I Physicists disagree wildly on what quantum mechanics says about real…

[gentzen]

I think we can present Bohr as modifying what subsequent measurements are possible after a given measurement, which in mathematical terms is equivalent to the construction of a Positive Operator-Valued Measure, a POVM, for a joint measurement at time-like separation. I present that mathematical version of Bohr's idea (which I of course hope Bohr would not dismiss out of hand if he were still with us) in an article

If I were you, I would not even try connect my own ideas to what Bohr might have ment by his obscure words:

The very nature of the quantum theory thus forces us to regard the space-time co-ordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features of the description, symbolizing the idealization of observation and definition respectively.

I have no idea what Bohr means by "definition". My own idea is that "preparation" is an important concept for QM that should better be disentangled from measurement. So I could reinterpret Bohr's "observation and definition" as "measurement" and "preparation", and claim that Bohr vindicates my ideas.

OK, let me check whether Howard's clarifications will be compatible with my reinterpretation:

the version of complementarity here introduced, between “space-time coordination” and the “claim of causality,” engenders confusion on the part of both those who, failing to hear the Kantian echoes in Bohr’s vocabulary, find the idea inherently obscure and those who ...

(Oh yeah, I guessed that Bohr might have believed his obscure words would echo Kant.)

Bohr always criticized Heisenberg for promoting the disturbance analysis, arguing that while indeterminacy implies limitations on measurability, it is grounded in “limitations on definability”

So Bohr complained that Heisenberg's uncertainty relations are primarily a limitation of possible quantum states, and only secondarily a limitation of possible classical measurements? But a "limitation of possible quantum states" means a "limitations of which states can be prepared", so my interpretation of Bohr's "definition" as "preparation" seems to work, no?
No, I am just kidding myself! Bohr's words are simply obscure. Just because I managed to read into them what I wanted doesn't mean that this is what Bohr had in mind!

 

[Fra]

I wonder, are we "using Bohr" to strenghten our own new ideas/interpretations...

OR

Are we honouring Bohr as one of the founders, by noting that he seems to have kept many doors open that are still beeing examined long time after? Rather than implying this or that, didnt Bohr just try to not say too much when we didnt know?

I personally think its the second option, as i doubt that many of the more werid or esotheric ideas around today was something that researchers gave much thought back then?

/Fredrik

 

[Peter Morgan]

If I were you, I would not even try connect my own ideas to what Bohr might have ment by his obscure words:

I have no idea what Bohr means by "definition". My own idea is that "preparation" is an important concept for QM that should better be disentangled from measurement. So I could reinterpret Bohr's "observation and definition" as "measurement" and "preparation", and claim that Bohr vindicates my ideas.

OK, let me check whether Howard's clarifications will be compatible with my reinterpretation:

(Oh yeah, I guessed that Bohr might have believed his obscure words would echo Kant.)

So Bohr complained that Heisenberg's uncertainty relations are primarily a limitation of possible quantum states, and only secondarily a limitation of possible classical measurements? But a "limitation of possible quantum states" means a "limitations of which states can be prepared", so my interpretation of Bohr's "definition" as "preparation" seems to work, no?
No, I am just kidding myself! Bohr's words are simply obscure. Just because I managed to read into them what I wanted doesn't mean that this is what Bohr had in mind!

Fun! Thanks! Whatever historical developments I partly associate myself with, there will be people who say I should start somewhere else?!? Bohr is problematic, but so is everyone else (including myself, inevitably), and I kinda like that we can use mathematics, in the form of the Naimark Dilation Theorem, to make sense of Don Howard's telling of the distinction between Bohr and Heisenberg. I like as well that Bohr comes out of that retelling smelling a little more of roses than one might expect, somewhat reflecting the second take that @Fra gives above: that we honor Bohr more than we use him to justify our own path. Bohr and many others could easily have done the math in my JPhysA 2022 article (and more accessibly on slides 17-20 in my Oxford talk), but he didn't and nor AFAIK have more than a very few other physicists, which in recent years I think is because decoherence has become so established as good enough.
In a more recent talk, for NSU Dhaka on May 18th (PDF of the slides here, which includes a link to YouTube), I present a slide that I like to think shows the difference of philosophy between Bohr and Heisenberg (and between Naimark and decoherence) well enough,

Naimark is still an FAPP approach, so it won't please anyone who will not accept anything else than a completely classical metaphysics, but I find it worthwhile to see how the two perspectives dovetail together.

 

[gentzen]

I present a slide that I like to think shows the difference of philosophy between Bohr and Heisenberg (and between Naimark and decoherence) well enough,

Sorry, I don't even see the names Bohr or Heisenberg on that slide. Also, the question is not so much the difference of philosophy between Bohr and Heisenberg, but rather what Bohr actually had in mind with his words.

Let me try to guess, how Bohr wanted me to interpret his words:

The very nature of the quantum theory thus forces us to regard the space-time co-ordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features of the description, symbolizing the idealization of observation and definition respectively.

I guess he wants space-time co-ordination to correspond to observation, and claim of causality to correspond to definition respectively. Because observation happens in normal 3+1 dimensional space-time, I guess he links it to space-time co-ordination. And because the Schrödinger equation describes a deterministic evolution in 3N-dimensional space, I guess he links it to claim of causality. And definition probably then simply means the wavefunction in 3N-dimensional space.

I don't want to deflate Bohr here. I just want to show what you get, if you try to interpret his words, assuming that he had a bit of trouble to clearly express himself. A disadvantage of this reading is that there is not much philosophy left. But maybe that is what Bohr really wanted, who knows?

 

[Herman Trivilino]

I don't want to deflate Bohr here. I just want to show what you get, if you try to interpret his words, assuming that he had a bit of trouble to clearly express himself

I think that's a fair assumption. Bohr was famous for coraling new physicists at his institute into joining him in his office to help him complete his thoughts. He tried this with Dirac, but if you know anything about Dirac's personality, it was bound to fail.

On Bohr's first attempt Dirac told him that as a child he was taught not to start a sentence until he knew how to finish it.

Bohr had to recruit someone else.

Whenever I read Bohr I'm usually left with the impression that he understands some underlying issue that I don't.

 

[Fra]

I don't want to deflate Bohr here. I just want to show what you get, if you try to interpret his words, assuming that he had a bit of trouble to clearly express himself. A disadvantage of this reading is that there is not much philosophy left. But maybe that is what Bohr really wanted, who knows?

Isnt' the philosophy just that it is impossible to even define a traditional dynamical law in a classical configuration space formed from distinguishable outcomes of definite single observations?

This may seem like an empty or trivial philosophy in that it does not attempt try to explain HOW to find an improved definition of dynamical law or states that brings more clarity.

Whenever I read Bohr I'm usually left with the impression that he understands some underlying issue that I don't.

Maybe Bohr able to hold that insight, without getting more confused than necessary and this is what he understood?

Given this "problem" we either need to a new understanding of "observation" or "causality" or both.

Also his reference to the "classical context" seems like a undeniable insight as well as ANY reconstruction of "observation" or "causality", wether it includes preparation procedures and instruments, must be build in a reference context that are not subject to the same uncertainy as the subatomic world.

Perhaps this is a thin philosophy? But that's why i find it honest and clean still, of minimalist type. But given that this insight, allows for slutions in many directions its not hard to see that many more "speculative interpretations" can still be "compatible" with this basic picture.

/Fredrik

 

[Lord Jestocost]

Let me try to guess, how Bohr wanted me to interpret his words:

There's no need to complicate things. Marian O. Scully, Berthold-Georg Englert and Herbert Walther have captured the essence of the 'Principle of Complementarity' in their paper “Quantum optical tests of complementarity” (Nature volume 351, pages 111–116 (1991)):

“Here then is the 'Principle of Complementarity':
For each degree of freedom the dynamical variables are a pair of complementary observables.
A less formal, less precise version in practical terms is:
No matter how the system is prepared, there is always a measurement whose outcome is utterly unpredictable.
Thus, in the microcosmos complete knowledge of the future in the sense of classical physics is not available.”

 

[gentzen]

Perhaps this is a thin philosophy? But that's why i find it honest and clean still, of minimalist type.

Maybe the trick to understand Bohr would be to focus on his discussions with other physicists and scientists, instead of trying to make sense of his writings. He loved discussions, something he had in common with Heisenberg.

When I look at Bohr's more famous discussions, my impression has always been that Bohr's focus on the details of the physical situations is the crucially important part of "his philosophy":

Obviously, this mixing up of theory and interpretation is one of the main reasons why QM causes so much confusion. Einstein wanted to interpret QM as incomplete. Bohr opposed this, by ... focusing on the details of the physical situations. Schrödinger wanted to reduce QM to a classical wave equation. Heisenberg disagreed, arguing for the discontinuity of QM phenomena.

The irony is that Bohr and Heisenberg interpreted QM differently. But they used the same theory and insisted on the completeness of this theory. For Bohr, this meant above all that Einstein was wrong in his interpretation. Heisenberg later described in great detail and with precision what he meant by completeness. Dirac then also described his view, drawing on and contrasting with Heisenberg.

To my surprise, Jan Faye seems to indicate that this contextuality might even have been a crucially important part of Bohr's beloved complementarity:

In general, Bohr considered the demands of complementarity in quantum mechanics to be logically on a par with the requirements of relativity in the theory of relativity. He believed that both theories were a result of novel aspects of the observation problem, namely the fact that observation in physics is context-dependent.

Let me also highlight Bohr's crucial part in the 1969 Nobel Prize in Physiology or Medicine for "discoveries concerning the replication mechanism and the genetic structure of viruses", in order not to reduce Bohr purely to discussions about the interpretation of QM.

---

But still, if Bohr's "claim of causality" has really such a simple interpretation, then he has essentially given up on causality. On the other hand, Heisenberg always defended QM for still respecting causality, if the fundamental limitations of our knowledge (imposed by QM) are properly taken into account.
Let me repeat here, what I learned recently about "Bob Coecke's" causality postulate:

I did research time-symmetric and retrocausal type interpretations quite intensely. I also studied "Picturing Quantum Processes" by Bob Coecke and Aleks Kissinger, because the calculus looks nicely time-symmetric too. Luckily for me, it turns out that Bob Coecke (et al?) found out how that time-symmetry gets broken (I think I know how to apply this "solution" to Consistent Histories): By "his" causality postulate:

So, we can more fundamentally interpret the causality equation as follows:
If a state is discarded, it may as well never have existed.

We can also interpret (6.32) directly:
If the output of a process is discarded, it may as well have never happened.
which is a straight generalisation of the interpretation we gave for causal states in Section 6.2.3.

We motivated causality with this motto:
if the output of a process is discarded, it may as well have never happened.
... (6.55)
This also means that if a processes is happening somewhere else, and its output never reaches us, we don’t need to care about it. As we already noted, this is crucial to being able to even do science, in that it allows us to safely ignore parts of the universe that won’t affect us.

Thus, the causality postulate (6.64) for a generic process guarantees that:
probabilities can be consistently assigned to branches.

Definition 8.8 is just a minor update to our original slogan for causality:
If we discard/delete all of the quantum/classical outputs
of a quantum process, it may as well have never happened.
Thus we have succeeded (as promised) in extending the interpretation of causality for quantum maps of Section 6.2.4, to quantum processes which may also involve classical inputs and outputs.

(I know I should make screenshots from his book to show just how seamless and natural that postulate works. In the meantime, I also tried to find out where he first published "his" causality postulate. I learned that it is actually not "his" postulate, but from Chiribella et al: the postulate itself in 2009, and the realization that this is actually "the causality postulate" in 2010.)

 

[gentzen]

There's no need to complicate things.

Hey, I was honestly proud that I seemed to have found an interpretation of "that specific quote of Bohr's words from Don Howard's paper" that seemed consistent to me.

I agree that Bohr's concepts are fine (most of the time), and that he could convey them in discussions. And the times when his concepts were not fine, he got attacked by Heisenberg (for his theory/paper with Slater and Kramers) or by Pauli (for Bohr's willingness to give up energy conservation). So those of Bohr's concepts which survived to the present day should be fine.

But Bohr's writing is absolutely terrible. Spelling this out explicitly is not "to complicate thing". It is just to be clear and honest. (And if others had realized that Bohr was giving up on causality in that obscure passage, maybe Heisenberg or Pauli, or somebody elso like Ehrenfest or Einstein would have actually attacked Bohr, and made it clear that giving up causality on such weak grounds is just a bad idea.)

 

[Herman Trivilino]

Maybe Bohr able to hold that insight, without getting more confused than necessary and this is what he understood?

Maybe, but it never made that clear, in my opinion.

be to focus on his discussions with other physicists and scientists, instead of trying to make sense of his writings.

When I spoke of his writings what I should have included is the written accounts of his discussions.

 

[Fra]

I wonder if anyone ever read a clear and brilliant writing about the conceptual foundations of QM?
I don't think I have.

/Fredrik

 

[Peter Morgan]

To my surprise, Jan Faye seems to indicate that this contextuality might even have been a crucially important part of Bohr's beloved complementarity:

In general, Bohr considered the demands of complementarity in quantum mechanics to be logically on a par with the requirements of relativity in the theory of relativity. He believed that both theories were a result of novel aspects of the observation problem, namely the fact that observation in physics is context-dependent.

Thanks for this, @gentzen. I found it on the CI of QM page for SEP. What I now find remarkable is that contextuality is a very natural classical concept that we can easily introduce into classical physics. In particular, Koopman's Hilbert space formalism for Classical Mechanics¹ allows us very easily to use the Poisson bracket to generate changes of experimental contexts — more generally than as only canonical transformations, as in conventional Hamiltonian CM. This is a natural extension of Bohr's insistence that we must describe experiments classically, insofar as it allows us to describe the expected statistics of many incompatible experiments in a single probabilistic structure.

Having introduced contextuality so easily into CM, we have to wonder what quantum fluctuations are in this larger classical world. Clearly they cannot be the same as thermal fluctuations. A first clue is that ℏ has units of action, whereas kT has units of energy, but this does not give much direction. Much more substantively, QFT is clear that the vacuum is Poincaré invariant, whereas thermal fluctuations are not invariant under boost transformations: this difference of symmetry properties under the action of the Poincaré group is perhaps the most natural and easiest distinction we could think of to introduce into classical physics.² With contextuality and quantum fluctuations added into CM, we have what I call 'CM+' in my AnnPhys 2020. Just these two additions give us a measurement theory for CM+ that is as empirically effective as that of QFT.
We can also take this construction in the other direction, following the example of Tsang&Caves in PRX 2012, in terms of Qunatum Non-Demolition measurement, which allows us to construct isomorphisms between the physically significant Quantum Optics (aka Quantum ElectroMagnetism, QEM) and what I call QND Optics.
This has been out in the literature for five years so far, and enough people think it and its further development has raised the bar significantly that I have given 19 talks to academic and other audiences since then, but I have clearly not yet raised the bar high enough for @Fra's standard:

I wonder if anyone ever read a clear and brilliant writing about the conceptual foundations of QM?

I more expect that these or similar ideas will make it into the Zeitgeist not through my obscure writing. More significant than understanding the relationship between QM and CM+ as about isomorphisms as well as about quantization is to me that CM+ thought of from the engineering perspective of signal analysis suggests how we can rethink renormalization, but about that I will not test your patience.

¹ Koopman introduced the idea that a Hilbert space formalism for CM is possible already in 1931, then it was immediately used by von Neumann and Birkhoff to prove the ergodic theorem, but thereafter it was almost unmentioned until Sudarshan in Pramana 1976. Since then, it's been used extensively in the dynamical systems literature (see "Modern Koopman Theory for Dynamical Systems", for example). The algebra of bounded operators that act on a Hilbert space contains the canonical transformations as a subgroup.
² Stochastic ElectroDynamics, SED, adopted this distinction already in the 1960s, when it introduced Zero Point Fluctuations, ZPF, but SED has failed to be compelling for most physicists, for ~60 years, I think because it does not have a measurement theory that includes contextuality.

 

[mad mathematician]

I’d like to see an AI trained only on the accumulated experimental data and ask it to come up with a logical and consistent theory of nature from scratch.

Computer says:No, none exists.
at least not consistent.
Either that, or it never halts....

 

[A. Neumaier]

I wonder if anyone ever read a clear and brilliant writing about the conceptual foundations of QM?

What about my paper Quantum tomography explains quantum mechanics?

 

[Fra]

What about my paper Quantum tomography explains quantum mechanics?

I read some of your work years ago and there is alot to like about it and from what I recall you did a good job to explain what you set out to do, such as operationally defined current they. Needles too say I symphatize with most of your motivation for coming up with the explanation/intepretation which is the ambigous operational basis for the statistical concepts.

But I was not satisfied with what handles for future development it offers, I think we to be a bit more radical to solve some open questions. But I'll try to get around to reading it again before I comment more, as i think it was some years since i read it. I'll get back later...

/Fredrik

 

[Morbert]

What about my paper Quantum tomography explains quantum mechanics?

What is the relation between this paper and your previous work on the thermal interpretation?

[edit] - I see section 10.6 probably answers this question.

 

[gentzen]

I wonder if anyone ever read a clear and brilliant writing about the conceptual foundations of QM?
I don't think I have.

Asher Peres (1978) Unperformed experiments have no results.
Rudolf Peierls (1991) In defense of „measurement“.

 

[sbrothy]

So, physics has never been "intuitive" in the sense you demand.

It's different to be guided by these things, than to demand that the eventual theory meets certain intuitive criteria. Also, Bohr and Heisenberg must have been guided by their intuition when they broke from classical thinking; while Schrodinger and Einstein's intuition was that QM must be incomplete.

This is back to the point I've made several times. If, like me, you study mathematics and then physics, then you come to the party with a very different sense of what's intuitive.

It's not clear where you draw the line. Perhaps the plane geometry of Euclid is inituitive? What about Minkowski geometry? Is that acceptable as a physical theory? What about more general curved spacetimes? What about complex numbers? Are we allowed to use those? Or, do we defer to those from the middle ages who decried them as imaginary?

What mathematics is acceptable as a basis for physics? And, just as important, why are you the arbiter of this? Why am I wrong because I can conceive of things you can't? What if you met a layman who dismisses all physics and mathematics? Does it have to satisfy their intuition?

I also found intuition of very limited use when talking about physics and why math models reality so successfully. The human brain wants to see patterns where there is none. I mean complex numbers? Who intuitively saw that coming?

 

[bhobba]

I read some of your work years ago and there is alot to like about it

There certainly is.

Well worth one's time.

Thanks
Bill

 

[A. Neumaier]

complex numbers? Who intuitively saw that coming?

Carl Friedrich Gauß!

 

[sbrothy]

Carl Friedrich Gauß!

Ah yeh. I love that (probably apocryphal) story of little Carl in elementary school where his math teacher tries to occopy the pupils by making them add up all the numbers from 1-50 (was it?). He leans back with his paper and thinks he has a little pause. A minute later little Carl says he’s finished and the teacher verifies his result in disbelief.

I can just imagine him thinking “aw cr..! A prodigy! No peace for me this year!”

 

[Fra]

What about my paper Quantum tomography explains quantum mechanics?

What I think is excellent is that I think you succeded in formalising how QM is in fact used and how it relates to the macroscopic information in a conservative sense (ie not modifying it). To formalise HOW information from the whole environment is used to make inferences about the quantum systems structure and dynamical law. You make this more operative and concrete by using tomograhic inference instead of fictional ensembles. This is an improvement and clarification I think, and I really like this. I like to see it from the inference perspecive is central to my own thinking.

The tomography is a special type of inference. In principle this is in the direction that I like, so there is alot to like. But your your paper is "conservative" in that you tried to characterize the process without changing or explaining the all structure.

What I miss, and the same critique applies also to Barandes perspective, is that I want to undersand the emergence of the "objective" constraints, or the objective tomography. But this admittedly NOT conservative, it is very radical, and as I understand your papers, your ambition is to avoid specilation but to clarify how the objective inference; rooted from in "classical domain"; is implemented via tomography but in a way that is consistent with the structure of quantum mechanics and hilbert spaces? If this is the ambition, I think your work looks great.

To just explain the radical perspective I personally seek, and how it will "corresponde" to you picutre in some limiting case, I'd put it like this.

You do away with "observers" and seek an objective inference.
I embrace observers and seek the true subjective inference.

The correspodence lies in where a population of agents/observers doing the subjective inference reached some sort of steady state, that can be described by some equivalence or objective inference, where intersubject variation are seems as some sort of gauge choices. (ie. QM assumes that all the parts in the environment are "consistent" and this to me mean they are in a steady state, or where they reach and agreement about how their subjective perspectives are consistent)

So given what I think you want to accomplish, I have no objections. The issue is only one of wanting to accomplish something difference. And the two are not in contradiction as far as I see.

The old basic copenhagen concepts was imo in line with neumaier lines out, but not beeing explcit. The tomography clarifies how this is accomplished. But I think conceptaully, this is still consistent with the copenhagen view, in that the quantum system is described from a perspective. Neumaier suggested a more detailed process description than just postualting an ensemeble with born rule.

But somehow THAT is not the main problem nagging my personal mind - i want to ask a slightly different question.

/Fredrik

 

[A. Neumaier]

to avoid specilation but to clarify how the objective inference; rooted from in "classical domain"; is implemented via tomography but in a way that is consistent with the structure of quantum mechanics and hilbert spaces?

I don't think quantum mechanics needs to be changed - only its interpretation must be made more rational. This is what I think I achieved.

I embrace observers and seek the true subjective inference.

The problem here is that observers are themselves quantum objects whose observations must be ultimately understood in terms of the unitary quantum evolution.
Thus, like measurements, observers must be explained rather than postulated.

the old basic copenhagen concepts was imo in line with neumaier lines out, but not beeing explcit. The tomography clarifies how this is accomplished. But I think conceptaully, this is still consistent with the copenhagen view.

As it must be since, within its scope, the Copenhagen view is extremely successful.

 

[Fra]

I don't think quantum mechanics needs to be changed - only its interpretation must be made more rational. This is what I think I achieved.

I agree you did a great job on that mission!

The problem here is that observers are themselves quantum objects whose observations must be ultimately understood in terms of the unitary quantum evolution.
Thus, like measurements, observers must be explained rather than postulated.

I Agree with all this.

This is why by "observers" i dont mean observer as per qm, because they are fiction. I mean a generalized notion of "observers" of which the quantum observer is a limiting case only. This limiting structure is sufficient for atomic physics as described from macroworld if you combine it with rhe effectice theory view.

But that limiting case gives me personally no grip on the nature of interactions and emergence of spacetime. I only see possible handles in the process before the limit is taken. Once the limiting case is considered you loose tracks of all ends and we end up having to fine tune things.

/Fredrik