Dear Dr. B: What are the requirements for a successful theory of quantum gravity?

“I've often heard you say that we don't have a theory of quantum gravity yet. What would be the requirements, the conditions, for quantum gravity to earn the label of 'a theory' ?

I am particularly interested in the nuances on the difference between satisfying current theories (GR&QM) and satisfying existing experimental data. Because a theory often entails an interpretation whereas a piece of experimental evidence or observation can be regarded as correct 'an sich'.

That aside from satisfying the need for new predictions, etc.

Thank you,

Best Regards,

Noa Drake”

Dear Noa,

I want to answer your question in two parts. First: What does it take for a hypothesis to earn the label “theory” in physics? And second: What are the requirements for a theory of quantum gravity in particular?”

What does it take for a hypothesis to earn the label “theory” in physics?

Like almost all nomenclature in physics – except the names of new heavy elements – the label “theory” is not awarded by some agreed-upon regulation, but emerges from usage in the community – or doesn’t. Contrary to what some science popularizers want the public to believe, scientists do not use the word “theory” in a very precise way. Some names stick, others don’t, and trying to change a name already in use is often futile.

The best way to capture what physicists mean with “theory” is that it describes an identification between mathematical structures and observables. The theory is the map between the math-world and the real world. A “model” on the other hand is something slightly different: it’s the stand-in for the real world that is being mapped by help of the theory. For example the standard model is the math-thing which is mapped by quantum field theory to the real world. The cosmological concordance model is mapped by the theory of general relativity to the real world. And so on.

But of course not everybody agrees. Frank Wilczek and Sean Carroll for example want to rename the standard model to “core theory.” David Gross argues that string theory isn’t a theory, but actually a “framework.” And Paul Steinhardt insists on calling the model of inflation a “paradigm.” I have a theory that physicists like being disagreeable.

Sticking with my own nomenclature, what it takes to make a theory in physics is 1) a mathematically consistent formulation – at least in some well-controlled approximation, 2) an unambiguous identification of observables, and 3) agreement with all available data relevant in the range in which the theory applies.

These are high demands, and the difficulty of meeting them is almost always underestimated by those who don’t work in the field. Physics is a very advanced discipline and the existing theories have been confirmed to extremely high precision. It is therefore very hard to make any changes that improve the existing theories rather than screwing them up altogether.

What are the requirements for a theory of quantum gravity in particular?

The combination of the standard model and general relativity is not mathematically consistent at energies beyond the Planck scale, which is why we know that a theory of quantum gravity is necessary. The successful theory of quantum gravity must achieve mathematical consistencies at all energies, or – if it is not a final theory – at least well beyond the Planck scale.

If you quantize gravity like the other interactions, the theory you end up with – perturbatively quantized gravity – breaks down at high energies; it produces nonsensical answers. In physics parlance, high energies are often referred to as “the ultra-violet” or “the UV” for short, and the missing theory is hence the “UV-completion” of perturbatively quantized gravity.

At the energies that we have tested so far, quantum gravity must reproduce general relativity with a suitable coupling to the standard model. Strictly speaking it doesn’t have to reproduce these models themselves, but only the data that we have measured. But since there is such a lot of data at low energies, and we already know this data is described by the standard model and general relativity, we don’t try to reproduce each and every observation. Instead we just try to recover the already known theories in the low-energy approximation.

That the theory of quantum gravity must remove inconsistencies in the combination of the standard model and general relativity means in particular it must solve the black hole information loss problem. It also means that it must produce meaningful answers for the interaction probabilities of particles at energies beyond the Planck scale. It is furthermore generally believed that quantum gravity will avoid the formation of space-time singularities, though this isn’t strictly speaking necessary for mathematical consistency.

These requirements are very strong and incredibly hard to meet. There are presently only a few serious candidates for quantum gravity: string theory, loop quantum gravity, asymptotically safe gravity, causal dynamical triangulation, and, somewhat down the line, causal sets and a collection of emergent gravity ideas.

Among those candidates, string theory and asymptotically safe gravity have a well-established compatibility with general relativity and the standard model. From these two, string theory is favored by the vast majority of physicists in the field, primarily because it has given rise to more insights and contains more internal connections. Whenever I ask someone what they think about asymptotically safe gravity, they tell me that would be “depressing” or “disappointing.” I know, it sounds more like psychology than physics.

Having said that, let me mention for completeness that, based on purely logical reasoning, it isn’t necessary to find a UV-completion for perturbatively quantized gravity. Instead of quantizing gravity at high energies, you can ‘unquantize’ matter at high energies, which also solves the problem. From all existing attempts to remove the inconsistencies that arise when combining the standard model with general relativity, this is the possibly most unpopular option.

I do not think that the data we have so far plus the requirement of mathematical consistency will allow us to derive one unique theory. This means that without additional data physicists have no reason to ever converge on any one approach to quantum gravity.

Thank you for an interesting question!