"The Alternate View" columns of John G. Cramer

Published in the July-August-2013 issue of

This column was written and submitted 2/4/2013 and is copyrighted ©2013 by John G. Cramer.

All rights reserved. No part may be reproduced in any form without

Computer simulations of
the real world are becoming better and better as computer CPUs become faster,
memories larger, and software smarter and more extensive.
The CGI effects in movies done with computers are becoming
indistinguishable from scenes filmed with large casts of extras and expensive
props. Computer games are becoming
ever more "realistic", even as the blood and violence of the games
increases. The online virtual
world * Second Life* simulates a mini-universe, complete with realistic
avatars, an economy, and real estate, and has reached 21.3 million registered
users. Movies like

Swedish philosopher
Nick Bostrom of St. Cross College, University
of *How do we know with any certainty
that our perceived real world is not a computer simulation?*
He considers the possibility that humanity will eventually reach a
"post-human" stage, which he considers to be a culture that has
mastered artificial intelligence and has achieved the capability of
"perfect" simulations of reality and human consciousness with
near-infinite computing resources. Iain
M. Banks’ “The Culture”, described in a series of his space-opera novels,
is an example of such a post-human civilization.

Bostrom asserts that
individuals in such a post-human civilization can, if they choose, perform
near-perfect "ancestor simulations" of the past, including our own
era. He presents arguments leading
to the conclusion that one of three alternative propositions must be true.
Either (1) The human species is very likely to go extinct before reaching
such a post-human stage; or (2) The fraction of post-human civilizations that
are interested in running a significant number of ancestor simulations is
extremely small; or (3) ** We are almost certainly living in
such a computer simulation rather than the real world**.

The logic that led
Bostrom to item 3 is a statistical one: if over a given time period there are
very many simulations of the present-day period of history, each containing
simulated sentient individuals who think that they are experiencing the real
world, then the probability that a given sentient individual is *actually*
experiencing true reality rather than simulated reality is extremely small.

A group of theoretical
nuclear physicists at the

Let me first explain what QCD lattice gauge calculations are. The Standard Model uses quantum chromodynamics (QCD) to provide a detailed description of the strong interaction, the color force that acts between quarks through the medium of massless gluons. Physics in general has the perennial problem that, although it may be possible to accurately describe in detail the forces of the universe, the actions of these forces as they act between many particles quickly becomes so complex as to make calculations difficult or impossible. Theoretical physicists have developed many calculation techniques for dealing with the electromagnetic and weak interactions, because they become smaller with distance. However, most of these techniques are worthless for the strong interaction, because it grows stronger and stronger as the distance between two strongly interaction particle like quarks increases. The strong force is rather like a stretched spring that pulls harder and harder as the spring is stretched.

Therefore, QCD
calculations require a new approach. Lattice
QCD, as the name implies, represents space-time as a 4-dimensional lattice, a
grid with some spacing ** a** between lattice points.
For the most accurate calculations, one makes the extent

The lattice must end
somewhere, and problems arise at the surface boundaries where the lattice stops.
Conventionally, this problem is dealt with by connecting the left
boundary of the lattice, in each of the space dimensions, to the right boundary,
so that no particles on the lattice encounter a region where the lattice simply
stops. If you do this to a
2-dimensional sheet of rubber, gluing the left edge to the right edge and then
gluing the top edge of the resulting cylinder to its bottom edge, you get a
torus, i.e., a doughnut shape. Similarly
connecting the spatial edges of a 4-dimensionl space-time lattice means that the
space-time being simulated is a hyper-torus, and if a particle moves far enough
in any space direction, it comes back to where it started.
This is a peculiarity of such simulations, but if the lattice size ** L** is large enough, it
doesn’t affect the quality of the calculation.

Of particular interest
in lattice gauge calculations are the masses mesons or baryons, combination of 2
or 3 quarks. For example, one might
place an up-quark and an anti-down-quark at nearby points on the lattice, turn
on the gluon interactions as described by QCD, and observe the mass of the
resulting mass of the resulting pi-plus meson.
Alternatively, one might place two up-quarks and one down-quark on the
lattice and predict the mass of a proton. Usually,
this would be done as a function of the lattice spacing ** a**,
the quark masses, and perhaps the number of color degrees of freedom.
One would look for the predicted values to converge to a definite answer
as

My colleagues at the
University of Washington, Silas Beane, Zoreh Davoudi, and Martin Savage (BDS)
have been extending the application of lattice QCD to nuclei, i.e. systems of
quarks that form more than one proton or neutron. This
allows them to predict the masses of light nuclei (deuterium, ^{3}He, ^{4}He,
...) and to check the models of nuclear forces that are more conventionally used
in theoretical nuclear physics. They
hope to gain better understanding of the nuclear forces that hold neutrons and
protons together in a nucleus and provide stability against radioactive decay.
Their simulations, on the 0.1 fm (10^{-16} m) scale, can be
considered to be at the very beginning of what could ultimately, with more
computing resources, become a completely accurate simulation of atoms,
molecules, people, and universes.

They argue that any
simulation of the universe on a hyper-cubic lattice on the smallest distance
scales brings with it certain artifacts of the lattice that should show up in
experimental results. In particular,
they examine three experimental results that could conceivably highlight the
difference between the real world and a computer simulation: (1) the
gyromagnetic ratio ** g
**of the m lepton (or muon), (2)
the fine structure constant

The m
lepton is an electron-like fundamental particle with an electric charge ±** e**,
a "spin" angular momentum of ½ħ,
and a dipole magnetic field associated with its spin.
If it were simply a classical spinning sphere of charge, it would have a
dimensionless gyromagnetic ratio

The
fine structure constant ** a** is a dimensionless physical constant
slightly larger than 1/137 that characterizes the strength of the
electromagnetic interaction in our universe.
Its value can be experimentally determined in two different ways: (1) by
measuring the gyromagnetic ratio

Another
lattice artifact that might be expected from a simulation performed on a
hyper-cubic lattice is that, at sufficiently small wavelengths, energetic
particles produced in high energy collisions would begin to "see" the
lattice structure and to develop preferences for certain directions, breaking
the intrinsic rotational symmetry of space.
In particular, the maximum attainable velocity of a charged particle,
limited by its collision with the abundant photons of the cosmic microwave
background, might be different along the lattice than across the lattice,
and this might produce observable effects for the highest energy protons of
cosmic rays. BDS examines the
evidence for this cutoff in cosmic ray data and concludes that **1 /a** > 1×10

The conclusion of this exercise is that if we live in a simulation, it is a very good one, and either uses extremely powerful computers capable of simulations many orders of magnitude larger and more fine-grained than present technology would support, or uses qualitatively better computers (e.g., quantum computers), or uses qualitatively better simulation algorithms than assumed by BDS.

So, do we indeed live
in such a simulation? It seems to me
that, contrary to Bostrom’s arguments, the BDS work in itself rules out that
possibility, simply on the basis of the physical size of the computer that would
be required. Any lattice simulating
our universe would be very large. The
whole universe, with a diameter of about 10^{27} m, would have to be
represented by the lattice. If the
simulation extends only out to the Oort Cloud, a diameter of 10^{16} m
would have to be included. Using the
largest BDS minimum lattice spacing of about 10^{-23} m, this
would mean that the simulation array for the universe would have to need about
10^{50} elements on a side, or 10^{39} elements on a side for
the Oort Cloud simulation. The each point on such a lattice would require the
storage of some minimum number of bits, say 20, to represent its state.

How densely could such
information be stored in some hypothetical post-human supercomputer?
Let’s extrapolate that the post-human supercomputer could be made of
matter of nuclear density, say collapsed-matter neutronium, with the individual
neutrons spaced 1 fm apart and that each neutron could somehow store 20 bits of
information. The universe
simulation, even neglecting the time dimension and using a 3-D cube rather than
a 4-D hypercube, would have to be a cube 10^{35} meters (or 6.7 x 10^{23}
light years) on a side. The Oort
Cloud simulation would have to be a cube 10^{24} meters (or 6.7 x 10^{12}
light years) on a side. There is not
enough matter in the universe to construct such an object, and if constructed it
would immediately collapse into a giant black hole.

I conclude that not
even Iain M. Banks' * Culture* could manage such a feat.
Unless there is something in the BDS assumptions that that is so wrong
that changes the ground rules by 20 or so orders of magnitude, there is no way
that our present world could be a computer simulation.

**References:**

**Simulating
Reality:
**

"Are You Living In a Computer Simulation?", Nick Bostrom,

Philosophical Quarterly, #211, 243-255 (2003).53

**Experimental
Tests for Simulations:
**

"Testing Constraints on the Universe as a Numerical Simulation", Silas R. Beane, Zohreh Davoudi, and Martin J. Savage,

Physical Review Letters, 153001 (2012).109

** SF
Novels by John Cramer: **
my two hard SF novels,

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