September 22, 2021

I, Science

The science magazine of Imperial College

If The Matrix was real how would we know? Could an experiment ever provide the answer?

“Take the blue pill and the story ends, you wake up and believe whatever you want to believe. Or take the red pill, stay in wonderland, and see how deep the rabbit hole goes” [Morpheus, The Matrix (1999)].

In the film The Matrix humanity has become confined to an existence within a highly detailed artificial reality. Over a decade later, the idea that we could be living in a computer simulation continues to intrigue us. Several years ago Oxford University professor Nick Bostrom postulated the simulation argument, and now physicists at the University of Bonn in Germany say it may be possible for us to actually test it.

The simulation argument, or hypothesis, put simply, is the postulation that our reality is a simulation and that we are unaware of this. The idea frequently features in some way in science fiction, most notably in Star Trek and in films such as The Truman Show and Inception. This concept can be thought of as similar to the holodeck in Star Trek, where the crew on board the spaceship can simulate an artificial reality that they can then play out scenarios within.

According to the physicists, if the universe is a simulation then it will have certain constraints, so we can find out if they are there. The team’s work, ‘Constraints on the Universe as a Numerical Simulation’, essentially involves studying a computer simulation of our universe, investigating the fundamental properties of its artificial construction and how that knowledge can be used towards the further understanding of our own reality.

The reasoning is that if the universe is just a mathematical simulation, then there should be clues around us, glitches in the system, which could reveal its true nature. The main problem with any simulation is that ultimately it is not smooth, not totally perfect. In order to model physical phenomena, including the laws of physics, the world has to be represented by numerous separate points in space and time. Even though the separation distance can be incredibly small, a three-dimensional grid structure always exists. So in a computer-simulated world there would be limits on the energy particles can have, because nothing can exist that is smaller than the spacing between these lattice points.

A limit like this does actually exist in our universe – high energy particles are subject to the well studied Greisen-Zatsepin-Kuzmin (GZK) cut-off condition. This limits the energy that cosmic rays can have, and results from particles losing energy due to interactions with the cosmic microwave background as they travel long distances across the universe.

The researchers created a detailed computer simulation of our universe, which models quantum chromodynamics (QCD). This theory describes how the strong nuclear force binds together quarks and gluons into protons and neutrons, which then form nuclei that interact. It describes the universe at a fundamental level, so it is believed that the QCD simulation is equivalent to simulating accurately the workings of our universe. In the simulation, spacetime, the fabric of the universe, is replicated by tiny cubic lattices in a process known as lattice gauge theory. At the moment the simulation only models nuclei and their interactions, but the researchers believe it could eventually be extended to include modelling of larger things like molecules and potentially even humans. The most interesting outcome is that the simulation is effectively indistinguishable from the real thing – at least on our level of understanding.

These QCD processes are complex, and so take a lot of computing power to model. Even using the world’s most powerful supercomputers, physicists have still only managed to simulate tiny regions of space (on the femtometre scale, that is, just a few quadrillionths of a metre).  It is likely that eventually, with greater computing power, physicists will be able to simulate larger regions of space. Even if they managed just a few micrometers, that would allow for the modelling of biological cells.

There’s also something else to look for. These cosmic rays would have a tendency to travel along the gridlines of the lattice, so they wouldn’t show up equally in all directions. This is something that can be checked using current technology, and the researchers point out that seeing this effect would be the same as seeing the lattice on which our universe is simulated.

However there are some limitations, and not finding evidence wouldn’t necessary rule out the theory of a computer-simulated world. The experimental research can only identify a certain type of simulation, which may well be different to the one we are searching for. The computer simulation, if it does exist, could be based on technology far superior to our understanding.  The cosmic rays’ theoretically preferred direction of travel would only be apparent if the lattice spacing is the same as the GZK cut-off. This occurs when the lattice spacing is about 10-12 femtometres – if it is smaller than that, there is no way of us finding it. Even if these conditions were found, it would be difficult to definitively say this is due to the universe being a simulation. It would be much more likely that the result arose from inaccuracies in the model. We may be able to create a highly accurate model of our own universe, including simulating ourselves, but still be unable to determine if we are likewise living in a simulated world.

In 2009 it was reported that the GEO600 gravitational wave detector had potentially given us a real insight into the theory of a simulated reality. Unexpected noise affecting the experiment was attributed to the fundamental limit of spacetime – the point where spacetime stops behaving as a smooth continuum and instead exists in a granular state. Theoretical physicists have long believed that the fabric of spacetime is grainy, similarly to pixels making up an image, and would have waviness due to energy fluctuations described by Heisenberg’s quantum-mechanical uncertainty principle.

The size of this granulation is billionths of billionths of the size of protons, defined by a distance known as the Planck length, which is 10-35 metres. This scale is far beyond the reach of any experiment, so finding evidence of it was unexpected. However, new investigative work on the noise has shown that it actually needs to be much smaller than that found by GEO600 to be confidently attributed to an artificial construct. Ongoing and future research work on detecting gravitational waves has the potential to also find evidence of an artificial reality, a far more fundamental property of nature.

Digital physics, a collection of theoretical perspectives postulating that that the world can be explained and therefore modelled as a computer program, offers an alternative approach to finding out the nature of reality. One aspect of this is a concept by John Wheeler called “it for bit” that states “everything in the universe derives its existence entirely from the outcome of yes/no questions, binary choices, digital bits”. This idea that the entire universe is effectively just a digital computer was actually first proposed by computer scientist Konrad Zuse in his 1969 book Calculating Space. This concept has gained some following in physics, with recent work showing that the mathematical equations we use to describe the laws of physics may contain elements analogous to computer code.

Whether our universe is a computer simulation or not, the reality is that we are not aware of the majority of the world around us. We can only see a small proportion of light, called the visible spectrum, and are mostly unaware of both the higher and lower frequency electromagnetic radiation that’s all around us. Similarly, we can only hear a small range of audio frequencies. We still have to explore the depths of the oceans, and are yet to venture far into space. Perhaps most poignant, we live on a tiny planet in an incomprehensively vast universe of which we only understand 4% despite all our scientific and technological advances. It seems we need to first find the rabbit hole before we can jump in and see how deep it goes.

IMAGE: ThomasThomas, flickr.