The Graviton as Aether

As I get closer to really understanding the theory (that is, knowing all the mathematical detail), I find myself becoming more and more of a string-theory fundamentalist, so I should attempt a response to this.

First, some basic quantum field theory. In quantum field theory, particles and fields are generally regarded as complementary. Particles are energy quanta from field modes, and field states are equivalent to certain superpositions of particle states. Every particle in the Standard Model corresponds to a field, and vice versa. But if you have to pick one description as more fundamental, it's probably the field, since the fundamental variables in the basic equation are field variables.

The classical theory of gravity is general relativity, and it's a field theory, so as a quantum field theory there should be gravitons. But as I just explained, a graviton state is a superposition of field states and vice versa.

The principal reason for the conceptual churn in quantum gravity, at least before string theory, was that quantum general relativity is nonrenormalizable, i.e. you cannot perform calculations with it. Renormalization (in its simplest, original forms) is a procedure for dealing with the divergent (infinite) integrals showing up in "perturbative quantum field theory", which is where the particle states show up. An elementary particle state may be regarded as a certain superposition of states of the noninteracting field. Perturbative approaches to interacting field theory are possible if the interaction is weak enough that the actual dynamics may be regarded as a correction to the free field dynamics. Feynman diagrams are a notation for these corrections which also symbolize some of the space-time processes appearing in the superpositions. But even in perturbative field theory, you still get infinite values for some of these corrections. You will be summing amplitudes over a variety of possible processes, and sometimes these sums just don't converge. Renormalization involves the assumption of fictitious processes whose integrals sum to infinities which cancel out the divergent integrals.

This is one of those concepts which is ubiquitous in popular exposition of physics but which sounds bizarre and which the expositors even describe as bizarre. However, the simplest way to understand the meaning of renormalization is to suppose that the theory you are working with (e.g. quantum electrodynamics) is incomplete, and that the complete theory (the complete set of interactions, which you do not know, and which may include completely unknown fields) is not divergent and undefined. The renormalization procedure is then a way of incorporating this hypothesis that a better theory has no divergences because other interactions cancel the infinities arising from the incomplete theory.

This is a practical process only because, in a renormalizable theory, only a finite number of parameters are required to define the divergence-cancelling "counterterms" at every order of perturbation theory (order corresponds to the complexity of the virtual processes entering into the amplitude sum over histories). When quantum gravity is said to be nonrenormalizable, what is meant is that an infinite number of parameters are needed to construct all the counterterms. In a renormalizable theory, the finite number of parameters are actually set by empirical values like observed mass and charge. But the infinity of parameters for quantum gravity renormalization render it unpredictive.

However, renormalization arose within a particular approach to making QFT calculations - the approximations of perturbation theory. One can instead aim to solve an interacting quantum field theory exactly. Just because perturbation theory breaks down, doesn't mean that the full unapproximated theory is undefined - just that you can't approximate the solution using that method.

So, back to the Standard Model, gravity, and fundamental theory. That gravity is not part of the Standard Model is an arguable proposition. The Standard Model is a codification of what is observed. The Standard Model without gravity consists of various matter fields and various force fields in interaction (and a Higgs field to provide mass; this is a hack and the Higgs has not been seen). All these interactions are renormalizable and so you can calculate with them. But gravity is also observed, of course, and we can write down an equation expressing the idea that the other Standard Model fields interact with a gravitational field as Einstein described it. We just can't do much with it as a quantum field theory, because gravity is nonrenormalizable. The Standard Model including gravity, however, as codified in that equation, really ought to be regarded as our empirically best theory of physics.

Beyond this, there have really been two directions of inquiry. One is unification of everything but gravity in various field theories with large symmetries which are then broken in some way; the other direction of inquiry focuses on quantum gravity, and has seen a great deal of formal invention and philosophical thrashing about, and even one solid result (Hawking radiation). The first path is the one pursued by particle physicists and quantum field theorists, and eventually they constructed unified field theories which did include gravity in a master symmetry; first supergravity, and then finally the string theories. The second path has been pursued by a lot of other people and does not have the methodological unity of the first path. The most substantial criticism of the first-path philosophy from the second path is that quantum field theory generally assumes flat Minkowski space and does not represent many effects from general relativity, such as black holes. However, this criticism has lost a lot of its impact across the years as physicists have learned to apply quantum field theory in curved spacetime backgrounds. There is still the objection that the philosophy of general relativity, in which matter and geometry react to each other, is lost in a philosophy which treats geometry as a classical "background" to quantum fields, but again, I see a slow remediation of this deficiency on the quantum side.

Now to string theory. Mathematically string theory is a work in progress. Tremendous progress has been made, especially when the various string theories of the 1980s were discovered in the 1990s to be intertransformable, but we do not yet know the fundamental variables of the unified string theory, in the way that the undamental variables of quantum field theory are the field degrees of freedom.

It is clear that string theory can produce something qualitatively like the Standard Model - though intriguingly, no-one has yet found a string "vacuum" which has exactly all the qualitative features of the Standard Model (dimensionality, number of generations, particular symmetries and so forth). The problem is that string theory can also describe a large number of other physical outcomes. It depends on what you do with all those dimensions. Until the previous decade (2000s) the mainstream of string research was always hoping that one geometric configuration would end up preferred, with everything else dynamically unstable, and that this would finally produce a falsifiable prediction. However, the anthropic approach crept into string theory in recent years, producing controversy. It seems clear that the answer to the question of string theory's ground-state geometry - is there just one, or are there many, and is the anthropic approach viable - depends on cosmology. The evolution from unstable geometries to stable ones occurs on cosmological scales, and if there are radically different geometries at different places in the universe, that too will only be understood once string cosmology is more advanced.

I think I'll stop there, since there are so many different issues which get raised in a discussion like this, and just field specific questions if there are any. I know I certainly haven't responded to everything in Tom's post, but I hope this clarifies a few things.

There's been a proposal by Verlinde of treating gravity as an entropic force which is pretty neat.

There might even be some "predictions" of things that we already know from it - see It from Bit.

I'm surprised that nobody's mentioned this yet - it was a bit of a blogosphere kerfuffle quite recently.

This is a standard semiclassical motivation as to why gravitons most probably exist (I think from Steven Weinberg "gravitation and cosmology" but I have since long lost the book so I am not sure): In the limit of weak gravitation GR looks similar to the Maxwell equations. In particular there should exist gravitational waves.. (Have not yet been detected experimentally but if GR is (at least approximately) correct they should exist.) This means that you could in principle build a gravitational wave microscope. Say you want to measure the position of a test particle using this microscope. Now if gravitational waves were actually classical you could use arbitrarily feeble waves and thus arbitrarily small recoil on the test particle. And thus measuring position and momentum of the test particle with lower unaccuracy of position times momentum (along a given direction) than allowed by the Heisenberg uncertainty relation. But if gravitational waves are quantized in gravitons of energy = h times oscillation frequency Heisenberg uncertainty relation will be satisfied (Heisenberg's original semiclassical derivation goes through for any wave quantised like this).

Posts like this shouldn't appear on this blog. Adequately considering the question requires a truckload of special knowledge that most visitors don't have and that is not associated with the topic of the blog.

The rhetoric that is visible on the surface (comparison with something ridiculous, etc.) strongly privileges a hypothesis (of the teacher's password opaque kind, no less -- to most readers), which in absence of understanding of the subject may as well be pure Dark Art.

Being contrarian doesn't mean that we should be interested in entertaining contrarian hypotheses any more seriously just because they are contrarian. This way lies madness.

There can only ever be one reality, and so there can only ever be one correct theory of reality.

I disagree with this. A theory is basically a model (or pertains to one). Models by necessity leave out details of the thing they're modelling (if you disagree, then the best model of reality is simply reality, and we already have that). So depending on which features of reality you think are relevant, you can have multiple models of reality bringing out each of those features. The theories based on those models will sometimes make different predictions, but if they're good models they'll agree most of the time, and you make predictions using the model that makes those sorts of predictions correctly most of the time.

As an illustration, look at maps of the surface of the Earth. There are multiple projections based on preserving different relevant information. If you want to plan a sea journey, you use one; if you want to plan a land journey, you use a different one. A globe represents both more accurately, but is harder to carry around / print out of a computer.

Surely our models of physics can have the same sorts of properties; what allows you to make predictions about gravity may not be the same model that allows you to make predictions about electromagnetism.

Loop quantum gravity actually does have at least one testable conclusion: non-constancy the speed of light at high energies. There's even some support for this as of a couple of weeks ago, with measurements from the Fermi telescope.

they were created by the influence of mediator particles called (respectively) gluons, W and Z bosons, and photons

The particles (and the specific number of particles for each force) are a consequence of how the different forces are modelled. The local gauge groups for the electromagnetic, weak and strong forces are U(1), SU(2) and SU(3) (this is a simplification, especially for the weak force).

The one dimensional U(1) generates a single force carrier, the photon, the three dimensional SU(2) generates three (W+, W- and Z), while the eight dimensional SU(3) generates eight (superpositions of gluons and anti-gluons with three different colours).

The existence of the graviton is a consequence of assuming that gravity can be modelled, in any way (some people have suggested E_8 as the gauge group) similarly to the other forces. So the graviton is not aether; its existence is predicted, perfectly sensibly, by a lot of theories, and is vital to the working of those theories.

In contrast, physicist came to realise you could discard aether without affecting their theories. So the non-existence of aether had no consequences, while the non-existence fo the graviton would have.

Tom, I upvoted this because I'm a fan of the LW "physics for rationalists" series that Eliezer started two summers ago. Interesting stuff.

My uneducated intuition is that you're right, and the graviton is the same naive-hypothesis-extension failure mode as aether.

But it's interesting to note that these two meta instances of reasoning-by-similarity are apparently acceptable:

• "Making a hypothesis about a different physical phenomenon by naively extending common properties of a group of well-understood physical phenomena is bad." (paraphrase)

• "Theories of physics have a known tendency towards elegance and simplicity."

I just found this: http://fqxi.org/community/articles/display/129

You correctly decry popularity as a non-rational measure of veracity, but to the extent that it expresses a sort of straw poll, it may be a good indicator anyway. The idea of expert futures markets comes to mind.

My point is related: is it not also a fallacy to assert it's GOT to be simple? That's awful close to demanding (even believing?) something's true because it ought to be, because we want it so bad. Occam's razor has worked like a champ all these years but inference is risky and maybe now, we find ourselves confronted with some hard digging. I too hope some crystalline simplification will make everything make sense, but I don't think we've a right to expect that, or should. What you and I want doesn't matter.

The analogy between æther and graviton has some appeal. Photons, W and Z are more or less directly detectable. There is no hope of doing that with graviton. Hence, speaking about graviton brings probably no good: such language has no direct correspondence to observed reality and there is a danger that it can enforce some incorrect intuitions. As far as it goes, I agree. But note also that neither gluons are directly observed.

What I disagree is that the new theories are "graviton-based". They are rather "gravitational-field-based". The gravitational field is an observed entity. For other three forces, a field is associated to particles (well, W and Z and gluon fields are also not directly observed, but at least they are very useful concepts for making theoretical predictions, field theory is more successful than once popular analytic S-matrix theory which worked without the idea of fields). So, we may reasonably assume that the gravitational field also behaves like particles in quantum regime. Maybe it is not the case, but the particle-like behaviour isn't the cornerstone of quantum gravity.

Also, why do you think that somebody has to be largely outside the academic system to solve the quantum gravity puzzle? Are there, in your opinion, some specific biases widespread in academia blocking the abilities to find a new successful theory?

Actually, E&M has been described as a warping of a 4+1-dimensional space-time (in combination with gravity). http://en.wikipedia.org/wiki/Kaluza–Klein_theory

It had some problems.

Interesting. I think there are fundamental things we don't know about gravity yet.

A basic physics question about light waves: I understand how water waves are a property of the medium. My analogy for how it works mechanically is potential energy and kinetic energy swapping in a (mostly) self-sustaining rhythm. I don't understand light waves though. What causes them to oscillate?

And finally, the Michelson-Morely experiment showed that the "aether" was always stationary relative to Earth, even though the Earth changed direction every six months as it moved about in its orbit! Shortly thereafter, the inconsistencies were resolved with Albert Einstein's Theory of Special Relativity, and everyone realized that aether was imaginary.

I actually think this is a misleading characterization. Those inconsistencies with resolved by positing that physical bodies contract as they move through the aether. Lorentz even gave us the math to show us how this worked. Then Einstein posited a theory empirically equivalent to Lorentz's. People liked Einstein's theory more for various reasons (good reasons, I think) but aether has never been ruled out in the way, say, phlogiston has been ruled out.

Theories of physics have a known tendency towards elegance and simplicity, and nothing we have come up with in the past forty years is either simple or elegant, let alone both.

I don't think the fact that all our false theories have been elegant and simple could possibly count as evidence that reality is, in fact, elegant and simple. And certainly those concerns aren't reasons to reject an approach that has been mind-blowingly accurate in it's predictions.

Of the explanations that have been proposed, string theory is currently the most popular. The idea that a theory of physics can have "popularity" should, in and of itself, be a warning sign.

Is it really? That is depressing. Though I don't at all have any problem with theories being popular or unpopular so long as the empirically invalid theories are always really unpopular. Why would there be something wrong with this?

Gravitons have, of course, never been detected.

Try jumping off the earth. :-)

The classical theory of gravity that we know works well, General Relativity, makes no mention whatsoever of gravitons, and describes gravity in terms of the curvature of space-time.

Sure if you don't mind having two totally different and wildly incompatible theories to describe reality.

While I think string theory is a mess too I don't think I see evidence here that all quantum gravity approaches are flawed.