Hossenfelder's beautiful idea resolves QG/QFT tension

[marcus]

Quote from page 1 of paper posted by Hossenfelder today:

"These difficulties can be circumvented by changing the quantization condition in such a way that gravity can be perturbatively quantized at low energies, but at energies above the Planck energy – energies so high that the perturbative expansion would break down – it becomes classical and decouples from the matter fields. The mechanism for this is making Planck’s constant into a field that undergoes symmetry breaking and induces a transition from classical to quantum. In three dimensions, Newton’s constant is G = [STRIKE]h[/STRIKE]c/m²_Pl, so if we keep mass units fixed, G will go to zero together with [STRIKE]h[/STRIKE], thus decoupling gravity. It should be emphasized that the ansatz proposed here does not renormalize perturbatively quantized gravity, but rather replaces it with a different theory that however reproduces the perturbative quantization at low..."

1208.5874

this paper is a bold bid to cut the Gordian knot and I find it remarkably persuasive.

I would like to think of Newton's G as, in fact, just [STRIKE]h[/STRIKE]c/m²_Pl. With a fixed standard mass. Since [STRIKE]h[/STRIKE]c is a standard force-area quantity---a standard amount of inverse-square coupling---G just says that two standard masses have that much interaction. So then if [STRIKE]h[/STRIKE] goes to zero at high energy then obviously so must G → 0.

One can imagine that nature wanted it this way So maybe this way of joining quantum geometry to QFT and the standard particle model will yield predictions that are practical to test!

I'm hopeful about this idea. Good for Hossenfelder!

 

[Physics Monkey]

Reminds me a lot of an old idea of David Finkelstein which he liked to describe as quantizing the imaginary unit. See section 1.4 of this draft of his https://www.physics.gatech.edu/files/u9/publications/quantumtime.pdf

Basically, his idea was that normally q and p commute with their commutator. This is bad for various reasons because the algebra has a central element and the resulting group is not semisimple. His observation was that one could get a nice algebra, either SO(3) or SO(2,1), by promoting [q,p] to a field that didn't commute with q or p.

Anyway, Hossenfelder's statements reminded me of this old idea, so I thought I'd mention it for your amusement.

 

[marcus]

Reminds me a lot of an old idea of David Finkelstein which he liked to describe as quantizing the imaginary unit. See section 1.4 of this draft of his https://www.physics.gatech.edu/files/u9/publications/quantumtime.pdf

Basically, his idea was that normally q and p commute with their commutator. This is bad for various reasons because the algebra has a central element and the resulting group is not semisimple. His observation was that one could get a nice algebra, either SO(3) or SO(2,1), by promoting [q,p] to a field that didn't commute with q or p.

Anyway, Hossenfelder's statements reminded me of this old idea, so I thought I'd mention it for your amusement.

Thanks for your response! It will be interesting to see how different people react to Bee's idea. I went over to her blog "Backreaction" and mentioned the paper, hoping to see some discussion of it before long.
http://arxiv.org/abs/1208.5874
http://backreaction.blogspot.com/2012/08/how-to-beat-cosmic-speeding-ticket.html

I guess I'll put the abstract here so a passerby can read it without going to the arxiv link:
A possibility to solve the problems with quantizing gravity
S. Hossenfelder
(Submitted on 29 Aug 2012)
It is generally believed that quantum gravity is necessary to resolve the known tensions between general relativity and the quantum field theories of the standard model. Since perturbatively quantized gravity is non-renormalizable, the problem how to unify all interactions in a common framework has been open since the 1930s. Here, I propose a possibility to circumvent the known problems with quantizing gravity, as well as the known problems with leaving it unquantized: By changing the prescription for second quantization, a perturbative quantization of gravity is sufficient as an effective theory because matter becomes classical before the perturbative expansion breaks down. This is achieved by considering the vanishing commutator between a field and its conjugated momentum as a symmetry that is broken at low temperatures, and by this generates the quantum phase that we currently live in, while at high temperatures Planck's constant goes to zero.
4 pages, 1 figure

So it would seem that if you go to high enough energy Planck's hbar just evaporates! It can't take the heat. But then if things cool back down it condenses again into some definite nonzero value or other. Just think, all that finicky non-commutativity and reciprocal uncertainty blown away in a blast from the transPlanckian furnace. But able to recrystallize, given the opportunity. I've always liked Bee, she posted here at PF even before she had her own blog, and I could be biased on that account, in the ideas favor.

 

[Paulibus]

I share your enthusiasm about this possible breakthrough, Marcus. I hope it generates some testable predictions. Until then, bear Meher Baba and Bobby McFerrin's suggestion in mind: "Don't worry, be happy" . Physics has two well-laid and beautiful theoretical foundation stones, GR and QM. Maybe in the end they'll prove to be compatible and sufficient to support its entire structure!

 

[Demystifier]

The Hossenfelder's idea is certainly very original, but the question is whether it is convincing and appealing. Her proposal is based on postulating the commutation relation Eq. (3), which in my view seems too ad hoc. But then again, the Heisenberg commutation relation also seemed too ad hoc when it was postulated for the first time. So who knows, maybe Hossenfelder is a new Heisenberg.

Her approach is also similar to the Higgs effect, predicting a new scalar particle - alpha particle. So maybe Hossenfelder is not only a new Heisenberg, but also a new Higgs.

For those reasons, if there is no any other related theory whose inventor has a second name beginning with H, I propose to call this theory HHH theory.

 

[Demystifier]

Another nice thing about this theory is the fact that the inventor currently lives in Stockholm. So if the theory turns out to be right, she will not need to take a long trip to pick up the prize.

 

[Demystifier]

Now more seriously, after a second reading of the paper, I see a serious problem with it.

Alpha(x,t) in Eq. (3) is a c-number field, not an operator. Hence, it should be distinguished from the operator alpha(x,t) satisfying the commutation relation between Eqs. (5) and (6). At least one should introduce two different notations for two different objects, but I am afraid that it would not be enough.

Namely, to make sense of alpha in (3), one should postulate that it is the average value of the operator alpha. But then the average depends on the quantum state.

At low energies we can say that the state is close to the vacuum, so there is no problem. But there is a problem at large energies.

In the case of large energies the paper studies the case of a well defined temperature, in which case the average alpha is also well defined. However, it is possible to have a high-energy state which is NOT close to the thermodynamic equilibrium. In this case, average alpha is NOT given by the minimum of (7).

My concern is, how to determine alpha in Eq. (3) for high-energy states which are not close to the thermodynamic equilibrium? This is a problem because alpha depends on the quantum state, while at the same time the quantization procedure, and therefore the quantum state itself, depends on alpha. This is a sort of a chicken-or-egg question, which I don't see how to resolve.

 

[hossi]

alpha is an operator valued field, not c-valued. If you are working in a mean field approximation you replace it with the expectation value at the minimum of the potential. Temperature changes the position of the minimum. If you can't make a mean field approximation things are more complicated. Then one can't use the expectation value. There are large fluctuations and it's not clear even what a phase transition would mean. It's that case I've been elaborating on when I talk about the expansion of the S-matrix towards the end of the paper, which you need for the general case. It's far from clear the series converges if you sum up all the quantum contributions because it depends on the potential (which doesn't have to be the one I wrote down, that was just the simplest example I could think of) and its loop corrections and so on. But it seems possible that it does. And that possibility is all I wanted to point out in my paper.

Thanks for your interest

 

[marcus]

But then again, the Heisenberg commutation relation also seemed too ad hoc when it was postulated for the first time. So who knows, maybe Hossenfelder is a new Heisenberg...

Yes, I think so in fact, and even better because she is good-looking and has a blog, neither of which perfections were attained by Heisenberg.

 

[marcus]

Hi[STRIKE] hossi[/STRIKE] Bee,
as an irresponsible lay bystander I expect G 't H will like this idea because he wants QM to have an underlying deterministic basis---your idea is in somewhat similar spirit, having a classical limit at high energy. It is not so much building QM on a deterministic basis as it is lowering QM from a hovering classical sky-crane. It is really really nice...really.

 

[jimgraber]

I also noted this paper and glanced through it quickly. I noticed in the acknowledgments that the participants in Physics Stack Exchange are thanked, so I spent a few minutes looking through PSE for a related discussion, but I did not find it. I would appreciate a pointer, if someone knows where I should look.
TIA.

 

[marcus]

Jim, I don't know of discussion at Stack Exchange but I imagine there WILL be public discussion at FQXI.
The arxiv paper, as I understand it, contains technical or supporting material for an essay that she will enter in the annual Essay Contest.
Here is a link to the essays already submitted:
http://fqxi.org/community/forum/category/31418
One approach would be to choose alphabetical ordering by author's surname, and scroll down to H.
I checked and it is not showing up yet. When the essay is turned in and listed, then clicking on the title will get you to a kind of blog-like discussion which will probably refer both to the essay and to the arxiv paper.

You may know more about the layout at the FQXI website than I do. Please share what know know or can find out, once the essay is online there. I've never registered there or bothered to find out about access. There may be two different tracks for people who want to discuss stuff. I'd just like to read some informed comment.

 

[atyy]

Does this mechanism need statistical mechanics to hold, since Boltzmann's constant seems to enter the equations?

If so, isn't that exchanging one mystery for another? I thought canonical typicality or some such quantum thing was going to resolve stat mech!

The commutation relations seem to emerge, but how about the Born rule?

 

[Demystifier]

The commutation relations seem to emerge,

No, they are POSTULATED by Eq. (3). But this commutation relation is more general than the usual canonical one with a constant Planck "constant", so what emerges is the constancy of the Planck "constant".

This is similar to the Higgs mechanism, by which the emergent thing is constancy of the mass. However, Higgs mechanism is in a sense more natural than the Hossenfelder mechanism, because the Higgs mechanism does not need an ad hoc postulate analogous to Eq. (3).

Another similarity is with the Brans-Dicke theory, in which the constantcy of the Newton "constant" is emergent, but again Brans-Dicke theory does not need an analogue of the ad hoc Eq. (3).

In short, I think that the idea that Planck constant is not a constant is an excellent idea. However, the concrete realization of that idea based on Eq. (3) is not so excellent. It's OK for a starting point, but one should think about more elegant realizations of the idea.

 

[Demystifier]

Does this mechanism need statistical mechanics to hold, since Boltzmann's constant seems to enter the equations?

The Boltzmann's constant does not appear in the fundamental assumptions of the theory, but only in a special case corresponding to the state of thermodynamic equilibrium. But to rephrase what hossi said in a response to my objection, it is not entirely clear whether de-quantization works when the system is not in the thermodynamic equilibrium.

 

[Demystifier]

Yes, I think so in fact, and even better because she is good-looking and has a blog, neither of which perfections were attained by Heisenberg.

Yes, but Heisenberg was much younger when he discovered his commutation relation than she is now. But to avoid misunderstanding, I am certainly not saying that she is not young. After all, she is about my age, and I am young.

 

[atyy]

So is this or is this not emergent quantum mechanics? In Eq 3, if that is classical, how can there be an operator valued field?

 

[John86]

This is Sabine Hossenfelder Essay

http://fqxi.org/data/essay-contest-files/Hossenfelder_fqxi_principle.pdf

 

[marcus]

Thanks John!,
if anyone wants to ask questions or comment, blog-style, it looks like you just go here:
http://fqxi.org/community/forum/topic/1477

There are already seven comments posted. It is a discussion thread devoted to that one essay.

 

[marcus]

Actually we might have a better discussion here, for a while, than what they have at FQXi. Since we have turned a page I will bring forward posts from earlier by Demystifier, Hossi, and Atyy.

=====quote Demy======
Now more seriously, after a second reading of the paper, I see a serious problem with it.

Alpha(x,t) in Eq. (3) is a c-number field, not an operator. Hence, it should be distinguished from the operator alpha(x,t) satisfying the commutation relation between Eqs. (5) and (6). At least one should introduce two different notations for two different objects, but I am afraid that it would not be enough.

Namely, to make sense of alpha in (3), one should postulate that it is the average value of the operator alpha. But then the average depends on the quantum state.

At low energies we can say that the state is close to the vacuum, so there is no problem. But there is a problem at large energies.

In the case of large energies the paper studies the case of a well defined temperature, in which case the average alpha is also well defined. However, it is possible to have a high-energy state which is NOT close to the thermodynamic equilibrium. In this case, average alpha is NOT given by the minimum of (7).

My concern is, how to determine alpha in Eq. (3) for high-energy states which are not close to the thermodynamic equilibrium? This is a problem because alpha depends on the quantum state, while at the same time the quantization procedure, and therefore the quantum state itself, depends on alpha. This is a sort of a chicken-or-egg question, which I don't see how to resolve.
===endquote===

===quote Hossi===
alpha is an operator valued field, not c-valued. If you are working in a mean field approximation you replace it with the expectation value at the minimum of the potential. Temperature changes the position of the minimum. If you can't make a mean field approximation things are more complicated. Then one can't use the expectation value. There are large fluctuations and it's not clear even what a phase transition would mean. It's that case I've been elaborating on when I talk about the expansion of the S-matrix towards the end of the paper, which you need for the general case. It's far from clear the series converges if you sum up all the quantum contributions because it depends on the potential (which doesn't have to be the one I wrote down, that was just the simplest example I could think of) and its loop corrections and so on. But it seems possible that it does. And that possibility is all I wanted to point out in my paper.

Thanks for your interest
===endquote===

===quote Atyy===
Does this mechanism need statistical mechanics to hold, since Boltzmann's constant seems to enter the equations?

If so, isn't that exchanging one mystery for another? I thought canonical typicality or some such quantum thing was going to resolve stat mech!

The commutation relations seem to emerge, but how about the Born rule?
==endquote==

===quote Demy===
"The commutation relations seem to emerge..."

No, they are POSTULATED by Eq. (3). But this commutation relation is more general than the usual canonical one with a constant Planck "constant", so what emerges is the constancy of the Planck "constant".

This is similar to the Higgs mechanism, by which the emergent thing is constancy of the mass. However, Higgs mechanism is in a sense more natural than the Hossenfelder mechanism, because the Higgs mechanism does not need an ad hoc postulate analogous to Eq. (3).

Another similarity is with the Brans-Dicke theory, in which the constantcy of the Newton "constant" is emergent, but again Brans-Dicke theory does not need an analogue of the ad hoc Eq. (3).

In short, I think that the idea that Planck constant is not a constant is an excellent idea. However, the concrete realization of that idea based on Eq. (3) is not so excellent. It's OK for a starting point, but one should think about more elegant realizations of the idea.
===endquote===

===quote Demy===
"Does this mechanism need statistical mechanics to hold, since Boltzmann's constant seems to enter the equations?"

The Boltzmann's constant does not appear in the fundamental assumptions of the theory, but only in a special case corresponding to the state of thermodynamic equilibrium. But to rephrase what hossi said in a response to my objection, it is not entirely clear whether de-quantization works when the system is not in the thermodynamic equilibrium.
==endquote==

 

[arivero]

THis thread somehow remembered me the work on Connes Tangent Grupoid. Good for quantisation, but nobody got the idea of trying gravity (either Newton or gen rel) inside. Nowadays the Red Book is free as a pdf in Connes website, so you can read there about it.

 

[hossi]

Hi Marcus,

I have great sympathy for 't Hooft's conviction that nature is deterministic, though this isn't what I aimed at with this paper. I write about a possible test in an earlier paper (1105.4326), but really has nothing to do with this one. Also note that in what I suggest the theory is never really classical, it just has a classical phase, but the quantization postulate is always present.

Sabine (aka hossi aka Bee)

 

[hossi]

Hi atyy,

It's not emergent quantum mechanics in the sense that quantization does not emerge from a fundamentally classical theory. It is instead a modification of the quantization procedure so that there are two phases: one which is classical and one which is quantized in the normal way. The theory is fundamentally neither classical nor quantized in the usual sense.

B.

 

[hossi]

Hi "Demystifier",

I connect the dots... You are right that it is not clear unquantization works if the mean field approximation cannot be used. I don't think I used the word thermodynamic equilibrium. This is what I alluded to in my elaboration at the end of the paper that to understand general highly energetic interaction processes the temperature dependence of the potential is not sufficient to tell the story. Whether the series converges or not depends on the quantum corrections of the potential, which in turn depends on the particle content. So I don't think there's an easy answer to this. However, all I wanted to say really is that the possibility exists and that I believe it is interesting enough to merit some thought.

B.

 

[John86]

Hi atyy,

It's not emergent quantum mechanics in the sense that quantization does not emerge from a fundamentally classical theory. It is instead a modification of the quantization procedure so that there are two phases: one which is classical and one which is quantized in the normal way. The theory is fundamentally neither classical nor quantized in the usual sense.

B.

You don't talk in emergent terms here about Quantum mechanics I am a wright ? But are you in some kind of way trying relativize the Classical framework to get Quantum mechanics or vice versa. Or are you asking more to question the search for a theory of Quantum gravity at all ?.

 

[marcus]

Hi John, your question is to Sabine, so I don't really answer but just make a comment on the side.

People can't think without concepts and dichotomies ("this or that" divisions) but every good thing has its disadvantages and our concepts can be a STRAIT-JACKET to creative thought.
We have this engrained distinction "classical determinist versus quantum indeterminist"

That mental structure could ultimately be laming disabling limiting cramping our style.

So you are talking about THIS emerging from THAT, or viceversa that emerging from this.

As if theories had to be ONE OR THE OTHER and then one of them could be FUNDAMENTAL and the other could emerge from it. And that could be wrong.

It could be that nature doesn't like this or that and that NEITHER can be fundamental.

Like the beautiful example of water. It is not fundamentally a solid or a liquid. The correct mathematical models to use for how water behaves depend on the phase. we don't say that it is fundamentally a solid and the liquid behavior "emerges" from the solid model. Or viceversa. There is something deeper that comprehends both.

So I think the essay is saying basically "let's take off our straitjacket and move around a little and see how it feels".
It might turn out to be a good idea, or it might not. You can only tell if you try.

 

[marcus]

So anyway Sabine has to answer your question but I will put in my two centsworth of interpretation. I think the idea is that a quantum mechanical theory cannot exist above a certain temperature because [STRIKE]h[/STRIKE] goes to zero.

And you make a certain bold guess or "Ansatz" that G is linked to [STRIKE]h[/STRIKE] by keeping a certain mass standard, so that if QM boils away as [STRIKE]h[/STRIKE] goes to zero you also have G dwindling to nothing. So at very high energy there is no coupling between geometry and matter! this is quite amusing to say the least

this idea could certainly certainly certainly be wrong. All good ideas can be wrong. But, to me, it is an extremely dangerous idea, which is why it is so good. It will be fun to see how this goes.

Anyway,I think the idea is classical and quantum are part of the same thing, which is neither of them. Neither are fundamental and neither emerges from the other. Because Planck's hbar constant is (or could be) a field. It freezes in a certain position (suddenly, like a modern dancer) when things cool down. But then, if things heat up, it could start dancing around again and regain zero-ness = symmetry.

Sabine will have my scalp if I have badly misrepresented her idea.

We should keep an eye on

http://fqxi.org/community/forum/topic/1477
and the blog
http://backreaction.blogspot.com
in case some discussion develops in those places

 

[Demystifier]

However, all I wanted to say really is that the possibility exists and that I believe it is interesting enough to merit some thought.

Yes, I definitely agree with that. As you have seen (not only on this forum), your paper inspired me to think about this by myself from a slightly different perspective.

 

[Berlin]

If at high energies h --> 0 it would also mean that the big bang would consist of a near classical bose gas of spin-0 particles without Pauli exclusion. The finite mass of the universe (~10^54 kg or so) would also mean that there should be a tiny bit of gravity left. This would imply a slowly starting big bang. But what would happen with the fermi statistics kicking in? Could we calculate the pressure of a developing fermi gas, maybe mimicking inflation? What would those poor infant-fermions, not able to find an unoccupied higher energy state, do? Would they condensate to composite-bosons, staying dark forever :)?

berlin

 

[atyy]

In normal spontaneous symmetry breaking, if the symmetry is continuous, there is a Goldstone boson. Is there anything like that here?

 

[Drakkith]

What exactly are the consequences of [STRIKE]h[/STRIKE] going to zero at high energies?

 

[Demystifier]

If at high energies h --> 0 it would also mean that the big bang would consist of a near classical bose gas of spin-0 particles without Pauli exclusion.

This suggests another argument against the hossi's proposal. If at high energies quantum fluctuations vanish, then the early inflationary phase of the Universe expansion cannot explain the primordial density fluctuations, which are needed to explain the observed inhomogenities in the spectrum of cosmic microwave background.

 

[Demystifier]

But what would happen with the fermi statistics kicking in? Could we calculate the pressure of a developing fermi gas, maybe mimicking inflation?

Fermi-Dirac statistics in the limit h->0 is still a Fermi-Dirac statistics. This limit does not turn the anti-commutator into a commutator.