The paradigm shift you didn’t notice

Inertia creeps.

Today, for the first time in human history a scientist has written this sentence – or so would be my summary of most science headlines I read these days. Not only do the media buy rotten fish, they actually try to resell them. The irony is though that the developments which really change the way we think and live happen so gradually you wouldn’t ever learn about them in these screaming headlines.

HIV infection for example still hasn’t been cured, but decades of hard work turned it from a fatal disease into a treatable one. You read about this in longwinded essays in the back pages where nobody looks, but not on the cover page and not in your news feed. The real change didn’t come about by this one baby who smiles on the photo and who was allegedly cured, as the boldface said, but by the hundreds of trials and papers and conferences in the background.

These slow changes also happen in physics. Quantum measurement is a decoherence process rather than collapse. This doesn’t break the ground but slowly moves it. It’s an interpretational shift that has spread through the community. Similarly, it is now generally accepted that most infinities in quantum field theory do not signal a breakdown of the theory but can be dealt with by suitable calculational methods.

For me the most remarkable shift that has taken place in physics in the last decades is the technical development and, with it, acceptance of renormalization group flow and effective field theories. If this sounds over your head, bear with me for I’m not going into the details, I just want to tell you why it matters.

You have certainly heard that some quantum field theories are sick and don’t make sense – they are said to be non-renormalizable. In such a theory the previously mentioned infinities cannot be removed, or they can only be removed on the expense of introducing infinitely many free parameters which makes the theory useless. Half a century ago a theory with this disease was declared dead and went where theories go to die, into the history aisle.

Then it became increasingly clear that such non-renormalizable theories can be low-energy approximations to other theories that are healthy and renormalizable. The infinities are artifacts of the approximation and appear if one applies the approximation outside its regime of validity.

These approximations at low energies are said to be “effective” theories and they typically contain particles or degrees of freedom that are not fundamental, but instead “emergent”, which is to say they are good descriptions as long as you don’t probe them with too high energy. The theory that is good also at high energies is said to be the “UV completion” of the effective theory. (If you ever want to fake a physics PhD just say “in the IR” instead of “at low energy” and “UV” instead of “high energy”.)

A typical example for an effective theory is the nuclear force between neutrons and protons. These are not fundamental particles – we know that they are made of quarks and gluons. But for nuclear physics, at energies too small to test the quark substructure, one can treat the neutrons and protons as particles in their own right. The interaction between them is then effectively mediated by a pion, a particle that is itself composed of two quarks.

Fermi’s theory of beta-decay is a historically very important case because it brought out the origin of non-renormalizability. We know today that the weak interaction is mediated by massive gauge-bosons, the W’s and the Z. But at energies so low that one cannot probe the production and subsequent decay of these gauge bosons, the weak interaction can be effectively described without them. When a neutron undergoes beta decay, it turns into a proton and emits an electron and electron-anti-neutrino. If you do not take into account that this happens because one of the quark constituents emits a W-boson, then you are left with a four-fermion interaction with a coupling constant that depends on the mass of the W-boson. This theory is not renormalizable. Its UV completion is the standard model.

Upper image: One of the neutron's quark constituents interacts via a gauge boson with an
electron. Bottom image: If you neglect the quark substructure and the boson-exchange, you get a four-fermion interaction with a coupling that depends on the mass of the boson and which is non-renormalizable.

So now we live and work with the awareness that any quantum field theories is only one in a space of theories that can morph into each other, and the expression of the theory changes with the energy scale at which we probe the physics. A non-renormalizable theory is perfectly fine in its regime of validity. And thus today these theories are not declared dead any longer, they are declared incomplete. A theory might have other shortcomings than being non-renormalizable, for example because it contains dimensionless constants much larger than (or smaller than) one. Such a theory is called unnatural. In this case too you would now not simply discard the theory but look for its UV completion.

It is often said that physicists do not know how to quantize gravity. This isn’t true though. Gravity can be quantized just like the other interactions; the result is known as “perturbatively quantized gravity”. The problem is that the theory one gets this way is non-renormalizable, which is why it isn’t referred to as quantum gravity proper. The theory of quantum gravity that we do not know is the UV-completion of this non-renormalizable perturbative quantization. (It cannot be non-renormalizable in the same way as Fermi’s theory because gravity is a long-range interaction. We know that gravitons, if they have masses at all, have tiny masses.)

But our improved understanding of how quantum field theories at different energies belong together has done more than increasing our acceptance of theory with problems. The effective field theory framework is the tool that binds together, at least theoretically, the different disciplines in physics and in the sciences. No longer are elementary particle physics and nuclear physics and atomic physics and molecular physics different, disconnected layers of reality. Even though we cannot (yet) derive most of the relations between the models used in these disciplines, we know that they are connected through the effective field theory framework. And at high energies many physicists believe it all goes back to just one “theory of everything”. Don’t expect a big headline announcing its appearance though. The ground moves slowly.