Tuesday, January 3, 2006

Pure quantum gravity cannot work

One of the simple - although not quite new - consequences of the "swampland" line of reasoning is that pure theories of quantum gravity cannot work.

This conclusion that we will justify below applies to various loop quantum gravities, spin foams, causal and acausal, dynamical and non-dynamical triangulations, tetrahedronizations, and any other misinterpretations of quantum gravity that you have heard of.

Quantum gravity cannot be studied separately from the other forces, and the other forces cannot be thought of as small corrections to quantum gravity.

On the contrary. In every consistent theory (and background) of quantum gravity,

in the sense that there must exist particles charged under any other kind of force for which the force of gravity is subdominant; their mass/charge ratio is smaller than for extremal black holes and the overall force between two copies of such a particle must be repulsive. This statement may be (and has been) justified by many arguments, for example:

  • the entropy bounds and the absence of remnants
  • the ability of extremal black holes to decay unless they are BPS
  • the continuous character of the magnetic monopole charge of all objects that can be described as black holes
  • the verification that the rule is satisfied in all classes of string theory backgrounds that have been looked at

According to our knowledge of string theory, it seems that there also cannot exist any backgrounds which only contain massless gravity but no massless gauge fields or scalars. See page 6 of the Swampland paper, for example. Pure quantum gravity does not seem to be an option. Moreover, we know that in the real world around us, gravity is not the only force - and the strength of the other forces does not go to zero, not even at the Planck scale.




Let us accept that pure gravity is not the final goal. Can it be a step towards getting a full theory, after we "add" the other forces such as electromagnetism as perturbations?

The answer is a resounding No.

When you add a force that you want to treat perturbatively, which should be possible if the success of QED is reproduced by your quantum theory of gravity and electromagnetism, then you are expanding around "g=0" where "g" is the gauge coupling. In quantum gravity, there is a new ultraviolet cutoff "g.M_{Planck}" above which the effective theory breaks down. If "g" goes to zero, then this scale goes to zero, too. The theory therefore breaks down at all scales. You can't expand around the point where gravity is the strongest force because a quantum theory of gravity in which gravity is stronger than other forces is inconsistent.

In unified theories - i.e. in string theory - this problem is avoided because the same coupling "g" also governs the strength of gravity, and setting "g=0" implies that "M_{Planck}" goes to infinity and the cutoff scale remains finite.

Well, I don't expect that the people who try to study "pure quantum gravity" will suddenly realize and accept these observations. But I do hope that many other readers will get the point. When the role of quantum mechanics is considered, other forces cannot be neglected when we try to include gravity. All forces must be studied simultaneously which is why a unified theory is necessary for a description of quantum gravity to be consistent.

This is the 17th known reason why string theory is the only tool to study quantum gravity, beyond the semiclassical approximation, that we have as of January 2006.