On Wed, Oct 10, 2012 at 09:27:25AM -0400, Richard Ruquist wrote:
>   The Measurement That Would Reveal The Universe As A Computer
> Simulation


> First, some background. The problem with all simulations is that the laws
> of physics, which appear continuous, have to be superimposed onto a
> discrete three dimensional lattice which advances in steps of time.

That's a load of rot! I was doing continuous space simulations during
my PhD. I'm doing continuous time simulations right now. OK - so I use
floating point arithmetic (which imposes its own discreteness), but in
principle there is nothing stopping one doing exact calculations by
implementing the same algorithm in a symbolic manipulator such as
Mathematica (its way slower, of course, and uses far too much computer
memory, so its not particularly practical). You can ask for your
results to as many decimal places as you wish after the simulation has

Lattice Gauge theories are an approximation of the standard model to
try to make them tractable. There is no requirement whatsoever that
any simulation we inhabit has to exhibit the same discreteness.

> The question that Beane and co ask is whether the lattice spacing imposes
> any kind of limitation on the physical processes we see in the universe.
> They examine, in particular, high energy processes, which probe smaller
> regions of space as they get more energetic
> What they find is interesting. They say that 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 do now with current technology. Finding the
> effect would be equivalent to being able to to 'see' the orientation of
> lattice on which our universe is simulated.

Even finding evidence of cubic lattice symmetry does not entail we are
living in a simulation (although that's another philosophical
question), but it would count as an interesting finding in itself.

> That's cool, mind-blowing even. But the calculations by Beane and co are
> not without some important caveats. One problem is that the computer
> lattice may be constructed in an entirely different way to the one
> envisaged by these guys.
> Another is that this effect is only measurable if the lattice cut off is
> the same as the GZK cut off. This occurs when the lattice spacing is about
> 10^-12 femtometers. If the spacing is significantly smaller than that,
> we'll see nothing.
> Nevertheless, it's surely worth looking for, if only to rule out the
> possibility that we're part of a simulation of this particular kind but
> secretly in the hope that we'll find good evidence of our robotic overlords
> once and for all.

All in all, just rampant speculation. There's no particularly good
evidence that we'd see anything but symmetric continuous space, so we
should be attempting to test that to the best of our experimental abilities.


Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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