The lattice spacing imposes a fundamental limit on the energy that particles can have. That’s because nothing can exist that is smaller than the lattice itself.
So if our cosmos is merely a simulation, there ought to be a cut off in the spectrum of high energy particles.
It turns out there is exactly this kind of cut off in the energy of cosmic ray particles, a limit known as the Greisen–Zatsepin–Kuzmin or GZK cut off.
This cut-off has been well studied and comes about because high energy particles interact with the cosmic microwave background and so lose energy as they travel long distances.
But Beane and co calculate that the lattice spacing imposes some additional features on the spectrum. “The most striking feature…is that the angular distribution of the highest energy components would exhibit cubic symmetry in the rest frame of the lattice, deviating signiﬁcantly from isotropy,” they say.
In other words, the cosmic rays would travel preferentially along the axes of the lattice, so we wouldn’t see them equally in all directions.
That’s a measurement we could be done with current technology.