Friday, August 14, 2020
The Beautiful Destruction of the Graviton
ABSTRACT:
In his paper titled "Aberration and the Speed of Gravity," S. Carlip argues that gravity propagates at light speed, and, its "action at a distance" and the lack of observed aberration is canceled by velocity dependent interactions. However, the underlying assumption of his thesis is that gravity is caused by gravitational radiation propagating at light speed. Another assumption held by much of the physics community is the quantization of gravitational waves will lead to a spin-2 massless particle known as the graviton. In this paper, I show why gravitational waves and gravitons are not the root cause of gravity. Gravity emerges from an entangled relationship between spacetime and matter.
Modern physics has two conflicting ideas: 1. gravity propagates at light speed, and 2. the equivalence principle. Why are these two ideas in conflict? The first proposes that gravity works in the following manner: a person holds a pen in his hand and drops it. Before it hits the floor, however, the floor must emit gravitons that propagate at c to create a field of gravity, so the pen can receive the gravitational information; otherwise, the pen won't fall.
The second idea is often set forth using a thought experiment where the person holding the pen is in a spaceship. The thrust of the engines cause the floor to accelerate toward the pen when the pen is dropped; otherwise, the pen would float freely in space and never make contact with the floor. In this scenario, no gravitons or gravitational field are needed. The floor is on a collision course with the pen and does not need to send a signal to the pen to let it know it's coming. According to Einstein, this is indistinguishable from gravity. Therefore, this great idea and the one that precedes it create a paradox: the first idea implies a force is causing the pen to fall, so a force-carrying particle is necessary. The second idea implies there is no force.
That begs the question: does gravity require gravitons? Let's examine what may be a source of gravitons and strong evidence that gravity's velocity is c: gravitational waves. Equation 2 below is a gravitational-wave equation:
From equation 2 we derive equation 3 which emphasizes that c is a component of rest-mass energy and not propagation speed.
Does gravity exist if there are no gravitational waves? To find out, we take angular frequency to zero. The time (t') it takes for no waves to propagate a distance r is also zero. The final result is equation 5:
Where there are no gravitational waves there is zero angular frequency and zero strain measured at distance r, but on the left side of equation 5 we see Newtonian gravity is not zero. Thus, the magnitude of gravitational acceleration does not depend on the magnitude of gravitational waves nor their quanta. Further, a zero time delay (t') implies action at a distance.
A comparison between electric waves and gravitational waves reveals why photons are observable and gravitons are not. The wave equation i below represents an electric field (photons) propagating at c. Equations ii through iv demonstrate how the removal of the electric field (photons) leads to no electromagnetic force:
By contrast, if the gravitational field (gravitons) is removed, Newtonian gravity still exists:
What's been shown so far is not surprising when you consider problems surrounding the hypothetical graviton:
1. Since electromagnetic force is around 1037 times greater than gravity, one might imagine a graviton with 1037 times the Compton wavelength of an electron. The graviton's wavelength would span much of the known universe! Not exactly quantum scale.
2. Or, one could imagine one graviton (with the same Compton wavelength as an electron and same speed as a photon) per 1037 photons. If it takes 1037 photons one second to interact with X number of atoms, the graviton would take 1037 seconds to interact with X number of atoms--many orders of magnitude longer than the age of the universe! Further, each graviton interaction would have the same strength as a photon interaction or electromagnetic force.
3. One expects gravitons to spread out to form a field. It is not clear how the gravitons of a black hole can escape each other (if they have a light-speed limit) and not clump together due to mutual attraction (caused by their spin, angular momentum, mass-energy equivalence, etc.).
4. Gravitational wave wavelengths are inconsistent with hypothetical graviton wavelengths.
5. There's a renormalization problem.
6. The graviton has never been observed.
Assuming gravitons are not the root cause of gravity, what exactly is? If we begin with the spacetime metric (equation 6), we can derive equations 9 and 10 below:
Imagine, for the sake of argument, there is a graviton propagating at velocity c. Equation 9 shows if the graviton's energy (E) changes, the spacetime must also change instantaneously; otherwise the constant c would have a different value during the time it takes the graviton to emit another graviton which then transports information to surrounding spacetime. In other words, if the speed of gravity is limited to c, there would be a time lag where c is no longer c! The same holds for Planck's reduced constant at equation 10. The very constants physics relies on would fail to be constant if gravity is required to propagate an information-carrying particle no faster than c.
A careful examination of equation 9 reveals the graviton's energy, when divided by Planck's constant, has the same dimension as frequency, and the spacetime has the same dimension as wavelength. Frequency and wavelength have an entangled relationship. If you measure the value of one, you instantaneously know the value of the other.
In the case of our graviton, a change in its energy instantaneously updates its surrounding spacetime. Our graviton does not need to emit a graviton--and neither does any particle, planet, star, or black hole.
Thus, if the graviton is ever discovered, it is not the root cause of gravity. Gravity is the result of an entangled relationship between matter and spacetime. Matter has a certain energy and moves in certain ways because of a certain configuration of spacetime, and spacetime has a certain configuration because matter has a certain energy and moves in certain ways. Like frequency and wavelength, one does not exist without the other. This new hypothesis is consistent with "action at a distance" observations but inconsistent with the highly contraversial Jovian deflection experiment (see endnote 22).
Acknowledgements:
Amber Strunk. Education and Outreach Lead. LIGO Hanford Observatory.
References:
1. Parikh, Wilczek, Zahariade. 2020. The Noise of Gravitons. arxiv.org.
2. Feynman, R.P. 07/03/1963. Quantum Theory of Gravitation. Acta Physica Polonica. Vol. XXIV.
4. Carlip, S. 12/1999. Aberration and the Speed of Gravity. arxiv.org.
5. Van Raamsdonk, M. 05/17/2010. Building up spacetime with quantum entanglement. arxiv.org.
7. Gravitational Wave. Wikipedia.
8. de Rham, C., Tolley, A.J. 03/17/2020. Speed of Gravity. arxiv.org.
9. Carroll, S.M. 12/1997. Lecture Notes on General Relativity. Enrico Fermi Institute.
14. Nix, E. 08/22/2018. Who Determined the Speed of Light. History.com.
15. Speed of Gravity. Wikipedia.
16. Tests of General Relativity. Wikipedia.
17. Decross, M. et al. Gravitational Waves. Brilliant.com.
18. Lawden, D.F. 1982. Introduction to Tensor Calculus, Relativity and Cosmology. Dover Publications, Inc.
19. Stefanovich, E. V. 09/16/2018. A relativistic quantum theory of gravity. arxiv.org.
20. Light-time correction. Wikipedia.
21. Liénard–Wiechert potential Wikipedia.
23. Faber, J. A. 11/24/2018. The Speed of Gravity Has Not Been Measured From Time Delays. arxiv.org.
24. Yin Zhu. 08/18/2011. Measurement of the Speed of Gravity. arxiv.org.
The matter weighed by its relatively short-range (light-hours and below) gravitational dynamics, fails to properly account for its own gravitational dynamics at galaxy cluster scale (later confirmed at galaxy scale, hundreds of light-years and above). Ever since Fritz Zwicky found that out 87 years ago, - a lot of smart people were looking for an explanation. The choice is between tweaking the law and tweaking the initial conditions (generally speaking, one can also do both). The mainstream explanation, dark matter, chooses to keep the law (Newtonian gravity) and tweak the initial conditions (distribution of mass, most of it implied and undetectable).
ReplyDeleteIt seems possible that it is, instead, Newtonian gravity law that is an approximation, - perfectly suitable at solar system scale yet increasingly inaccurate (requiring a more general law) beyond that. What would a generalization like that look like? Could it be, for example, that Newtonian gravity represents an attractive force partially screened, at short distances, by repulsion - repulsion that decays somehow at longer distances?
At that stage, I slapped my forehead and went searching for publications about anti-gravitons and galaxy rotation curves. Almost immediately, a paper popped up (see the link at the bottom of this message) that explored the idea in 2014.
The Wong paper postulates (among many other things) Yukawa potentials to graviton (attractive) and anti-graviton (repulsive) fields. In exchange, they do away with the assumption that there is any conveniently distributed invisible matter. Several of the paper's postulates appear to be a big stretch, and derivations are somewhat wobbly, - as you can no doubt see better than I can. Nevertheless, the fit with experimental data is rather good with just two more-or-less free parameters. Of course, fitting smooth data with two parameters is relatively easy - but incomparably harder than it is for dark matter models with their inexhaustible supply of free parameters (invisible mass distribution).
I think the Wong model might be developed into a more consistent/rigorous one by replacing the assumptions of the Wong paper with a different set of assumptions about behavior of gravitons and anti-gravitons. I personally, and perhaps naively, gravitate towards the idea of anti-gravitons decaying (on the galaxy scale) faster than gravitons, while also differing from gravitons in either the emission rate or the cross-section of their interaction with regular matter (or both).
A model like this might combine dark matter and dark energy into one repulsive force field. Maybe more importantly, it may lead to reconsideration of interpretations of observational data (including the data that has suggested dark matter and dark energy in the first place). Much more importantly, it will lead to falsifiable (read scientific) predictions regarding currently available observational data.
I am nowhere near qualified to develop a model like this in necessary detail. I wonder if you 1) see an undertaking like this as worthy, and 2) know somebody who might be willing and able to handle it.
https://www.researchgate.net/publication/280835039_Discovery_of_the_antigraviton_verified_by_the_rotation_curve_of_NGC_6503
Everything is Elliptical. 🙏 Thank you for sharing
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