The key to quantum gravity from a cosmological perspective is the correspondence between neutrino masses and the peak temperature of the radiation that permeates our sky, the cosmic microwave background (CMB).

In June 2010, I was calculating the rest masses of right handed neutrinos using the simple parameters of Koide and Brannen. These were posted on my physics blog, Arcadian Functor. Although I was very keen to relate fundamental rest masses to the CMB temperature, I was not thinking about the actual numbers. Luckily, the keen astrophysicist Graham Dungworth was reading my blog. At the time, he was a well known supernovae hunter on the Galaxy Zoo forums. He immediately noticed that the central right handed mass, which was 0.00117 eV in standard units, exactly corresponded with the present day CMB temperature. All one has to do is multiply kT, where k is Boltzmann’s constant, by the constant of Wien, which applies to black body radiation. The CMB is nature’s most perfect black body spectrum.

It was a stunning clue to the true nature of the quantum universe. In no time at all, Graham was figuring out all kinds of consequences on the Galaxy Zoo forums. We cared about things like the derivation of the mass of the observable universe. Such a possibility was totally ludicrous from the perspective of the reigning cold dark matter picture, which imagines a universe evolving in a mostly classical way from a Big Bang epoch, and for which the CMB temperature takes a random value due to the arbitrary cosmic time that has elapsed until our present.

For many years, Graham and I were the only researchers who publicly took the neutrino CMB correspondence seriously. Although I did not know it at the time, this began to change in 2015. While at the University of Auckland, I heard a rumour that Marni was not thinking about the CMB any more, which was entirely untrue, and I realised that certain forces had figured out that the neutrino CMB picture was correct, theoretically.

In 2017, I managed to make good progress on the mathematical foundations of the theory, working alone in my tent in the forest. I had cut myself off from negative influences for a few years. Within a few months, I was invited to the United States to give lectures. It was obvious now that people were very interested in understanding the quantum vacuum from this point of view.

Since the mathematics is quite sophisticated, attempts would naturally be made to fit the neutrino results into the string theory framework. But the new view is not string theory. It is much closer to condensed matter physics, which uses diagrams and quantum logic to analyse interesting laboratory systems, like superconductors or the fractional quantum Hall effect. The new cosmology does not require dark matter or dark energy, because these are artefacts of the incorrect application of Einstein’s general relativity to the universe at large. Only ordinary matter, meaning particles in the Standard Model of particle physics, shows up in the axioms that we need. Moreover, the principle of mass localisation uses both a local scale and a cosmological scale, which is what happens in the model of quantum inertia, studied by Mike McCulloch and collaborators. Quantum inertia can easily derive the so called MOND (modified Newtonian dynamics) solution for anomalous galactic rotation curves, without the need for dark matter.

So why are neutrinos special? Neutrinos are the only electrically neutral fundamental particle. Neutrons, which live in the nuclei of atoms, are composed of up and down quarks, which are charged. Neutrinos appear in beta decay, like in a radiating uranium atom, when a neutron turns into a triplet of particles: an electron, an antineutrino and a proton. Observe that in this decay, many things balance out. The charge on both sides of the equation is zero, because the electron contributes -1 while the proton contributes +1. There is also a lepton number. Electrons and neutrinos are leptons, with lepton number +1. But the antineutrino is an antiparticle, and it has a lepton number of -1. So on both sides of the equation, the total lepton number is zero. This is how particle physics works. Conservation laws beyond the conservation of energy and momentum govern what interactions are permitted to take place.

The difficulty is that neutrinos have mass. We know this from many neutrino oscillation experiments, whose data all fit a simple quantum mechanical model with mass states for neutrinos. And yet the old Standard Model wants neutrinos to be completely massless, because unlike electrons, the neutrinos only appear locally with one handedness, relative to the direction of propagation. Since the experiment of Wu, to test the early theory of Lee and Yang, we have known that neutrinos are the reason why the parity symmetry of spacetime is broken by nature.

Where are the right handed neutrinos? Most theorists believe they must exist in some form, because they are useful in attempts to explain why the masses of neutrinos are so much smaller than the masses of other fundamental particles. In the Standard Model, particles gain mass through the Higgs boson, which was discovered at the LHC in 2012. But it makes no sense to use the Higgs boson for neutrino masses, which require a theory beyond the Standard Model.

We study neutrino masses using quantum information theory, and consider the possibility that neutrino mass itself underlies the mass of the Higgs boson. The numbers work nicely: if you take the geometric mean of the neutrino mass scale and the high energy Planck scale, you get the observed Higgs scale. The Planck scale is a natural cut-off for high energy physics, and the neutrino scale introduces an infrared cut-off at low energy, now associated to cosmic phenomena. Cut-offs are big business in particle physics, and accounting for them properly complicates the mathematics. They are also absolutely necessary, because nothing is well defined without them. Our CMB cut-off suggests that the quantum boundary of our cosmos can be studied without appealing to the classical causality of the hypothesised early universe. After all, we are observers. We view our cosmos from the present.

Now the three neutrino mass states cannot be the same as the three neutrino states that participate locally in the electroweak interactions. The latter are called the electron, muon and tau neutrinos, after their partner charged leptons. A left handed electron neutrino is a mixture of the three mass states, as are the other electroweak neutrinos. We imagine multiple mass states coming out of one interaction point, but then the conservation of energy and momentum is problematic, and it is essential to consider Heisenberg’s uncertainty principle. You could say that the neutrinos are more quantum than other particles. Because they don’t interact with anything as they travel from the source beam to the detector, which can be a very long way, all three mass states propagate stably, and it is easy to model their behaviour.

To put this theory on a firmer footing, we need more than one amazing numerical coincidence. This we get by looking closely at the right handed states. Since our list of states corresponds closely with those observed in the Standard Model, it is natural to assign three masses to a left-right pair of electrons: the electron, the muon and the tau mass. The Higgs mechanism usually requires us to pair left and right handed states, but this does not apply to neutrinos, and so we are free to assign three masses to the left handed neutrinos and another three masses to the right handed neutrinos. The quantum information model does this neatly using only a basic arithmetic phase difference of 30 degrees. This is how we get the 0.00117 eV mass amongst the right handed masses. Then we consider that this local CMB photon has a non local sterile neutrino partner, given by the redshifted temperature, where we choose the redshift of z=1100 back to the CMB creation time. The resulting sterile mass is 1.3 eV, which amazingly agrees exactly with well known anomalies in the oscillation data.

The theory also solves another long standing problem. The horizon problem asks how the CMB temperature can be so uniform across our sky, when photons coming from opposite directions seem to originate in places that never had causal contact. The answer is that the CMB temperature is a fundamental variable in quantum gravity, related to rest masses, which are derived from first principles using quantum mechanics.