I Confused by nonlocal models and relativity

[A. Neumaier]

While contributions to quantum gravity by quantum foundations can't be ruled out a priori, I don't see it in recent literature. Is there some recent review that explores potential connections?

For example,

• Rovelli, C. (1996). Relational quantum mechanics. International Journal of Theoretical Physics, 35, 1637-1678.

The paper is not very recent, but has 269 citations in Google Scholar since 2022.

I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the measurement problem) could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion that generates the unease with quantum mechanics is the notion of observer-independent state of a system, or observer-independent values of physical quantities.

Two recent papers are

• Carroll, S. M. (2022). Addressing the quantum measurement problem. Physics Today, 75(7), 62-63.
• Cavalcanti, E. G., Chaves, R., Giacomini, F., & Liang, Y. C. (2023). Fresh perspectives on the foundations of quantum physics. Nature Reviews Physics, 1-3.

See also my comments from 2017 here (Point 12).

You have to bump up against the nomological character of a physical theory at some point. A theory that completely determines future outcome from an initial state + dynamics would not explain why those dynamics are correct, as opposed to some alternative scheme.

The unification of relativistic QFT and general relativity is already so constrained that any successful unification would count as the most correct one, since it explains the most experiments! The question of assessing alternatives arises only if there are several competing successful unifications.

 

[vanhees71]

Correctly but not completely. It is not shown why the unitary quantum dynamics gives rise to unique macroscopic outcomes. This is an open problem that you simply ''solve'' by making the metaphysical assumption of intrinsic quantum randomness. But this is hiding the problem under the carpet, not solving it.

But there's not the slightest hint that this assumption is not correct. You can speculate a lot, but without empirical guidance unlikely to find more comprehensive theories. It's even not clear, whether there should be such a more comprehensive theory. All the Bell tests speak against it.

 

[Fra]

Few researchers search in the region backed by experiment.

Which specific region would you suggest this is?

I ask because there extrapolation from experimentally accessible domain to the hypothetical domain is rarely unique, it is often dependent on interpretation or in what form you seek the answers.

/Fredrik

 

[A. Neumaier]

But there's not the slightest hint that this assumption is not correct.

Neither is there the slightest hint that your assumption is correct. Both are metaphysical assumptions until someone finds a positive solution.

 

[A. Neumaier]

Which specific region would you suggest this is?

https://www.physicsforums.com/threads/confused-by-nonlocal-models-and-relativity.973876/post-6968312

I answered this already. See also the last paragraph here.

 

[vanhees71]

Neither is there the slightest hint that your assumption is correct. Both are metaphysical assumptions until someone finds a positive solution.

Of course, both are metaphysical assumptions, but there's huge empirical evidence for the correctness of the assumption that Nature is inherently random and none to the opposite.

 

[A. Neumaier]

Of course, both are metaphysical assumptions, but there's huge empirical evidence for the correctness of the assumption that Nature is inherently random and none to the opposite.

No. There is huge empirical evidence for randomness, but not the slightest evidence for inherent randomness.

 

[vanhees71]

So, how do you interpret all the confirmations of QT against "local realistic HV theories"?

 

[Morbert]

You have to bump up against the nomological character of a physical theory at some point. A theory that completely determines future outcome from an initial state + dynamics would not explain why those dynamics are correct, as opposed to some alternative scheme.

The unification of relativistic QFT and general relativity is already so constrained that any successful unification would count as the most correct one, since it explains the most experiments! The question of assessing alternatives arises only if there are several competing successful unifications.

I should have clarified: My statement was about the position that outcomes following probabilistically from their antecedents needs explanation while outcomes following deterministically from their antecedents can be accepted without controversy.

 

[A. Neumaier]

So, how do you interpret all the confirmations of QT against "local realistic HV theories"?

They are confirmations of the minimal interpretation of quantum mechanics, but not of your metaphysical extension that claims irreducible randomness.
They confirm equallly well the thermal interpretation, in which no irreducible randomness exists.

 

[vanhees71]

So you claim that the confirmation of QT against local realism is compatible with the assumption of determinism? If so, then you'd need to provide a (then necessarily non-local) deterministic HV theory compatible with the violation of Bell's inequalities that is consistent with Einstein causality, as is relativistic microcausal QFT.

 

[A. Neumaier]

My statement was about the position that outcomes following probabilistically from their antecedents needs explanation while outcomes following deterministically from their antecedents can be accepted without controversy.

Well, if something is determined, why ask for a reason for its value? The determinstic law is the reason! But if something is not determined but can take several values, curiosity arises as long as we can point to no law for the precise value.

 

[A. Neumaier]

So you claim that the confirmation of QT against local realism is compatible with the assumption of determinism? If so, then you'd need to provide a (then necessarily non-local) deterministic HV theory compatible with the violation of Bell's inequalities that is consistent with Einstein causality, as is relativistic microcausal QFT.

The N-point functions of a relativistic QFT satisfy the deterministic but nonlocal Schwinger-Dyson equations and describe everything observable about QFT.

The Schwinger–Dyson equations (SDEs) or Dyson–Schwinger equations, named after Julian Schwinger and Freeman Dyson, are general relations between correlation functions in quantum field theories (QFTs). They are also referred to as the Euler–Lagrange equations of quantum field theories, since they are the equations of motion corresponding to the Green's function.

 

[vanhees71]

The Wightman functions of local observables do not imply determinism for the observables but only for the probabilities of their outcome when measured or rather you can calculate these probabilities using them.

Also, I don't know, what you mean by "non-local" here. If it comes to observables, these must be represented by local field operators, obeying the microcausality condition.

 

[A. Neumaier]

The Wightman functions of local observables do not imply determinism for the observables

The observable macrovariables are all given by locally smeared 1-point functions, without thinking about probabilities. They are fully determined by the Wightman functions.

but only for the probabilities of their outcome when measured or rather you can calculate these probabilities using them.

Deterministic equations and hidden variables are always for beables!

I thought we had agreed that the beables in quantum theory are the probability distributions and not the individual outcomes.

Also, I don't know, what you mean by "non-local" here. If it comes to observables, these must be represented by local field operators, obeying the microcausality condition.

In the thermal interpretation, the observables are the N-point functions and what can be computed from them. Every quantum phycisists known how to observe these observables for sufficiently stationary objects, at least for N=1 and N=2.

A 2-point function is already nonlocal since the two arguments can be arbitrarily far apart. Such observables are not allowed in Bell's local hidden variable analysis.

 

[vanhees71]

The observable macrovariables are all given by locally smeared 1-point functions, without thinking about probabilities. They are fully determined by the Wightman functions.

These are the expectation values not the outcomes of measurements. We discussed this already some time ago: When you measure the spin-$z$ component of an electron prepared to have the spin-$x$ component determined to be, say, +1/2, you don't get the expectation value $\langle s_z=0 \rangle$ when measuring $s_z$ accurately but $s_z=\pm 1/2$ with probability 1/2 for each outcome.

Deterministic equations and hidden variables are always for beables!

Can you say, what you mean? We just have discussed that "beables" is an undefined word play by Bell!

I thought we had agreed that the beables in quantum theory are the probability distributions and not the individual outcomes.

I don't know, what "beables" are. I talk about measurement outcomes in a lab. The probability distribution can of course be measured by preparing "statistical samples" as proxies of the corresponding "ensembles". The probability distributions are of course determined but not the outcome of measurments on observables (except those, which are determined in the given state of course).

In the thermal interpretation, the observables are the N-point functions and what can be computed from them. Every quantum phycisists known how to observe these observables for sufficiently stationary objects, at least for N=1 and N=2.

The $N$-point functions do not predict with certainty the outcome of measurements but the probabilities/expectation values of the measured observables given the state you use to evaluate the corresponding expectation values.

A 2-point function is already nonlocal since the two arguments can be arbitrarily far apart. Such observables are not allowed in Bell's local hidden variable analysis.

Of course, measurement devices can be placed arbitrarily far away from each other. E.g., the two-point function of the electric field describes two-photon detection (see, e.g., Garrison&Chiao Sect. 6.6.2), used in the Bell tests (coincidence measurements on two entangled photons). That doesn't make the QFT non-local. Also in Bell's LHV analysis he considers of course the same, i.e., the measurement of parts of a system at far-distant places.

 

[A. Neumaier]

When you measure the spin-$z$ component of an electron

This is not a macrovariable. The corresponding macrovariable actually measured is the amount of silver on the plate, and this is a smeared 1-point function of the silver density field.

Can you say, what you mean? We just have discussed that "beables" is an undefined word play by Bell!

No. We discussed that it is a defined word in a paper about beables. All his foundational work is about the consequences of having beables. His hidden variables are the parameters characterizing his beables, and he proves that local beables must satisfy his inequalities.

I don't know, what "beables" are.

For the present discussion (which at the moment is about the thermal interpretation), the beables are the N-point functions, and since you know what the latter are, you know what I mean by beables in the thermal interpretation!

I talk about measurement outcomes in a lab.

Bell's beables are theoretical generalizations of macroscopic things - pointer positions, colors, image patterns - the things that one can read off with certainty from the equipment in the lab, before one translates them into properties of invisible objects like electrons. He said that in Maxwell's theory, the electromagnetic fields are beables (in contrast to the vector potential); their smeared values are measurable with certainty.

The $N$-point functions do not predict with certainty the outcome of measurements

The 1-point function of an electromagnetic current predicts with certainty the current read from a current meter. Thus it is a beable in bells sense.

Of course, measurement devices can be placed arbitrarily far away from each other. [...] That doesn't make the QFT non-local.

Not the QFT but 2-point function are nonlocal. Since the Schwinger-Dyson equations couples the N-point functions for all N, their deterministic dynamics is Bell nonlocal. Thus there is no contradiction with Bell's theorem, since the latter assumes Bell locality.

This Bell nonlocality has nothing at all to do with the fact that relativistic QFT is local in the sense used by field theorists. It only has to do with the form of the deterministic equations!

 

[Fra]

Well, if something is determined, why ask for a reason for its value? The determinstic law is the reason!

I disagree and this is think again a symptom of that we seek answers of different forms.

My view towards this is summarized well be this philosophical quote from Charles Sanders Pierce, that Lee Smolin quoted in one of his papers of evolution of law.

"...To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformities are precisely the sort of facts that need to be accounted for. Law is par excellence the thing that wants a reason. Now the only possible way of accounting for the laws of nature, and for uniformity in general, is to suppose them results of evolution..."
-- https://arxiv.org/abs/1201.2632

/Fredrik

 

[A. Neumaier]

this philosophical quote from Charles Sanders Pierce, that Lee Smolin quoted in one of his papers of evolution of law.

"...To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformities are precisely the sort of facts that need to be accounted for. Law is par excellence the thing that wants a reason. Now the only possible way of accounting for the laws of nature, and for uniformity in general, is to suppose them results of evolution..."
-- https://arxiv.org/abs/1201.2632

I reject this view. The fundamental physical laws are eternal, since they are supposed to hold in the whole universe at all times. Thus they cannot evolve. Only our understanding of them evolves.

 

[Fra]

I reject this view. The fundamental physical laws are eternal, since they are supposed to hold in the whole universe at all times. Thus they cannot evolve. Only our understanding of them evolves.

I figured you would. This is also why I see why it follows that you view some of my views as circular.

One of the reasons why I tend to consider physical interrelations in material nature beyond human knowledge, is that its the only conceptual way I found to explain for example entanglement correlation and therefore its for personally me a heavy argument. We know from Bells inequality that human ignroance can not explain this (unless one adds even MORE strange things that instant actions etc, that i dont see adds any explanatory value at all) there seems to be an ignorance built into the physical interactions themselves. And its these, that I still in principle that is evolving, and the fixed laws we de facto are aware of in the limited domain of validity are of natures self-organisation to mutual understanding. But all this is "interpretations" of course.

/Fredrik

 

[A. Neumaier]

I tend to consider physical interrelations in material nature beyond human knowledge,

But the physics community is human and knows a huge amount about the physical interrelations in material nature - much more than you do. So I don't think your view carries any weight.

 

[Fra]

But the physics community is human and knows a huge amount bout the physical interrelations in material nature

But apparently not enough to have found a unified theory of interactions.

Alot of intelligent people has spent alots of time on these problems for many decades and still many hard unsolved problems. Perhaps new different thinking is required.

/Fredrik

 

[PeterDonis]

But apparently not enough to have found a unified theory of interactions.

We do have one for all the interactions except gravity. It took only a couple of decades for that unified theory to be developed and tested.

Alot of intelligent people has spent alots of time on these problems for many decades and still many hard unsolved problems.

This has always been true and will always be true.

Perhaps new different thinking is required.

And if you think this, you should go do it. But PF is not the place for it, since PF is not for discussion of personal research. Get your new different thinking published in a peer reviewed paper and then we can talk. But unless and until you do that, there is no point in just continuing to wave your hands and assert that you're not satisfied with what we have now. Yes, we know that. But it offers no basis for useful discussion here.

 

[Fra]

We do have one for all the interactions except gravity. It took only a couple of decades for that unified theory to be developed and tested.

There is no distinguished unification of QCD and electroweak theory that would reduce the number of free parameters.

/Fredrik

 

[PeterDonis]

There is no distinguished unification of QCD and electroweak theory that would reduce the number of free parameters.

You're quibbling. We have a unified theory of all the interactions except gravity. It might not meet your idiosyncratic requirements, but why should I care?

In any case, as I said, if you think our current theories are incomplete, go do research to help complete them. Complaining about it in a PF thread is pointless and adds no value. So please stop doing it.

 

[bhobba]

The problem is which region? Is there any empirical evidence of a quantum-gravitational effect?

Would Hawking radiation count? My understanding is it can be explained by the Effective Field Theory (EFT) of gravity, which is valid to about the Plank scale.

I agree that QM is incomplete because we only have a quantum theory of gravity as an EFT. But then again, I thought the modern view was all our field theories are EFTs. So I think it may go beyond just gravity.

Thanks
Bill

 

[bhobba]

In any case, as I said, if you think our current theories are incomplete,

Ditto.

Thanks
Bill

 

[PeterDonis]

Would Hawking radiation count?

Not as empirical evidence since it has not been observed and there is no prospect of it being observed any time soon.

 

[PeterDonis]

I thought the modern view was all our field theories are EFTs.

Yes, that is correct. So our modern field theories offer no evidence for QM being complete.

 

[Fra]

In any case, as I said, if you think our current theories are incomplete, go do research to help complete them. Complaining about it in a PF thread is pointless and adds no value. So please stop doing it.

Surely never meant to "complain".

I thought discussing in a constructive but critical way the current state of the art theories and in partucular their foundations and was what we did here - but without adding personal speculation, which I try carefully to not do even if everyones way of reasoning is naturally slighly coloured by personal,bias.

If adding perspectives adds no value to anyone then fine with me. I personally enjoy understanding other perspectives even if I don't share them.

/Fredrik

 

[PeterDonis]

I thought discussing in a constructive but critical way the current state of the art theories and in partucular their foundations and was what we did here

Sure, we do that, but your post that I objected to was not that; it was vague handwaving: "perhaps new different thinking is required". As far as I can tell, nobody in this discussion is claiming that our current theories are complete and can never be improved on. So stating that they aren't complete adds nothing to the discussion.

And, as I have said, whatever "new different thinking" might be required is, or will be if it happens, original research, which is not what PF is for. If you have any specific new ideas, you should be doing the original research and getting it published in a peer-reviewed journal; then we can discuss it here. If you don't have any specific new ideas, what point is there in saying you would like some?

 

[Fra]

Sure, we do that, but your post that I objected to was not that; it was vague handwaving: "perhaps new different thinking is required". As far as I can tell, nobody in this discussion is claiming that our current theories are complete and can never be improved on. So stating that they aren't complete adds nothing to the discussion.

And, as I have said, whatever "new different thinking" might be required is, or will be if it happens, original research, which is not what PF is for. If you have any specific new ideas, you should be doing the original research and getting it published in a peer-reviewed journal; then we can discuss it here. If you don't have any specific new ideas, what point is there in saying you would like some?

By this I referred to what neighbourhoods in theoryspace we should or should not include in the search for improvements of our agreed incomplete theories. I felt we should not a priori exclude search areas. And the search areas I suggest are less common, but not totally original. Smolins reference is in that area. We seemed to disagree on which should be included! This is what I meant by "new" thinking. I find it interesting to argue and understand why, based on different types of answers we reject diffetent areas.

/Fredrik

 

[PeterDonis]

Smolins reference

Yes, you've already given it, and that's fine as far as it goes.

However: as you will see if you read the guidelines for this subforum, topics that are discussed in this subforum by their very nature are not resolvable by discussion. That means all such discussions come down to expressions of opinion. And once you've expressed your opinion, it is pointless to keep repeating the same opinion.

This is what I meant by "new" thinking.

Yes, but Smolin himself is still trying to turn this "new thinking" into something actually testable, and he hasn't yet, as far as I know, succeeded. So there's not much more we can say about his paper other than "keep trying". We're certainly not going to carry out the kind of research he is describing here at PF; as I've already said, that's not what PF is for.

 

[Fra]

Yes, but Smolin himself is still trying to turn this "new thinking" into something actually testable, and he hasn't yet, as far as I know, succeeded. So there's not much more we can say about his paper other than "keep trying".

Using neutron stars and primordial black holes to test theories of quantum gravity​

"Three observational tests of cosmological natural selection, a theory that follows from some hypotheses about quantum gravity, are described. If true, this theory explains the choices of the parameters of the standard model of particle physics. The first, the observation of a pulsar with mass greater than 2.5M∘, would cleanly refute the theory. The second and third, having to do with primordial black holes and early massive star formation, could do so given likely developments in the near future. However given present knowledge these arguments do not presently refute the theory. This shows that cosmological natural selection has not so far been refuted, in spite of being very vulnerable to falsification by possible observations."
-- https://arxiv.org/abs/astro-ph/9712189

Originally he said the estimated limited was 1.6 solar masses, but the exact limite was unclear, he latest increased it a bit. But a heavy pulsar found is: PSR J0952–0607 with 2.35 Solar masses that may or many not falsify smolins theory, I supposed it has to do with the confidence intervals of the limits in the theory as they estimates as they rely on models themselves. There a few papers on this, also with people objecting to the predictions. It is as interesting to read the proponents as the opponents critique.
But the purpose of CNS was not be be the detailed full theory he seeks, it was as I see it just a "example" of how a theory of such type can provide falsifiable predictions. The task of getting an actual theory of this form is clearly extremely hard at least, it's not what the CNS papers are about. So if CNS holds or not does not matter.

A more revent multiauthor paper, Smolin among them from 2021, if someonen wants to discuss any of it, it touches some QM foundational questions for sure, also including another interpretation .

The Autodidactic Universe​

"This paper is one of a growing number that attack the question of why these laws? Why these gauge groups, why these fermion and scalar representations, why the mysteries of chirality, CP violation, and baryogengesis? Why the vast hierarchies of scale and why the particular ratios of parameters of the standard model, setting the values of the masses and mixing angles? It is sobering to contemplate that not one problem of this type has ever been solved, going all the way back to the measurements of the electron’s mass and charge. Roughly speaking, we are faced with a single stark choice:
Either: There are no rational reasons for any of these choices. The universe might have been very different, but there will never be a reason why it took the path we observe it on.
Or: There is at least one rational explanation - in which case we are obligated to find it.
...
Achieving any of this would be a stunning advance. So it is with trepidation and caution that we mention two more paths these ideas might motivate, each wildly more ambitious than what we have just mentioned. Imagine if we could use the correspondences discussed here to construct learning machines out of the degrees of freedom of gauge and gravitational fields. Perhaps one version of this would be to construct a quark computer which computes using the spins and isospins of quarks and gluons as qubits. But beyond that, the correspondences suggest that the effective degree of freedom of the actual vacuum of a quantum gravity or gauge field might naturally evolve to become an autodidactic learning system. This might be part of the explanation for the choices of gauge fields and representations and values of the coupling constants of the standard model. Since the correspondence organizes a landscape of theories, it might lead to a search
in such a landscape, which might lead to discoveries of note, or might even serve as a model for what the universe might be doing. The results here are tiny, baby steps towards these hypotheses, to be further explored in future work."
-- https://arxiv.org/abs/2104.03902

/Fredrik

 

[vanhees71]

Using neutron stars and primordial black holes to test theories of quantum gravity​

"Three observational tests of cosmological natural selection, a theory that follows from some hypotheses about quantum gravity, are described. If true, this theory explains the choices of the parameters of the standard model of particle physics. The first, the observation of a pulsar with mass greater than 2.5M∘, would cleanly refute the theory. The second and third, having to do with primordial black holes and early massive star formation, could do so given likely developments in the near future. However given present knowledge these arguments do not presently refute the theory. This shows that cosmological natural selection has not so far been refuted, in spite of being very vulnerable to falsification by possible observations."

I can't say much about these speculations, but the problem concerning neutron-star theory is not so much quantum gravity but the quest for the equations of state of strongly interacting matter. We have 2 solar-mass neutron stars and equations of state, which allow for them. So there's no problem with them.

-- https://arxiv.org/abs/astro-ph/9712189https://arxiv.org/abs/astro-ph/9712189

 

[Fra]

I can't say much about these speculations, but the problem concerning neutron-star theory is not so much quantum gravity but the quest for the equations of state of strongly interacting matter. We have 2 solar-mass neutron stars and equations of state, which allow for them. So there's no problem with them.

I see Smolins CNS as a sample theory "from an interesting category", so the details aren't that important for me (I don't share the specific idea of CNS). But the idea is that the CNS hypothesis as per smolin, predicts that our universe are tuned for "maximal offspring" in number of black holes. And as the fate after a supernova depends on the maximal mass for a neutron star, which supposed relates to finetuning the strange quark mass, he came up with an upper bound. The idea is that there is some gap where it could "in principle" be varied.

"CNS implies a prediction that neutron stars are Kaon-condensate stars and that the upper mass limit for neutron stars is Muml 1.6Msolar[15]. This comes about because the strange quarkmass can be varied to raise and lowerMuml without strongly affecting the processes that lead to massive star formation and supernovas[8]."
-- https://arxiv.org/abs/hep-th/0612185

To the extent a full theory of quantum gravity would help understand things of hypothetical more dense states than neutron stars (quark stars or something else) or explain the mass gap between the smallest observed black holes and the most massive neutron starts is possibly a separate discussion.

Interesting, but not something that I think makes a different for me at aleast about the more general issue the sort of thinking Smolin raises. The issue raised applies not only to QG, but also to just finding a GUT. But I think the evolutionary approache, naturally relates both the high energy limit and the low energy limit; as opposed to have to "fine tune" the high energy limit to get the right low energy limit, which was the issue string theory has had for ages.

/Fredrik

 

[PeterDonis]

The first, the observation of a pulsar with mass greater than 2.5M∘, would cleanly refute the theory.

Maximum mass limits on neutron stars are not a prediction unique to Smolin's theory. They have been understood to be a prediction of GR plus relativistic degeneracy since the 1930s.

Generally speaking, predictions of this type are not predictions of specific theories but of general frameworks. So observations that refute such predictions, if they were made, would not just refute one particular theory but our whole general framework for understanding gravitationally bound objects. So I don't see this as carrying much weight in terms of falsifiability of Smolin's theory in particular. In this respect his theory is just betting that our current general framework is correct as far as it goes (i.e., it is most likely incomplete and we might at some point discover a more fundamental theory that has our current framework as an approximation in some appropriate limit), which is a pretty safe bet.

When it comes to trying to make more specific predictions that actually are unique to Smolin's theory, what we get is more like this:

Originally he said the estimated limited was 1.6 solar masses, but the exact limite was unclear, he latest increased it a bit. But a heavy pulsar found is: PSR J0952–0607 with 2.35 Solar masses that may or many not falsify smolins theory

The 1.6 solar mass limit was indeed significantly different from the limit predicted by the standard understanding. If we take Shapiro & Teukolsky's classic work from the 1980s as a good example of the standard understanding, it was talking about maximum mass limits for neutron stars in the 2.5 to 3 solar mass range (the uncertainty was mainly due to uncertainty about the exact equation of state for neutron star matter in the relevant density range).

But what actually happened when the 1.6 solar mass limit was refuted? Did Smolin abandon his theory as falsified and go try something else? No, he adjusted the parameters to predict a new limit of 2.5 solar masses, as shown in what I quoted from you at the top of this post. In other words, his theory was not actually making very tight predictions at all; it could be fudged to change the limit from 1.6 to 2.5 solar masses, i.e., from a prediction significantly different from the standard prediction, to one that is indistinguishable from the standard understanding.

In short, I don't share your optimism about this line of research.

 

[vanhees71]

Maximum mass limits on neutron stars are not a prediction unique to Smolin's theory. They have been understood to be a prediction of GR plus relativistic degeneracy since the 1930s.

The main problem is the uncertainty concerning the equation of state of strongly interacting matter. It's a subject of current research in the intersection between particle, nuclear, and astrophysics.

From the nuclear-physics side the investigations are with relativistic heavy-ion collisions as conducted at the LHC, RHIC, and GSI/FAIR. It's not so much about the highest collision energies as at the LHC, where one explores strongly interacting matter under conditions, which are more similar to the very early universe, where one has a (nearly) net-baryon-density free quark-gluon plasma (QGP), undergoing the cross-over transition to a hadron-resonance gas at a time of some ms after the Big Bang. Unfortunately there's no direct observable of this transition left in the cosmic microwave background. So here we indeed rely on the heavy-ion collision data at the highest beam energies available in our accelerators (particularly the LHC). There a blob of a few fermi extension of strongly interacting matter is created for a few fm/c, and one needs many data and a lot of different theorertical models (QCD at finite temperatures, effective hadronic models, relativistic transport theory and hydrodynamics) to analyze these data.

Concerning the phase diagram what's known is not too much. From the theoretical point of view the most is known for the above described LHC/early-universe conditions, i.e., at zero net-baryon density ($\mu_{\text{B}}=0$), where one can directly use lattice QCD at finite temperature to get that there's a cross-over between a (still strongly coupled) QGP and a hadron resonance gas at a pseudocritical temperature of about 160 MeV, and that's confirmed by experimental observations in the sense that the chemical-freezeout conditions that are determined by hadron (and even light anti-(hyper) nuclei!) abundances, which are well described by the statistical hadronization model with indeed a temperature close to 155 MeV and $\mu_{\text{B}}=0$.

For "neutron star matter" the pendant in heavy-ion collisions is rather at the lower beam-energies, where matter at higher net-baryon density is produced. This is explored particularly in the beam-energy-scan (BES) program at RHIC. Whether or not there is a first-order-phase-transition line with a second-order critical endpoint, as predicted by various effective chiral models, is not yet really conclusive, let alone at which temperatures and $\mu_{\text{B}}$ this might be.

For the neutron stars you have of course also a large isospin chemical potential, because it's "neutron-rich matter", and there are equations of states, that are consistent with all the constraints given by the above described experiments, which allow for the so far predicted large-mass neutron stars (with masses around $\gsim 2 M_{\text{Sun}})$.

The long-standing puzzle, how to accomodate strangeness with the large neutron-star masses seems also to be close to a solution. The trick is that effective chiral models that realize chiral symmetry in the parity-doublet scheme, where the bulk mass of the hadrons is due to the trace anomaly ("gluonic") and only a small part from the "nuclear $\sigma$ term", which means that at the chiral transition the hadrons do not get massless but only the mass difference between chiral partners vanishes. This also leads to stiffer equations of state, including hyperrons, allowing for the larger neutron-star masses.

Besides the well-known mass-radius relations following from GR + equations of state calculations, there is also the observation of neutron-star-neutron-star collisions and the gravitational-wave signals, which also need the nuclear equation of state (in this case also at finite temperature) as input for corresponding simulations. The highlight was GW170817, where not only the gravitational-wave signal was observed but also the elecromagnetic signals in a wide range of frequencies.

 

[Fra]

The long-standing puzzle, how to accomodate strangeness with the large neutron-star masses seems also to be close to a solution. The trick is that effective chiral models that realize chiral symmetry in the parity-doublet scheme, where the bulk mass of the hadrons is due to the trace anomaly ("gluonic") and only a small part from the "nuclear $\sigma$ term", which means that at the chiral transition the hadrons do not get massless but only the mass difference between chiral partners vanishes. This also leads to stiffer equations of state, including hyperrons, allowing for the larger neutron-star masses.

Curious about your opinion on these ideas?

Quantum gravity effects on compact star cores​

"Using the Tolman-Oppenheimer-Volkoff equation and the equation of state of zero temperature
ultra-relativistic Fermi gas based on generalized uncertainty principle (GUP), the quantum gravitational effects on the cores of compact stars are discussed. Our results show that 2m(r)/r varies with r. Quantum gravity plays an important role in the region r ∼ 10^3 r_0, where r_0 ∼ beta_0 lp, lp is the Planck length and beta_0 is a dimensionless parameter accounting for quantum gravity effects. Furthermore, near the center of compact stars, we find that the metric components are g_tt ∼ r^4 and g_rr = [1−r^2/(6(r_0)^2)]^(−1). All these effects are different from those obtained from classical gravity. These results can be applied to neutron stars or denser ones like quark stars. The observed masses of neutron stars (≤ 2M⊙) indicate that beta_0 can not exceed 10^37, not as good as the upper bound beta_0 < 10^34 from simple electroweak consideration. This means that incorporating either quantum gravity effects or nuclear interactions, one obtains almost the same mass limits of neutron stars."
-- https://arxiv.org/abs/1110.5550

/Fredrik

 

[PeterDonis]

Curious about your opinion on these ideas?

As the last sentence you quoted notes, these ideas have no significant effect on our estimates of the upper mass limit for neutron stars. This is to be expected since pretty much all possible equations of state for matter in this density regime have already been studied and our estimates of the upper mass limit already take all that information into account. Shapiro & Teukolsky's classic work from the 1980s contains a good review of that research.

 

[vanhees71]

The equation of state of strongly interacting matter, including in the regime valid for neutron stars/neutron-star merger physics is subject to vigorous current investigation. It's not yet fully understood.

 

[PeterDonis]

The equation of state of strongly interacting matter, including in the regime valid for neutron stars/neutron-star merger physics is subject to vigorous current investigation. It's not yet fully understood.

In the sense that we don't know its exact form, yes. But we know the range of possibilities well enough to know the range of possible maximum mass limits.