## Monday, 17 February 2014

### Belief in Quantum Gravity (and Cosmology)

Recently a few discussions have alerted me to the role of belief when it comes to theories of quantum gravity. This comes about essentially because of the huge energy scales involved in quantum gravity: because we have no (direct) experimental access to the Planck scale.

Firstly, what is the Planck scale? We need to a short lesson on units to get there. The Planck scale is what we assume to be the natural scale in gravity. As a mass scale it is approximately the square root of 1/G, where G is Newton's constant (I normally prefer to include a factor of 8 pi and call this "reduced Planck scale" simply "the" Planck scale, but that is a matter of preference, although as we are discussing, preference is a driving factor here...). Planck noticed that "natural" units for physics can be established based on a few fundamental constants, that is, we measure things in units of those constants. The first is Planck's constant itself, h (or "h-bar" if you divide it by 2 pi), which measures units of angular momentum (Joules per second in SI), and is the fundamental constant associated to quantum mechanics. Next is the speed of light, c, which measures units of speed (duh!) (metres per second in SI), and is the fundamental constant associated to relativity. Finally, then, comes Newton's constant, G, which measures the force of the gravitational field of body of fixed mass (per unit distance squared from that body, per unit mass of that body, per unit mass of the test particle feeling the force, which all follows from Newton's famous law of gravitation). Newton's constant also appears in Einstein's theory of general relativity, and so is associated to all gravitational physics (it is inserted by hand into general relativity to fix the units and the weak limit, but by consistency carries through the rest, and in all that spectacularly verified glory).

Here's where the fun starts: we can measure *all* dimensionful quantities in physics in terms of these three constants. Let's focus on the Planck mass. First of all, notice it involves masses, in particular, two masses, and so mass squared (hence why we took the square root above). All the other things it involves can be expressed as appropriate powers of c and h. We can get acceleration from using the units of c and part of h (the seconds bit), and we can also use c (via E=mc^2) to turn energies, i.e. the Joules part of h, into masses. That leaves G just a measure of 1/mass^2, and the mass it measures is the Planck mass.

Now, gravity is a very weak force. What does that mean? It means that for all the fundamental particles we know if you consider the force between any two of them then the gravitational force is far weaker than any of the other forces (yes, even the Weak force). But, if there were a particle that weighed a Planck mass (which is about 10^18 times the mass of the proton, or the same mass as about one ten thousandth of a gram, judging roughly from a mole of hydrogen which contains 10^23 protons) then the strength of the force of gravity between those particles would be equal to the strength of all the other forces.

There is also that sneaky "per unit distance squared form that body", which means if you bring the particles closer together, gravity gets stronger. When you compute that change in force taking account of the appropriate quantum mechanics (the renormalisation group flow) then we find that all the forces not only change in this simple high-school physics way, but also fundamentally, as we go to short distances. The constants of nature "flow" with energy scale (though h and c, and debatably G, do not). This means that in addition gravity becomes of comparable strength to other forces on very short distance scales, in fact at the Planck length (using our units we can change mass into length too). (If you want to read more about all of this, go and read Frank Wilczek's great book "The Lightness of Being")

Normally in computing quantum effects we can ignore gravity because it is so weak, but at the very high energies of the Planck scale, gravity becomes so strong that we cannot ignore it, and this is therefore the scale at which a theory of quantum gravity is needed. At all the energies below the Planck scale gravity was so weak that we could treat it as a "classical background". (It is a common misconception that physicists "cannot treat quantum mechanics and relativity at the same time".  We're actually very good at it: we can do so-called "quantum field theory in curved space-time", but to do this we always treat both halves separately, that is we have "classical space-time")

Okay, so now we are finally there and we can discuss why quantum gravity involves belief. It involves belief because the Planck scale is so very big. It is 10^18 GeV in particle physics units. The rest energy of a proton is about 1 GeV. The LHC runs at about 10^4 GeV. The biggest machine physicists can even think of making in the foreseeable future is about 10^5 GeV, which is still a very long way from the Planck scale. (I read somewhere that a particle accelerator capable of reaching the Planck scale would have to be the size of the solar system and use a large fraction of the sun's total output. I don't know where I read that, or how the maths was done) At these comparatively low energies we can don't need to specify our theory of quantum gravity in order to do calculations in normal theories. As long as the quantum theory reduces to general relativity in the right limits, pretty much anything goes (although some things may not, they may "resist embedding", as recently and elegantly discussed in this paper).

The enormity of the Planck scale means we cannot do experiments to test quantum gravity directly. And this means that for the most part whether you think string theory is a better theory than loop quantum gravity, or vice versa, is based on your aesthetic opinion about those theories. The role of aesthetics in physics *is* important, and helps guide us towards new laws (for more on this read/watch Feynman's "Character of Physical Law", or read Weinberg's "Dreams of a Final Theory"). It is precisely that aesthetics that has even got us as far as being able to contemplate quantum gravity, but beliefs about aesthetics diverge at the edges of our knowledge.

I came to think about this recently during a conversation with colleague. We were discussing what kind of indirect evidence could possibly be considered as for or against a given theory of quantum gravity, where by indirect I mean evidence discovered well below the Planck scale, either in cosmology or in a spectrum of new particles that could be found at foreseeable collider. I was primarily thinking of whether this evidence could support a complex theory of quantum gravity with many possible solutions, in particular, the "string landscape". Certain solutions and low energy physics scenarios appear "more likely" (in quotes because of the notorious measure problem: there is a *lot* to discuss here) in the landscape, and I argued that seeing such signals could be indirect evidence for the landscape (I do argue this a lot, and was particularly inspired by Paul Langacker's recent colloquium at PI on this subject, which you can see here). My colleague replied:

"In [theory of quantum gravity] which I believe in, the situation is..."

and we went on to try and interpret (unsatisfactorily in my opinion) all such results in light of said theory. And so, it has become abundantly clear to me how important our beliefs are in interpreting indirect evidence. I guess this is obvious, but it does get a little worse. Earlier the same day I had discussed during a mini-conference this exact topic of indirect evidence pointing to string theory and the landscape. I asked the audience, "if we discovered ultra-light axions in cosmology would you consider this a good pointer towards string theory and the landscape?". An audience member replied:

"No, I would try and interpret it in light of [theory of cosmology]"

I found this very honest, but depressing. The role of belief is so strong in the far and esoteric reaches of cosmology and quantum gravity that even when faced with a nominal prediction and hypothetical evidence for that prediction, someone cannot be convinced away from their beliefs. I'm not trying to be above all of this. I admit to being in a similar situation myself. I *believe* that the landscape is unavoidable, and that this behooves us to interpret the world in light of this. Why? Because, following Gell-Mann "anything that isn't forbidden is mandatory" (quoted from that same elegant paper linked to above) the landscape has a much wider space of what is possible, and thus not forbidden, and is therefore an interesting playground that forces us to question all possible assumptions. As a phenomenologist this is daunting, but I love the challenge of trying to find tell-tale needles in this haystack.

I wonder, even if we could do experiments up at the Planck scale, if all parties could ever be convinced? If scattering carried a uniquely stringy character (there are some, but I don't know them) could this still be "interpreted in light of [theory]"? On the flip-side, and this is more important to me, what types of evidence would I consider as being counter to my own beliefs that might force me to revise them?