Gravity Can Be Neither Classical nor Quantized by Sabine Hossenfelder

Hello again Bee

Thanks for your reply.

When I wrote of Planck's constant "varying", I wasn't thinking carefully about the circumstances. Variation with either space or time would be worth understanding. As to "normalizing", perhaps I had better read your arxiv paper before writing more.

About choice of potential: you suggest two criteria.

The first, causing symmetry breaking, sounds worthwhile, but if there is any symmetry breaking potential then there will probably be very many such. It would be good to have a criterion which constrains the form of the potential much more. The second, convergence of the perturbative expansion, sounds rather ad hoc. It seems based on a model of calculation which excludes every conceivable model which is not just a simple perturbation of some basic state.

These are not criticisms of your essay. As far as I can tell, the entire main stream of current physics theory is developed around models described by such perturbations. The problem of convergence haunts them all. Even more serious: this approach excludes the possibility of models which are not such perturbations. The form of model suggested in my submission avoids this issue, which is one reason why I thought it worth writing. As things stand in current theory, the entire structure of most theories proposed these days is constrained by the very specific syntax which is available for describing Lagrangians in the notation inherited from a century-old form of maths. This aspect of theoretical physics has some catching up to do.

Best wishes

(Patrick) Alan H.

Thanks for the answers! I didn't realize until I checked your thread that it was you who posted as "Bee" over on my thread... I wrote some remarks there too. Anyway, you have some very good ideas... things I had never thought of before. Take care,

Ben

What do you mean with "masses are quantized"?

Hi Harlan,

As I already wrote in a comment above, in principle you are correct that since Planck's constant is dimensionful, one should take a ratio and then talk about a dimensionless quantity. The most natural thing to do seems to divide it by the measured (low energy) value of Planck's constant (\hbar_0). However, this would make the notation less intuitive, so I haven't done that for the sake of readability. I don't know what your referral to discreteness means. Best,

B.

Bee,

Thanks for the response.

The idea of discreteness comes from using planck's constant in hilbert space. The purpose of the constant is to transform an otherwise continuous spectrum into discrete spectrum. For instance

[math]e^{iHT}[/math]

which contains two continous quantities is modified into

[math]e^{(i/h)HT}[/math]

which now allows us to talk about integer components with respect to h (everything to the left of the decimal point e.g. x.yyyy where the integers are to the left of the decimal). When talking of infinties, the specific value of h isn't important, its that we now have discretized the product space HT. Since T is usually unbounded, HT is unbounded, so talking in infinities makes sense. Cantor showed that there is a definite distinction between discrete and continuous infinities.

This is the basis of the remark, the value of h isn't particularly important, so it isn't useful to discuss it changing with respect to time.

A very interesting question!

Say in this toy cosmos there are only the commonly known particles and atoms composed of them. The atoms have quantized masses in acordance with QM.

If the masses of all objects in this toy cosmos are quantized (not continuously variable masses, but definite masses, and in the case of atoms multiples of a unit mass), then are the gravitational interactions between and among them quantized by default, i.e., the interactions cannot be other than quantized even though GR is classical?

I do not see how to ask the question in a simpler or more straightforward way. For those seeking to quantize gravitation, this would seem like one of the most obvious first questions to ask of nature.

This is interesting, thanks Bee (BTW a prior 2nd-place winner.) The welcome defying of typical dichotomies reminds of my own insistence, the previous contest, that reality was neither digital nor analog (i.e., not fully representable by any kind of actual math.) Considering the big troubles that trying to conjoin GR and QM have provided, why not try a whole new attitude?

BTW I submitted a new essay for this contest, late Friday night so it hasn't shown up yet. The title gives a hint, it's about quantum measurement: "Can repeated interactions show more about a photon than current theory allows?"

PS: Is there a general contest discussion thread, like there was last time? I can't find one. tx. Cheers and good "luck" to all.

Sabine,

Is c1 lower than c or is c1 equal to c? You were not so timid a few years ago when we discussed the same problem:

http://backreaction.blogspot.com/2006/08/lee-smolins-trouble-with-physics.html

"Pentcho, Unfortunately I have the impression you aren't even trying to listen to what I say. I am pretty damned close to deleting all your nonsensical comments, as they are plainly wrong, and I don't want my blog to contribute to distributing your erroneous believes. Would you please consider for one moment to think about what I say, or otherwise restrain yourself from commenting garbage, thanks, B."

Pentcho Valev pvalev@yahoo.com

Sabine,

I have followed some of the concepts you have presented for several years. In 2008, I sent you an email about a proposed paper, which was published by the IEEE in 2011, "A methodology to define physical constants using mathematical constants". That paper is cited in my essay, topic 1294, and I provide links in the comments. It describes a fundamentally different way to apply mathematics to physical law.

In your essay, first section, subsection 3, you state, "As Hannah and Eppley have argued [2], the attempt to do such a coupling leads either to a violation of the uncertainty principle (and thus would necessitate a change of the quantum theory) or to the possibility of superluminal signaling, which brings more problems than it solves."

Although not a part of my essay, a paper titled, "The helical structure of the electromagnetic gravity field" ( Helical Electromagnetic Gravity ) describes a simple mechanism how superluminal influence can exist. Please note that in 2004, the authors of references [6] and [7], cited in the paper, established a mathematical basis why gravity has an electromagnetic (EM) origin. All the authors of [6] and [7] needed was a description of the EM field structure that provides an attractant only force; my paper does that.

Dear Sabine,

For almost any choice, people tend to think that it should either be one, or the other. I liked your point that, in the case of "classical" vs. "quantized", the fundamental theory can be neither. I am interested myself in ways in which quantum can emerge from something else. Maybe is both "classical" and "quantized", where the quantum comes from some topological or cohomological properties or something like this. In a different direction, in my present essay, Did God Divide by Zero?, I develop the idea that singularities exist in classical general relativity, but are nicely behaved, and as a bonus they seem to provide a way of regularization for quantum gravity.

Best wishes,

Cristi Stoica

Your essay is interesting and food for thought. Gravitation is not given by a compact Lie group, which makes unitary principles problematic. The holographic principle makes the argument that quantum information is conserved. However, we have no general theory for how quantum information is conserved without unitarity. My essay is an attempt to address this matter. Quantum gravity might in the end be a bit of a misnomer.

In general I agree that gravitation will not be quantized at all in the standard way.

Cheers LC

Lawrence and Sabine. The force/energy of inertia and gravity has to be equivalent and balanced in order for there to be fundamental quantum gravity. (Light is known to be quantum mechanical in nature.) A smaller space must be made larger, and a larger space (on balance) must be made smaller. All relevant opposites must be balanced, included, and combined. Completeness and balance are essential in physics (and theory/ideas). Balanced and equivalent attraction and repulsion is a must too.

Also, please see the additional information in my prior/above post in this matter.

Have either of you given any thought to the ideas of feeling, touch, AND vision as they can converge (fundamentally/basically) in relation to BOTH gravity and electromagnetism? Would this not fundamentally, meaningfully, and significantly tell us more about space, force, and energy (as seen, felt, and touched) taken together? We do need to begin with basics.

True/real quantum gravity demonstrates F=ma fundamentally and fundamentally includes instantaneity as well. Inertia and gravity must be balanced and equivalent. There is no getting around this. You have to demonstrate fundamentally stabilized distance in/of space.

My essay, soon to be posted, represents a major and fundamental breakthrough in waking AND dream physics (including gravity) FUNDAMENTALLY. I would appreciate your ratings and comments on this too. Thanks.

Bee,

As usual, you display a marvelous facility for clearly reducing a problem to its essentials. Delightful reading.

I have to point out, though "If Planck's constant is a field ..." your proposal for unification is unambiguously classical. We've always known that if Planck's constant were zero, that we live in a classical world. So if " ... quantum corrections which would normally diverge ... cleanly go to zero ..." spacetime geometry (actually, topology) is enough and we don't need quantization at all, for a fundamentally unifying theory.

I do hope you get a chance to visit my essay site.

Best,

Tom

Hello Bee,

Congratulations on a wonderful essay. I could not agree more with your position on which I quote:

"This mismatch between the quantum field theories of the standard model and classical general relativity is more than an aesthetic problem: It signifies a severe shortcoming of our understanding of nature. This shortcoming has drawn a lot of attention because its resolution it is an opportunity to completely overhaul our understanding of space, time and matter."

Perhaps the complete overhaul might require backing away from general relativity in favor of a single mathematical foundation that cleanly integrates the fundamental forces of Gravitation and Electrodynamics, with directive qualities on just what the remainder of things must look like. The quantum side of nature might reveal itself in a different guise within the very same structure.

There is a nascent concept that does just this. It is the subject matter of my essay The Algebra of Everything. I show in this essay the relativistic characteristics of Electrodynamics are not unique to a 4D split-signature Minkowski space-time, but also within an Octonion Algebra governed 8-space. The increase in dimensions allows Electrodynamics to be only a subset of the presentation, as it must to be unified with something else. You might consider the move to Octonion Algebra as flatting out the second rank tensors employed, and instead of having only their symmetric and anti-symmetric structures, the full structure of Octonion Algebra is in play.

I would love for you to take a look and comment, for I value your opinion.

Regards,

Rick

Dear Sabine

I found very intriguing your idea of theories that are neither quantum nor classical.

However I have a concern regarding the your proposal.

I remember from my time as a student some old discussions about the issue of constancy of $h$. At that time we were talking about a proposal made by mi advisor.

The paper was E. Fischbach, G.L Greene, and R.J. Hughes, "New test of QM: Is Planck's constant unique ?", Phys. Rev. Lett. 66, 256 (1991))

One issue I recall from that discussion was the argument indicating that, as all one can measure in physics are dimessional ratios, the issue of the

variation of dimensional constants was not well defined. This is contrast with variations that could be casted in terms of variations of dimensionless ratios ( i.e. the variation of the Plank-time could be expressed as a variation of the ratio $t_{Pl}/ t_{cesium}$).

In other words, it only made sense to say some constants do vary if one specified exactly how the quantities that are used define the units we employ are supposed to behave under such change.

Consider that we take a cesium atom oscillations to define the unit of time, and define the unit of length by setting the sped of light in vacuum to be $c=1$. Furthermore imagine we define the unit of energy so that $h=1$ and use Eintein's $E=mC^2$ relation to define the unit of mass.

In that case, to say that $h$ varies would be simply meaningless.

Of course one could talk about potentially observable effects ( say a variation of the energy levels of an hydrogen atom) in terms of dimensionless constants or dimensionless ratios ( i.e. variations of $e$ or of $m_{electron}/M_{proton}$). Note however that the self consistency of the proposal would require that when we consider the Cesium atom (and in particular the transition used to define de unit of time) that the changes one is considering would lead to no modification of its frequency.

Best regards Daniel

I still don't know what you mean with "quantized masses in accordance with QM."

Hi Harlan,

Operators can have continuous spectra. Best,

B.

Hi Tom,

Thanks for the kind words. My proposal is not fundamentally classical, the quantization condition is always present. You're right, we might not need quantization for a fundamentally unifying theory. But we clearly need quantization, or something very much like it, to reproduce the world that we see. I'll check out your essay. Best,

B.

Hi Daniel,

Thanks for your interest. I did address this point in my paper, and also in two comments above. It is true of course that Planck's constant is dimensionful and one should not speak of it varying. Note however that I have another constant of the same dimension, which is the low-energy vev \hbar_0. You can divide the field by that constant and be left with a dimensionless quantity. Think of ASG: Strictly speaking it doesn't make sense to speak of the variation of the Planck mass either for the same reason, it's dimensionful. It does make sense however to speak of the ratio between the low energy and the high energy coupling. It's the same here. Best,

Sabine