Gravity Can Be Neither Classical nor Quantized by Sabine Hossenfelder

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

Unfortunately, Dr. Laurent Nottale and Dr. Jin He quantized gravity many years ago:

Quantum Gravity Based on Mach Principle and Its Solar Application

http://vixra.org/abs/1101.0076

Einstein Field Equation: the Root of All Evil? Quantum Gravity, Solar Application

http://arxiv.org/abs/astro-ph/0604084

I see.

Never mind.

I'm wondering if there would also be effects at low energies. If you consider some amplitude of a process written as a path integral then you now divide the Lagrangian L by hbar inside the space-time integral over the fields, as hbar is now a dynamical field. Then, even though you have some potential for h that effectively contrains it to the standard value, if you consider some process with a very small amplitude (like some rare decay process), it seems to me that there could be significant contributions to this via fluctuations in the h-field. The penalty against this due to the the h-potential may then be outweighed by the L/h part making a larger contribution.

Sabine,

Do you consider the electrostatic force exerted between two electrons to be quantized, classical or neither? The reason for asking this question is that I am going to make the argument that there is also a gravitational force between the two electrons and this gravitational force is closely related to the electrostatic force. In other words, my proposal is the gravitational force must be classified the same way as the electromagnetic force. To support this contention I offer my essay available here. This essay offers previously unknown equations showing that these two forces are closely related. This close relationship becomes obvious when the forces between fundamental particles are expressed using the wave properties of the particles and referencing Planck force. Furthermore, these equations were predicted by a wave-based analysis of both particles and forces. In this analysis all quantized processes ultimately result from the transfer of a quantized unit of angular momentum.

Dear Sabine

Thanks for your reply. I am afraid however that I might not have made my point 100%

clear, as I do not think that these points were really covered in the previous discussions.

The issue is what is the meaning (or to be more precise the operational significance ) of a varying value of $h$?

Say we chose to base our units of time and energy one some particular aspects of atomic physics. In that case, were $h$ to change form one space-time point to another the meaning of our units would change from one space-time point to another.

Say we define a the ``second" as the N times the oscillation period connected with a certain atomic transition. Then it is clear that

if $h$ ware to change from one space-time point to another point that particular atomic transition would be modified and the meaning of what we call one ``second" would be modified as well.

Consider a simpler situation where we limit ourselves to space and time.

(Example 1) Say, again, that we define the units of time and of length in terms of the wavelength and frequency of a certain photon

( say the photon emitted in the 2P-1S transition of hydrogen as seen in the rest frame of said atom). What would be the meaning of saying the speed of light changes from space point to another?. If we measure such speed using that particular photon, it seems that, by definition, the seeped measured in those units can not change.

Another example of the difficulties I see is the following:

( Example 2) Consider a proposal where we say that the until of length changes with length. Imagine we say that a meter is only a meter for the first 150 meters but is only half a meter after that. Well one can make that meaningful by saying: Take a collection of sticks placed at the origin, and make sure each one of the sticks when placed there coincides with the unit meter we take from that place in France. Then in measuring a distance to the origin, the first 150 sticks would count as one meter, and every stick after that would count as 1/2 meter.

To make the proposal feel defined, one would have to indicate the point playing the role of the origin from where one starts counting. O.k.

but at what point is the proposal a meta definition and at what point would one be saying something about the nature of the world?

These are issues that seems inescapable when contemplating such proposals. In particular the notion of variation of $h$ with energy seems delicate in the manner similar to that of Example 2.

Therefore my point is that a proposal such as yours would need to be made much more precise in order to make it clearly meaningful.

I am not saying it is impossible, but that taking care of issues like those is, in my view, essential.

Best regards Daniel

Dear Saibal

I think you are overlooking my main point:

Suppose we do as you say and choose units $\hbar =1$ and there a is a new filed $\psi$,

Now Suppose I want to measure that filed

at a certain point.What do I do?

Suppose for instance that I conclude that such modified value of the filed would modify the energy levels of an Hydrogen atom. Now suppose I want to measure that! The point is that I need something to compare with. Perhaps the energy level of a different atom. But how can I be sure that what I use that as a comparison has not change in the same fashion. In other words my w question is What is the experiment that I need to do in order to say unambiguously if $\psi$ has changed or not!

Furthermore you say this filed that replaces $\bar h$, which presumably controls the commutation relations between a particle's position and its conjugate momentum,

has a certain vev at low energies and different vev (0) at high energies. But the issue is: energies of what? of the particle involved? If so in which frame should that energy be evaluated?

Moreover could I use a high energy particle to localize beyond the uncertainty provided by the low energy vev of $\psi$ the sit ion and momentum of a low energy particle?

Would that not contradict the low energy uncertainty relationship?

Hi Bee,

Yes, I agree that we need " ... something very much like ..." quantization to explain the observed world. I am reminded that Einstein (The Meaning of Relativity, Appendix II) allowed that a more complex field theory than general relativity may be explained by " ... (increasing) the number of dimensions of the continuum. In this case, one must explain why the continuum is *apparently* restricted to four dimensions."

In the same respect, the idea of Planck's constant as a field has to explain why action is apparently quantized.

Best,

Tom

Dear Ms. Sabine

I do not agree with Your ideas. The key for rejection is hidden in Duff's idea that constants h, c, and G does not exist physically. It is only possible that masses of particles increases, but You did not mentioned this possibility.

Problems with singularities can be solved on different way. Brukner, Zeilinger, Feynman, and other claim, that finite information is hidden inside of finite volume. So also singularities do not exist.

But your article is useful as thought experiment as why G, h, and c do not exist. So variation of h does not influence on variation of G.

Regards, Janko Kokosar

My essay

p.s.

I found some grammar mistakes: "violate unitary", "tought experiment", "gravitty". I hope that you will return this favour. :)

Hi Sabine,

It's long bothered me as to how many insist that gravity needs to be quantilized to have it consistent with the standard model, since it's apparent neither vision of reality represent being the final word on matters. With that said it's also undeniable that within their relative domains each stand as very successful theories which lend a great deal of insight into the workings of the physical world respective of their predictive power and conceptual imagery.

However it's always puzzled me that when we are talking about the very beginning of things, that is to enter terra incognita, there be reason for either conceptualization of things as thought needing to be particularly relevant. So I find your essay to resonate with this concern of mine, as it gives no special significance to either; that is other than as to ponder as to how each of these characteristics of our world has emerged as a consequence of conditions not needing to be governed by the mandates of either.

Regards,

Phil

Sabine

"a severe shortcoming of our understanding of nature... ...resolution it is an opportunity to completely overhaul our understanding of space, time and matter."

Beautifully and clearly written, and I very much agree, but wonder if you've overhauled understanding enough, and nothing has emerged with anything of the clarity of your writing.

I hope you may be able to read my own essay, which steps back a few more paces for greater overview and finds a pattern which does match observation, leading to a conceptual ontological construction. It has no singularities or evaporation, but Lagrangian points and recycling, via a mechanism not violating uncertainty. The model also redefines black holes as equivalent to AGN's. (elucidated in other papers).

I fear it's to unfamiliar for mainstream to recognise, but hope that, as you seem to understand the problem, you may recognise a solution. The model has kinetic logic foundations, and you need to understand each of a set of components to build the consistent model.

But anyway, your essay is worth a good score, even, or perhaps because, it clearly makes and deals with a limited point, rather the opposite of my own.

Best wishes and good luck

Peter

Dear Sabine,

I suppose that at the atomic level of matter there is acting strong gravitation . Then we can quantize the equations of Lorentz-invariant theory of gravitation in the same way as Maxwell equations. At last strong gravitation may be used for modeling of strong interaction. What do you think about it?

Sergey Fedosin

Sabine,

You are a world-renowned expert in energy-dependent but observer-independent (yes we all believe in relativity, relativity, relativity) speed of light and I thought the problem of variation/costancy of the speed of light in a gravitational field might be relevant here. Other Einsteinians treat the problem in a contradictory way: some say the speed of light varies like the speed of cannonballs, others say it does not vary at all, and the most illuminated quote general relativity where it is shown that light falls with twice the acceleration of cannonballs:

http://www.speed-light.info/speed_of_light_variable.htm

"Einstein wrote this paper in 1911 in German. (...) ...you will find in section 3 of that paper Einstein's derivation of the variable speed of light in a gravitational potential, eqn (3). The result is: c'=c0(1+phi/c^2) where phi is the gravitational potential relative to the point where the speed of light co is measured. (...) You can find a more sophisticated derivation later by Einstein (1955) from the full theory of general relativity in the weak field approximation. (...) Namely the 1955 approximation shows a variation in km/sec twice as much as first predicted in 1911."

http://www.mathpages.com/rr/s6-01/6-01.htm

"Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential phi would be c(1+phi/c^2), where c is the nominal speed of light in the absence of gravity. In geometrical units we define c=1, so Einstein's 1911 formula can be written simply as c'=1+phi. However, this formula for the speed of light (not to mention this whole approach to gravity) turned out to be incorrect, as Einstein realized during the years leading up to 1915 and the completion of the general theory. (...) ...we have c_r =1+2phi, which corresponds to Einstein's 1911 equation, except that we have a factor of 2 instead of 1 on the potential term."

http://arxiv.org/pdf/gr-qc/9909014v1.pdf

Steve Carlip: "It is well known that the deflection of light is twice that predicted by Newtonian theory; in this sense, at least, light falls with twice the acceleration of ordinary "slow" matter."

Pentcho Valev

Dear Sabine,

I find this essay to resonate for me it's long bothered me as to how many insist that gravity must be quantilized to have it consistent with the standard model, as it's apparent neither vision of reality represents being the final word on matters. With that said, as you've pointed out, it's also undeniable that within their relevant domains they each present as very successful theories, which lend a great deal of insight into the workings of the physical world respective of their predictive power and conceptual imagery. However it's always puzzled me that when we are talking about the very beginning of things, that is to enter terra incognita, there be any reason to be convinced that either conceptualization of things as thought needing to be particularly relevant. So I find your essay to resonate with this long held concern of mine, as it giving no special significance to either, that is other than to ponder how each of these characteristics of our world has emerged as a consequence of conditions not necessarily needing to be governed by the mandates of either, but rather serve as having the fundamental aspects with would allow for both.

"In relativity, movement is continuous, causally determinate and well defined, while in quantum mechanics it is discontinuous, not causally determinate and not well defined. Each theory is committed to its own notions of essentially static and fragmentary modes of existence (relativity to that of separate events, connectable by signals, and quantum mechanics to a well-defined quantum state). One thus sees that a new kind of theory is needed which drops these basic commitments and at most recovers some essential features of the older theories as abstract forms derived from a deeper reality in which what prevails in unbroken wholeness."

-David Bohm, "Wholeness and the Implicate Order", Introduction p-xviii

Regards,

Phil

Bee,

Thanks for the comment! I never discussed the representation as being an operator in the comment. If you chose to make that connection yourself that is fine, but you're projecting your own thoughts into the meaning of these things, which is fine too, but it does lead to a lot of miscommunication.

All you have to do is go look at how h is defined and used in the quantum mechanics versus quantum mechanics.

If classical mechanics is arrived at when we reduce h, what does that mean? First of all this is already well known (page 19 of A. Zee QFT), so we shouldn't confuse that continuous spectrum emerge in classical limits against the effect of dividing through by a constant.

If we seriously look at h as it is to describe a single entity it does in fact describe wave like properties in terms of expected position and momentum. However, the only way we can reduce h in the classical realm is through process related to mutual information, defined as:

[math](\rho^{ab}) = S(\rho^{a}) S(\rho^{b}) - S(\rho^{ab})[/math]

Which is understood in terms of relative entropy as:

[math](\rho^{ab}) = S(\rho^{ab}|| \rho^{a} \otimes \rho^{b})[/math]

As the wikipedia article on quantum mutual information states:

"if we assume the two variables x and y to be uncorrelated, mutual information is the discrepancy in uncertainty resulting from this (possibly erroneous) assumption."

It is easy to assume that when we are talking about classical variables, such as position and momentum, uncertainty does not scale with the number of systems, so as more and more systems are added, mutual information increases, so the uncertainty in larger systems decreases and the system becomes more classical...e.g. the classical world emerges as we scale up with more systems.

I might even be tempted to declare it a law, but that would be an easy way out.

In any case, this is sufficient to begin discussions about how the objective world of Einstein is a world dependent all the component density matrices, and the world as we know it is an emergent property in the limit of vanishing uncertainty.

This is also best explained by understanding the relationship of Wigner's function and the Moyal equation to Liouville's equation (http://en.wikipedia.org/wiki/Density_matrix#.22Quantum_Liouville.22.2C_Moyal.27s_equation)

As mutual information increases with the number of systems, the uncertainty decreases, this would appear as a decrease of the uncertainty (represented with h) in the equivalent classical phase space. So the classical world eventually starts to emerge in the limit of large systems.

This is probably closer to the concept you are trying to articulate in the article.