I must admit that spin 2 gravitons make no concrete sense to me as fundamental particles because they seem to be composed of more fundamental sub-components.
I can imagine fundamental concepts for spin 1/2 and spin 1 because it is difficult to break them up into smaller components.
When a volume gets trapped in a film or surface, it must spin around twice to conserve angular momentum.
A photon may be a swirling volume while an electron is a spinning surface, like a spinning bubble, and when they have the same amount of angular momentum, the bubble (fermion, electron) will spin around twice as fast as the volume (boson, photon).
In more intuitive terms, when a spinning bubble pops, the remaining volume will be spinning around at half the rate of the bubble.
Whatever a spin 2 particle is must be something that completes the geometric sequence:
Higgs nothingness (spin 0) ->
electron bubble (spin 1/2) ->
photon volume (spin 1) ->
graviton tesseract or toroid (spin 2)
and this something is a volume with a hole in the middle.
It would have to spin around only by a quarter as much as a cube-shaped bubble would have to spin around to return to the original state.
In less abstract terms, a spin 2 particle is sort of like a donut. It is a volume with a hole in the middle.
Do these things actually exist in nature at the fundamental scale, or are people just trying to use them to show off or to paper over things they don’t understand? When gravitons are translated from the language of spin into the language of dimensions, one certainly gets that impression. For example, the spin 2 graviton can be thought of as something that exists in a fifth dimension, but what does that really mean?
An apple sitting on a table and doing nothing exists in four dimensions; X, Y, and Z stay constant, but T ticks away. If you pick up the apple and throw it, the four dimensions, X, Y, Z, and T all change at the same time, however, one could also say that when the apple was thrown, it entered the 5th dimension because it now possesses energy. The five dimensions of the apple are X, Y, Z, T, and E.
If you are a promoter of a fashionable theory of gravitons like loop quantum gravity or spinfoam, you might say that the apple on the table exists in five dimensions, even when you don’t throw it, simply because the apple possesses the property of mass and mass is the fifth dimension in their theory. But since mass is equivalent to energy times a constant, this isn’t a major divergence from the simple example in the first paragraph. The energy of the fifth dimension refers to the stuff that is moving within the apple and/or the motion of the apple relative to you.
Saying “five dimensions” over and over like a magic incantation which opens the door to enlightenment is a parlor trick which physicists use in order to make themselves look more mysterious, interesting, and powerful than they really are. All that saying “the apple exists in five dimensions” really does is provide a trumped-up, short-hand way of saying – the apple or the stuff inside of it is moving.
I know that spin 2 particles have been used to win a Nobel Prize for explaining the quantum Hall effect in terms of a theorem about bubble geometry, but they didn’t come out and relate that collective effect to gravity. I wonder why.
I think I will go ahead and do that.
A deformed bubble interacts with its own oscillation in a predictable fashion described by the Berry phase, as long as the motion is not in a non-linear regime. The deformations act like a drag that warps the surrounding space, giving rise to electric and magnetic fields.
If one thinks of the initial, driving oscillation that deforms the bubble as the cause of its ability to gravitationally attract other bubbles, then, since the Berry phase shift results from this oscillation, this is a way to mathematically describe how electromagnetism and gravity are linked.
A driving, gravitational oscillation with spin 2 gives rise to drag around a bubble surface with spin 1 which causes an electromagnetic oscillation of a volume with spin 1/2.
Doesn’t this mean that a graviton is merely a combination or conflation of a photon and an electron?…. and isn’t this similar to how a photon or an electron is a conflation of a particle and a wave?
If so, a graviton is a composite object that is not truly fundamental. It is a collective effect and misdefined as being a fundamental particle. It may represent the photon-like energy radiated by bubbles oscillating in synch and at the same time be a description of the energy exchanged between a vibrating volume and a bubble composed of smaller bubbles. They are two sides of the same coin.
I don’t like the post-war trend of conflating abstract concepts and then conflating the conflations. I know that it is just a (contorted) way to express a recursive system, but I think we should get rid of this opaque, modern definition of a graviton and restore it to its clearer pre-war definition in terms of the Laplacian and precession.
… stop here if you don’t want to run into the limits of my ability to ramble about this topic ….
The Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. That sounds a bit abstract, but “the divergence of the gradient” could also be written as “the change of a rate of change”, as in, you are swinging back and forth on a swing and someone pushes or pulls on you.
I have to tie math to a physical thing to understand what it means.
“The Laplace operator is named after the French mathematician Pierre-Simon de Laplace (1749–1827), who first applied the operator to the study of celestial mechanics, where the operator gives a constant multiple of the mass density when it is applied to a given gravitational potential. Solutions of the equation Δf = 0, now called Laplace’s equation, are the so-called harmonic functions, and represent the possible gravitational fields in free space.”
Laplace operator – Wikipedia
The Laplacian operator tells you what will happen to the mass density within a given gravitational potential energy well. If the arrows in the operator point out, the mass density decreases and if they point in, the mass density increases. When the oscillating mass density is constant on average, you can predict the gravitational fields at a distance from the distribution as a sum over harmonic functions.
In other words, the mass density responsible for gravity can be described as a localized oscillation. Light can be described as a non-localized oscillation. With gravity, you have localized oscillations that radiate non-localized oscillations which add up harmonically to create the gravitational potential energy well.
“One can consider harmonic functions which transform under irreducible representations of the conformal group or of its subgroups (such as the group of rotations or translations). Proceeding in this fashion, one systematically obtains the solutions of the Laplace equation which arise from separation of variables such as spherical harmonic solutions and Fourier series.”
Potential theory – Wikipedia
In potential theory, you have things like Liouville’s theorem about how the emittance of a distribution never gets smaller and this can be connected to statistical theories like entropy.
The Laplacian, the Lagrangian, and the Hamiltonian formalisms can all be used to describe the same system, but the Hamiltonian is what everyone uses for modern physics because it keeps conjugate variables orthogonal and describes things in terms of momentum, whereas the Laplacian describes things in terms of velocity and mass density. The Laplacian seems like a more fluid description that motivates intuition about gravity very well, but since the Hamiltonian formalism is typically used to describe quantum systems and anything with a relativistic process, the intuition behind the Laplacian has been buried in many sub-fields of physics, even within general relativity. This is ironic because Minkowski space comes from generalizing the Laplacian to non-Euclidean space, but that is probably to be expected since the Laplacian is like a Fourier transform or inversion of Newtonian physics and we don’t have a Fourier transform of general relativity because it doesn’t conserve energy.
In simpler language, Laplace found the mass density from the potential at some point outside of the object while Newton found the potential outside of the object given a certain mass density. Laplace saw that, as in Stokes’ theorem, the gravitational potential outside of the sphere containing the mass is a harmonic function satisfying the Laplace equation —regardless of the distribution of the mass density. It was an inversion of Newton, just like the Fourier transform is an inversion of the time domain into the frequency domain.
For gravity, the Laplacian operator represents the fundamental jiggle of our reference frame which is the same jiggle behind everything from quantum mechanics to the cosmic microwave background radiation. For electricity, it shows how a smoothly changing external field from a light wave gives rise to discrete, concentrated flows of current in matter.
More generally, when you have a Laplacian matrix instead of just a Laplacian operator, you are using smooth, global properties at a distance to calculate the discrete, concentrated, local properties of multiple objects – instead of just one. It is related to the problem of renormalization and the philosophical implications of boundary conditions.
Whereas a photon is a quantized amount of radiation from a bubble-like electric charge that breathes or oscillates within a jiggling volume, the graviton is a quantized amount of radiation from a bubble-like collection of charged particles that breathe or oscillate within a jiggling volume.
Geometrically, they are both defined by a bubble-like surface interacting with a volume and that combination of a spin 1 and a spin 1/2 object is described by a spin 2 object. It is a lot like how a laser works, except it is a laser that is shaped like a sphere that radiates short wavelengths in all directions that add up to create very long wavelengths.
If one thinks of a graviton as a quantized gravitational force mediator which could be incorporated into the standard model in the same way that photons are treated as electrostatic force mediators, then it will necessarily be too small to be detected by any of the methods at our disposal in the near and distant future. Photon detectors are of the scale of electrons and graviton detectors would need to be of the scale of planets.
Instead of holding onto the idea of an unmeasurable particle called a graviton, we could throw this quantum graviton in the trash and reclaim the word by redefining it with a straightforward analogy from gravitoelectromagnetism:
Electrons repel, magnets attract and repel, electromagnetic waves make atoms stable
Mass attracts, gravitons repel and attract, gravitational waves make orbits stable
Gravitational moments are classical descriptions of the change in angular momentum of a nonuniform distribution of mass in a solid object which is under the influence of a gravitational field. They describe the precession of a rotating, revolving object.
One can define a graviton in relation to the gravitational moment in the same way that a magnet is related to the magnetic moment.
In this picture, a magnet is caused by a current of charge and a graviton is caused by a current of mass.
In quantum systems, we can connect the magnetic moment to the angular momentum, a quantity which depends on gravitational moment.
- Electron magnetic moment is the rate of change of angular momentum experienced by an electron in a magnetic field. It is given by the Bohr magneton, a constant derived from the relativistic mechanics of the Dirac equation. The gyromagnetic ratio between the magnetic moment and the angular momentum is twice what one would expect for a classical spherical volume of charge, but it is equal to what one would expect for a classical spherical surface of charge.
By making an analogy with planetary systems, one might interpret the square root of the gravitational constant divided by the speed of light as a sort of conversion factor between the gyromagnetic ratios of bubble-like surfaces and volumes.
It has been known for a long time, particularly from the work of Schuster, Sutherland and H. A. Wilson, though lately little regarded, that the magnetic moment P and the angular momentum U of the earth and sun are nearly proportional, and that the constant of proportionality is nearly the square root of the gravitational constant G divided by the velocity of light c. We can write, in fact, where p is a constant of the order of unity.
https://www.nature.com/nature/journal/v159/n4046/pdf/159658a0.pdf
Back in the 1940s, scientists like Patrick Blackett believed that there was a relationship between angular momentum and magnetic moment in an extension of Maxwell’s laws to gravitation.
But later in his career, after witnessing the horror of the world wars and the atomic bomb, he concluded based on experiments with magnetometers that there was no relationship. He subsequently won a Nobel Prize for his work on the cosmic rays from outer space which are akin to the particles emitted from an atomic bomb blast.
I think that Blackett didn’t get enough statistics in his experiments and that he was on the right track early in his career with the simple equation relating angular momentum and magnetic moment.
The idea that there is a simple analogy (gravitoelectromagnetism) to be made for Maxwell’s equations and gravity just went out of fashion and I’m trying to figure out why. I think it was caused by a switch from Cartesian space to Riemannian space. In short, I blame Einstein and relativity, but I think that post-war politics and million dollar Nobel Prizes played a role as well.
It is widely believed that Blackett did a laboratory test which ruled out this equation. However, his experimental paper described a static test in which a 15 kg gold cylinder was placed at rest and presumed to pick up an induced current (producing a small, but measurable magnetic field) from the rotation of the earth.
[the author, S P Sirag goes on to describe measurements in astronomy which support the equation and suggests that the measurement be re-done with SQUID magnetometers]
Gravitation and Cosmology: From the Hubble Radius to the Planck Scale
This book was written in 2003 and it costs 200 EUR!!!
Honestly, 15 kg of gold back in the 1970s sounds like a good way to embezzle some serious scientific funding.
Some people are still researching how planetary mass and magnetic moment are correlated and it might lend some support to bringing back Blackett’s moment – if only as an expectation value in a quantum system.
Kirsten Hacker 