No Road to Quantum Gravity: On the Incommensurability of Cosmology and Physics

For some bizarre reason, without any action of the will, I got to thinking about general relativity.

There were two things that had me thinking. The first, historical, the other, philosophical. I will make some brief remarks regarding both.

I have been looking at the relationship between big science and society, especially with reference to the space programme and the development of ballistic missile technology. But this had me thinking about the renaissance of general relativity, which I think was facilitated by the space age and but which general relativity itself helped to facilitate. Of course, there were intellectual reasons behind the renaissance of general relativity, most especially the Penrose-Hawking singularity theorems and the big bang-steady state controversy. However, general relativity and cosmology became a “big science” during the space age, and it’s hard to imagine that all the big experiments that were developed to test general relativity would have been so lavishly funded in the absence of a space programme whose key justification, presented to the public, was both scientific and exploratory.

In turn, the renaissance of general relativity helped to fuel the space age because it led to a popular revival of interest in the space sciences. For example, in the 1960s one of the most iconic aspects of Star Trek reminded one of general relativity, that is “warp drive.” In the 1970s there was much popular interest in black holes. There seemed to be a symbiotic relationship between the space programme and general relativity.

When we speak of big science and physics we generally speak of particle physics, and the large particle accelerators associated with it. This is ironic, I suppose, given that general relativity and cosmology are the sciences of the very large and particle physics is the science of the very small. There are good reasons for focusing inquiry on particle physics, as particle physics became “king” as it were. Before 1960 general relativity was a backwater. But we forget that general relativity also became a big science, and I content that the space age was crucial here. There are not too many studies that explore this symbiotic relationship.

Okay, so that’s the historical part. No great intellectual wonder there, but interesting in the context of the relationship between science and society.

The other, more philosophical, focused on incommensurability in the philosophy of science. My view of scientific revolutions is a bit different to Kuhn’s. I tend to think that scientific revolutions resolve incommensurability because they overcome paradigmatic disjuncture. One aspect of science becomes disjunct from another, the prevailing paradigm fissions into incommensurable parts, and attempts are made to patch them together but, ultimately, revolution occurs when the sciences are reunited through a conceptual revolution. To be sure the new paradigm is incommensurable with the previously prevailing, but this is not important and far too much focus is given to it. That’s progress.

So I tend to think that the, original, scientific revolution occurred because astronomy, or cosmology if you will (the solar system was *their* universe), and physics became incommensurable. What we call the Copernican revolution in astronomy undermined the hitherto prevailing Aristotelian physics. The scientific revolution was a sort of longue duree which eventually, through Newton, led to the unification of cosmology and physics but this came at the price of a complete, revolutionary, overhaul of physics and of our notions of the physical.

Something very much similar happened with physics and chemistry, ultimately culminating in quantum mechanics. Chemistry was not reduced to physics so much as unified with physics, and again that unification required a revolution in physics.

I tend to think that cosmology and physics are again incommensurable. Now there are anomalies in cosmology, that is in the standard big bang model, and their resolution through inflationary cosmology looks shaky, but what I am speaking of is much deeper.

The picture of cosmology that both Newton and Einstein left us with is that, when it comes to the large scale structure of the universe, gravitation is the key physical mechanism. But we know now, with the accelerating expansion of the universe, that this is not so. A type of anti-gravity, not understood, is more significant. This is associated with the cosmological constant, but the cosmological constant does not flow naturally from general relativity. Furthermore, the predicted value of the cosmological constant arising from quantum field theory is completely at odds with experiment, the worst discrepancy between theory and experiment in the history of physics.

Physics no longer provides us with a working model of the large scale structure of the universe, that is with a working model of the universe. That means physics and cosmology are incommensurable. The prevailing model of the universe is the Lambda-Cold Dark Matter, and we’ve just been talking about lambda. It looks like the other half, cold dark matter, is in trouble too.

The standard view regarding the resolution of our incommensurability has it that a quantum theory of gravity, which supersedes general relativity, will solve this mystery.

This view also holds that the unification of quantum mechanics and general relativity requires general relativity to buckle, leaving quantum mechanics unscathed and unsullied. It is supposed that the singularity theorems require this, because singularities are associated with infinite physical quantities. Yet infinite physical quantities also appear in quantum field theory which sweeps them under the rug through renormalisation. It is argued that singularities led to a break down in physics, with the break down of predictably, causality and so on. Spacetime singularities are philosophical problematical because they demonstrate that general relativity is incomplete. However, would this be as serious a concern if the cosmic censorship hypothesis, the last outstanding problem of classical general relativity, is demonstrably correct? Not only that, but quantum mechanics, through the measurement problem, has its own philosophical conundrums to deal with.

It is also often said that quantum field theory leads to stunningly precise predictions that are confirmed through experiment, showing that something deep lies within. However, general relativity also leads to stunningly precise predictions confirmed by experiment. Not only that, but this neglects the woeful cosmological constant prediction.

It seems to me that the arguments made for buckling general relativity whilst leaving quantum field theory intact are not as strong as often presented, but nonetheless it has become a type of dogma underpinning the search for a quantum theory of gravity. Quantum field theory has more problems than general relativity does.

The quest for a quantum theory of gravity has something like a 70 year history, and yet we still don’t have one and none appears on the horizon. That suggests maybe there isn’t one to be found. The cosmological problem is a problem for both theories, and perhaps the incommensurability between physics and cosmology requires revolutionary upheaval in our conceptions of the physical. The physical mechanism, or the physical principle, that underpins the cosmological constant could well require physics that goes beyond general relativity *and* quantum mechanics. Unification of these two theories won’t provide us with this. It seems to me that the search for quantum gravity is based on views and hopes that are not as defensible as claimed.

We need some new principle, say like the principle of equivalence, that points us down the right road. Lee Smolin once wrote of three roads to quantum gravity. Perhaps there are no roads to quantum gravity, and the sooner we recognise this the sooner shall we stumble upon the right road.

I suspect that the key lies in considerations regarding the big bang singularity, especially if you hold that inflationary cosmology is also problematical. But that’s another topic.