How do entanglement experiments benefit from QFT (over QM)?

[vanhees71]

Well, I think the first step to understand these things is to look at what's done in the lab. You have a very concrete setup consisting of a laser and certain types of birefringent crystals which through nonlinear optics enables you to create entangled photon pairs. That's the preparation procedure. This is also well understood by effective QED descriptions, i.e., using some constitutive parameters to describe the down-conversion process. It's all based on phenomenological experience and then brought into an efficient formalism to understand "how it works".

Then you have other equipment to measure polarization. In the most simple case you just use some polarization foil like "polaroid" in a certain orientation letting photons with some linear-polarization state through and the ones in the perpendicular polarization are absorbed. These filters you use on both sites where the photons are registered (or not registered). Then you can established in a series of measurements that the single-photon polarization is completely indetermined. Taking accurate measurement protocols to ensure that you can check the correlations of each of the entangled photon pairs you find a 100% correlation between polarization measurements in the same direction. The only thing that has to do with a human experimenter is that he decides what he wants to measure, and there's no subjective element in this, if that's what's behind your question.

The very idea that this is an interesting measurement is a prediction of the theory, but it's finally defined if you can set up such a concrete experiment to measure it. There's no more you can expect from natural science. What in addition do you expect? Why are such questions never asked about classical mechanics or electrodynamics? You never ask why Newton's postulates describe the Newtonian world accurately (and indeed that's true, i.e., within the now known limits of applicability Newtonian mechanics is a very good description of the corresponding phenomena observed in nature)? But why don't you ask? Is it, because the classical-physics description has no irreducible probability element in it? Isn't it a as pretty weird idea to think that everything is strictly deterministic, compared to our daily experience of pretty random events?

 

[Jimster41]

That all makes sense. And I've heard others make that argument, that we can't grasp irreducible probilistic-ness. We aren't wired to... I think that's possible. But I'm not sure I'm willing to give up on that intinct just yet. It does smack of fatalism - and I think there are too many things left un-detailed, if not un-explained.

to which, I thought you were going to say, "it will propagate until it hits something that it must interact with"... so I've been trying to hone my question.

We can enumerate things that would meet that qualification and imagine how they might arrive in some sense in the way of our experimental infinitely propagating two-photon. And that we will never know when that happens, can't ever know. Fine, but how did those things come into existence. Or were they already there. Well, they got made in the Big Bang or shortly thereafter... particles etc. Distributed by the inflationary period, condensed from... some...

what, Quantum?
Yes, it broke down, condensed, collapsed, interacted. Space started getting bigger. Whatever, hence the ever rambling Pachinko machine of the universe full of billiard balls drifting or zooming around... entropy-ing. It's all quite... linear.

But then what causes situations of negative entropy?

It's maleable, and has ... random non-linear fluctuations.

What allows for maleability of the general process, why didn't it just run down completely right off? What governs that maleability? Whence maleable? Why not maleable? Why any non-linearity?

Accidents of interaction, rarities and anomalies, tunneling, non-perturbative effects. Sometimes in a Pachinko machine the balls bounce up.

Oh, can I make a Pachinko machine where the balls bounce up more? What if I make one Pachinko machine that works just right and another one and compare them - but find they are different... like two relativistic observers with identical physics. What common laws govern the designs of those two different machines?

Space-time rules.

What governs those space-time rules. What are those?

I don't know, Einstein said c.

How does c get worked out by space-time?

 

[Lord Jestocost]

How does that explain the mechanism controlling the evolution between that preparation and the actual later (and or space-like separated) event when they get measured and “display” said correlation.

There is no mechanism, because the “photon”, for example, is merely an encodement of a set of potentialities or possible outcomes of measurements, viz. a mental conceptual link between particular macroscopic preparation devices and a series of macroscopic measurement events.

 

[Jimster41]

There is no mechanism, because “phonons”, for example, a merely an encodement of a set of potentialities or possible outcomes of measurements, viz. a mental conceptual link between particular macroscopic preparation devices and a series of macroscopic measurement events.

Aren't they also involved in the heat capacity of materials... as in giving different materials different heat capacity. Heat capacity is pretty important to me... on a daily basis.

Sorry, did you mean phonons or photons?

 

[Lord Jestocost]

Sorry, I mean of course "photon".

 

[Jimster41]

You think with photons. We all do. I'm going to go ahead and call myself (and you for that matter) and all this here. Real as it gets. Don't mean to sound snippy. Cognitive dissonance.

We need to lean on the concept of photons and all these conceptual links to reality with all our weight I think. I don't see any way around it. That's why I keep coming here making an idiot out of myself.

And to try to respond to the point being made - which seems to be kind of that there is nothing universally interesting about our enumeration of observables - they are things we invented so we are mesmerized by them. That just seems pretty solipsistic.

Maybe our two photon hits a two photon made by some experimenters we don't know. We are now connected by space-time's rules... I get it's useless to either of us as a random number but the connection is physical, isn't it? It has physical implications for what happens next.

 

[Lord Jestocost]

You think with photons.

As a working physicist, just for FAPP! From a philosophical point of view, I don't mistake the map for the territory, an instrumentalist's point of view.

 

[DrChinese]

Isn't it a as pretty weird idea to think that everything is strictly deterministic, compared to our daily experience of pretty random events?

I agree with this with no reservations. Human experience is demonstrably NOT deterministic, and yet there is obviously a strong desire to provide rules and order for everything else.

 

[A. Neumaier]

Human experience is demonstrably NOT deterministic, and yet there is obviously a strong desire to provide rules and order for everything else.

Casting dice is also demonstrably NOT deterministic, and yet Laplace provided rules and order for them that remained valid until the advent of quantum theory..

 

[atyy]

But it would represent the measurement process (which is what vanhees71 means) and, at least in the thermal interpretation, tell what happens.

But the thermal interpretation is not (yet?) a standard interpretation. I do agree that what you say would likely be true of an interpretation that solves the measurement problem (eg. maybe something like Bohmian Mechanics or the thermal interpretation, but that is also not a standard interpretation at this time).

 

[DrChinese]

Of course the formalism does not supply a causal mechanism for the correlations in the sense you seem to imply (but not explicitly mention to keep all this in a mystery ;-)), because there is no causal mechanism. The causal mechanism is the preparation procedure...

I "think" what you mean is that the causal mechanism (such as it is, what you can control) essentially ENDS when the 2 photon entangled state begins. Because there is no known root cause (in any theory I know of) that explains* what the entangled outcomes would be for the various possible observations. In other words: you might be able to create the entanglement initially, but what happens "next" cannot be considered causal or deterministic via the formalism. And I naturally agree with that view, if I am close to what you mean.

And you have then said that "leads to a two-photon state, where both the momenta and the polarization of these photons are necessarily entangled." And you agree that 2 photon state is not classical, so we are in good agreement to this point. The only gap remaining is acknowledging that whatever happens next is an example of a) apparent randomness; and b) quantum nonlocality, things which MUST be present/embedded in any theoretical framework - even if to say the mechanism is unknown currently. We don't know a) why you get spin up, for example (or any value of a measurement on an entangled basis). And we don't know how the system evolves from a 2-photon state (spin/polarization undefined) to 2 matching 1-photon pure states whose distance/separation precludes influences limited by the light cone defined by a measurement.

You don't see a) and b) as mysteries, OK. We can agree that mysteries are in the eye of the beholder. *Even in MWI there is no explanation of why we see a particular outcome; and in BM there is no possibility of observing the pilot wave that guides a particular measurement outcome.

 

[Jimster41]

but what happens "next" cannot be considered causal or deterministic via the formalism.

And just because it's not deterministic doesn't mean we can have no more knowledge about it. There are plenty of statistical systems we can characterize partially (like thermodynamic ones).

To me it all leads to chemistry and there are plenty of mysteries w/respect to how chemistry does what it does - like create observers who think up a name for it called "chemistry" then notice that it has to behave with relativistic symmetry and think up names for all the symmetries involved, but can't figure out how it does it.

 

[A. Neumaier]

But the thermal interpretation is not (yet?) a standard interpretation. I do agree that what you say would likely be true of an interpretation that solves the measurement problem (eg. maybe something like Bohmian Mechanics or the thermal interpretation, but that is also not a standard interpretation at this time).

Well, there is only one standard interpretation, printed in many different textbooks, and that is obviously far too idealistic, for example claiming measurements to be described by exact eigenvalues attained via Born's rule rather than by POVMs. (See the quote from Asher Peres in another thread.) Thus one cannot base arguments solely on the standard interpretation.

The thermal interpretation, though nonstandard, indeed solves the measurement problem, without introducing variables not already ubiquitous in QM and QFT. See Section 3 of Part IV of my sequence of papers.

 

[DarMM]

The only thing that has to do with a human experimenter is that he decides what he wants to measure, and there's no subjective element in this

But why don't you ask? Is it, because the classical-physics description has no irreducible probability element in it?

These are closely linked.

It's because the quantum formalism says the statistics of the variables you choose to measure are not marginals of the set of variables in general. Thus if in an experiment on entangled particles we can measure $A, B, C, D$ ($A,B$ being Spin measurements on the first particle and $C, D$ being spin measurements on the second) then if we measure $A, C$ we find $p(A,C)$ is not a marginal of $p(A, B, C, D)$.

That's the difference between QM and even a stochastic classical theory. It means the sample space is determined by your choice of what to measure.

 

[RUTA]

Of course the formalism doesn not supply a causal mechanism for the correlations in the sense you seem to imply (but not explicitly mention to keep all this in a mystery ;-)), because there is no causal mechanism. The causal mechanism is the preparation procedure. E.g., two photons in the polarization-singlet state are created in a parametric downconversion event, where through local (sic) interaction of a laser field (coherent state) with a birefringent crystal a photon gets annihilated and two new photons created, necessarily in accordance with conservation laws (within the limits of the uncertainty relations involved of course) leads to a two-photon state, where both the momenta and the polarization of these photons are necessarily entangled. There's nothing mysterious about this. The formalism thus indeed describes and in that sense also explains the correlations. By "explaining" in the sense of the natural sciences you always mean you can understand it (or maybe not) from the fundamental laws discovered so far. The fundamental laws themselves (in contemporary modern physics mostly expressed in terms of symmetry principles) are the result of careful empirical research and accurate measurements, development of adequate mathematical models/theories, their test and, if necessary, refinement.

We know how to create and test a Bell basis state, that is not in dispute. It looks like you conflate the causal mechanism for creating a Bell basis state with the causal mechanism needed to account for the conservation principle it represents. As it turns out, the mechanism that creates the Bell basis state provides no mechanism to account for its conservation outcomes, which caused Einstein to believe quantum mechanics is incomplete (Smolin going so far as to claim it's "wrong").

For example, suppose we're talking about the (fallacious) "classical counterpart" to the spin singlet state, i.e., we have conservation of angular momentum in the classical sense. Alice and Bob would measure variable deflections through their SG magnets corresponding to some hidden underlying value of L for each particle, the sum of those hidden, underlying L's being zero per the creation of the state via conservation of L. In that case, the mechanism creating the state also provides a mechanism to explain the subsequent measurement outcomes in each trial of the experiment. Of course, with the real spin singlet state the conservation principle only holds on average when Alice and Bob make different measurements, since they both always measure +1 or -1 at all angles (no partial deflections as in the classical case, which uniquely distinguishes the quantum and classical joint distributions). [See our paper here or video summary here or here.] There is not anything in the mechanism creating the spin singlet state that also provides a mechanism to account for this manner of conservation.

I realize you don't need a causal mechanism to account for the average-only conservation to feel as though you "understand" quantum theory. But, the plain and simple fact is that others do. Thus, they don't understand why you're happy and you don't understand why they're not happy. The psychological needs of these two camps are different, that's all.

I'm writing all this because psychologically speaking, I've a foot in each camp. That is, I can live with acausality at the fundamental level, but I want a principled ontology for it. That's introduced in these two episodes of the video series (Episode 1 and Episode 2).

It is impossible to explain any physics without invoking "the formalism". This is as if you forbid to use language in communicating. It's impossible to communicate without the use of the adequate language, and the major breakthrough in men's attitude towards science in the modern sense is to realize, as Galileo famously put it, that the language of nature is mathematics (particularly geometry), and this is the more valid with modern physics than ever.

We have the formalism and have seen that it maps to the experiments, which is the first step in understanding the phenomenon. That doesn't explain the phenomenon for everyone, as I just stated, but it is a necessary first step.

 

[bhobba]

Quantum theory breaks Kolmogorov's axioms. A quantum state and a context induce a Kolmogorov model via a Gelfand homomorphism.

Yes - you can look on QM as a generalized probability model, or, as is usually done, ordinary probability plus other rules eg at the semi popular level:
https://www.scottaaronson.com/democritus/lec9.html

I suspect it's trying to tell us something - what I have no idea. I do know that QM as we know it requires continuity in pure states, which you can't do in ordinary probability theory. This allows many powerfull theorems right at the foundations of QM eg Wigner's theorem. But why is nature so mathematically accommodating? I have a sneaky suspicion nature is running us in circles on this one because it turns out to be equivalent to requiring entanglement.
https://arxiv.org/abs/0911.0695
Thanks
Bill

 

[bhobba]

But the thermal interpretation is not (yet?) a standard interpretation. I do agree that what you say would likely be true of an interpretation that solves the measurement problem (eg. maybe something like Bohmian Mechanics or the thermal interpretation, but that is also not a standard interpretation at this time).

Personally I would use not well known rather than standard. I do not think there is any standard interpretation other than the math itself. And yes I do realize you need some kind of interpretation of probability to apply it but that's true of many areas that use probability. You can prove all sorts of interesting things from the Kolmogorov axioms alone such as Brownian Motion is continuous but not differentiable anywhere (thats as far as I got with rigorous probability theory) but applying it is another matter as Ross's Probability Models makes only too clear (groan some of his problems are HARD - I took it at uni only because I liked the lecturer - never did like the subject).

Thanks
Bill

 

[A. Neumaier]

I do know that QM as we know it requires continuity in pure states, which you can't do in ordinary probability

Brownian motion is continuos on the level of pure states.

Don't take the finite dimensional caricature of QM presented by quantum information theory as the full truth!

 

[vanhees71]

Personally I would use not well known rather than standard. I do not think there is any standard interpretation other than the math itself. And yes I do realize you need some kind of interpretation of probability to apply it but that's true of many areas that use probability. You can prove all sorts of interesting things from the Kolmogorov axioms alone such as Brownian Motion is continuous but not differentiable anywhere (thats as far as I got with rigorous probability theory) but applying it is another matter as Ross's Probability Models makes only too clear (groan some of his problems are HARD - I took it at uni only because I liked the lecturer - never did like the subject).

Thanks
Bill

The standard interpretation is still one of the Copenhagen flavors, usually without the collapse postulate. It's pretty close to the minimal interpretation and usually dubbed "the orthodox interpretation". With "standard interpretation" I mean the interpretation used by the majority of theoretical and experimental physicists (even in the quantum optics/AMO community, which are closest to the foundations).

 

[vanhees71]

I "think" what you mean is that the causal mechanism (such as it is, what you can control) essentially ENDS when the 2 photon entangled state begins. Because there is no known root cause (in any theory I know of) that explains* what the entangled outcomes would be for the various possible observations. In other words: you might be able to create the entanglement initially, but what happens "next" cannot be considered causal or deterministic via the formalism. And I naturally agree with that view, if I am close to what you mean.

And you have then said that "leads to a two-photon state, where both the momenta and the polarization of these photons are necessarily entangled." And you agree that 2 photon state is not classical, so we are in good agreement to this point. The only gap remaining is acknowledging that whatever happens next is an example of a) apparent randomness; and b) quantum nonlocality, things which MUST be present/embedded in any theoretical framework - even if to say the mechanism is unknown currently. We don't know a) why you get spin up, for example (or any value of a measurement on an entangled basis). And we don't know how the system evolves from a 2-photon state (spin/polarization undefined) to 2 matching 1-photon pure states whose distance/separation precludes influences limited by the light cone defined by a measurement.

You don't see a) and b) as mysteries, OK. We can agree that mysteries are in the eye of the beholder. *Even in MWI there is no explanation of why we see a particular outcome; and in BM there is no possibility of observing the pilot wave that guides a particular measurement outcome.

The entangled state is as causal as any other. QT is a causal theory, as any dynamical theory of physics. The entangled state evolves according to the standard dynamical laws of QT as any other state.

You are always insisting on classical interpretations, not I! That's the main source of our mutual misunderstandings and quarrels. I just take QT seriously and I deny any necessity of classical interpretations. Particularly Bell's class of local deterministic (usually dubbed "realistic", which is a misleading term however) are ruled out with humongous significance while QT is confirmed!

The theory also clearly says what's random and what is not random. An observable takes a determined value according to the state preparation if and only if the outcome of the measurement leads to one value with 100% probability. Otherwise it's indetermined, and the outcome of any individual measurement is irreducibly random. When repeated on an ensemble of equally prepared systems the outcomes of these measurements are distributed according to the probabilities the state describes, and the state describes these probabilities and nothing else. According to QT, and confirmed by all Bell tests with high significance, there's nothing "behind the curtain" which could "determine" values of such observables.

Ad a) The randomness is not apparent but an objective fact of the behavior of nature.

Ad b) Interactions are local. What's called "nonlocal" refers to correlations between far distant parts of a quantum system described by entanglement.

There's nothing weird with this. It's just what we have figured out over the last 500 years about how nature behaves.

 

[vanhees71]

These are closely linked.

It's because the quantum formalism says the statistics of the variables you choose to measure are not marginals of the set of variables in general. Thus if in an experiment on entangled particles we can measure $A, B, C, D$ ($A,B$ being Spin measurements on the first particle and $C, D$ being spin measurements on the second) then if we measure $A, C$ we find $p(A,C)$ is not a marginal of $p(A, B, C, D)$.

That's the difference between QM and even a stochastic classical theory. It means the sample space is determined by your choice of what to measure.

Yes sure, but it's an established fact of 100 years testing QT. For me that's the only conclusion I can come to in view of all the Bell tests disproving local deterministic HV theories and confirm QT.

 

[vanhees71]

We know how to create and test a Bell basis state, that is not in dispute. It looks like you conflate the causal mechanism for creating a Bell basis state with the causal mechanism needed to account for the conservation principle it represents. As it turns out, the mechanism that creates the Bell basis state provides no mechanism to account for its conservation outcomes, which caused Einstein to believe quantum mechanics is incomplete (Smolin going so far as to claim it's "wrong").

For example, suppose we're talking about the (fallacious) "classical counterpart" to the spin singlet state, i.e., we have conservation of angular momentum in the classical sense. Alice and Bob would measure variable deflections through their SG magnets corresponding to some hidden underlying value of L for each particle, the sum of those hidden, underlying L's being zero per the creation of the state via conservation of L. In that case, the mechanism creating the state also provides a mechanism to explain the subsequent measurement outcomes in each trial of the experiment. Of course, with the real spin singlet state the conservation principle only holds on average when Alice and Bob make different measurements, since they both always measure +1 or -1 at all angles (no partial deflections as in the classical case, which uniquely distinguishes the quantum and classical joint distributions). [See our paper here or video summary here or here.] There is not anything in the mechanism creating the spin singlet state that also provides a mechanism to account for this manner of conservation.

I realize you don't need a causal mechanism to account for the average-only conservation to feel as though you "understand" quantum theory. But, the plain and simple fact is that others do. Thus, they don't understand why you're happy and you don't understand why they're not happy. The psychological needs of these two camps are different, that's all.

I'm writing all this because psychologically speaking, I've a foot in each camp. That is, I can live with acausality at the fundamental level, but I want a principled ontology for it. That's introduced in these two episodes of the video series (Episode 1 and Episode 2).
We have the formalism and have seen that it maps to the experiments, which is the first step in understanding the phenomenon. That doesn't explain the phenomenon for everyone, as I just stated, but it is a necessary first step.

There is no classical counterpart of spin. Spin is generically quantum, but that's semantics.

Indeed, I think the great merit of the scientific method is that it doesn't care about our psychological needs but establishs clear facts about what's real. Obviously the worldview of classical physics is not describing reality accurately. QT describes it at least more accurately. It may be psychologically problematic for you to face this reality, but I indeed wonder why.

 

[bhobba]

Brownian motion is continuos on the level of pure states. Don't take the finite dimensional caricature of QM presented by quantum information theory as the full truth!

Good point. I even mentioned it in one of my posts. But while continuous is nowhere differentiable. Still the paper I posted making the claim 'If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one.' is not correct - it should include differentiability.

Thanks
Bill

 

[A. Neumaier]

Good point. I even mentioned it in one of my posts. But while continuous is nowhere differentiable. Still the paper I posted making the claim 'If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one.' is not correct - it should include differentiability.

This is too much required - wave functions need not be differentiable, only square integrable.

 

[bhobba]

This is too much required - wave functions need not be differentiable, only square integrable.

Yes (we won't go into Rigged Hilbert Spaces because it only makes it worse for my position) - but not nowhere differentiable because we have Schrodinger's Equation. I need to review the number of places I have seen it. But this it getting off-topic. I will need to look at the papers that state it first.

Thanks
Bill

 

[A. Neumaier]

but not nowhere differentiable because we have Schrodinger's Equation.

Schrödinger's equation for $N$ particles and expectations $\psi^*H\psi$ make sense in the Soboloev space of once weakly differentiable functions on $R^{3N}$. It contains the piecewise linear finite elements that could be used (in principle) to solve it numerically. I don't know whether this space contains nowhere differentiable functions but wouldn't be surprised.

 

[A. Neumaier]

Yes [...] but not nowhere differentiable because we have Schrodinger's Equation.

Schrödinger's equation for $N$ particles and expectations $\psi^*H\psi$ make sense in the Soboloev space of once weakly differentiable functions on $R^{3N}$. It contains the piecewise linear finite elements that could be used (in principle) to solve it numerically. I don't know whether this space contains nowhere differentiable functions but wouldn't be surprised.

Indeed, since $3N>1$, the Soboloev space $H^1(R^{3N})$ contains nowhere differentiable functions. See the answer to my question Do Sobolev spaces contain nowhere differentiable functions? on MathOverflow.

 

[Auto-Didact]

Of course the formalism doesn not supply a causal mechanism for the correlations in the sense you seem to imply (but not explicitly mention to keep all this in a mystery ;-)), because there is no causal mechanism.

This is a philosophical statement, not a scientific one, and certainly not a statement concerned with finding the complete pure mathematical theory for which QT is 'applied mathematics', i.e. the currently unknown uniquely correct mathematical model capable of capturing all of QT without any glaring conceptual problems.

From the history of physics, we have learned that all physical theories have such a unique form of pure mathematics underlying them: for Newtonian mechanics it is calculus, for Maxwell theory it is vector calculus, for GR it is Riemannian geometry, for Hamiltonian mechanics it is symplectic geometry, etc.; for QT we have not yet found the correct form of pure mathematics, this is still work in progress.

Having a unique mathematical theory underlying a physical theory - which moreover typically can easily directly be mathematically generalized (i.e. not merely heuristically e.g. through perturbative methods, linearizations or small angle idealizations) in a plethora of ways and directions - means that the physical theory can be derived from first principles and unified with other mathematical and/or physical theories; this means that there are no conceptual problems in the foundation of that physical theory.

All fundamental physical theories known so far were capable of being derived from first principles eventually, all except for QT, which moreover cannot easily be generalized or unified with other physical theories without extreme heuristics e.g. perturbation theory in the case of QFT.

The causal mechanism is the preparation procedure. E.g., two photons in the polarization-singlet state are created in a parametric downconversion event, where through local (sic) interaction of a laser field (coherent state) with a birefringent crystal a photon gets annihilated and two new photons created, necessarily in accordance with conservation laws (within the limits of the uncertainty relations involved of course) leads to a two-photon state, where both the momenta and the polarization of these photons are necessarily entangled. There's nothing mysterious about this. The formalism thus indeed describes and in that sense also explains the correlations. By "explaining" in the sense of the natural sciences you always mean you can understand it (or maybe not) from the fundamental laws discovered so far. The fundamental laws themselves (in contemporary modern physics mostly expressed in terms of symmetry principles) are the result of careful empirical research and accurate measurements, development of adequate mathematical models/theories, their test and, if necessary, refinement.

It is impossible to explain any physics without invoking "the formalism". This is as if you forbid to use language in communicating. It's impossible to communicate without the use of the adequate language, and the major breakthrough in men's attitude towards science in the modern sense is to realize, as Galileo famously put it, that the language of nature is mathematics (particularly geometry), and this is the more valid with modern physics than ever.

The causal mechanism is not the preparation procedure; what you have offered is not an actual explanation but instead just a heuristic description of the phenomenology retrofitted into a post-hoc-ergo-propter-hoc statement; while such heuristics sound nice and help pragmatic experimentalists not to worry about the foundations, it is completely fallacious and therefore unacceptable for anyone really interested in rigourous explanation and understanding at an academic level.

Your heuristics import your philosophy into the practice of physics, because you are assuming that the axioms for QT that you have chosen are necessary, sufficient and capable of giving a complete conceptual description, while in actuality your chosen axioms are purely pragmatic heuristics; even worse when extended beyond their range of applicability they end up being patently fallacious and therefore fundamentally incapable of giving a complete description of the physics.

This is the danger of making a hurried premature axiomatization of a physical theory instead of finding the correct derivation from first principles i.e. constructing a new form of pure mathematics tailor-made for that physical theory which dovetails with the rest of pure mathematics: von Neumann et al. just bum-rushed a premature axiomatization of the physics into the foundation of QM and we are suffering to this day because of that.

The lesson to take away from this is that an axiomatization of a theory typically almost offers nothing of substance directly for the construction or discovery of new mathematics, especially if done sloppily/incorrectly because an axiomatization can easily so just end up being a meaningless game in formal mathematics; in other words axiomatization is an art form and not all axiomatizations are works of art, far from it.

Any physical theory which can not be based on a principle which is conceptually coherent by itself as a mathematical theory should always be looked at with the necessary cautionary suspicion; this is for me the same reason to be suspicious of string theory and also the same reason to be suspicious of the highly artificial mathematical constructions (i.e. non-pure) in mathematical economics and econometrics.

To demonstrate that your axiom-based heuristic view for QT without any coherent underlying principles - i.e. the minimal interpretation - is not a necessary way of looking at QT, others, in particular Popescu and Rohrlich have actually given a completely different way of changing the foundational structure of QT by changing the roles of axioms, postulates and principles: https://doi.org/10.1007/BF02058098

Indeed, I think the great merit of the scientific method is that it doesn't care about our psychological needs but establishs clear facts about what's real. Obviously the worldview of classical physics is not describing reality accurately. QT describes it at least more accurately. It may be psychologically problematic for you to face this reality, but I indeed wonder why.

Psychologically problematic aspects of any explanation - especially a scientific explanation which can be put into mathematical form - implies conceptual problems within that explanation.

Conceptual problems in science practically always means that the particular chosen form of mathematics used in the explanation is not sufficient to fully describe the phenomenon that that form of mathematics is aiming to describe i.e. a more sophisticated form of mathematics is needed to naturally model/capture/explain that phenomenon.

I would say that it is pretty obvious that the problems in the foundations of QT are precisely of this nature: in the absence of glaring experimental deviations, we always needed a new form of mathematics to help solve the remaining conceptual issues and there is no reason whatsoever to suspect that the case is different for QT; on the contrary because of the unexplained introduction of complex numbers into the foundation of physics there is all the reason to suspect that a new form of mathematics is needed to resolve the problems in the foundations of QT.

 

[A. Neumaier]

for QT we have not yet found the correct form of pure mathematics, this is still work in progress.

For quantum mechanics, it is functional analysis in Hilbert spaces. Only for quantum field theory, clear mathematical foundations are fragmentary. The interpretation is a completely disjoint issue.

 

[Auto-Didact]

For quantum mechanics, it is functional analysis in Hilbert spaces. Only for quantum field theory, clear mathematical foundations are fragmentary. The interpretation is a completely disjoint issue.

It is explicitly an assumption that the interpretation is a disjoint issue: all interpretative issues in physics always change when mathematical foundations change; the removal of Newtonian absolute space and time from the foundations of physics due to relativity theory is the prime example of this. Feynman spoke a lot about the resolution of such conceptual issues by changing foundations in The Character of Physical Law, among his many works and lectures.

Functional analysis in function spaces is only a necessary but not sufficient ingredient of the pure mathematical apparatus required to describe QT in full, exactly as you say.

 

[A. Neumaier]

It is explicitly an assumption that the interpretation is a disjoint issue:

Your arguments are also full of assumptions solely based on your faith, none of them verifiable.

all interpretative issues in physics always change when mathematical foundations change; the removal of Newtonian absolute space and time from the foundations of physics due to relativity theory is the prime example of this.

But there is not the slightest hint that there is a deeper nice theory ''deforming'' quantum mechanics to something of which the latter is a limiting case. If it existed, it would have been found by now.

 

[Auto-Didact]

Your arguments are also full of assumptions solely based on your faith, none of them verifiable.

Alas, making assumptions is necessary in order to progress. Making assumptions in and of itself isn't problematic if one is aware that they are making assumptions; I am fully aware that I am doing this, not just reflectively but strategically: making your assumptions explicit directly opens them up to falsification. This is a formal reasoning strategy I learned in medical practice called diagnostics.

But there is not the slightest hint that there is a deeper nice theory ''deforming'' quantum mechanics to something of which the latter is a limiting case. If it existed, it would have been found by now.

Not if the wrong conceptualization is missing; it of course only needs to be found once. Discovery of new pure mathematics in the absence of empirical guidance is not a trivial technical problem which can be resolved by throwing more money and man-power at it; if that was so all the Millenium Prizes in mathematics would have been solved ages ago.

It instead requires a careful solving of the conceptual issue in tandem with the construction of a novel mathematical concept; these events are exceedingly rare occurrences and they require creativity, imagination, vision and boldness beyond mere technical mastery taught in schools and upon which graduate students are selected for. Newton, Euler, Gauss and Grothendieck are prime examples of mathematicians who displayed all the required characteristics to achieve such things.

 

[vanhees71]

All fundamental physical theories known so far were capable of being derived from first principles eventually, all except for QT, which moreover cannot easily be generalized or unified with other physical theories without extreme heuristics e.g. perturbation theory in the case of QFT.

Since I don't care about psychology, which is far too complicated for me as a physicist, let me just pick this quote.

I don't know, what you mean by "first principles". For me what turned a posteriori after about 400 years of scientific research since Galilei and Newton to be something like "first principles" are symmetry principles, and a great deal of QT relies on these principles. I don't know, in which sense you mean that QT were not derivable from "first principles" in contradistinction to classical physics.

 

[Auto-Didact]

Since I don't care about psychology, which is far too complicated for me as a physicist, let me just pick this quote.

I don't know, what you mean by "first principles". For me what turned a posteriori after about 400 years of scientific research since Galilei and Newton to be something like "first principles" are symmetry principles, and a great deal of QT relies on these principles. I don't know, in which sense you mean that QT were not derivable from "first principles" in contradistinction to classical physics.

Derivation from first principles is a foundational research methodology used in theory construction which integrates the conceptual, the mathematical and the axiomatic based on an empirical fact. It can be done at multiple levels of completion; an example of a complete derivation from first principles would be inventing calculus, using it to define force and axiomatically defining space, time and mass all in tandem with each other in order to give a complete model of motion, an empirical phenomenon.

 

[PeterDonis]

Derivation from first principles is a foundational research methodology

This is getting way off the topic of this thread. Please confine discussion to the thread topic.