# B Quantum Mechanics is not a theory?

1. Nov 28, 2017

### Zafa Pi

"... quantum mechanics isn’t a complete physical theory in its own right, but rather a framework for the construction of physical theories."

I found this in Michael Nielsen's blog and elsewhere. I am perplexed. In what fundamental way does it differ from Newtonian Mechanics (Theory) in not being a theory? What about Probability Theory?

2. Nov 28, 2017

### PeroK

In my opinion, you are not going to find established definitions of "theory" and "framework" on which everyone agrees. When is a framework not a theory? When the particular author who is writing the piece wants or thinks it to be so.

3. Nov 28, 2017

### Zafa Pi

I'm sure you're right, but I wonder what Nielsen and others mean when they say QM is not a (complete physical) theory.
Do you think Probability Theory is a physical theory of Newtonian ilk?

4. Nov 28, 2017

### PeroK

These questions do not interest me in the least, I'm sorry to say. As soon as someone starts to play about with words like this I switch off.

5. Nov 28, 2017

### Zafa Pi

That's fair. Yet Hossenfelder and Aronson use them, and I wonder if Feynman said it would you feel different? And would you feel different after 4 shots of whiskey, or if you were on one of your mountain peaks?
I wonder about a lot of stuff, even you.

6. Nov 28, 2017

### A. Neumaier

It just means that you need to specify the collection of relevant observables (positions, momenta, fields, Hamiltonian, etc.), their properties (typically a set of commutation relations and/or other equations relating the observables), and a Hilbert space on which they are represented in order to make definite predictions.

Last edited: Nov 28, 2017
7. Nov 28, 2017

### Demystifier

If quantum mechanics is just a framework and not a theory, then Newtonian mechanics is also just a framework and not a theory. In this context, a theory is something in which the Hamiltonian $H(x,p)$ is not an arbitrary function, but a specified function such as $H=x^2+p^2$.

8. Nov 28, 2017

### martinbn

I would have thought that it is a theory in the first case and an example in the second.

9. Nov 28, 2017

### hilbert2

The basic framework of QM contains the axioms of momentum-position commutation relation (more generally, the Poisson bracket-commutator connection), the fact that the Hamiltonian is the generator of time translation, and that observables are Hermitian operators. Then there's some requirements of mathematical reasonability, like that the spectrum of the Hamiltonian must be bounded from below. These are already quite strict limitations for the physical models that are possible within the framework.

10. Nov 28, 2017

### A. Neumaier

No; this is the case only in certain important models of QM. For example, all of quantum information theory concerns finite-dimensional Hilbert spaces, in which there is no position operator. and no Poisson bracket. Quantum mechanics on curved manifolds also lack position operators.

11. Nov 28, 2017

### Karolus

The Ptolemaic system is a framework (according to certain points it is true), the Copernican system is also a framework.
None of them is more true than the other, although we certainly prefer to adopt the Copernican system than the Ptolemaic.
The quarks theory is a framework just as the first two.
Today, we prefer to talk about framework, compared to theory (though certainly the word "theory" is still used as a set of mathematical statements or "laws")
The subject is not simple.
To make it simple: The theory was used by the physicists until the late 1800s, according to which a theory in some way corresponds to a truth, to an objective reality.

12. Nov 28, 2017

### Staff: Mentor

In most cases the choice of terms is simply historical rather than linguistic. It is a playground for philosophers and linguistic researchers and people with a political agenda, in case of evolution. Those who know what is inside rarely care how you name it.
Call it stochastic.

13. Nov 28, 2017

### Staff: Mentor

But do note that Nielsen's assertion is preceded by "Note, incidentally, ..." and is completely contained in a parenthesized digression. I doubt that there's much more to be read into it than the original context: depending on how one chooses to axiomatize and interpret the mathematical formalism of QM, it may be difficult to apply the CTD principle to QM.

14. Nov 28, 2017

### Strilanc

He means it in the same sense that someone might say "statistics is a framework for the construction of physical theories" or "calculus is a framework for the construction of physics theories". It is a general mathematical idea/area/tool that can be fruitfully investigated in its own right, independent of experiments and observations. Then, when you want to do physics, you bring in extra details about how you are mapping your experiments and observations into ideas from statistics / calculus / quantum.

15. Nov 28, 2017

### Fra

If you take really seriously the idea, not only that computing is a physical process, but also that any physical process can be considered as some kind of computation - and thus by extension, the rules of computations are the rules of physical law, then there is indeed alot of wish from quantum mechanics as it stands, but part of this "problem" is indeede shared with classical mechanics and even probability theory if you look at stochastic models.

My personal "interpretation" of QM, that of course hides a large ambition, is that any physical process can be understood as a "physical inference process", and that happens to quite be related to computation ideas, and i am partly symphatetic to the the idea of using a CTD idea as a guiding principles to finding physical law.

Anyway, if you TRY to understand quantum mechanics as it stands today - in these terms - there are several obstables that needs to be solved to make progress.

1) Uncountable numbers.

Most physics is based on calculus and real numbers. So is probability theory. You can surely do inference, in contiuum terms, but it makes the algorithmic descriptions more difficult as you have to first go through the problem of finding the countable structures WITHIN the continuum models that correspond to the physical inferences. This is most probably possible, but is of little help for a physicists, but probably very fun for mathematicians.

2) Coding of the "computational rules"

Quantum mechanics is still constructed via a still not (conceptually) understood quantization procedure, also using the classical placeholders for physics: lagrangians or hamiltonians with extra constraints. Their content is basically put in by hand, rather than be a principal inference from interaction history.

I would say these two things are major issues, that might be a possible meaning of QM not beeing a complete theory from the point of view of computation. But indeed this is shared by classical mechanics.

A possible route to a solution i see is
1) Starting from distinguishable states and limited memory, physics at the microlevel is discrete computation, and continuum physics is emergent at large complexity limit.
2) the computational rules are selected by evolution of law, in the sense of beeing selected for the algoritms of "best computability" given the memory constraints (here i think we can benefit from a discrete correspondences to Ads/CFT which is a dualit of theories with different computation complexity). I think there are interesting links to that here. Computational complexity is proabalby the more interesting part of these dualities.

Once can idenfity constraints here that can be traced to requirements of "inferrability" which in this case is closely related to "computability".

/Fredrik

16. Nov 28, 2017

### Staff: Mentor

Don't be - its just semantics.

In the sense of generalized probability models its a framework:
https://arxiv.org/abs/1402.6562

In the sense of studying an actual book on QM its a theory.

Its just the semantics people use given the context. I wouldn't say in any given context people use the same semantics either as I am sure you have noticed. People are often loose in what they say, but we generally get the meaning, drift or whatever you want to call it.

As another example take the principle of relativity - the laws of physics are the same in all inertial frames. People call it a law - and it is. But a law about laws - whats that - its actually a meta law. But people don't worry about that and just say its a law. I worked in computing for many years and you have this thing called a data dictionary. Really it contains meta data - data about data - but nobody ever calls it that - its just data.

Regarding Newtons laws, I have mentioned it before - take law 1 - it follows from law 2 which is just a definition. What's its physical content then? Its simply a framework that says - get thee to the forces. But nobody worries about it - they still call it a law. I used to worry about it - but then again I am weird. However John Baez in a discussion we had about it pointed this all out to me and now I couldn't really care less - except when trying to explain to someone the real basis of classical mechanics is in fact QM - in which case understanding this is rather crucial - but that is another story.

Thanks
Bill

Last edited: Nov 29, 2017
17. Nov 29, 2017

### Zafa Pi

Thanks to all of you for your generous and thoughtful replies. Team PF/QM is awesome.
Many of the responses contain a similar notion of semantics. I offer a germane anecdote:

Last summer a neighbor bought a large above ground circular swimming pool. He planned to use low chlorine and empty it once a week for his neighbor's garden.
He asked me how it would affect his water bill. I made two measurements (using a Hermitian tape), checked how the water company charged, and gave him the answer.
He was impressed and asked if I used physics theory. I told him I used arithmetic theory.

As some of you argue, perhaps arithmetic theory should be called a computational framework and when specific actualizations are provided (e.g. diameter, and depth) it becomes a theory with profound predictive power.

Though the opening quote by Nielsen (whose book I admire) is parenthetical, it makes me all the more curious why he chose to make it. So armed with a link to this thread I will try to ask him.

18. Nov 29, 2017

### atyy

It is not just semantics. Nielsen says "complete physical theory", meaning that the bare axioms of quantum mechanics do not make predictions about specific systems until further specifications are added. This is the point made above by A. Neumaier (post #6) and Demystifier (post #7).

19. Nov 29, 2017

### vanhees71

Another example cementing my prejudice against philosophy ;-)). It's a totally empty and irrelevant statement whether you call quantum mechanics a framework or a theory. Quantum mechanics is a special case of general quantum theory for non-relativistic systems.

20. Nov 29, 2017

### Staff: Mentor

On that note, time to close.