Smolin: Realistic and anti-realistic interpretations of QM

[PeterDonis]

In #56, vanhees said "there's a probability distribution of its location" not a probability distribution of measurement outcomes.

As his later posts make clear, by "probability distribution of its location" he meant "probability distribution of measurement outcomes when you measure its location". You need to take people's posts in context instead of fixating on a particular phrase.

I specifically asked about *where* in spacetime you claim the free electron is *between measurements* to avoid this dodge.

It's not a dodge, it's a refusal to accept your claim that your categories are logically exhaustive. Your categories are interpretation dependent.

 

[samalkhaiat]

According to QT the electron doesn't take a determined position, no more no less.

Exactly. And the uncertainty principle is the reason why probability enters QM, full stop. Why do need to participate in this kind discussions? Let me just tell you that if this Smolin guy gave that talk in London or Oxford/Cambridge, he would be, after 15 minutes, talking to an empty lecture theatre in Oxford/Cambridge or get booed in London.

 

[charters]

As his later posts make clear, by "probability distribution of its location" he meant "probability distribution of measurement outcomes when you measure its location". You need to take people's posts in context instead of fixating on a particular phrase.

It's not a dodge, it's a refusal to accept your claim that your categories are logically exhaustive. Your categories are interpretation dependent.

Then he should have simply continued to agree to this instrumentalist position we were focusing on in the #40s, instead of rejecting it in the #50s (this is the more complete context). The overall categories I gave are exhaustive, and I accept what you suggest here is a logically possible option - in these later posts I am merely assuming some winnowing has taken place. The problem we've had is as soon as I try to get a firm, particular commitment to move us along, they backtrack on the commitment in order to reject the implications of the commitment that would lead to the measurement problem.

I think this is just not an effective medium/format for the socratic approach I was trying, with the strictly linear comment thread.

 

[PeterDonis]

Then he should have simply continued to agree to this instrumentalist position we were focusing on in the #40s, instead of rejecting it in the #50s (this is the more complete context).

The term "instrumentalist" is also interpretation dependent (as are Smolin's terms "realist" and "anti-realist"). This kind of labeling game does not strike me as a good way to make progress.

The overall categories I gave are exhaustive

I don't think they are, and apparently @vanhees71 doesn't think they are either. The Aristotelian game of stating a set of categories, claiming they are logically exhaustive, and then trying to force every claim into one of them also does not strike me as a good way to make progress.

 

[charters]

I don't think they are, and apparently @vanhees71 doesn't think they are either. The Aristotelian game of stating a set of categories, claiming they are logically exhaustive, and then trying to force every claim into one of them also does not strike me as a good way to make progress.

It is widely agreed any interpretation of QM is a) psi-ontic, b) psi-epistemic, or c) instrumental, and that this is exhaustive. A pseudo-exception are d) dynamical modification a la GRW/Penrose, but this is no longer an interpretation of quantum theory per se, but instead a new (but no less problematic) theory in its own right. See for example Aaronson's classification at the end of this article for an endorsement of the classification scheme: https://www.nature.com/articles/nphys2325?draft=journal&platform=oscar

However, you or vanhees can easily change my mind by presenting a concrete counter-example - just summarily saying this quite standard classification scheme is incomplete is unfair. But so far, this thread has not shown a counter example. It has just been a sort of whack-a-mole game of shifting between the familiar views, though too quickly for me to hone in on the version of the measurement problem most salient to each (which is all I was hoping to do).

It is easy to deny the significance of the measurement problem when one picks and chooses only the good parts of different, incompatible philosophical stances at the necessary times. The hard thing is sticking to a firm commitment, being clear eyed about the weird or difficult implications of it, and then working on a solution.

 

[PeterDonis]

you or vanhees can easily change my mind by presenting a concrete counter-example - just summarily saying this quite standard classification scheme is incomplete is unfair.

You already gave a counterexample: dynamical modification. In other words, not believing that QM as it currently exists is a final theory. (The specific example you give is just one particular case of this.) The classification scheme you describe assumes that it is. Calling the contrary belief a "pseudo-exception" seems just as unfair to me as summarily saying that the classification scheme you describe is incomplete seems to you.

 

[charters]

You already gave a counterexample: dynamical modification. In other words, not believing that QM as it currently exists is a final theory. (The specific example you give is just one particular case of this.) The classification scheme you describe assumes that it is. Calling the contrary belief a "pseudo-exception" seems just as unfair to me as summarily saying that the classification scheme you describe is incomplete seems to you.

Dynamical modification exists in order to solve the measurement problem in textbook quantum theory. It is not an option for someone whose stance is to deny the significance of the measurement problem in textbook QT, which is where we began back in #20 and #22. And I've seen no indication in this thread that anyone here actually wants to advocate something like this, which requires replacing the Schrodinger equation with something non-unitary.

So, I think this is a misrepresentation of vanhees position, and these approaches are irrelevant here. But if it somehow is what he meant, then it is a concession that my only point (the measurement problem is real) has been correct all along.

 

[PeterDonis]

Dynamical modification exists in order to solve the measurement problem in textbook quantum theory.

Only in the trivial sense that, if you have a different theory, it obviously doesn't have to share whatever problem you think you see in textbook QM.

It is not an option for someone whose stance is to deny the significance of the measurement problem in textbook QT

Why not? Doesn't saying "QT is not a fundamental theory, so there's no point in even worrying about any measurement problem it might have" (which is basically what I read @vanhees71 as saying) count as denying the significance of the measurement problem in textbook QT?

 

[charters]

Why not? Doesn't saying "QT is not a fundamental theory, so there's no point in even worrying about any measurement problem it might have" (which is basically what I read @vanhees71 as saying) count as denying the significance of the measurement problem in textbook QT?

Sure, you can say you don't *care* about the issue because you think QT will be replaced (though in reality there is no good reason to believe this as a serious possibility given the nature of quantum gravity research, where no popular and closely studied approach tries to replace QT as the overarching framework).

But that's not what vanhees is saying. In #22: "There's no contradiction in the sense of logic nor in the empirical evidence for this probabilistic interpretation of the formalism." They clearly think QT *as is* has no logical/conceptual inconsistencies, in particular not the inconsistency as set up in the Wallace quote I began with.

The argument has been QT is fine, not that we shouldn't care whether or not it is fine.

 

[PeterDonis]

that's not what vanhees is saying. In #22: "There's no contradiction in the sense of logic nor in the empirical evidence for this probabilistic interpretation of the formalism." They clearly think QT *as is* has no logical/conceptual inconsistencies, in particular not the inconsistency as set up in the Wallace quote I began with.

The Wallace quote you began with talks about a problem with QT if it is a fundamental theory. It says so right there in the quote. So his argument obviously doesn't apply to any interpretation of QT that does not treat it as a fundamental theory. I read @vanhees71 as saying that if textbook QT is treated as an effective theory that makes correct predictions in its domain but nothing more, then there are no logical/conceptual inconsistencies.

 

[charters]

The Wallace quote you began with talks about a problem with QT if it is a fundamental theory. It says so right there in the quote. So his argument obviously doesn't apply to any interpretation of QT that does not treat it as a fundamental theory. I read @vanhees71 as saying that if textbook QT is treated as an effective theory that makes correct predictions in its domain but nothing more, then there are no logical/conceptual inconsistencies.

Well, I don't read the thread that way, and you're also misreading Wallace, who certainly does not think the measurement problem is only relevant to strictly fundamental theories. You can look into his many papers and find this out for yourself.

But at this point I'm tired of this. So all I will say is, if your presentation of vanhees's argument is correct, it's quite a bit of wishful thinking to assume or expect quantum theory writ large will be replaced by anything, let alone by something that happens to magically make the measurement problem moot.

 

[PeterDonis]

you're also misreading Wallace, who certainly does not think the measurement problem is only relevant to strictly fundamental theories

If I am, it's certainly not evident from what you quoted. When I have time I'll take a look at his papers to get a more complete view of what he is saying.

 

[PeterDonis]

it's quite a bit of wishful thinking to assume or expect quantum theory writ large will be replaced by anything, let alone by something that happens to magically make the measurement problem moot.

It seems to me to be wishful thinking to assume that a framework for thinking about quantum theory, the one that points up the measurement problem as being the fundamental issue, will suddenly turn out to solve the problem after making no progress on it for many decades.

To put it another way, I would describe the fundamental problem not as "the measurement problem" but as "the quantum foundations problem"--is QM a fundamental theory or not? If it is, then nobody knows how to make it a consistent fundamental theory. If it isn't, then nobody knows what could possibly replace it. Talking about "the measurement problem" basically means you've chosen the first path--QM is a fundamental theory, the problem is how to make it a consistent one. But that problem doesn't even show up on the radar if you choose the second path--QM is not a fundamental theory, the problem is what to replace it with.

 

[charters]

To put it another way, I would describe the fundamental problem not as "the measurement problem" but as "the quantum foundations problem"--is QM a fundamental theory or not? If it is, then nobody knows how to make it a consistent fundamental theory

This is a topic for another thread, but I think at least one philosophically consistent/acceptable version of QT exists for both fundamental, non-fundamental, and non-physics (i.e., quantum information) applications of QT, so the situation is less bleak than you suggest. However, this comes through reckoning with the measurement problem and biting some bullets, not wishing the problem away and hoping the future will offer some return to classicality. Even if I'm wrong, and the situation is totally bleak, it's still unfair to equate kicking the can with actively trying to do our best with the theory we have right now. Its more honest and responsible to keep trying to make sense of QT, given the highly likely case it doesn't get supplanted. So I don't see these two approaches you outline as equally meritorious.

 

[PeterDonis]

This is a topic for another thread, but I think at least one philosophically consistent/acceptable version of QT exists for both fundamental, non-fundamental, and non-physics (i.e., quantum information) applications of QT

Yes, this would be a topic for another thread.

 

[vanhees71]

This post demonstrates a clear misunderstanding of what it means to have an ontology: having an ontology means having an actual existence and being ontic simply means actually existing.

Example: Unicorns (one-horned horses) don't have an ontology (or aren't ontic) in the science of biology.

Similarly, any state that actually exists in any literal sense is by definition an ontic state.

If you don't accept this explanation, you are implicitly committing to option 2 from post #63.

Quantum theory provides clear ontics. The actual existence of, e.g., elementary particles is not in question by the probabilistic description of QT. An electron actually exists in the description of relativistic QFT and is described by a quantum field. It doesn't exist as visualized by classical physics as a "point particle" of course, but that's because there's progress in science going way beyond a naive picture based on our experience with macroscopic objects which behave, under the circumstances of everyday life, to an excellent approximation as descxribed by classical physics.

 

[vanhees71]

Then he should have simply continued to agree to this instrumentalist position we were focusing on in the #40s, instead of rejecting it in the #50s (this is the more complete context). The overall categories I gave are exhaustive, and I accept what you suggest here is a logically possible option - in these later posts I am merely assuming some winnowing has taken place. The problem we've had is as soon as I try to get a firm, particular commitment to move us along, they backtrack on the commitment in order to reject the implications of the commitment that would lead to the measurement problem.

I think this is just not an effective medium/format for the socratic approach I was trying, with the strictly linear comment thread.

Well, you must allow me to have my point of view. It doesn't need to fit into one of your isms. Philosophy is indeed utmost inappropriate to shed light on the modern findings of the natural (and also structural) sciences. I'll take @samalkhaiat 's advice, not to participate in such fruitless discussions anymore. It's useless.

 

[vanhees71]

Exactly. And the uncertainty principle is the reason why probability enters QM, full stop. Why do need to participate in this kind discussions? Let me just tell you that if this Smolin guy gave that talk in London or Oxford/Cambridge, he would be, after 15 minutes, talking to an empty lecture theatre in Oxford/Cambridge or get booed in London.

Well, I think you are right. I shouldn't waste my time anymore to discuss philosophical issues in this forum. It's kind of fighting against religious beliefs rather than having a constructive scientific discussion.

 

[Auto-Didact]

I'll take @samalkhaiat 's advice, not to participate in such fruitless discussions anymore. It's useless.

You might enjoy pretending that the practice of physics and science at large, is free from this kind of foundational disagreement that we have as with foundations of QT; nothing could be further from the truth.

The best known case in the history of physics, where problems and paradoxes in the theory led to as much confusion as they do in QM foundations today, was in the 18th and 19th century in fluid mechanics, d’Alembert’s paradox; in fact, this problem can be restated as a problem of the interpretation of the ontological versus epistemological status of a central object in the theory, namely boundary layers - exactly like the problem with $\psi$ in QM foundations.

It is therefore nothing short of a tragedy that this tale isn't universally known among physicists; here a brief retelling is quoted from (Bush, 2015):

And lest the longevity of the quantum paradoxes be mistaken for their insurmountability, fluid mechanics has a cautionary tale to tell. In 1749, d’Alembert’s paradox indicated that an object moving through an inviscid fluid experiences no drag, a prediction that was clearly at odds with experiments on high–Reynolds number gas flows. The result was a longstanding rift between experimentalists and theorists: For much of the nineteenth century, the former worked on phenomena that could not be explained, and the latter on those that could not be observed (Lighthill 1956). D’Alembert’s paradox stood for over 150 years, until Prandtl’s developments (Anderson 2005) allowed for the resolution of the dynamics on the hitherto hidden scale of the viscous boundary layer.

 

[Auto-Didact]

Quantum theory provides clear ontics.

You are outright disagreeing with all the experts in the world on this matter, but keep telling yourself that if it makes you sleep better at night.

The actual existence of, e.g., elementary particles is not in question by the probabilistic description of QT. An electron actually exists in the description of relativistic QFT and is described by a quantum field. It doesn't exist as visualized by classical physics as a "point particle" of course, but that's because there's progress in science going way beyond a naive picture based on our experience with macroscopic objects which behave, under the circumstances of everyday life, to an excellent approximation as descxribed by classical physics.

This isn't under question at all. I don't see the need to keep bringing it up. Maybe it would be instructive to state that 'practical physics' purely focussed on applications (i.e. physics as an extension of engineering) is pretty much the opposite of 'foundational physics', wherein everything that has been swept under the rug is exposed so that it can be fixed. See the above post #89.

Why do need to participate in this kind discussions? Let me just tell you that if this Smolin guy gave that talk in London or Oxford/Cambridge, he would be, after 15 minutes, talking to an empty lecture theatre in Oxford/Cambridge or get booed in London.

Again, just because you don't find fundamental physics important, doesn't mean it isn't important.

Smolin actually devotes an entire chapter to discussing what the experts over at Oxford (Deutsch, Greaves, Myrvold, Sauders, Wallace et al.) think about the matter; he refers to their collective stance as critical realism, or more specifically the Oxford interpretation. Oxfordians - like Copenhagenists before them - have the same core belief but disagree to differing degrees on different specific points.

Simply stated, Oxfordians believe that decoherence, a irreversible statistical concept, is completely sufficient to solve the measurement problem. Smolin - like Bell, Shimony, Penrose and @A. Neumaier before him - keenly demonstrates that this argument is actually insufficient because it introduces observers into the foundations of the theory.

The problem with decoherence as a solution to the measurement problem is that if unitary evolution is fundamental to QT, then complete decoherence is impossible because decohered states will recohere if we wait long enough due to the Poincaré recurrence theorem; this is literally the same reason why entropy can increase.

Now if we are only interested in times shorter than it takes to recohere - that is if we are only interested in an approximate description of measurements for all practical purposes (FAPP) - then decoherence works, but as a matter of principle - i.e. as a question of foundational and mathematical physics - decoherence outright fails as a complete explanation.

 

[stevendaryl]

To put it another way, I would describe the fundamental problem not as "the measurement problem" but as "the quantum foundations problem"--is QM a fundamental theory or not? If it is, then nobody knows how to make it a consistent fundamental theory. If it isn't, then nobody knows what could possibly replace it.

That's a very good way to summarize the situation.

 

[stevendaryl]

The problem with decoherence as a solution to the measurement problem is that if unitary evolution is fundamental to QT, then complete decoherence is impossible because decohered states will recohere if we wait long enough due to the Poincaré recurrence theorem; this is literally the same reason why entropy can increase.

Now if we are only interested in times shorter than it takes to recohere - that is if we are only interested in an approximate description of measurements for all practical purposes (FAPP) - then decoherence works, but as a matter of principle - i.e. as a question of foundational and mathematical physics - decoherence outright fails as a complete explanation.

To me, there is possibly another problem with decoherence, and that is that, as I understand it, decoherence involves splitting the universe into three parts:

1. The system of interest, which might be a single electron
2. The measuring device
3. Everything else (the "environment")

After making such a split, you can trace out the environmental degrees of freedom, and what you find for the reduced density matrix is that it rapidly evolves into a mixed state. That mixed state can be interpreted as the situation: The measuring device nondeterministically goes into a definite "pointer" state, with probabilities given by the Born rule. So decoherence seems to give the same result as a "measurement collapses the wave function" interpretation without introducing a separate collapse event.

However, it seems subjective to me to split the world into the three parts that way. And it seems inconsistent to interpret a state that you know is an improper mixed state (due to tracing out environmental degrees of freedom) as if it were a proper mixed state (due to ignorance of the actual state).

 

[Auto-Didact]

To me, there is possibly another problem with decoherence, and that is that, as I understand it, decoherence involves splitting the universe into three parts:

1. The system of interest, which might be a single electron
2. The measuring device
3. Everything else (the "environment")

After making such a split, you can trace out the environmental degrees of freedom, and what you find for the reduced density matrix is that it rapidly evolves into a mixed state. That mixed state can be interpreted as the situation: The measuring device nondeterministically goes into a definite "pointer" state, with probabilities given by the Born rule. So decoherence seems to give the same result as a "measurement collapses the wave function" interpretation without introducing a separate collapse event.

However, it seems subjective to me to split the world into the three parts that way. And it seems inconsistent to interpret a state that you know is an improper mixed state (due to tracing out environmental degrees of freedom) as if it were a proper mixed state (due to ignorance of the actual state).

Agreed. Incidentally, that is more or less the same argument Penrose made 20 years ago against decoherence in The Road To Reality.

 

[akvadrako]

The problem with decoherence as a solution to the measurement problem is that if unitary evolution is fundamental to QT, then complete decoherence is impossible because decohered states will recohere if we wait long enough due to the Poincaré recurrence theorem; this is literally the same reason why entropy can increase.

Now if we are only interested in times shorter than it takes to recohere - that is if we are only interested in an approximate description of measurements for all practical purposes (FAPP) - then decoherence works, but as a matter of principle - i.e. as a question of foundational and mathematical physics - decoherence outright fails as a complete explanation.

Why, what's wrong with recoherence as part of the complete story? Presumably for a system like our universe the recoherance time could be far enough in the future that all structure would have long ago been lost due to heat death.

 

[Auto-Didact]

Why, what's wrong with recoherence as part of the complete story?

If decoherence solves the measurement problem per the Born rule, then it should be effectively completely irreversible; the fact is that decoherence is always incomplete and therefore, per Poincaré recurrence, reversible. Ergo, it cannot solve the measurement problem.

In orthodox QM, the act of measurement is de facto irreversible. Upon measurement, unitary evolution restarts again with effectively 'new initial conditions'; this process is not reversible even if unitary evolution itself up to this point is reversible. In other words, decoherence is patently insufficient to solve the measurement problem.

 

[A. Neumaier]

Well, you must allow me to have my point of view. It doesn't need to fit into one of your isms. Philosophy is indeed utmost inappropriate to shed light on the modern findings of the natural (and also structural) sciences. I'll take @samalkhaiat 's advice, not to participate in such fruitless discussions anymore. It's useless.

Its fruitless because you insist on your own rules. You preserve a sort of effective consistency by the same sort of vagueness of language that you criticize in Bohr's writing. You adhere to a conceptual uncertainty principle, with no attempt to match your concepts to those used by the community that discusses foundational questions in a more precise way. This makes foundational discussions with you frustrating for all participants.

 

[vanhees71]

It's also very frustrating for me, because I never get comprehensible explanations from the philosophical side. And it's not "my rules", but the way modern Q(F)T is successfully applied for nearly 100 years now, including the most modern applications in quantum optics and quantum information physics, which are both closest to these fundamental topics as it can be as far as the physics is concerned.

I think it's just impossible to discuss the issue strictly staying in the realm of physics without distorting the subject by philosophical arguments which are completely irrelevant for the scientific side of the matter, which could be interesting, but I give up these discussions from now on.

 

[A. Neumaier]

it's not "my rules"

Everyone but you (even Ballentine) allows for collapse, and everyone but you (even Peres) acknowledges that there is a problem applying the statistical interpretation of QM to large systems such as the solar system, whose preparation cannot be replicated multiple times.

I give up these discussions from now on.

Yes, it is fruitless.

 

[akvadrako]

If decoherence solves the measurement problem per the Born rule, then it should be effectively completely irreversible; the fact is that decoherence is always incomplete and therefore, per Poincaré recurrence, reversible. Ergo, it cannot solve the measurement problem.

Why do you define the "measurement problem" this way? I think most people consider it to be something different; it just needs to describe our universe. What unitary QM predicts, at least considering the other assumptions of Poincaré recurrence (maybe finite dimensionality) is that eventually recoherance will happen. You seem to be a priori ruling that out.

 

[A. Neumaier]

What unitary QM predicts, at least considering the other assumptions of Poincaré recurrence (maybe finite dimensionality) is that eventually recoherance will happen.

Can you point to a theorem proving a recurrence theorem in the quantum case?

Poincaré recurrence is for finite-dimensional bounded dynamical systems only. Already a single hydrogen atom violates both assumptions, let alone the universe.

 

[akvadrako]

Can you point to a theorem proving a recurrence theorem in the quantum case?

Poincaré recurrence is for finite-dimensional bounded dynamical systems only. Already a single hydrogen atom violates both assumptions, let alone the universe.

I was just assuming it holds for the sake of @Auto-Didact's argument, and trying to argue that it's irrelevant as a way to rule out unitary QM holding exactly.

 

[A. Neumaier]

I was just assuming it holds for the sake of @Auto-Didact's argument, and trying to argue that it's irrelevant as a way to rule out unitary QM holding exactly.

The real problem with decoherence alone is that the standard axioms of QM provide no relationship at all between the state vector of the universe and the state vector of a subsystem. But experimental predictions are always made with fairly small subsystems of the universe

 

[Auto-Didact]

Why do you define the "measurement problem" this way?

The measurement problem is essentially why the Born rule (describing irreversible measurements) exists in addition to unitary evolution (describing reversible non-measurements).

I think most people consider it to be something different; it just needs to describe our universe. What unitary QM predicts, at least considering the other assumptions of Poincaré recurrence (maybe finite dimensionality) is that eventually recoherance will happen. You seem to be a priori ruling that out.

Not me, but orthodox QM. The theory of QM = unitary evolution AND the Born Rule; the fact that they BOTH lay claim to describing Nature is the entire problem with QM, because they are mathematically deeply inconsistent with each other. This just means that we cannot find (or it is impossible to find) a single particular theory from pure mathematics which can simultaneously naturally describe both concepts.

If QM was just unitary evolution, no one would even give QM foundations a second thought and vanhees would be completely correct in his criticism about discussing QM foundations.

Can you point to a theorem proving a recurrence theorem in the quantum case?

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.18.2379The proof is a single page.

 

[A. Neumaier]

The theory of QM = unitary evolution AND the Born Rule; the fact that they BOTH lay claim to describing Nature is the entire problem with QM, because they are mathematically deeply inconsistent with each other.

I don't see any direct inconsistency. unitary evolution is claimed for an isolated system only, and the Born rule for a measurement only (during which the system measured is surely not isolated).

Can you point to a theorem proving a recurrence theorem in the quantum case?

Poincaré recurrence is for finite-dimensional bounded dynamical systems only. Already a single hydrogen atom violates both assumptions, let alone the universe.

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.18.2379The proof is a single page.

This proof assumes a Hamiltonian with discrete spectrum, which is a very special situation.
No molecules, no quantum fields - not a good model for the universe...

Even for a Hamiltonian with discrete spectrum, recurrence in the 2-norm (which is proved in the paper quoted) says very little - e.g., it says nothing about how close the mean position of a particle comes to the initial mean position.

 

[Auto-Didact]

I don't see any direct inconsistency. unitary evolution is claimed for an isolated system only, and the Born rule for a measurement only (during which the system measured is surely not isolated).

The reason you aren't seeing an inconsistency is because you are carefully seperating out two aspects as two idealizeable systems; isn't the universe as a whole is an isolated system?

From the perspective of a mathematical physics basing itself upon the theory of complex analysis, QM - i.e. unitary evolution and the Born rule - as a mathematical model is as inconsistent as it gets; this is because unitary evolution is a completely holomorphic notion, while the Born rule involves complex conjugation, i.e. is distinctly non-holomorphic.

This proof assumes a Hamiltonian with discrete spectrum, which is a very special situation.

Smolin (or more accurately his book) is my source for the argument of quantum Poincaré recurrence. I can argue for or against discrete spectra or whether or not he was referring to the universe as a quantum system peri-Big Bang, but I suggest you take it up with him.