## Tuesday, December 10, 2013

### Some Physics Conjectures Related To Gravitons And Mass

Observations

* If gravity is indeed conveyed via a graviton particle, we know that it does not couple merely to mass, because gravity bends light.  It must, instead, couple to mass-energy (with an E=mc^2 interaction).

It follows from the existence of Black Holes, however, that gravitons must not couple to other gravitons, just as photons don't couple to photons (this also seems to theoretically grossly disfavor massive graviton theories).  But, this is odd.

Photons couple to electric charge and lack electric charge themselves.  Gravitons couple to mass-energy.  Yet, surely if gravity is transmitted via bosons, they must have energy which is seemingly one of the things that they couple to.  The definition of energy is the capacity to apply force to move things, which gravitons, if the exist, can surely do.

FWIW, I'm not terribly clear on whether gravitational energy self-gravitates in GR itself.  If it doesn't it isn't clear to me how matter-energy conservation is not violated, however.  Discussions of this issues can be found here and here with seemingly with a contradictory conclusion here.  More discussion here (gravity self-gravitates but does not generate gravity the way that other matter-energy does in the equations).

* Both quantum gravity transmitted by gravitons and ordinary classical GR gravity, propogate at the speed of light, not instantaneously.  So, the gravitational interactions of two objects can be decomposed into two parts.  The generation of a gravitational pull from a source object that has an impact at its destination (both proportionate to mass-energy apparently), and the destination object's pull in the other direction.  This is sometimes called a distinction between active and passive gravity.  For objects in motion the source object and the destination object gravitational impacts on each other are at a time-gap to each other.

* The coupling of gravitons to mass-energy, if they exist, is also odd because it does not always couple with the same strength to a particle of a particular type.  The coupling of a photon to an electron or W boson is always identical.  The coupling of a photon to an up type quark is always identical.  The coupling of a photon to a down type quark is always identical.  The strong force coupling of a gluon of one of the eight types of gluons to any of the six flavors of quark with a particular color charge is always identical.  The coupling of a W boson or Z boson to a fermion is always a function of that kind of fermion's weak force charge.

* The Higgs boson coupling constants are such that the "sum of the square of each of the fundamental boson masses, plus the sum of the square of each of the fundamental fermion masses, equals the square of the Higgs vacuum expectation value to a precision of 0.012%."

In other words, the sum of the Yukawa's giving the proper definition of the Higgs boson self-coupling, equals one (empirically true, but not theoretically required by the Standard Model), i.e. 2λ +g2/4+(g2+g'2)/4+sum over all fermions(yf/2)= 1, where λ, g, g′ and yf being, respectively, the eﬀective and renormalized scalar (i.e. Higgs self-coupling), gauge (i.e. W and Z boson couplings) and Yukawa couplings of the twelve Standard Model fermions to the Higgs boson.

But, while the Higgs boson coupling to a fundamental particle, i.e. it's "Higgs charge", also called its Yukawa,  does not come in integer or simple integer ratio units the way that electric charge, weak force charge, and strong force color charge do, the Yukawa does not.

* The electromagnetic coupling constant, the weak force coupling constant, the strong force coupling constant and the Higgs field properties, as well as the masses of the fundamental particles, all "run" with the energy level of the interaction.  The mass of a quark in a low energy interaction is not the same as the mass of that same quark in a high energy interaction.  But, while masses and bosonic coupling constants do run, electric charge, weak force charge, color charge do not (see e.g. here).

Still, any given kind of particle at any given energy scale, always has a particular mass.  Indeed, particle mass is indifferent to (1) whether a particle is ordinary matter or antimatter (something that flips the electric charge of a particle to the opposite charge), (2) it is indifferent to its parity (which impacts its weak force charge), and (3) it is indifferent to the color of a quark (all charm quarks, for example, have the same mass at a given energy level, without regard to whether it has red, blue or green strong force color charge).

This is not true in the case of gravitons.  For example, in general relativity, an electron travelling at 0.1 times the speed of light and an electron travelling at 0.5 times the speed of light give rise to different gravitational effects because they have differing amounts of kinetic energy, and the direction of the gravitational pull is not a function just of the location of the electron, as it would be in the case of Newtonian gravity who gravitons would be spin-0 bosons transmitting a scalar gravitational field, but also of the direction in which the electron is traveling.  The fact that a particle's vector momentum, vector angular momentum, and vector photon flux, as well as its scalar rest-mass and other elements all contribute to gravitational pulls in general relativity is why a general relativity graviton would have to be a spin-2 boson giving rise to a tensor field, rather than the spin-0 boson of a Newtonian gravity or the spin-1 vector bosons of electromagnetism, the weak force and the strong force.

Note that the cosmological constant of GR can be conceptualized as a scalar field, however, possibly with its own spin-0 boson.

* This particularly problematic because the absolute among of energy of a matter-energy field is not a well defined universal quantity even for a particular matter-energy field.  Kinetic energy is a function of velocity which is a function of the reference frame of the person describing it.  So is potential energy in a variety of fields.  Discussion of the arguable non-gravitation of potential energy is found here.  General relativity copes with this problem by being formulated mathematically in a background independent way that essentially dependents on the differences in energy between two points in the GR field, neatly cancelling out differences in intermediate quantities like absolute energy level that don't produce physical observables.

But, it isn't obvious to me how gravitons acting in isolation can do the same, although I suppose it can base its properties on it in reference to its source, and it in reference to its destination, using itself as an intermediate reference frame.

Maybe the Beta function running of particle masses and coupling constants with energy level solves some of these issues in the Standard Model, but it is my understanding that beta functions derive from the renormalization proceedure, and not from general relativity.

Still, a graviton, at a minimum, is engaged in a far more sophisticated interaction than any other force carrying boson.  The other force carrying bosons need only respond to one universal property of a particle.  The graviton must measure what we would ordinarily consider to be multiple properties of a particle at once as it interacts with it, some of which must be measured in a way that is relative to the graviton's source.  No other particle in the Standard Model has properties that depend upon the source of the particle in this way - the particle itself has a tiny number of individual properties that fully characterize it regardless of its source (apart from quantum entanglement).

What a GR graviton delivers is not merely a pull in a particular direction.  It can deliver elaborate twisting and turning.

* One way that a Higgs boson is often conceptualized is as something that gives rise to the inertial mass of fundamental particles.  But, in principle, at least, it seems as if the inertial mass of a fundamental particle due to its Higgs field interaction may differ from the gravitational mass of that same fundamental particle which derived from both the mass and the energy of the particle, seemingly violating the principle of equivalence (although perhaps equivalence merely means that the inertial mass component of a particle's mass-energy is identical to the gravitational mass component of a particle's mass-energy disregarding the energy component of  particle's mass-energy).

Presumably, the running of fundamental particle energies with energy scale also impacts the gravitational mass of those particles, although it isn't obvious to me how mass-energy conservation is maintained in this context.

* Particles that don't have weak or electric charge (i.e. photons and gluons) don't have rest mass, empirically, in the Standard Model.

* The mass of a composite particle, like a proton, is not simply the sum of the fundamental particles that make it up.  Those only make up about 1% of the total mass.  The other 99% of the mass comes from the energy of the strong force gluon fields between the quarks in the composite particle, although the amount of the composite particle mass isn't entirely independent of the mass of the fundamental particles that go into it in a non-linear way.  I've heard authoritative sources (maybe at the Of Particular Significance blog) state that even in the absence of fundamental particle mass, a proton would have mass, although it would be much less than it is in reality, which means that not all of the mass of composite particles is derivative in some way of the Higgs field interactions of the constituent fundamental particles.

* If particles in the Standard Model are truly point-like, they would be singularities in GR.  But, they only need to be smeared over a sub-Planck length distance by some means to escape this fate.  This is one basic issue that we would expect any quantum gravity theory to solve.

* The black hole firewall debate illustrates the deep problems involved in trying to mix classical GR and the quantum SM.

* Would hypothetical gravitons differ in energy like photons do via particle frequency (equivalent to particle wavelength), or do they have identical energy?  Arguing that they do see, e.g., here and here (with a caveat since energy is not localizable in GR) and here.

Analysis

The point of the observations is to reach some personal speculative conclusions and conjectures about quantum gravity.

1.  The transmission of gravity via a graviton if gravity reduced to general relativity in the classical limit, then the properties of a graviton and its interactions seem much more complex and non-straightforward in their fit to a particle model than the other Standard Model interactions.  This tends to disfavor particle oriented theories of quantum gravity (a la SUGRA and supersymmetry) over quantum gravity formulations that reside in an emergent space-time fabric (e.g. Loop Quantum Gravity) rather than a particle.

2.  The process by which fundamental particles are endowed with inertial mass via the Higgs field is not equivalent to or identical with gravitational mass.  There are gravitational mass-energies which do not have their source in the Higgs field (e.g. photons, gluon fields, kinetic energy) and the Higgs field does not generate everything that contributes to even a fundamental particle's gravitational impact.  This also suggests a need for stronger experimental tests of the equivalence of inertial and gravitational mass in systems in which Higgs field generated inertial mass is not overwhelmingly predominant.

3.  Is it sensible to imagine a fundamental particle (e.g. a sterile neutrino) that acquires inertial mass via the Higgs field, but lacks other Standard Model interactions?  There is certainty room, even given the precision of the fundamental particle Yukawa measurements and the conjecture the the sum of all Yukawa's equals one, for this to be the case for a keV mass particle, for example.  But, this doesn't fit well with a notion that the Higgs boson may in some sense be a combination of the four electroweak bosons as its mass and other properties seem to suggest (suggesting that each of the boson interactions contribute to its field and that particles that interact with none of the fields shouldn't interact with the Higgs field either, something that is otherwise true).

Note on Wiggle Room in GR Confirmation

Some of the nuances on what non-mass energy quantities are properly included in General Relativity calculations aren't very well confirmed experimentally relative to other experimentally well confirmed predictions of GR.  In many circumstances in astronomy observations, energy contributions are so modest relative to mass contributions that they can be effectively disregarded, and gravitational energy contributions, for example, would be too tiny to observe for the most part.

Maju said...

And what if gravitons simply don't exist. I know that they are needed for the SM to extend its reach and become a ToE (of sorts, space-time would still be unexplained) but so far the only theory of gravity that works is not "materialist", i.e. it is totally unrelated to quantum mechanics - but it does work well anyhow.

I feel that quantum mechanics obviate the fundamental problem of space-time, taking it as a given, and that is an intrinsical limit to its potential scope, even in the unlikely case that gravitons would happen to be real and not just, as I strongly suspect, a hopeless myth.

Shouldn't we try instead to explain QM from the fundamentals of space-time relativity? After all a quantum and a photon are nearly impossible to distinguish, so what if photons/quanta are just conformations of space-time?, for example. I bet there are some interesting theories from this PoV, although I, in my relative ignorance, am not privy to them. Anonymous said...

Andrew,
Once again, I commend you on trying to find order within the existing Standard Model, rather then inventing new dimensions or new classes of particles.

I agree with the first comment and the gist of the post.

I think that it's best to assume that there is no graviton until one is found experimentally. The problem of self-coupling and blackholes begs the question of how the graviton could get out of the blackholes, and as such it's better to think of gravity as the bending of space-time.

In addition, there are other reasons to think that there's a graviton.

To be specific, right now, we have 12 fundamental (i.e. spin 1) bosons (photon, Z, W-, W+, and the 8 gluons.) We also have 12 fermions (3 classes of 4 fundamental fermions: up quark, down quark, electron,and e-neutrino.)
This counting ignores anti-particles...and may be only rough. It also doesn't include the well established spin 0 Higgs boson (which is the only fundamental particle of spin not equal to 1/2 or 1.)

But with that having been said, it's interesting that there are so far 12 spin 1 and 12 spin 1/2 particles. (A total of 24.) 24 is the number of symmetry operations of the Permutation group of order 4, S(4). The sub-groups of this group have order: 1,2,2,4,4,4,8,3,6, and 12.
This group has conjugacy classes of order 1,3,8, 6,6.

As such, my 'educated, but not expert' guess is that the photon corresponds to the class of size 1, the 3 weak bosons correspond to the class of size 3, the 8 gluons correspond to the class of size 8, the 6 quarks correspond to one class of size 6, and the 6 leptons correspond to the other class of size 6.
The reason to suspect a S(4) symmetry group of nature is that there are four forces and 4 dimensions of space-time.
Where does this leave the Higgs Boson, the graviton, dark matter, and dark energy?
Not really sure, but I suspect that there isn't a graviton, that the Higgs field is what causes the weak force to separate from the photon and become time irreversible...and hence for time to separate from space (even though space-time dimensions would all be the same if there weren't a Higgs field...and it's associated Higgs boson)
As for dark matter, I think that the best guess is that it's either a heavy neutrino or the anti-particle (i.e. sterile form) of a neutrino. (As you have stated many times on your blog.)
And as for dark energy, my guess is that it's just the expansive of space-time due to an increase in space-time when there's an increase in the number of particles...i.e. the weak-nuclear force assymetrically causes heavier mass particles to decay into more and lighter particles. Which would mean that the weak-nuclear force couples with space-time...i.e. that the gravitational force causes bending of space-time and the weak-nuclear force causes the expansion of space-time.
It's like saying: we live in a 3+1D universe that would be 4-D symmetric if it weren't for the Higgs field.
This is obviously just speculation and it can't explain a lot, but it seems more grounded than most speculation nowadays (i.e. supersymmetry.)
These thoughts are scattered through the physics-related posts of my blog over the last ~3 years. I'm working on putting it together into a single post.

Let me know your thoughts on anything discussed above. Anonymous said...

I found a typo in my previous comment. The third line should read:
"In addition, there are other reasons to think that there is no graviton."
The "no" was missing.

andrew said...

@Maju

We need a quantum theory of gravity of some kind because there are inconsistencies between the Standard Model and General Relativity (mostly in areas where our ability to observe phenomena with the necessary accuracy is absent). Realistically, both are a little bit wrong in areas that don't matter too much.

But, quantum gravity doesn't have to have a graviton (which string theory is famous for suggesting), although it is a very logical extrapolation of the SM and GR (which supposes that gravity propogates in waves moving at the speed of light).

The alternatives focus either on breaking up into discrete chunks the fabric of space-time itself (loop quantum gravity aka LQG and kindred theories), or in describing how the world works a distances so small that conventional understandings of separations of time or space as so "out of focus" that they no longer work.

In some LQG-like theories, matter itself is simply an excited and scrunched up piece of space-time rather than something in space-time.

LQG is the newcomer to the party and making great progress, but it has not yet been determined if the program can really be carried out to its logical conclusion without running into some sort of contradiction either theoretically or compared to the universe.

andrew said...

@ Eddie.

I doubt that we will ever have directly detection of an individual graviton even if they do exist. The core issue is whether someone can come up with a quantum gravity theory that otherwise works - if that theory has a graviton then they probably exist even if we don't detect them directly until much later or never directly detect them (in the tradition of the neutrino and Higgs boson which were predicted long before they were directly observed). I don't think that enough work has been done to kick the tires of a graviton model in detail yet, however. A fatal flaw could certainly be discovered, and if one isn't found the target particle at least would be very well defined just like the Higgs boson. The graviton is the hypothetical particle most likely to exist IMHO (also to be clear, LQG and gravitons are not necessarily inconsistent although they are strictly emergent and not put in by hand in LQG-family models where they are present).

Ultimately, I don't find the numerology considerations you offer to be very persuasive, even though they are interesting to consider.

Importantly, we already know that we are missing something really important - a fundamental force or modification to a fundamental force or a new non-SM particle or some combination thereof, because we need to explain dark matter phenomena. This argues strongly against the proposition that the particles and three fundamental forces of the SM are a complete set.

On the other hand, I don't think that SUSY/SUGRA or string theory will be the Theory of Everything in the end, even if the TOE that may be ultimately discovered may borrow some elements from it (e.g. I discussed in a previous post the idea that a keV mass gravitino with spin-3/2 might exist as a dark matter particle even though no other SUSY particles do).

My current flavor of the weak is graviweak unification models, but there are a variety of viable proposals out there.

Maju said...

What you say about LQG (loop quantum gravity, right?) sounds very interesting, Andrew. I have to get a basic grasp of the theory however.

andrew said...

A typical formulation of loop quantum gravity (kindred theories are also called e.g., causal dynamic triangulations or spin-foams), assumes that space-time is made up of vertexes (aka nodes) in a network each connected via three or four links to other nodes, that the four dimensional version of space-time in which locality is a concept that makes sense is emergent from this network because on average nodes are approximately local, and that gravity and inertia are a function of all of the possible paths in the network between node A and node B in the network calculated in a manner similar to the path integrals used in the Standard Model.

In the real world, some of the important consequences of this are the existence of a minimum unit of length (from one node to a connected node), would provide a physical justification for some of the mathematical tools used (non-rigorously) in the Standard Model, and an absence of true singularities (i.e. infinities) in the theory. Hence, e.g., the event horizon of a black hole wouldn't be absolutely inescapable and the Big Bang would be replaced by a Big Bounce.

andrew said...

Footnote: the point-particle singularity of the Standard Model isn't too serious. For a particle of Planck length radius to form a GR singularity would require a mass of about 10^19 GeV. The heaviest SM fundamental point-like particle, weighs 173 GeV more or less.

The radius necessary for a top quark (or even a top quark-antitop quark pair) to form a GR singularity is many orders of magnitude less than the Planck length. And, the Heisenberg uncertainty principle may "smear" this mass over a volume at least as great as a Planck length sphere.

andrew said...

A black hole of electron mass would have a radius of 1.5*10^-57 meters, far smaller than the Planck length. If particles are in any sense wave-like excitations (perhaps of space-time itself) rather than pure points, this makes all sorts of sense.