Gravity Can Be Neither Classical nor Quantized by Sabine Hossenfelder

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

Daniel,

You are making things way too complicated here by mixing the freedom to choose a unit system with the actual physics. While I can't speak for Sabine here, let me suggest to you may favorite way of dealing with these sorts of problems.

First switch to natural units c = hbar = G = 1. This defines unambiguously a consistent unit system, so no problems with that here. Unlike in, say, the SI units system you don't have any freedoms to express time, masses etc. relative to some arbitrary scales, so you now don't have compensating constants like c, hbar and G that compensate for such freedoms.

Then where hbar were to appear if you wanted it to put back, you put in your equations written in these natural units, a field phi. Also, where G would appear you put a factor phi. Since you are still working within the same natural unit system, all issues regarding measurments etc. are unambiguously defined.

In Sabine's theory, phi gets a vacuum expectation value of 1 at low energies, and at high energies the expectation value tends to zero.

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.

typo...

[math](\rho^{ab})[/math]

should be

[math]I(\rho^{ab})[/math]

Dear Sabine

What is your attitude to fundamental constants and Planck units?

My attitude is special....

See essay 1413

Do yo familiar with Frank Wilczek attitude?

See Wilczek articles

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits388.pdf

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits393.pdf

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits400.pdf

Is trinity sacred?

Sabine wrote: "Concretely, consider that Planck's constant ¯h is a field whose value at high energies goes to zero.

In four space-time dimensions, Newton's constant is G = ¯hc/m2

Pl, so if we keep mass units fix, G will go to zero together with ¯h, thereby decoupling gravity. If gravity decouples, there no reason for singularities to form. If gravity becomes classical, there's no problem with the perturbative expansion. So this possibility seems intriguing, if somewhat vague. I will now make this idea more concrete and then explain how it addresses the previously listed problems with quantizing gravity."

Sabine, i reminding you about Wilczek doubt concerning Planck units:

"An appealing feature of atomic and strong units, in contrast to Planck

units, is that the characteristic length, time, and mass can be constructed

without taking square roots. It is disconcerting to imagine that we must extract roots in order to express the basic units in terms of fundamental

parameters. (Sophisticates will recognize that extracting roots is a

nonanalytic procedure, in the technical sense.) The fact that G, \, c can be expressed in terms of mp, \, c without extracting roots, but not vice versa, on

the face of it suggests that the strong units are more fundamental than

Planck units. (I find it remarkable that a similar conclusion is suggested

by string theory, where the closed string gravitational coupling naturally

appears as the square of the open-string gauge field coupling"

http://ctpweb.lns.mit.edu/physics_today/phystoday/Abs_limits388.pdf

A most enjoyable essay. I found it delightful reading.

Sometimes we have to step back at take a more general look at things. Here is a more simplistic look (perhaps too simplistic) at the nature of gravity. I have posted it on a couple of essay pages.

Einstein, who, more than anyone else gave us our current view of the nature of gravity, said that gravity is not a force and yet in most of contemporary physics gravity is treated as if it were. It appears that the presently held view of gravity is that it does not pull you into the chair in which you are sitting but rather, because of the curvature of space-time, it pushes you into the chair. This is a bit absurd; Gravity is either a force or it isn't, it simply can't be both.

Einstein used the example of a man jumping from a building. The man would feel no force pushing or pulling him. The only way he would know he is moving is by the motion of the building that seems to be moving up and the friction of the wind. While nobody challenges this it seems to be almost universally ignored. The example of the man falling is a good one but gravity can be proved to not be a force by use of a very simple, basic physical law.

Suppose I hold a ball of a given weight stationary in the air. The understanding of vectors tells us that a force equal to the force I am supplying must be pushing down on the ball. Vector analysis also tells us that a resulting vector will appear in a direction opposite the acute angle formed by the two vectors. The acceleration of the resultant vector, if the forces are constant, is dependent upon the sine of the acute angle formed by the two vectors. In the case of my holding the ball the angle formed by my pushing up and the alleged force of gravity pushing down is 180°. The sine of 180° is zero so the resultant vector is zero. It is important to remember that the force and acceleration of both vectors is still very real.

Newton's second law of motion says that Force is equal to Mass times Acceleration - F=ma. If I hold a ball ten times heavier the force I supply must be ten times stronger as well. In order to the stationary position of the ball I must also increase the downward force ten times. Herein lies the problem.

Acceleration is dependent on force and mass. The only way acceleration can be changed is to alter either the force or the mass. We know that acceleration in a gravitational field is a constant. On the earth it is 32 feet per second squared. If the gravity of the earth is a force and created by the curvature of space-time then this force too must be constant. The only thing that is a variable is the mass however, if we change the mass we change either the force or the acceleration. Thus either heavier objects fall more slowly than lighter objects or the acceleration changes as a result of the change in mass. We know empirically that this cannot be true as both force and acceleration are constant. Therefore gravity cannot be a force.

The ball is now ten times heavier and thus the gravitational field (if indeed that is the correct term) is ten times as strong. The curvature of the space-time created by the ball is greater and so, if gravity is a force, the ball is pulling the earth with a stronger force. Actually the acceleration of the earth toward the ball has increased and so the earth is falling toward the ball at a greater velocity. We can see this in Newton's other formula: F = G(m1m2/r2) While this does not exactly hold in GR it is sufficient for this argument. The increase in the apparent attraction of the earth and the ten pound ball is so small as to be virtually immeasurable.

If gravity is not a force why do we feel our weight when sitting in a chair? Consider a situation where two opposing vectors are both forces, such as two cue sticks pushing on a billiard ball at two points in direct opposition.

The change in the position of the ball is zero and we can state that this is the resultant force of the two primary vectors. We have the mass of the cue ball and the force applied by the cue sticks. This means that there is in both cases an acceleration. An object can have any number of independent motions and in this case the ball is moving in two directly opposite directions but the ball is moving. The second law of motion states that force and mass will produce an acceleration. These two opposing accelerations do not 'cancel each other'. They create a vector with zero acceleration. Perhaps it may be more correct to say that they produce no vector.

Since gravity behaves much like a force, we feel our weight in a chair because we are still falling. Just because the chair stops a change in position does not mean we are not still falling. Our feeling of weight comes from momentum. A falling body has a certain momentum even if it does not actually change its position. It is this momentum we feel when sitting in a chair.

Since gravity is not in any way a force it has none of the properties of a force. It does not propagate. It would only propagate if it were a force. Contemporary physics not only thinks of gravity as a force but appears to think of it as an electromagnetic force. Many, many hours have been spent by really brilliant people trying to reconcile the 'force' of gravity with such forces as magnetism. The mass of an atom does not create the curvature of space-time any more than the nucleus creates the electron. The curvature is an integral part of the atom that was created when the atom was created. It cannot be modified nor removed.

Newton, when he worked out his gravitation theories, was concerned with action at a distance. Even though gravity is ubiquitous through the universe there is no action at a distance because there is no action. Gravity does not do anything, it simply is. It is not one of the elementary forces as it is not a force. There is no need for energy mediating bosons to mediate the force ergo, thus there is no graviton. I seriously doubt that the Large Hadron Collider will find any evidence of a massless, spin-2 boson.

It has been said that if the sun were to suddenly disappear we would not be aware of it for eight and a half minutes. That is true but has nothing to with the curvature of space-time and thus gravity. If the sun were to disappear instantly the curvature would disappear instantly as well. We would not sense this in any way, since the path of earth around the sun is a geodesic nothing would have changed; we would still be traveling in a straight line. Eight and a half minutes later everything would become instantly dark and start to quickly become very cold. That we would certainly sense and then we would know that the sun had disappeared.

The extent of a gravitational field appears to be limitless. It diminishes as described by the inverse square law but never completely disappears. Thus the entire universe is one large structure formed of a myriad of space-time curvatures.

Finally; since gravity is not a force why it is considered along with magnetism, the strong nuclear force and the weak nuclear force to be one of the primary force interactions of physical reality? Gravity is not a force, it is a condition.

If indeed gravity is not a force, are we correct is thinking that gravity functions at the quantum level? Does an elementary particle warp the space-time or is the concept of space even valid at the quantum level. It seems quite possible that gravity at quantum level may be a mathematical concept that would only be valid if gravity is a force.

Wilczek:"we must extract roots",

"can be taken outside the square roots",

"In the strong system of units no square roots

at all appear in [M], [L], [T ]."

http://arxiv.org/abs/0708.4361