The Inverse Problem. Sorry, we don’t have experimental evidence for quantum gravity.

The BICEP collaboration recently reported the first measurements of CMB polarization due to relic gravitational waves. It is presently unclear whether their result will hold up and eventually be confirmed by other experimental groups, or if they have screwed up their data analysis and there’s no signal after all. Ron Cowen at Nature News informs the reader carefully there’s “No evidence for or against gravitational waves.”

I’m not an astrophysicist and don’t have much to say about the measurement, but I have something to say about what this measurement means for quantum gravity. Or rather, what it doesn’t mean.

I keep coming across claims that BICEP is the first definite experimental evidence that gravity must be quantized. Peter Woit eg let us know that Andrew Strominger and Juan Maldacena cheerfully explain that quantum gravity is now an experimental subject, and Lawrence Krauss recently shared his “Viewpoint” in which he also writes that the BICEP results imply gravity must be quantized:

“Research by Frank Wilczek and myself [Lawrence Krauss], based on a dimensional analysis argument, suggests that, independently of the method used to calculate the gravitational wave spectrum, a quantum gravitational origin is required. If so, the BICEP2 result then implies that gravity is ultimately a quantum theory, a result of fundamental importance for physics.”

We previously discussed the argument by Krauss and Wilczek here. In a nutshell the problem is that one can’t conclude anything from and with nothing, and no conclusion is ever independent of the assumptions.

The easiest way to judge these claims is to ask yourself: What would happen if the BICEP result does not hold up and other experiments show that the relic gravitational wave background is not where it is expected to be?

Let me tell you: Nobody working on quantum gravity would seriously take this to mean gravity isn’t quantized. Instead, they’d stumble over each other trying to explain just how physics in the early universe is modified so as to not leave a relic background measureable today. And I am very sure they’d come up with something quickly because we have very little knowledge about physics in such extreme conditions, thus much freedom to twiddle with the theory.

The difference between the two situations, the relic background being confirmed or not confirmed, is that almost everybody expects gravity to be quantized, so right now everything goes as expected and nobody rushes to come up with a way to produce the observed spectrum without quantizing gravity. The difference between the two situations is thus one of confirmation bias.

What asking this question tells you then is that there are assumptions going into the conclusion other than perturbatively quantizing gravity, assumptions that quickly will be thrown out if the spectrum doesn’t show up as expected. But this existence of additional assumptions also tells you that the claim that we have evidence for quantum gravity is if not wrong then at least very sloppy.

What we know is this: If gravity is perturbatively quantized and nothing else happens (that’s the extra assumption) then we get a relic gravitational wave spectrum consistent with the BICEP measurement. This statement is equivalent to the statement that no relic gravitational wave spectrum in the BICEP range implies no perturbative quantization of gravity as long as nothing else happens. The conclusion that Krauss, Wilczek, Strominger, Maldacena and others would like to draw is however that the measurement of the gravitational wave spectrum implies that gravity must be quantized, leaving aside all other assumptions and possibly existing alternatives. This statement is not logically equivalent to the former. This non-equivalence is sometimes referred to as “the inverse problem”.

The inverse problem is finding the theory from the measurements, the inverse of calculating the data from the theory. Strictly speaking it is impossible to pin down the theory from the measurements since this would imply ruling out all alternative options but one, and there might always be alternative options - unknown unknowns - that we just did not think of. In practice then solving the inverse problem means to rule out all known alternatives. I don’t know of any alternative that has been ruled out.

The so-far best attempt at ruling out classical gravity is this paper by Ashoorioon, Dev, and Mazumdar. They show essentially that it’s the zero-point fluctuations of the quantized metric that seed the relic gravitational waves. Since a classical field doesn’t have these zero-point fluctuations, this seed is missing. Using any other known matter field with standard coupling as a seed would give a too small amplitude; this part of the argument is basically the same argument as Krauss’ and Wilczek’s.

There is nothing wrong with this conclusion, except for the unspoken words that “of course” nobody expects any other source for the seeds of the fluctuation. But you have practice now, so try turning the argument around: If there was no gravitational wave background at that amplitude, nobody would argue that gravity must be classical, but that there must be some non-standard coupling or some other seed, ie some other assumption that is not fulfilled. Probably some science journalist would call it indirect evidence for physics beyond the standard model! Neither the argument by Ashoorioon et al nor Krauss and Wilczek’s for example has anything to say about a phase-transition from a nongeometrical phase that might have left some seeds or some other non-perturbative effect.

There are more things in heaven and earth, Horatio, than annihilation and creation operators for spin-two fields.

The argument by Krauss and Wilczek uses only dimensional analysis. The strength of their argument is its generality, but that’s also its weakness. You could argue on the same grounds for example that the electron’s mass is evidence for quantum electrodynamics because you can’t write down a mass-term for a classical field without an hbar in it. That is technically correct, but it’s also uninsightful because it doesn’t tell us anything about what we actually mean with quantization, eg the commutation relations between the field and its conjugate. It’s similar with the Krauss’ and Wilczek argument. They show that, given there’s nothing new happening, you need an hbar to get the dimensions work out. This is correct but in and by itself doesn’t tell you what the hbar does to gravity. The argument by Ashoorioon et al is thus more concrete, but on the flipside less widely applicable.

Don’t get me wrong there. I have no reason to doubt that perturbatively quantized gravity is the right description at weak coupling, and personally I wouldn’t want to waste my time on a theory that leaves gravity unquantized. But the data’s relevance for quantum gravity is presently being oversold. If the BICEP result vanishes you’d see many people who make their living from quantum gravity backpedal very quickly.