# 9 Reasons Quantum Mechanics is Incomplete

I argue that all interpretations of quantum mechanics (QM) are incomplete, each for its own reason. I also point out that for some interpretations (those marked with (*)) this incompleteness is in fact a good thing because in principle this incompleteness may be resolved experimentally.

**Shut up and calculate logical positivism:**It’s OK to talk about the meaning, it’s just not OK to talk about it when one is doing science. Therefore science is incomplete. Assuming that QM is a science, it follows that QM is incomplete.**Old Copenhagen:**There is a quantum micro-world and there is a classical macro world. Therefore QM is incomplete. (It is not specified where exactly the borderline between micro and macro is, so even QM and classical physics together are incomplete. (*) )**QBism, relational, and other information-based interpretations:**There is an objective reality out there, but QM has nothing to say about it. Therefore QM is incomplete.**Statistical ensemble interpretation:**Individual measurement outcomes exist, but QM has nothing to say about them. Therefore QM is incomplete.**Von Neumann collapse:**Consciousness causes collapse, but nobody knows what consciousness is. Therefore QM is incomplete.**Objective collapse:**One should add some additional terms to the Schrodinger equation, but there is no consensus on what these additional terms are. Therefore QM is incomplete. (*)**Many worlds:**To derive the Born rule one needs some additional axioms, but there is no consensus on what these axioms are. Therefore QM is incomplete.**Consistent histories:**All the allowed questions have unambiguous answers, but some questions are explicitly forbidden. Therefore QM is incomplete.**Bohmian mechanics:**Only fundamental objects have trajectories. For instance, a phonon (the quantum of sound) doesn’t have a trajectory. It is not known yet what the fundamental objects are, so QM is incomplete. (*)

(*) This kind of incompleteness is in fact good because different choices lead to different measurable predictions. In the Bohmian case see https://lanl.arxiv.org/abs/1811.11643

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Theoretical physicist from Croatia

One can exclude point charges from the theory.Then how do you handle a blob of matter? It is usually done by breaking it into a lot of infinitesimal size bits. But even aside from that if you want to exclude point particles a theory that requires that is not complete.

Thanks

Bill

That is the conventional wisdom. But we have some curios things classically indicating classical physics is incomplete eg the a-causal runaway solutions of the Dirac-Lorentz equation:

https://arxiv.org/abs/gr-qc/9912045One can exclude point charges from the theory.

The distinction between classical electrodynamics and quantum mechanics is that the former is intrinsically complete (detailed experimental data is needed to show it is incomplete), while the latter is intrinsically incomplete (even without deviations from detailed experimental data, we know it is incomplete because measurement is considered to be a special process).That is the conventional wisdom. But we have some curios things classically indicating classical physics is incomplete eg the a-causal runaway solutions of the Dirac-Lorentz equation:

https://arxiv.org/abs/gr-qc/9912045

My view is that each layer of the onion has issues that can only be resolved by the next layer.

I am also expressing the view it is never ending – that may of course be wrong – there may be a final theory, but certainly we do not know it at present.

Thanks

Bill

Very nice article, well articulated and thought provoking. Thank you for writing this. After reflecting on the issues for a couple days, the question at the top of my mind is,

Which physical theories are complete?1. Classical mechanics?

2. Classical electrodynamics?

3. Classical thermodynamics?

4. Quantum statistical mechanics?

5. Classical (Newtonian) gravity?

My tendency is to consider classical mechanics as the shining example of excellence in a physical theory to which other scientific ideas should be compared. But by your criteria (2), the inability to clearly articulate a boundary between systems where classical is applied and where quantum is applied means that neither theory is complete. But if we are dogmatic about this criterion, are there any complete theories at all anywhere in science?The distinction between classical electrodynamics and quantum mechanics is that the former is intrinsically complete (detailed experimental data is needed to show it is incomplete), while the latter is intrinsically incomplete (even without deviations from detailed experimental data, we know it is incomplete because measurement is considered to be a special process).

Although the source of incompleteness is different, there is a similar distinction between classical electrodynamics and quantum general relativity. Quantum general relativity is intrinsically incomplete, even without deviations from detailed experimental data, because we can see that it is mathematically undefined at high energies. (I think Zee says something like this in his QFT text.)

Thus QM and quantum gravity provide open problems to theorists, even before they have been experimentally falsified. They are incomplete on almost purely "logical" grounds.

Because a photon in air or in glass is something different from a photon in vacuum (and similarly for an electron). Already their speed is different, and since all QED photons travel with the speed of light in vacuum, photons in a medium must have a different nature – they are quasiparticles only. Their nature changes each time they change the medium.Are there photons in a medium? I thought on entering the medium they become a quasi particle – a phonon if I recall correctly.

Thanks

Bill

Which physical theories are complete?That's pretty much Dirac's view – it's simply just a progression of what's gone before rather than the paradigm shifting idea of Kuhn and advocated by Heisenberg and others. Its my view as well for what its worth.Thanks

Bill

I just want to mention Ensemble also has the same issue as Copenhagen – namely it assumes a classical world for the outcome to be an ensemble of.

Decoherent histories, while these days subsumed into Consistent Histories, tries to explain why some questions cant be asked – but it still has issues. Will those issues be resolved? Who knows.

Thanks

Bill

Very nice article, well articulated and thought provoking. Thank you for writing this. After reflecting on the issues for a couple days, the question at the top of my mind is,

Which physical theories are complete?1. Classical mechanics?

2. Classical electrodynamics?

3. Classical thermodynamics?

4. Quantum statistical mechanics?

5. Classical (Newtonian) gravity?

My tendency is to consider classical mechanics as the shining example of excellence in a physical theory to which other scientific ideas should be compared. But by your criteria (2), the inability to clearly articulate a boundary between systems where classical is applied and where quantum is applied means that neither theory is complete. But if we are dogmatic about this criterion, are there any complete theories at all anywhere in science?

Mmm, can you elaborate on that? Why wouldn't a photon I observe be fundamental?Because a photon in air or in glass is something different from a photon in vacuum (and similarly for an electron). Already their speed is different, and since all QED photons travel with the speed of light in vacuum, photons in a medium must have a different nature – they are quasiparticles only. Their nature changes each time they change the medium.

Electrons and photons in a medium (i.e., all electrons and photons we observe here on earth) are quasiparticles only. Do they have trajectories?Mmm, can you elaborate on that? Why wouldn't a photon I observe be fundamental?

What mean a QM interpretation?

A classical version of QM? A classical understanding of QM?

There need not be such thing.An ontology, like any physics theory has. Of course, an ontology doesn't need to be classical.

What mean a QM interpretation?Any explanation of QM beyond pure operationalism.

What means a QM interpretation?https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

What mean a QM interpretation?

A classical version of QM? A classical understanding of QM?

There need not be such thing.

''Bohmian mechanics: Only fundamental objects have trajectories.''

Electrons and photons in a medium (i.e., all electrons and photons we observe here on earth) are quasiparticles only. Do they have trajectories?Thanks for asking, they don't have trajectories in my view of BM (which somewhat differs from the standard view of BM).

''Bohmian mechanics: Only fundamental objects have trajectories.''

Electrons and photons in a medium (i.e., all electrons and photons we observe here on earth) are quasiparticles only. Do they have trajectories?

A possible variant of Old Copenhagen:

Everything can be described by quantum mechanics, but not everything at once, therefore QM is incomplete.This variant of old Copenhagen is quite in spirit of modern consistent histories.

Looks interesting, I have two rather naïve questions.

1) What do you mean by completeness? Is it a term you use colloquially, or with a precise technical meaning?I use it colloquially.

2) Can Gödel incompleteness have anything to do with it?No.

A possible variant of Old Copenhagen:

Everything can be described by quantum mechanics, but not everything at once, therefore QM is incomplete.

Looks interesting, I have two rather naïve questions.

1) What do you mean by completeness? Is it a term you use colloquially, or with a precise technical meaning? On wikipedia I see for example a definition

a formal system is calledWhich makes me wonder, is quantum mechanics (or its interpretations) a formal system?completewith respect to a particular property if every formula having the property can be derived using that system.2) Can Gödel incompleteness have anything to do with it?