Will QG leave GR unchanged or QT?

[Demystifier]

As he points out, while the coupled equations (his equations 1.3) are nonlinear, the standard probability interpretation of $\psi$ remains consistent.

The standard probability interpretation involves also the collapse postulate, but the collapse postulate is not consistent in nonlinear QM.

 

[PeterDonis]

the collapse postulate is not consistent in nonlinear QM

Why not?

 

[Lord Crc]

He mentions the quantum potential, but I think that Bohmian mechanics is best understood without the quantum potential. For instance, incorporating spin into the quantum potential scheme is a total mess. On the other hand, in my "Bohmian mechanics for instrumentalists" you can see that incorporating spin is trivial in the scheme without the quantum potential.

He said the Bohm potential was a surprise he did not expect. Given that,could one recast the version with potential to the version without? I didn't have time yet to read your paper, and didn't see the connection (if any) while skimming.

 

[Demystifier]

He said the Bohm potential was a surprise he did not expect. Given that,could one recast the version with potential to the version without?

I don't know, I didn't study his paper.

 

[Demystifier]

Why not?

See my http://de.arxiv.org/abs/0707.2319
especially Introduction and Sec. 4.

 

[martinbn]

See my http://de.arxiv.org/abs/0707.2319
especially Introduction and Sec. 4.

I don't understand. Why do the $\psi_a$ have to be solutions?

 

[Demystifier]

I don't understand. Why do the $\psi_a$ have to be solutions?

Please quote the exact statement in the paper that you don't understand.

 

[martinbn]

Please quote the exact statement in the paper that you don't understand.

Thus, to determine the subsequent post-measurement properties of the system, it is sufficient to know only that component. However, in the nonlinear case, it is not a solution, so to know that component one actually needs to know the whole solution.

The whole section 4 is just two paragraphs, this is the first one.

 

[Demystifier]

The whole section 4 is just two paragraphs, this is the first one.

A simple answer: After the collapse, the wave function is supposed to be $\psi_a(t)$ for all $t$ after the collapse. But it cannot be so if $\psi_a(t)$ is not a solution of the Schrodinger equation.

 

[martinbn]

A simple answer: After the collapse, the wave function is supposed to be $\psi_a(t)$ for all $t$ after the collapse. But it cannot be so if $\psi_a(t)$ is not a solution of the Schrodinger equation.

Well, no. After the collapse the wave function is $\psi_a(x, t_0)$ at that instant of time. Then, this is the initial data for the Schrodinger's equation, it will evolve to a solution $\psi(x, t)$.

 

[Demystifier]

Well, no. After the collapse the wave function is $\psi_a(x, t_0)$ at that instant of time. Then, this is the initial data for the Schrodinger's equation, it will evolve to a solution $\psi(x, t)$.

Sure, but if $\psi_a(x, t)$ is a solution, then your $\psi(x, t)$ will be equal to my $\psi_a(x, t)$. So in that case, we can say that the wave function collapsed to $\psi_a(x, t)$ for any $t$, so the actual time of collapse $t_0$ is irrelevant and hence unphysical. We can even interpret it as if the collapse happened before the measurement, as in the delayed choice experiments. That's why one cannot associate with a collapse a definite time of collapse, which is related to the fact that collapse cannot be used for instantaneous communication.

If, on the other hand, $\psi_a(x, t)$ were not a solution, then we could determine a definite time of collapse and associated nonlinearity could be used for instantaneous communication.

One way of understanding it is this. Formally, a collapse is always nonlinear. But if there is no way to determine the time of collapse, then the time of nonlinearity is unphysical so for practical purposes one may interpret collapse as mere information update not corresponding to any actual nonlinear event. By contrast, if there is a way to determine the time of collapse, then the collapse is an actual physical event with measurable consequences, including instantaneous communication. If the Schrodinger equation is nonlinear, then the additional nonlinearity induced by collapse becomes physical and cannot longer be interpreted as mere information update.

For a related discussion see also https://www.physicsforums.com/threa...-for-the-probabilistic-interpretation.991365/

 

[Lord Crc]

I don't know, I didn't study his paper.

I was curious if there was a general way, I take your answer to mean there is not.

Thanks!

 

[martinbn]

Sure, but if $\psi_a(x, t)$ is a solution, then your $\psi(x, t)$ will be equal to my $\psi_a(x, t)$. So in that case, we can say that the wave function collapsed to $\psi_a(x, t)$ for any $t$, so the actual time of collapse $t_0$ is irrelevant and hence unphysical. We can even interpret it as if the collapse happened before the measurement, as in the delayed choice experiments. That's why one cannot associate with a collapse a definite time of collapse, which is related to the fact that collapse cannot be used for instantaneous communication.

If, on the other hand, $\psi_a(x, t)$ were not a solution, then we could determine a definite time of collapse and associated nonlinearity could be used for instantaneous communication.

One way of understanding it is this. Formally, a collapse is always nonlinear. But if there is no way to determine the time of collapse, then the time of nonlinearity is unphysical so for practical purposes one may interpret collapse as mere information update not corresponding to any actual nonlinear event. By contrast, if there is a way to determine the time of collapse, then the collapse is an actual physical event with measurable consequences, including instantaneous communication. If the Schrodinger equation is nonlinear, then the additional nonlinearity induced by collapse becomes physical and cannot longer be interpreted as mere information update.

For as related discussion see also https://www.physicsforums.com/threa...-for-the-probabilistic-interpretation.991365/

I still don't understand. You are being too vague and as written it is at best ambiguous. When you make a measurement you get and eigenvalue of the corresponding operator, the state collapses to an eigenstate (using the standard formulation as in the forum's guidelines). In general the evolution (under the Schrodinger's equation) will not preserve the eigenstates. So it is very confusing, to put it politely, to say that the wave function collapsed to $\psi_a(x, t)$ for any $t$! May be it is clear to you what you mean, but not to me. It just sounds incorrect. And this has nothing to do with non-linear equations. It seems incorrect even with a standard linear equation QM.

 

[Demystifier]

I still don't understand. You are being too vague and as written it is at best ambiguous. When you make a measurement you get and eigenvalue of the corresponding operator, the state collapses to an eigenstate (using the standard formulation as in the forum's guidelines). In general the evolution (under the Schrodinger's equation) will not preserve the eigenstates. So it is very confusing, to put it politely, to say that the wave function collapsed to $\psi_a(x, t)$ for any $t$! May be it is clear to you what you mean, but not to me. It just sounds incorrect. And this has nothing to do with non-linear equations. It seems incorrect even with a standard linear equation QM.

OK, here is a more precise way to explain what's going on in the nonlinear case, based on the idea of quantum cloning. The proof of the no-cloning theorem rests on the assumption of linearity. Hence in nonlinear QM cloning may be possible. But if cloning is possible, then there is a protocol that can be used for instantaneous communication. To explain the protocol, I present a few paragraphs from the book by Schumacker and Westmoreland:

 

[atyy]

Carlip doesn't seem to be making that strong a statement. He seems to be saying that, while treating GR as an effective field theory approximation to some quantum gravity field theory is one option, another option is to accept gravity as a classical potential in the Schrodinger-Newton equation sourced by the expectation value of the mass density. As he points out, while the coupled equations (his equations 1.3) are nonlinear, the standard probability interpretation of $\psi$ remains consistent. Ruling out (or confirming, depending on how the results turned out) this latter option would require experimental tests along the lines Carlip suggests, which are not yet quite within our capabilities.

I don't think so, because what we would need is not Schroedinger-Newton but "Schroedinger-GR" (I made up te term). However, we don't have a working version of Schroedinger-GR, not even at the physics level of rigour. If Schroedinger-GR exists, then presumably Schroedinger-Newton is an approximation to Schroedinger-GR, so he uses Schroedinger-Newton to estimate the deviations predicted by Schroedinger-GR.

On the other hand, GR as an effective quantum field theory is a working theory, at least at the physics level of rigour.

 

[Fra]

Moreover, I think that there is also a justification for this asymmetry.

Indeed there is a justifiction for the assymmetry - the fact that QT and the standard model of particle physics is by definition, formulated to describe a small subsystem, from the perspective of a controlled classical environment, where processes can be prepared and repeated in a controlled and fapp unlimited manner. Noone has yet constructed a quantum theory without a classical background. Bohr understood this from day one, but for some reason sometimes deeep insighs tend to get lost and misinterpreted. This btw, is also the reason for the timeless laws and absence of cosmological time in QT. Without diverging into the philosophy, many people argue that this must apply for a "scientific theory", as no "scientific results" can be attained without the contact of repeatability and confident statistics etc.

The problem is that one can argue that this justification breaks down for cosmological observations; or to put i more precisely, for "inside observers", that are not necessarily classical systems or are classical but can not encode enough information about the environment to comply to the requirements of the construction of the framework. Does mean that non-classical observers can not do science, or are cosmology not science? Well maybe not. Or maybe there is something wrong with the question we ask - I argue there is. But this is a much more painful insight, further adding to the assymmetry.

Classical GR has singularities, so it is known from the start to be wrong, it has to be replaced by a different theory.

If you adhere to my second paragraph above, one can similary conclude from start that "QT must be wrong". Or rather than "wrong", correspond to a a special limiting class of observers, that makes us unable to scale the framework to arbitrary observer frames required for full unification.

/Fredrik

 

[andresB]

By the way, your claim is wrong, the theory (combined in the straightforward way with the SM) predicts quantum effects, classical GR not. Semiclassical GR is inconsistent as a theory, thus, does not count. Thus, GR quantized as an effective field theory in harmonic coordinates on $\mathbb{R}^4$ predicts things not predicted by classical GR or any other non-quantum theory of gravity.
...
In general, one claims success if one has solved some scientific problem. That there was no theory able to predict as what GR predicts as well as the quantum effects was a scientific problem, not? But we have now a theory which solves this problem. So, success.

Those predicted things could very well not be in nature at all. I can't share your eagerness to call it a "success". Promising, might be a better word.

 

[Sunil]

Indeed there is a justifiction for the assymmetry - the fact that QT and the standard model of particle physics is by definition, formulated to describe a small subsystem, from the perspective of a controlled classical environment, where processes can be prepared and repeated in a controlled and fapp unlimited manner. Noone has yet constructed a quantum theory without a classical background.

The conclusion would have to be, that once GR certainly has to be modified (given the singularities) and to modify both at the same time leaves us completely without any guidance, to accept that we need a classical background too.

The problem is that one can argue that this justification breaks down for cosmological observations;

What follows from the Copenhagen-QT-inherent conflict between the classical and the quantum part depends on the interpretation. Different interpretations handle cosmology differently. The realist interpretations extend the classical part to everything - they introduce a continuous configuration space trajectory $q(t)\in Q$ into the quantum part too.

Is there, similarly, also a wave function of the universe? A consistent epistemic interpretation would deny this. Can such a consistent epistemic interpretation describe the whole universe completely? Formally not, there has to be that part containing the incomplete information about the system. But that "incomplete information" we somehow have to know completely, assuming we have only incomplete information about that incomplete information smells paradoxical.

For what happens in practice, we have the example of thermodynamics, statistical mechanics in the Bayesian approach, where entropy describes no physical property of a system but our incomplete knowledge of the trajectory of that system. The picture is the same - the observer is outside the system. Can we do thermodynamics for cosmology? Obviously. But we would have to handle the internal observer on that planet Earth as something external. Could we handle Earth as completely internal too? That's possible too, simply use some far away alien civilization as the observer, and take out that alien planet somewhere in Andromeda instead of Earth. Both no essentially nothing about each other, beyond some general approximate information (say about the actual properties of the background radiation), so FAPP this is completely harmless. But the cut between observer and observed is there, and remains there, and I see no chance to get rid of it.

Once the conceptual problems related with this cut can be nicely considered based on thermodynamics, it makes sense to study them first in thermodynamics instead of quantum theory, and then to apply the results of what necessarily follows (say, that such a cut is unavoidable anyway) to quantum mechanics too. Simply it would not make sense to require from QT more than from statistical mechanics. If (or better once) we have a satisfactory situation in statistical mechanics, all we need is a consistent Bayesian approach to QT. Which exists, Caticha's entropic dynamics (ignoring with its existence, following the traditions of dBB theory, a lot of impossibility theorems like the many variants of PBR). It interprets $|\psi(q)|^2$ as required by the Born rule and the phase in terms of the entropy of the system in dependence given the information available outside the system. But it has also the continuous configuration space trajectory $q(t)\in Q$ which defines the ontology.

Does mean that non-classical observers can not do science, or are cosmology not science? Well maybe not. Or maybe there is something wrong with the question we ask - I argue there is. But this is a much more painful insight, further adding to the assymmetry.

I see no potential here for a serious conflict. In Caticha's interpretation we objectively have a trajectory $q(t)\in Q$. The aliens from Andromeda can apply QT to describe that trajectory based on the incomplete information they have. In this sense, we are "quantum observers", and I see no problem with this.

If you adhere to my second paragraph above, one can similary conclude from start that "QT must be wrong". Or rather than "wrong", correspond to a a special limiting class of observers, that makes us unable to scale the framework to arbitrary observer frames required for full unification.

I see here only a problem with the "full unification" idea, which runs into the same problem already in the Bayesian variant of statistical mechanics where everything else is well understood. Nothing comparable with GR singularities in seriousness.

 

[Fractal matter]

Yes, I've been trying Lorentz covariant Bohmian mechanics too, and published a few papers, but eventually gave up of that approach.

I heard Basil Hiley made a covariant formulation. Also there is a recent qft model of the de Broglie's Double solution theory https://www.frontiersin.org/articles/10.3389/fphy.2020.00300/full

 

[Fractal matter]

Summary:: I argue that there are good reasons to expect that QG will be indeed a standard quantum theory, the general principles of QT remaining unchanged, instead of a modified, generally covariant modification of quantum theory.

I agree with that.

Recent works of Padmanabhan tell, that GR has the same status as thermodynamics.
There is also the work of B. L. Hu, that says "general relativity can be viewed as the hydrodynamic limit of quantum gravity"

But nevertheless, i suppose GR have a clue as to what QM really is.

 

[Fra]

to modify both at the same time leaves us completely without any guidance

Yes I agree this is the difficulty, and the first impression.

But rejecting the full problem due to difficulties and work on an alternative problem which avoids the real issue is not appealing to me. As i have been thinking about this problem for some time I disagree that there is no guidance.

I see here only a problem with the "full unification" idea, which runs into the same problem already in the Bayesian variant of statistical mechanics where everything else is well understood. Nothing comparable with GR singularities in seriousness.

Singularities and infinities are precisely the kind of pathologies that can arise when you assume an infinite encoding and processing capacity of the observing system - which ultimately is associated with the "classical background". Because it is in the background, that processing of statistics and emergence of "equivalence classes" take place. Let's not confuse the statistical patterns in the eye of the beholder, that influences the action of the beholder, with constraints on the parts.

If you apply the constrained physical perpective of measurement and information processing, a natural cutoff tied to the observing system is likely to exist.

The same mechanism can in principle explain why "randomness" is a matter of perspective as there is no such thing as "true randomness". This can also give us a hint how to handle the paradoxal situation of complete knowledge of the ignorance. It also makes it clear that there are good reasons to expect that all the classical GR conclusions from cosmology, are unlikely to make sense when we are talking about say hypothetical Planck scale black holes. That a cosmological black hole has no hair relative to a hovering observer, does not mean a microscopic black hole does not, relative to a massive lab fram. This is a generic insight one can draw without detailed models if to bring computational capacity of the parts into play,

QG has two main challenges

1) trying to understand cosmology and GR in a quantum framework, ie. construct a quantum theory in terms of the inside observer

2) trying to understand hypothetical "planck scale" black holes in terms of regular quantum theory in a classical lab frame.

Usually these two problems are worked on independently, but they may well be connected.

/Fredrik

 

[robwilson]

I'm only a mathematician, but it seems to me that attempts to convert GR to QM have failed after many years of strenuous efforts, and attempts to convert QM to GR likewise. My conclusion from this is that neither will survive, once a unified theory is found. The trick for unification, then, is to find how to tweak both of them so they meet in the middle. That's much harder than tweaking one to fit the other, of course, but it seems that it has to be done.

 

[Fra]

My conclusion from this is that neither will survive, once a unified theory is found. The trick for unification, then, is to find how to tweak both of them so they meet in the middle. That's much harder than tweaking one to fit the other, of course, but it seems that it has to be done.

I agree.

From the conceptual perspective, it is quite clear that both QM and GR foundations are missing some important things. So if anyone managed to actually combine them sort of as is, and solved all the problems, in a sensible way without reconstructing them both would be remarkable or even unreasonable IMO.

/Fredrik

 

[robwilson]

I agree.

From the conceptual perspective, it is quite clear that both QM and GR foundations are missing some important things. So if anyone managed to actually combine them sort of as is, and solved all the problems, in a sensible way without reconstructing them both would be remarkable or even unreasonable IMO.

/Fredrik

Yes. Few people are really thinking about unification, because we really have no clue where to start. I started thinking about symmetry, simply because that's what I know about. My preliminary conclusions as of now are in arxiv:2009.14613. For 12 fundamental fermions and 12 fundamental bosons, one needs at least a group of order 24. I tried the obvious ones, and one of them "worked", to give something like the standard model, but with a tweak to QCD and another tweak to electroweak mixing. It may also give GR, with a tweak also, but I need to do more work on that. Also I shouldn't discuss my pet theory here.

 

[martinbn]

I'm only a mathematician, but it seems to me that attempts to convert GR to QM have failed after many years of strenuous efforts, and attempts to convert QM to GR likewise. My conclusion from this is that neither will survive, once a unified theory is found. The trick for unification, then, is to find how to tweak both of them so they meet in the middle. That's much harder than tweaking one to fit the other, of course, but it seems that it has to be done.

This is the probably what will happen, but are there any attemts at addapting QM to GR?

 

[robwilson]

This is the probably what will happen, but are there any attemts at addapting QM to GR?

I don't know. I tried, and you can read about my attempts on my blog. But I can't say I succeeded.