different question from philosophy.stackexchange.com/questions/6670/… , my answer to it would be pretty much the same. –  Nathaniel May 4 '13 at 10:59
This is too vague to answer. Questions are expected to show some research effort. Point us to information about the point of view you're attributing to these people. –  Ben Crowell May 4 '13 at 13:06
I will reedit with details, Ben. I think it is NOT vague question though. –  riemannium May 4 '13 at 23:50

Possibly this is just a different way of making the same points Nathaniel alluded to in his comment.

A physical theory is just a mathematical model. When constructing the theory we devise some mathematical model, compare it with experiment, and if our model predicts the correct results we announce it to the world. If our model fails to match observations we go back to the blackboard and try a different mathematical model. For example, both general relativity and QM are just mathematical models that describe the world well enough to have earned the status of theories.

However some mathematical models feel more natural than others. General relativity is an often quoted example because the assumptions at its core seem to be minimal and elegant. By constrast the mathematical model that is quantum mechanics feels somewhat contrived and unnatural.

People respond to this in different ways. Most of us don't care as long as it works (which it does!). Some regard the apparent unnaturalness of QM as a failure on our part and a naive attempt to impose our limited understanding on the world. However some believe that a more natural mathematical model to describe QM must exist and that we will one day discover it. This is the motivation for regarding QM as an effective theory.

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Jim Graber says he can't speak for 't Hooft, Smolin or Penrose. Neither can I. But surely these physicists can and do speak for themselves.

't Hooft lists some "motivations for studying the ontological nature of quantum mechanics" (http://arxiv.org/abs/quant-ph/0701097), among them - the problems related to the "collapse of the wave functions" and the problems with quantum gravity (mentioned by Jim Graber).

Smolin gives his list of arguments suggesting "that quantum mechanics is an approximation to a deeper theory" (http://arxiv.org/abs/quant-ph/0609109), among them - the "unresolved difficulties in extending quantum theory to cosmology" and the "difficulties in solving the measurement problem".

I don't have Penrose's book, but he was quoted as follows (http://timfolger.net/penrose.pdf): “Quantum mechanics gives us wonderful predictions and experimental confirmations for small-scale scenarios, but it gives us nonsense at ordinary scales,” so perhaps he is not happy with the mainstream treatment of the collapse problem.

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Obviously, I can't speak for 't Hooft, Smolin or Penrose, but I think that they and many other physicists think the inability to reconcile quantum mechanics (QM) and general relativity (GR) (the so-called quantum gravity problem) indicates that it is at least worth considering possible alternatives to QM. The fact that, as you note, QM is spectacularly successful (as is GR), means that the alternative must be very close to QM, or perhaps even identical. One can seriously argue whether identical, or close but not identical, is a better pathway to progress.

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Conversely to Smolin, Penrose, etc there are other physicists who think that the business of unifying QM and QR is actually going not that bad ... –  Dilaton May 10 '13 at 22:43

In my opinion it is not only philosophy that is powering these alternative searches but also the human psychological set up. Inherent in us, and particularly the great technicians in the sample, is the drive to invent a better mousetrap.

't Hooft for example has great mathematical tools which he used brilliantly in his early career. Such honed tools "ask" to be used and in the case of a physicist the "better" research horizon is alternative theories that will blend with existing ones at the interface.After all that is how physics developed over the centuries, if one ignores the tiny but very important detail that it was the data that pushed for an alternative to classical theories. As original thinkers they do not follow the slow and laborious beaten path of the bulk of theorists . They use their tools hoping to preempt/predict future discoveries, and if they succeed it will probably be the first time in the history of physics.

The above for the true physicists, because there also exists the profile of the crank. In the human sample there exists also the aggrandizing one's self impulse :the biggest fish, the largest boar etc and unfortunately there are such humans fishing in the waters of physics .

This answer is a long way of saying this question does not have a physics answer.

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I once heard from one of my professors one convincing argument about QM being a non fundamental theory. If you look at Classical Mechanics, for example, you have just one dynamics governing all systems at any time. If it explained every experiment it would be a pretty nice fundamental theory. In Quantum mechanics, instead, one of the weirdest things from a theoretical point of view is that you have two dynamics: Schroedinger evolution and wavefunction collapse; how can you tell which one of the two is acting in a given time $t$, only in terms of fundamental processes (and not, for instance, introducing hard-to-define measurements)?

There are some models that try to fix the dynamics of the wavefunction, but they are either self-consistent but non verifiable through experiments (e.g. Bohmian Mechanics) or not yet verified or falsified by experiments, but verifiable experimentally (e.g. the GRW theory).

To this, one has to add problems in quantum gravity, non-locality effects and everything starts to sum up and explain why a lot of people are exploring theories that try to go beyond QM.

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Below is my answer to a different question, but I think most of the points I make there are relevant here as well. My answer can be summarised as "there might not be an underlying theory, but then again there might, and if we don't look for it then we'll never find it." Not everybody has to participate in such a search, but it would be foolish not to take the chance of having a few people working on it.

My answer to the other question follows:

Edwin Jaynes argued that Niels Bohr's original version of the copenhagen interpretation was exactly that: a theory that only makes epistemological statements and refuses to say anything about an ontological world. However (according to Jaynes) most people didn't really understand what Bohr was saying, so what we normally think of as the Copenhagen interpretation is a misinterpretation of the interpretation, in which Bohr's epistemological statements become ontological facts about the world.

In any case, it is certainly possible to interpret the formalism of quantum mechanics that way. In fact I would say that it's the only reasonable way to interpret the mathematical formalism. Quantum mechanics is basically a formalism for predicting the outcomes of experiments. Everything you calculate is an operationally defined probability of the form "if you do this experiment, these are the outcomes that can occur". However, the mathematical formalism has nothing to say about any ontological process that would cause those particular outcomes to occur with those particular probabilities. This is exactly why there is so much room for "interpretation" of the equations.

However, I would argue (along with Jaynes) that this doesn't mean we should throw ontological thinking out the window just yet. It might be that, for some reason, we live in a Universe that (in some yet-to-be-clearly-stated sense) fundamentally has no ontological reality. But then again, there might be an underlying ontological reality, and if there is then knowing about it would lead to new fundamental physics. We know from Bell's theorem and similar results that if this underlying reality does exist then it must have certain (arguably counterintuitive) properties, but its existence cannot be ruled out entirely at this point. Depending on your philosophical outlook you might consider the existence of such a thing to be more or less unlikely, but you'd have to be pretty hard-line to discount it entirely. If we don't look for it we'll never find it, so it seems wise to have at least a few smart people thinking about the possibility.

As an analogy, the Lorentz transforms were already worked out (by Lorentz) before Einstein, but their interpretation was unclear. We could just have stopped there - we had the equations after all, and so why not remain content to interpret them operationally? But Einstein's ontological interpretation led not only to a more elegant way of understanding the mathematics but also to matter-energy equivalence and ultimately to general relativity. It would be hard to argue in that case that the search for an ontological interpretation was a useless concept leading down a philosophical rabbit hole to nowhere.

It is my hope (not belief, just hope) that one day something similar will be done for quantum mechanics, enabling us to see, if not the underlying ontological reality then at least one level further down. This requires more than just an interpretation of the equations - it requires a new theory that makes testable predictions, while also reducing to quantum mechanics in some appropriate limiting case. It is my suspicion that many of the biggest unsolved issues in physics (and in particular the unification of quantum mechanics with general relativity) will not be fully resolved unless we can accomplish this.

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I'm hoping I can get away with cross-posting this answer, because the other version is on a different Stack Exchange site. –  Nathaniel May 5 '13 at 5:10
In classical physics the state of a system is a vector $x \in V_{2m}$ in a $2m$ dimensional phase. The physics is encoded by the symplectic group $Sp(2m,R)$. Classical physics is the study of a finite dimensional representation of $Sp(2m,R)$ carried on the phase space $V_{2m}$. $$x'^{i}=g^{i}_{j}x^{j}$$ where $g\in Sp(2m,R)$.
Quantum physics is the study of infinite-dimensional unitary representations of $Sp(2m,R)$ carried on Hilbert space. $$\psi'^{a}=[U(g)]^{a}_{b}\psi^{b}$$ This clean account is muddied by the Groenwald van Hove theorem which says that the unitary representations don't exist in many cases of interest. However, I believe that this description is morally sound. It says that quantum mechanics is not the collection of poorly motivated axioms that trouble some researchers; it's just another representation of the symplectic group and, looked at in this light, is completely natural.