A symmetry argument for multiverses

Penrose tiles by MonkstoneThe multiverse hypothesis is that what we used to see as the Universe (which is supposed to be all that there is) may be part of something larger, that includes other universes like, or unlike our own. This is not a hypothesis that was proposed to conveniently solve the Anthropic paradox (we don’t know why the Universe can support life at all whereas it could be a lot more hostile and sterile than it already is, as far as we can tell). It does solve that problem, but wasn’t proposed for that reason. It emerges, actually, in four different forms, as a necessary consequence of scientific theories for which we have very good evidence. Some levels of multiverse are more controversial than others, of course, but in this post, I want to bring forward another argument in favor of multiverses, based on symmetry.

Symmetry is central to modern physics, and helped us make some of the most important discoveries of the 20th and early 21st centuries. General Relativity comes from Lorentz covariance, which is the idea that the laws of physics look the same no matter where and when you test them, and no matter how fast you’re moving (physicists will forgive this oversimplification, I hope). Antimatter was predicted by Dirac when he applied Relativity to the Schrödinger equation that rules quantum systems. The discovery that high energy particles can be mapped to interesting mathematical groups helped us understand the fields they are associated with, and in turn, unfilled positions in these symmetry groups led to predictions of new particles, that were later discovered to exist. Pretty much every time that the equations describing a system seemed to be more symmetrical than observation, we’ve discovered that something was missing from our observation.

Another interesting discovery of modern physics is spontaneous symmetry breaking. This phenomenon happens when a system’s potential energy is distributed in such a way that the most symmetrical state of the system is not that of lowest energy, and when there are multiple states of lowest energy, that are in principle equally probable.

Imagine a perfectly round igloo, on top of which you drop a ball. If you place the ball exactly at the top point of the igloo, will the ball fall? If it does, can you predict on what side of the igloo? The answers are yes and no: The ball is going to fall because even the tiniest environmental fluctuation (and quantum mechanics assures us that there will be fluctuations) will push it in one direction or the other. You can’t predict where the ball will fall because the system is perfectly symmetrical except for those perturbations that will cause the ball to fall.

This is a case where the problem is perfectly symmetrical, but none of the solutions are: it’s the set of solutions that has the same symmetries as the problem.

Something similar, but a bit more abstract, happened at a cosmic scale during those events we call the Big Bang. Electromagnetism and the weak interaction used to be one and the same force, perfectly SU(2) x U(1) symmetrical, and then the whole universe decayed in a lower energy state where the symmetry was broken, giving rise to photons, W±, and Z0 bosons, and giving a mass to electrons, protons, and neutrons through the Higgs mechanism. We think something similar happened when the symmetry between the strong and electroweak interactions was broken, and maybe also when those broke up with gravitation.

This raises a question however: in our silly igloo example, there are outside perturbations. In the case of the Universe, no such thing exists, by definition. So why does our universe exhibit those specific symmetry-broken results? More importantly, does the whole set of solutions, which is symmetrical, exist? What makes our particular decayed universe more real than those other solutions?

There is no particular reason why we see this particular symmetry breaking: this tells us more where we are in the multiverse than it tells us anything profound about our particular solution to the equations. The whole set of solutions probably exists just as much as our own, and what makes ours real is that we’re in it, that’s all. A gap in the observed set of solutions that should be filled according to the symmetries of the system is indicative that there is something in there that we haven’t found yet.

So there you have it: there is a multiverse because the laws of physics are more symmetrical than our observable universe is.