Can Quantum Mechanics be postulated to exclude humans?

[dextercioby]

TL;DR Summary

The axioms of a physical theory are the set of irreducible assumptions from which every result/statement of that theory follows as a theorem applying separately formulated definitions and rules of mathematical logic.

An axiomatization of classical mechanics such as the one by McKinsey et al. (1) does not contain any reference to humans or experiments, and does not contain the magic (irony!) words of quantum mechanics, i.e. observables and measurements.

(1) McKINSEY, J. C. C., et al. “Axiomatic Foundations of Classical Particle Mechanics.” Journal of Rational Mechanics and Analysis, vol. 2, Indiana University Mathematics Department, 1953, pp. 253–72, http://www.jstor.org/stable/24900331.

If this article is out of your reach, then let's go back to standard college education and Newton's laws. Any reference to human-made actions (laboratory, experiments, measurements, observables) is missing from the 3 laws.

If Classical Mechanics can be postulated in the absence of humans, and Quantum Mechanics can't (see the standard axioms of QM here), why do we then perceive QM as being the necessary completion of CM (in the microscopic regime, I may add), when it can't even be formulated in the absence of human intervention?

This is not an argument against "QM interpretations", just a question: any QM interpretation involves human actions. Can we void the axioms of QM of any human actions (results of actions) and formulate them in full, perhaps abstract, generality?

Even the postulation of Schrödinger's equation contains humans, if you think about it (you have to link it to the von Neumann-Lüders collapse axiom): "In the absence of measurements (subsequently understood as being performed by humans in a desirably controlled environment) the abstract state vector evolves in time according to this equation (...) until there is a new measurement (again understood to be performed by humans) which discontinuously changes the state vector to a fixed one".

I didn't mean this to sound philosophic, I apologize in advance.

N.B. Sure, in classical mechanics, the definitions which accompany Newton's three laws can be made "operational", i.e. from the perspective of human tools (such as clocks and rulers) and actions ("measurements"). But the axioms are still void of any explicit human action.

 

[andrewkirk]

There certainly appears to be a distinction along the lines you suggest.
But I think it dissolves when one looks at it more closely, at least if one does so from a decoherence perspective.

As you point out, the direct distinction between the two axiom sets is not about humans, but about measurements. The humans come in when we assume the humans make the measurements.

Under the decoherence perspective, we view a measurement as the interaction between the system being studied ("subject system") and a much larger system - the measuring apparatus. That interaction causes a very rapid evolution of the combined system's state that we loosely think of as 'collapse of the wave function'.

So we can interpret the 'in between measurements' proviso in rule 3 as meaning 'in the absence of any interactions with other systems'.

It seems to me that we make the same assumption in classical mechanics. Consider a Newtonian model of the motion of the sun and its eight planets. We would construct that allowing only for the gravitational interactions between these bodies. We implicitly assume no gravitational interactions with other bodies, whether distant stars or smaller local bodies like moons, comets, asteroids, planetoids, satellites, rubble and dust. That is, we apply the laws assuming the absence of interactions with other systems, just as we do with Schrodinger's law.

If the universe were finite, and we didn't have the known incompatibility between QM and GR, we could theoretically make a classical mechanics model of it, that didn't have the 'excluding other interactions' proviso, and we could do the same with a QM model, because there is no possibility of interaction with other systems (because the subject system encompasses everything).

The last four of the seven rules you linked all relate to measurements, ie interactions with systems other than the subject system. They have no analog in the CM axioms, because in CM we always exclude outside influences. We can do that because those outside influences are nearly always tiny. We can't do that in QM because an outside influence, through decoherence, is usually profound, and cannot be ignored. In theory we could do it if the subject system was the whole universe. But in practice we can't, because the universe is too complex to construct a meaningful QM model, and we know it would be wrong anyway, because of the incompatibility of QM with GR.

 

[Demystifier]

any QM interpretation involves human actions.

That is simply not true. Counterexamples are Bohmian mechanics, GRW, relational interpretation, many worlds. See also
https://arxiv.org/abs/2008.04930
https://physicstoday.scitation.org/doi/10.1063/1.882184
https://physicstoday.scitation.org/doi/10.1063/1.882241

 

[vanhees71]

I think if quantum theory tells us one important thing about nature then it is that to observe the phenomena you need to interact with the objects you want to observe. Now one of the lessons we learned is the atomistic structure of matter, and thus we cannot make the interactions necessary to observe the phenomena arbitrarily small. Particularly when we observe "atoms" we need indeed at least one more "atom" to observe its properties, and the interaction to do so necessarily will have a non-negligible influence on the measured "atom", and this is utmost successfully described by the mathematical formalism of quantum theory, it is "a symbolism for atomic measurements" (Schwinger). The resulting "contextuality" implied by quantum theory thus is not a bug but a feature.

Of course, you don't need humans or consciousness to explain these features, simple measurement devices and their interactions with the measured objects without any esoterics are sufficient to understand the meaning of the quantum formalism.

 

[EPR]

QM can be postulated to exclude humans. The question is would it stand scrutiny. Would there be "particles" observed(measured and perceived) if there were no sentient beings to do measurements?
The evidence is not very conclusive.
Being sentient must be a very special feature(result) of measurements as it kind of does not fit anywhere in the formalism.
If it's the which-path information that forces a quantum state to a single outcome, then possibly observers are entangled with the measured system and are essential to the observed "classical" outcomes.

 

[Lord Jestocost]

Can Quantum Mechanics be postulated to exclude humans?​

One should, as John von Neumann has done, merely rely on the unambiguous mathematics constituting quantum theory. The quantum mechanical time evolution is valid for all "physical systems". Simply follow John von Neumann's quantum-mechanical measurement chain in case physical systems are interacting which each other. And then?

 

[WernerQH]

The axioms of a physical theory are the set of irreducible assumptions from which every result/statement of that theory follows as a theorem applying separately formulated definitions and rules of mathematical logic.

Do you expect the axioms to be unique? After centuries, even Euclid's axioms were found to be deficient. And geometry is a more narrowly circumscribed field than physics.

I think the foundational problems of QT, especially of course the infamous measurement problem, derive from the inclusion of "measurement" as an "irreducible" concept in its axioms. There is no reason to assume that prophets like Bohr or von Neumann have once and for all identified the most appropriate concepts for the description of quantum processes. IMHO quantum (field) theory is more appropriately seen as a theory of events in spacetime.

If Maxwell had chosen to axiomatize electrodynamics, no doubt the axioms would have been about the properties of the ether. For Maxwell the existence of the ether was as self-evident as the existence of elementary particles is for us today. (In the year before his death he inquired about the possibility of using eclipses of Jupiter's satellites to determine the rest frame of the ether.) In the case of electrodynamics it took only four decades to identify (or "purify") a concept more appropriate than the ether: fields.

 

[dextercioby]

That is simply not true. Counterexamples are Bohmian mechanics, GRW, relational interpretation, many worlds. See also
https://arxiv.org/abs/2008.04930
https://physicstoday.scitation.org/doi/10.1063/1.882184
https://physicstoday.scitation.org/doi/10.1063/1.882241

Thank you very much, I will read the three of them.
EDIT: see the other reply just under, my original message focused only on the given references.

 

[dextercioby]

That is simply not true. Counterexamples are Bohmian mechanics, GRW, relational interpretation, many worlds. See also
https://arxiv.org/abs/2008.04930
https://physicstoday.scitation.org/doi/10.1063/1.882184
https://physicstoday.scitation.org/doi/10.1063/1.882241

Sorry, do you know any axiomatical treatment of "Bohmian mechanics, GRW, relational interpretation, many worlds", i.e. exact literature references?

 

[vanhees71]

It's not axiomatic, but the great book by Dürr has been translated to English recently:

https://www.springer.com/gp/book/9783030400675

 

[Demystifier]

Sorry, do you know any axiomatical treatment of "Bohmian mechanics, GRW, relational interpretation, many worlds", i.e. exact literature references?

No, but the book by Durr mentioned by @vanhees71 is quite mathematical.

 

[*now*]

For a relational interpretation, this is an early treatment https://arxiv.org/pdf/quant-ph/9609002.pdf but I think there has been development since.

In comparisons between different approaches in different areas of physics, the OP touched on frames of reference and some possibly implicit referential inclusion in physical interaction accounts. I think there may be some frame of reference involved in accounts of any physical interaction and it could be that this is more explicit in some areas. If this were the case, then any special human status could be neutralised by accepting any physical system involved in interaction may be a frame of reference and so not limited to humanity or anything of that nature. Wiki says relativity’s frames of reference was inspirational for RQM.

 

[Demystifier]

It's not axiomatic, but the great book by Dürr has been translated to English recently:

https://www.springer.com/gp/book/9783030400675

Since this book is at odds with your own view of quantum mechanics, may I ask why exactly do you think it's great?

 

[gentzen]

I think if quantum theory tells us one important thing about nature then it is that to observe the phenomena you need to interact with the objects you want to observe. Now one of the lessons we learned is the atomistic structure of matter, and thus we cannot make the interactions necessary to observe the phenomena arbitrarily small.

Indeed, interaction is central. But what would happen if it were an interaction between a quantum sensor of a quantum computer instead of an interaction with a classical measurement device? The quantum computer might do some processing of the sensor input on the quantum level, and in the end could output a combination of classical measurement results and special quantum output states. It might also use classical measurements as part of its error correction scheme to ensure accurate quantum processing. But we can ignore those classical intermediate results, because they don't contain meaningful information.

Since here the output of the quantum computer was a combination of classical and quantum information, it makes sense to assume that the input too can be a combination of classical and quantum information. The difference is that quantum information cannot be cloned, while classical information can be copied at will and even be permanently recorded.

Quantum Computation and Quantum Information by Michael Nielsen and Isaac Chuang present axioms for quantum mechanics (and especially measurements) which fit well to the possible outputs of such a combination of quantum sensor with a quantum computer described above. (It doesn't include the mixing of classical and quantum input, which would only make the presentation more complicated without adding anything substantial.)

Of course, you don't need humans or consciousness to explain these features, simple measurement devices and their interactions with the measured objects without any esoterics are sufficient to understand the meaning of the quantum formalism.

I guess the question is less about consciousness and esoterics than about the fact that performing an experiment is an intentional human action, and measurement devices seem to be artifacts of human culture. And the combination of quantum sensor and quantum computer I described above doesn't fix this. What it does fix is that the interaction is now allowed to be a combination of quantum and classical, and it clarifies the role of the classical as the part that can be copied without restrictions.

The problem with the role of humans in the formulation of quantum mechanics is the subjective element they contribute. But the decision which information can be regarded as classical FAPP is indeed subjective. The decision about what is the system and what is the environment is subjective too. (But it also exists in classical mechanics: For example, we decide that the solar system with its planets (and moons of the planets, and water on the planets) is the system, and random influences like small asteroids and remaining forces from outside are the environment. The only difference is that quantum systems are typically less well isolated from their environment.)

 

[vanhees71]

There is no subjective element only because there are interactions between a measurement device and the measured system. Also there is no classical-quantum cut as you suggest. Of course, in modeling it is to some extent arbitrary what you call "environment". The only thing you have to make sure is that you include all relevant interactions between the measured system and the "environment", including the interaction with the measurement device.

 

[EPR]

But QT postulates only observables and measurements. The environment and measuring devises are all subjects to these measurements.

It seems there are no apparati and environment outside the measurement framework. Namely, there are classical measuring devices because there's colossal amount of measuring going on all the time.
Hence, we can't postulate the measuring devices as the causes of the appearance of classical reality because they depend on the act of measurement for their own existence. The real question remains - what makes the measurements in the absence of anything classical.

 

[Lord Jestocost]

Regarding the Heisenberg cut, it is a “purely epistemological move without any counterpart in ontology” (as N.P. Landsman characterizes Heisenberg’s and Bohr’s reasoning with respect to the Heisenberg cut in his paper “Between classical and quantum”).

Wolfgang Pauli in „Aufsätze und Vorträge über Physik und Erkenntnistheorie“, chapter „Die philosophische Bedeutung der Idee der Komplementarität“:

„Während die Existenz eines solchen Schnittes eine notwendige Bedingung menschlicher Erkenntnis ist, fasst sie die Lage des Schnittes als bis zu einem gewissen Grade willkürlich und als Resultat einer durch Zweckmäßigkeitserwägungen mitbestimmten, also teilweise freien Wahl auf.“
(While the existence of such a cut is a necessary condition for human knowledge, its location is to some extent arbitrary as a result of a pragmatic and thereby partly free choice.)

 

[Lord Jestocost]

The only thing you have to make sure is that you include all relevant interactions between the measured system and the "environment", including the interaction with the measurement device.

The math of quantum mechanics is unambiguous: The system is sucked into a vortex of entanglement and no longer has its own quantum state.

 

[gentzen]

There is no subjective element only because there are interactions between a measurement device and the measured system.

I have a hard time parsing this sentence. However, I see that what I meant by "subjective element" might be better captured by "is to some extent arbitrary" as in Lord Jestocost's quotes.

But the decision which information can be regarded as classical FAPP is indeed subjective.

So instead of "... FAPP is indeed subjective" it might have been better if I had written instead "... FAPP is to some extent arbitrary".

Also there is no classical-quantum cut as you suggest.

Did I suggest such a cut? All currently relevant quantum computer designs make a very clear distinction between the quantum and the classical parts. Only the quantum part is operated at near zero temperatures, the classical control logic operates at higher temperatures. The exact point of the transition from quantum to classical information is simply very explicit and intentional in a quantum computer.

But the purpose of introducing the quantum computer was less to suggest a classical-quantum cut, but to allow to leave the measurement interaction fully in the quantum domain, and decouple it from the decision whether the measurement result output should be more quantum or more classical. Have you heard of Mermin's paper "Copenhagen computation: How I learned to stop worrying and love Bohr"?

 

[vanhees71]

I thought you suggest a quantum-classical cut, because you make the somewhat enigmatic distinction between classical and quantum information. There is information as a very important concept in physics, but I've no clue, how you distinguish between classical and quantum information. Also it's clear that macroscopic systems in thermal equilibrium at not too low temperatures behave classical, but that's not a surprise but a pretty obvious approximation you can directly read off the Bose-Einstein or Fermi-Dirac distribution functions.

I don't know that paper by Mermin.I'm surprised that he learned to love Bohr. Maybe it's an interesting read ;-).

 

[WernerQH]

I guess the question is less about consciousness and esoterics than about the fact that performing an experiment is an intentional human action, and measurement devices seem to be artifacts of human culture.

I find it strange a strange idea that humans should play a special role here. Nature "does its thing". (Not her's, that's too anthropocentric! :-) Why should it matter whether or not humans arranged it to happen?

 

[dextercioby]

No, but the book by Durr mentioned by @vanhees71 is quite mathematical.

I still can't get over the fact that you/one cannot fully define Bohmian Mechanics by 3 to 6 axioms.

 

[Demystifier]

I still can't get over the fact that you/one cannot fully define Bohmian Mechanics by 3 to 6 axioms.

Nobody said that it can't be done, it's just that Bohmians are not much interested in that. In fact, it's very easy to do that. Roughly, the idea is the following. (i) Start from the usual axioms of nonrelativistic QM, written in the form such that one of them (usually the last one) is the collapse axiom. (ii) Remove the collapse axiom. (iii) Add the guiding formula for particle trajectories to the list of axioms.

If you want more details, cite a reference with an axiomatization of standard QM and I will tell you how exactly this axiomatization should be modified to make it Bohmian.

 

[dextercioby]

It is here quoted in the 1st post. A summary by Arnold Neumaier with input from other PF users. (7 rules).

 

[Demystifier]

It is here quoted in the 1st post. A summary by Arnold Neumaier with input from other PF users. (7 rules).

I don't like this particular form of axiomatization. I would be more happy if you would take axiomatization from some better known textbook.

See also https://arxiv.org/abs/1704.08017, Sec. 1 can be thought of as axiomatization of Bohmian mechanics, while the rest of the paper are consequences of those axioms. In this paper the Born rule for particle positions is an axiom, but in some Bohmian approaches the Born rule is considered an approximate derived feature.

 

[gentzen]

I find it strange a strange idea that humans should play a special role here. Nature "does its thing". (Not her's, that's too anthropocentric! :-) Why should it matter whether or not humans arranged it to happen?

Well, QM and QFT are formalisms invented by humans. To to get experimentally verifyable predictions from them, various strategies suggest themselves:
1) You could study small well isolated systems. And if nature does not provide them in sufficient number, then humans can just prepare them theirself. No real mystery how humans acquired a special role here, from my POV.
2) You study the statistics of systems with many degrees of freedom, in some sort of local equilibrium. Since your predictions can only be approximate in those cases, the decision if they are good enough FAPP is to some extent arbitrary. Here the arbitrariness seems to bring in a human element. Maybe it is possible to eliminate it, maybe not.
3) ...

Since QM and QFT are human inventions, it might be interesting to understand why they are so robust against missing details and other inaccuracies. Why are they good tools to predict results of experiments? How much is the focus on pure states an obstacle towards a better understanding in this direction?

 

[Lord Jestocost]

I find it strange a strange idea that humans should play a special role here. Nature "does its thing".

One shouldn’t mix up different levels of thinking when discussing the role of conscious human beings. Of course, “Nature” does its thing, that’s trivial. However, the object of our scientific studies isn’t “Nature” as it is “in-itself” or “Nature” as it is “when nobody looks”. The object of our studies are our perceptions of “Nature”, the relation between conscious observers and “Nature”.

N. David Mermin citing Schrödinger in “Making Better Sense of Quantum Mechanics”:

“Quantum mechanics forbids statements about what really exists — statements about the object. It deals only with the object-subject relation. Although this holds, after all, for any description of nature, it appears to hold in a much more radical and far-reaching sense in quantum mechanics.”
(Schrödinger to Sommerfeld, 11 December, 1931, in Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, Springer Verlag, 2011. English translation by N. David Mermin and Rüdiger Schack)

 

[WernerQH]

it might be interesting to understand why they are so robust against missing details and other inaccuracies.

They are the result of evolution. Unsuccessful theories have been forgotten along with the concepts that they relied on.

How much is the focus on pure states an obstacle towards a better understanding in this direction?

Very good question! In my view the focus on the wave function is misguided. The Heisenberg picture with its focus on operators (ensembles) is a much better starting point. The wave function is but a single piece of a bigger mathematical apparatus (and is always traced over, except in situations involving idealized experiments).

 

[WernerQH]

The object of our studies are our perceptions of “Nature”, the relation between conscious observers and “Nature”.

Of course you can call the publications of the Particle Data Group summaries of their "perceptions". But most physicists would presumably consider that rather silly and prefer to think of those publications as expressing facts about really existing objects.

Schrödinger's remark

Quantum mechanics forbids statements about what really exists — statements about the object.

seems to contradict this. The fundamental problem is that we tend to think of the world around us as made up of "objects", be they planets or electrons. But electrons must be "objects" in a very different sense. It is misleading to think of them as objects (particles), because the term carries too many inappropriate connotations. For example that objects have properties, that an electron must always have a position.

 

[PeterDonis]

The fundamental problem is that we tend to think of the world around us as made up of "objects", be they planets or electrons. But electrons must be "objects" in a very different sense. It is misleading to think of them as objects (particles), because the term carries too many inappropriate connotations. For example that objects have properties, that an electron must always have a position.

I think part of the issue here is that there are two possible attitudes towards our experiences and observations of macroscopic objects that are in tension.

One attitude is that we should be able to derive the behavior of macroscopic objects, and the fact that that behavior looks "classical" to us, using some sort of approximation scheme from the underlying quantum laws. On this view, a statement like "objects have properties" would be an approximation that is understood to only apply to macroscopic objects, and to not be a fundamental law. QM itself can then be viewed as a complete fundamental theory.

The other attitude is that our experiences and observations of macroscopic objects, including the fact that we observe such objects to have properties that are "there" whether or not we observe them at a particular moment, are the basic ground from which we derive any physical theory, including QM. So if QM ends up telling us that macroscopic objects don't have properties, or only have them in some approximation, that means that QM cannot be viewed as a complete fundamental theory.

 

[AndreiB]

The fundamental problem is that we tend to think of the world around us as made up of "objects", be they planets or electrons. But electrons must be "objects" in a very different sense.

Can you be more specific here? In what sense are electrons objects?

It is misleading to think of them as objects (particles), because the term carries too many inappropriate connotations.

OK, how one should think of them?

For example that objects have properties, that an electron must always have a position.

Are you saying that electrons don't have properties? Why are you calling them electrons then instead of neutrinos or pink rabbits?

 

[vanhees71]

They are the result of evolution. Unsuccessful theories have been forgotten along with the concepts that they relied on.

Very good question! In my view the focus on the wave function is misguided. The Heisenberg picture with its focus on operators (ensembles) is a much better starting point. The wave function is but a single piece of a bigger mathematical apparatus (and is always traced over, except in situations involving idealized experiments).

I agree that too much focus on pure states can be misleading. Particularly it is hard to make clear that not Hilbert space vectors (or wave functions in the wave-mechanics formulation) are the states but unit rays in Hilbert space. That's why I think one should introduce statistical operators as the representants of states early and the pure states as the special case, where the statistical operator is the special case of being a projection operator.

I'm not so sure about which approach to QM should be used first. For quite a while I was thinking, that the most simple approach is to start with some finite-dimensional cases like spin 1/2 (problematic for a first encounter, because it's hard to explain what spin is without having a concept of QM first) or polarization of photons (problematic for a first encounter, because you have somehow to introduce the concept of photons, and this all too easily leads to the very wrong idea that photons were in any sense "particles", but it's in principle doable). I've started by intro QM lectures twice in such a way, but my experience is that this is too abstract. The students don't get a good idea what QM is about. The same holds for using the Dirac approach, i.e., using "canonical quantization" with abstract operators and representation-free Hilbert-space formalism using the Heisenberg picture of time evolution. Though I think that this is the most "natural" approach, but that's true provided you have a good understanding of the formulation of classical mechanics in terms of the Hamiltonian formulation with Poisson brackets with an emphasis on its algebraic structure and its natural relation with the Lie groups underlying the space-time symmetries (Galilei symmetry, which however is not so easy too, and you cannot start an intro lecture in QM with Lie group and algebra representation theory, needing complicated concepts as unitary ray representations and central extensions). With all this experience I'm back at the old-fashioned heuristic approach via wave mechanics, using the de Broglie approach postulating the free-particle dispersion relation for the wave via the energy-momentum relation and then discussing wave mechanics in position and momentum representation first. This works quite well as a heuristic, and the math is well known from the electrodynamics lecture the students had just one semester before the QM lecture. Then you can introduce the abstract Hilbert space formalism a la bras and kets later as a generalization. Of course then you naturally have the Schrödinger picture of time evolution first.

 

[WernerQH]

I think part of the issue here is that there are two possible attitudes towards our experiences and observations of macroscopic objects that are in tension.
[...]
So if QM ends up telling us that macroscopic objects don't have properties, or only have them in some approximation, that means that QM cannot be viewed as a complete fundamental theory.

I think that's going a bit too far. :-)
QM cannot be telling us that macroscopic objects don't have properties.

Nobody doubts that electrons have a mass of 511 keV and spin 1/2, whereas properties like position and spin direction are questionable (at least not permanent, or "uncertain"). The former properties are better viewed as properties of the Dirac propagator, whereas the latter arise in interactions with detectors and should perhaps be better called attributes (or observables), because they depend on the detector as much as on the "object" being measured. I think that at the fundamental level it is best to avoid the talk of "objects" altogether.

 

[vanhees71]

In classical physics, position, momentum and classical spin components (for extended bodies) also take different values in different "states" and only intrinsic properties like their mass don't change. If nothing would change, we'd not have any kinematics and dynamics. Of course, also in quantum theory systems have properties, described by the state.

 

[WernerQH]

So, where's the difference between classical and quantum mechanics in your opinion?
Is it just that c-values are replaced by q-values, and one has to be careful in interpreting the "states" of systems? I'm interested to understand the physical, not the formal differences.