Can Gravity Be Quantized? by Vesselin Petkov

George Ellis

typo: string analogies

[deleted]

Vesselin,

This is a great essay and I enjoyed reading it. I fully agree with your central thesis that the gravitational field cannot be quantized because there is no field as such but rather a global curvature effect related to the mass distribution on geodesics. However, I do have one question regarding the non existence of gravitational energy. I understand that there is no energy associated with a gravitational field because there is no such field. However, there is an energy (given by mc^2) associated with geodesic motion and the rest mass which could be seen as a consequence of Mach's principle stemming from the gravitational (curvature)effects of the universe. Might one not call this gravitational energy?

Paul O'Hara

Vesselin Petkov

Thank you, Paul. The mass of a particle whose worldline is geodesic is inertial - for example, a falling particle (its worldline is geodesic) moves by inertia and when prevented from doing so (say when it hits the ground) it resists the change in its inertial motion; the measure of that resistance is precisely its inertial mass. Traditionally (before GR), that mass had been called passive gravitational mass since it is the coefficient of proportionality between what had been called the gravitational force or the weight of the particle (in GR that force is inertial) and the gravitational acceleration.

Mach essentially claimed that inertial mass was gravitational, whereas GR showed that it is the opposite - the passive gravitational mass and the gravitational force acting on a particle at rest on the Earth's surface (i.e. the particle's weight) are inertial. In this way GR gave a natural explanation of the equivalence of inertial and gravitational masses and forces.

That is why it is not surprising that in 1954 Einstein wrote to a colleague: "As a matter of fact, one should no longer speak of Mach's principle at all" (A. Pais, Subtle Is the Lord: The Science and the Life of Albert Einstein (Oxford University Press, Oxford 2005) p. 288).

In fact, Mach's relativism should have been immediately abandoned in 1907-1908 after Minkowski's four-dimensional formulation of special relativity where he provided rigorous criteria for inertial and accelerated motion - a particle moving by inertia is represented by a straight timelike worldline, whereas the worldline of an accelerating particle is curved. Minkowski wrote at the beginning of Section III of his paper "Space and Time:" "Especially the concept of acceleration acquires a sharply prominent

character." Indeed, acceleration is absolute in special relativity (and in GR as well) since it reflects an absolute geometric property of the worldline of an accelerating particle - its curvature (or rather its deformation) - in full agreement with the absolute (i.e. experimental) fact that a particle resists its acceleration; therefore the absoluteness of acceleration does not imply that a particle accelerates with respect to some absolute space.

In such a way Minkowski's spacetime representation of special relativity unequivocally supported Newton's view of absolute acceleration and disproved Mach's arguments that acceleration, like velocity, is also relative. Mach argued that one could not say whether or not a single particle in the Universe accelerates. By contrast, that situation in spacetime is crystal clear - the worldline of a single particle in the Universe is either straight or deformed, which means that the particle is either moving by inertia or is accelerating.

Best wishes and good luck in the contest,

Vesselin

[deleted]

Vesselin,

I have read your essay again and I still do not find the conclusive proof that you claim. You state numerous different ways that a falling particle moves without resistance. Another variation is that a falling accelerometer reads zero acceleration. The alternative explanation that you never address is that a falling particle experiences no net force because it achieves equilibrium between two opposing forces. Suppose an electron is prevented from following a geodesic because it is held stationary relative to the Earth by a tailored electric field gradient. An electrostatic force opposes what is commonly called a gravitational force. Now the electric field is turned off. Does the gravitational force on the electron immediately disappear also? The alternative that you never discuss is that the gravitational force continues but the electron is accelerating compared to the local CMB rest frame. If the electron possesses intrinsic inertia, then the 9.8 m/s2 acceleration generates an opposing inertial force. Equilibrium is achieved and the electron experiences no net force even though the gravitational force continues.

The reason that I am so convinced of this alternative is that I have actually derived gravity, inertia, etc. from simple starting assumptions. From this perspective your arguments appear to originate with a widely held but erroneous physical interpretation of general relativity equations. My derivation has generated previously unknown equations relating the gravitational force to the electromagnetic force. The limitations of this blog do not allow me to duplicate these equations, but they are available here. In particular compare equations 6 and 7. These equations show an important relationship between these forces that originated as a prediction from my derivation. I claim that they imply that gravity is a real force. However, that also is a physical interpretation of equations and subject to alternative interpretations.

Vesselin Petkov

John,

"The alternative explanation that you never address is that a falling particle experiences no net force because it achieves equilibrium between two opposing forces."

This is incorrect for two reasons:

1. Unfortunately, this is a common misconception. Take as an example a particle at rest on a table (explained by Newton's gravitational theory). There is no net force on the particle - the gravitational force (the particle's weight) is balanced by the normal reaction coming from the table. The whole point is the very force (the particle's weight) with which the particle acts on the table - the particle resists its state of rest. So the balancing of forces does not mean that the particle does not resist its state of being prevented from falling; on the contrary - the very existence of the balancing force (the normal reaction) proves the existence of the force with which the particle presses the table.

Another example is the same particle accelerated by a force. By Newton's second law the application of the force is only needed to overcome the resistance the particle offers to its acceleration. So the active force is balanced by the inertial (resistance) force; this dynamic equilibrium is called the principle of d'Alembert (in many textbooks it is not mentioned at all since it appears simpler to talk only about active forces => if the sum of such forces is different from zero, there is acceleration).

2. Both special and general relativity showed that only four-dimensional (4D) quantities represent real properties of the world. The 4D (curved-spacetime) acceleration of a falling particle is zero, which means that no force is causing the fall of the particle. When the particle is on the table its 4D (curved-spacetime) acceleration is different from zero (the table acts on the particle by preventing it from falling) and the particle resists its change in its inertial motion. That is why the weight is an inertial force in general relativity. The observed apparent acceleration of the falling particle is not real (i.e. not caused by a force) since it is caused by the spacetime curvature. Please note - all this is not just playing with mathematics as looking at the whole picture presented by general relativity (theory experiment) proves.

When I read your paper I will be first interested in what testable predictions it makes.

All the best,

Vesselin

Vesselin Petkov

"You have not offered any experimental proof that gives a conclusive yes or no answer to whether gravity is a force"

John, please analyze (or see the explanation in the essay) the single experimental fact - falling particles move non-resistantly. That is the proof that no gravitational force is bringing them down.

And this is only the most spectacular piece of experimental evidence that gravity is not a force. All experiments that confirmed different predictions of general relativity also proved its core - that there is no gravitational force. That is why this is an established scientific fact and science never goes backwards.

All the best.

Vesselin Petkov

Thank you, Michael. Now I will be able (finally) to start reading the essays I have downloaded so far, including yours.

Good luck in the contest.

Vesselin Petkov

I am sorry; I posted it below, but it should be here.

"You have not offered any experimental proof that gives a conclusive yes or no answer to whether gravity is a force"

John, please analyze (or see the explanation in the essay) the single experimental fact - falling particles move non-resistantly. That is the proof that no gravitational force is bringing them down.

All the best.

Vesselin Petkov

Thank you, Armin. Good luck in your studies and in the contest,

Vesselin

Vesselin Petkov

Thank you, George. I think even if the Weyl tensor were regarded as representing gravity the situation in gravitational physics would remain the same since the Weyl tensor also represents spacetime curvature (like the Riemann tensor).

In the essay I have tried to employ explicitly and with a strong emphasis the Galileo-Einstein research approach - physics comes first (before deciding which formalism suits the proposed physical picture). This approach directly leads to the core of general relativity (GR) - gravitational phenomena are manifestations of the spacetime curvature, but the curvature is not a physical field. In this sense, as the Weyl tensor represents the curvature of spacetime it does not represent a gravitational field. At best the Weyl tensor describes a geometrical field. But such a field does not possess energy.

I believe all who maintain that there is gravitational energy in GR should address the two contradictory assumptions which have been coexisting peacefully in GR for about twenty years:

1. The geodesic hypothesis (confirmed by the experimental fact that falling particles move non-resistantly, i.e. by inertia) - a particle, whose worldline is a timelike geodesic, is a free particle moving by inertia.

2. The neutron stars in a binary pulsar system, say the famous system PSR 1913+16 discovered by Hulse and Taylor in 1974, emit gravitational energy despite that they move by inertia (that is, without any loss of energy!) since their worldlines are geodesic (the neutron stars were "modelled dynamically as a pair of orbiting point masses" by Hulse and Taylor).

Best wishes and good luck in the contest,

Vesselin

Vesselin Petkov

The above post was posted incorrectly here; now it is posted after:

John Alan Macken replied on Aug. 24, 2012 @ 18:42 GMT

[deleted]

Dear Vesselin Petkov,

I understand that this was addressed to John Macken. But you keep repeating this kind of argument:

"John, please analyze (or see the explanation in the essay) the single experimental fact - falling particles move non-resistantly. That is the proof that no gravitational force is bringing them down.

You have not made your case. I understand also that you consider your case so obvious that you feel no obligation to discuss this with me. However, you cannot take an error that leads to a theory and then use that theory to prove the error.

General relativity predictions follow from that theory, just as any professional theory would do, by mimicing mathematically the patterns observed in empirical evidence. The properties interpreted to be responsible for those patterns can be false and yet the equations, even with false names and artificial units, will fit the patterns for which they were designed to fit.

The reason why there is no deformation of an object in free-fall is because there is evenly applied acceleration to all parts of it simultaneously. Those parts do not move their positions relative to one another. There is no cause for feeling or observing what you refer to as resisting accleration.

James Putnam

[deleted]

A superb essay. Extremely simple to follow, and full of information. High rating.

[deleted]

"The reason why there is no deformation of an object in free-fall is because there is evenly applied acceleration to all parts of it simultaneously."

James, this is *absolutely* falsified by experiment. Why do you not understand the lack of horizontal acceleration in the Galilean model that was explained in detail? Extended to Newtonian mechanics and then to relativity, we do not find *any* force of acceleration compelling a mass -- no matter what trajectory it follows. Spacetime geometry is necessary and sufficient.

Tom

[deleted]

Vesselin,

Yuri Rylov

Dear Vesselin Petkov,

I agree with your conclusion that the gravitation should not be quantized. However, your arguments are insufficiently fundamental. You deal with apical consideration, although the contest is devoted to fundamental problems.

Actually your conclusion follows from fundamental changes in approach to geometry and to the relativity principles. There is a conceptual mistake in transition from nonrelativistic particle dynamics to the relativistic one. At this transition nonrelativistic dynamic equations were substituted by the relativistic ones, whereas the description of the particle state remains to be nonrelativistic. The nonrelativistic description of the particle state is available for description of deterministic relativistic particles, but it is not available for statistical description of nondeterministic particles. In the nonrelativistic case the state of a statistical ensemble is described as a function of a point in the phase space, whereas in the relativistic case it is described as a 4-vector in the space-time [1,2]. As a result at the consequent relativistic approach the quantum mechanics may be obtained as statistical description of random motion of a relativistic particle. At nonrelativistic description of particle state one cannot obtain quantum mechanics as a result of statistical description. One was forced to postulate quantum principles and introduce new quantum essences.

Explaining quantum mechanics as a statistical description of nondeterministic particles, a question on the indeterminacy reason arises. (This question does not arise at axiomatic introduction of quantum mechanics). To answer this question, one is forced introduce discrete space-time geometry, where the free particle motion appears to be stochastic. Statistical description of such a stochastic motion leads to Schroedinger equation provided the quantum constant is proportional to the squared elementary length of the discrete geometry [3]. Thus, the quantum effects appear to be geometrical effects. The particle world line is now a broken line (world chain). The length of its link is proportional to the particle mass. The particle mass is now a geometrical characteristic of the particle. We come to geometrization of physics in microcosm. In such a situation, when quantum quantities are not fundamental essences, it is useless to quantize gravitational field, because it is only a property of the space-time geometry.

We see that a use of relativistic particle state changes cardinally approach to physical phenomena in microcosm. We do not use any hypotheses. We only transit correctly from nonrelativistical dynamics to relativistic one. This admits one to resolve freely such problems as existence of tachyons and dark matter. For instance, fermions appear to be tachyons having helical world line with timelike axis. Dark matter is explained freely as a tachyon gas. See my essay http://fqxi.org/community/forum/topic/1367

Of course, it looks as a focus, because modern theorists are used to deal with apical conception which does not concern fundament of physics (in particular, relativistic concept of particle state). They do not believe that one can solve most problems of microcosm physics and cosmology without introduction exotic hypotheses.

Discrete space-time geometry [4] is a second change of fundamental physics.. Such properties of a discrete space-time geometry as additional geometric parameter (elementary length, connected with quantum constant) and stochastic motion of free particles were not known. We did not know, if the space-time geometry is continuous or discrete in microcosm. We can only observe appearance of geometrical properties in the particle dynamics.

In the discrete space-time geometry the particle state is described by its skeleton ((n+1) points) [5]. n(n+1)/2 distances between skeleton points contain all information on the particle (mass, charge, spin, etc.) It is more natural and simpler, than to invent particle characteristics taken from exotic symmetries.

References:

[1] Yu.A. Rylov, Quantum Mechanics as a theory of relativistic Brownian motion. Ann. Phys. (Leipzig). 27, 1-11, (1971)

[2] Yu.A. Rylov, Uniform formalism for description of dynamic, quantum and stochastic systems. e-print /physics/0603237v6.

[3] Yu.A. Rylov , Non-Riemannian model of the space-time responsible for quantum effects. Journ. Math. Phys. 32(8), 2092-2098, (1991).

[4] Yu.A. Rylov, Geometry without topology as a new conception of geometry. Int. Jour. Mat. & Mat. Sci. 30, iss. 12, 733-760, (2002), (e-print /math.MG/0103002 ).

[5] Yu. A. Rylov, Discrete space-time geometry and skeleton conception of particle dynamics IJTP, 51, 1847-1865,(2012), http://arXiv.org/abs/1110.3399v1

With my best wishes

Yuri Rylov

[deleted]

Vesselin,

In the above post to me you talk about a particle at rest on a table having no net force. The table's electric field gradient extends only a few Angstroms above the surface. An accelerometer on a table registers acceleration because only a few electrons at the bottom of the accelerometer are interacting with the table. If there was some way of exerting an opposing force on every particle that makes up the accelerometer, then the accelerometer would register zero acceleration even though it is in the earth's gravity. The analogy is that a free falling body can register zero acceleration and still have two opposing forces exerted on every particle.

Your argument is essentially the following: Curved spacetime is absolutely equivalent to acceleration. If a person agrees with this statement, then your essay eloquently makes the point that gravity is not an interaction and searching for quantum gravity is a waste of time. However, you admit that the mechanism for producing curved spacetime is not understood. I claim that there is a long list of points relating to the gravitational force that are not understood. For example, the properties of spacetime itself are not understood. My quantum mechanical model of spacetime incorporates impedance (Zs = c3/G), a frequency dependent bulk modulus, elasticity, a large energy density of vacuum energy, an unusual type of pressure, etc. The point is that a more nuanced understanding of spacetime and particles has resulted in the derivation of gravity without making any analogy to acceleration. In fact, one conclusion is that curved spacetime is not equivalent to acceleration. My essay contains previously unknown equations that support this conclusion.

Thomas Ray

"The alternative explanation that you never address is that a falling particle experiences no net force because it achieves equilibrium between two opposing forces."

John, if this were true, Galilean relativity would be falsified, let alone Newtonian mechanics and Einstein relativity.

Missing in your equations is a dynamical spacetime. By imlicitly quantizing spacetime to an absolute length 1, you assume counterfactually that quantum mechanical unitarity is a universal initial condition. This is the very flaw that Vesselin discovered in *every* particle-based model of fundamental physics.

Petkov's case is not one of interacting particles; it is one of free particles interacting with spacetime curvature. I have expressed this in a more radical way (in venues other than my current essay) by making the point that it is not possible in principle to experimentally differentiate a conscious agent acting with free will, from a bound agent following a prescribed trajectory.

In fact, IIRC, Einstein in a reflective mood at his Princeton Institute office was said to have wondered if the Canada geese migrating past his window were following an invisible path through Earth's magnetic field. (I've lived in New Jersey on that same migratory route, so I appreciate the beauty of the spectacle.) Considering Einstein's own early work on Brownian motion, would he have also wondered if the state preparation of those pollen grains might determine their subsequent motion -- I'd like to think so, especially considering his work in the physics of river meanders (cf. contemporary research in the connections between fractal geometry and physics) and Einstein's lifelong quest to know "His thoughts."

Point is, we can get particle physics from classical physics, assuming no more than initial condition and continuous functions. Though it remains to be seen whether these assumptions are self-similar to the cosmological initial condition (which a positive result to Joy Christian's proposed experiment would prove), it seems to me more than reasonable that the classical models of Christian, Ellis, Petkov and others are more in line with how Nature works at a fundamental level -- because they don't depend on getting, or assuming, the continuum from an a priori assumption of primordial matter. Space and time are sufficient. Complex interactions follow dynamically.

Back to Galilean relativity -- it should be simple enough to see that bodies falling freely at the same rate from the same initial condition yet in different trajectories, are subject to no acceleration horizontal to the plane of reference; we cannot separate the physics of time from that of space, which means that neither time nor space are independent in their physical properties; i.e. not physically real. Therefore, one cannot set the universal initial condition at length 1, t = T, and get physical dynamics, without a number of ad hoc assumptions.

Tom

[deleted]

Gravity is much different than other forces. It is also claimed by You that

gravity is not a force. I agree that when comparing it with other forces, it is

necessary to be constantly aware that it is different. It is necessary

to analyze this distinction and to publish it, what is done by You

[1, 2].

''Gravity as not a force'' is an unexplained phenomenon, similarly ignored as

''unexplained physical causes for consciousness''.

I also claim that gravitational force does not exist (in some

sense). But I claim that gravity should be quantized, where virtual

gravitons do not exist. I also claim that space-time is emergent. This

is published in [3], in comments and resume is published in Vixra [4] and in references therein.

I suggest also that You comment articles of Baez [5] and Curiel [6], if it is

possible to add something. I suggest also thesis of Hadley [7], because

it has similar ideas as You. He also refuses gravitational

radiation, similarly as You. After reading of Baez, I still ever do not understand precisely enough, what is in Gravity that is different as energy?

But, there are examples how ''gravity is not a force'' is incorrectly understood by people. For instance, when a photon flies close to the Sun it changes its direction. But it also gives its changed momentum to the Sun. But some people claim that the photon only moves by geodesic curve and it does not give any momentum to the sun.

It is not precisely clear to me, why do you refuse gravitational

radiation - either because of energy loss or because of possibility to

define gravitons?

What is possibility that tidal friction could explain pulsar PSR 1913+16.

Namely, tidal friction cannot give only one possible result, but

gravitational radiation gives only one possible result.

References:

[1] Petkov, V. (2012) Can Gravity Be Quantized?, http://fqxi.org/community/forum/topic/1371.

[2] Petkov, V. (2011) Continuous and Discrete Aspects of Nature, http://fqxi.org/community/forum/topic/909.

[3] Kokosar, J. (2012) Postulates and Prejudices in Fundamental Physics, http://fqxi.org/community/forum/topic/1418.

[4] Kokosar, J. (2012) Principles for quantization of gravitation,

http://vixra.org/abs/1209.0005.

[5] Weiss, M & Baez, J. (2011) Is Energy Conserved in General Relativity?, http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html.

[6] Curiel, E. (2009) On Tensorial Concomitants and the Non-Existence of a

Gravitational Stress-Energy Tensor, http://arxiv.org/abs/0908.3322.

[7] Hadley, M. J. (1997) A Gravitational theory of Quantum Mechanics, Doctor thesis, University of Warwick,

http://www2.warwick.ac.uk/fac/sci/physics/staff/academic/mhadley/papers/thesis/thesis.pdf.Attachment #1: QG_resume.pdf

[deleted]

Appendix:

It is known that there are problems of interaction between of classical and quantum fields, for instance Sabine Hossenfelder:

"All quantum fields carry energy so they all need to couple to the gravitational field, but we do not know a consistent way to couple a quantum field to a classical field. 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. While Mattingly has argued [3] that Hannah and Eppley's thought experiment can not be carried out in our universe, that does not address the problem of consistency"

http://fqxi.org/community/forum/topic/1477

Do You have any comment for this problem?

My suggestion, as I wrote, is that quantum interactions (virtual gravitons) are not necessary, but the principle of uncertainty (UP) is necessary. I claims that UP is more basic than wave functions and virtual photons. (This problem of interactions between classical and quantum fields is an example, how UP is important.)

Best regards,

Janko Kokosar

p.s. Can You suggest any essays in this forum, which are connected with your ideas or that You esspecialy agree with them?

Vesselin Petkov

Thank you for your comments, Janko. I was able to start reading properly the essays here hardly this week (as indicated above); so I can't recommend any essays.

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