The underappreciated value of boring truths

My primary reaction to any new idea on the arXiv is conviction that it’s almost certainly wrong, and if I can’t figure out quickly why it’s wrong, I’ll ignore it because it’s most likely a waste of time. In other words, I exemplify the stereotypical reaction of scientists which Arthur Clarke summed up so nicely in his the three stages of acceptance:

1. “It’s crazy — don’t waste my time.”
2. “It’s possible, but it’s not worth doing.”
3. “I always said it was a good idea.”

Maybe I’m getting old and bold rather than wise and nice, but when it comes to quantum gravity phenomenology, craziness seems to thrive particularly well. My mother asked me the other day what I tell a journalist who wants a comment on somebody else’s work which I think is nonsense. I told her I normally say “It’s very implausible.” No, I’m not nice enough to bite my tongue if somebody asks for an opinion. And so, let me tell you that most of what gets published under the name of quantum gravity phenomenology is, well, very implausible.

But quantum gravity phenomenology is just an extreme example of a general tension that you find in theoretical physics. Consider you’d rank all unconfirmed theories on two scales, one the spectrum from exciting to boring, the other the spectrum from very implausible to likely correct. Then put a dot for each theory in a plane with these two scales as axes. You’d see that the two measures are strongly correlated: The nonsense is exciting, and the truth is boring, and most of what scientists work on falls on a diagonal from exiting nonsense to boring truths.

If you’d break this down by research area you’d also find that the more boring the truth, the more people work on nonsense. Wouldn’t you too? And that’s why there is so much exciting nonsense in quantum gravity phenomenology - because the truth is boring indeed.

Conservative wisdom says that quantum gravitational effects are tiny unless space-time curvature is very strong, which only happens in the early universe and inside black holes. This expectation comes from treating quantum gravity as an effective field theory, and quantizing it perturbatively, ie when the fluctuations of space-time are small. The so quantized theory does not make sense as a fundamental theory of gravity because it breaks down at high energies, but it should be fine for calculation in weak gravitational fields.

Most of the exciting ideas in quantum gravity phenomenology assume that this effective limit does not hold for one reason or the other. The most conservative way to be non-conservative is to allow the violation of certain symmetries that are leftover from a fundamental theory of quantum gravity which does not ultimately respect them. Violations of Lorentz-invariance, CPT invariance, space-time homogeneity, or unitarity are such cases that can be accommodated within the effective field theory framework, and that have received much attention as possible signatures of quantum gravity.

Other more exotic proposals implicitly assume that the effective limit does not apply for unexplained reasons. It is known that effective field theories can fail under certain circumstances, but I can’t see how any of these cases play a role in the weak-field limit of gravity. Then again, strong curvature is one of the reasons of failure, and we do not understand what the curvature of space-time is microscopically. So sometimes, when I feel generous, I promote “implausible” to “far-fetched”.

John Donoghue is one of the few heroically pushing through calculations in the true-but-boring corner of quantum gravity phenomenology. In a recent paper, he and his coauthors calculated the quantum contributions to the bending of light in general relativity from 1-loop effects in perturbatively quantized gravity. From their result they define a semi-classical gravitational potential and derive the quantum corrections to Einstein’s classical test of General Relativity by light deflection.

They find a correction term that is suppressed by a factor ℏ G/b² relative to the classical result, where b is the impact parameter and G is Newton’s constant. This is the typical result you’d expect from dimensional reasons. It’s a loop correction, it must have an extra G in it, it must have an inverse power of the impact parameter so it gets smaller with distance, thus G/b² is a first guess. Of course you don’t get tenure for guessing, and the actual calculation is quite nasty, see paper for details.

In the paper the authors write “we conclude that the quantum effect is even tinier than the current precision in the measurement of light deflection”, which is an understatement if I have ever seen one. If you are generous and put in a black hole of mass M and a photon that just about manages to avoid being swallowed, the quantum effect is smaller by a factor (m_p/M)² than the classical term, where m^p is the Planck mass. For a solar mass black hole this is about 70 orders of magnitude suppression. (Though on such a close approach the approximation with a small deflection doesn’t make sense any more.) If you have a Planck-mass black hole, the correction term is of order one – again that’s what you’d expect.

Yes, that is a very plausible result indeed. I would be happy to tell this any journalist, but unfortunately news items seem to be almost exclusively picked from the ever increasing selection of exciting nonsense.

I will admit that it is hard to communicate the relevance of rather technical calculations that don’t lead to stunning results, but please bear with me while I try. The reason this work is so important is that we have to face the bitter truth to find out whether that’s really all that there is or whether we indeed have reason to expect the truth isn’t as bitter as it said on the wrapping. You have to deal with a theory and its nasty details to figure out where it defies your expectations and where your guesses go wrong. And so, we will have to deal with effective quantum gravity to understand its limits. I always said it was a good idea. Even better that somebody else did the calculation so I can continue thinking about the exciting nonsense.

Bonus: True love.