Do we live in a simulation? One little known theory proves Elon Musk wrong

What if the world around us was not real? Could it be that the screen you’re looking at, the air you’re breathing, the ground beneath your feet and even the smallest particles that make up your body do not really exist?

Is it possible, maybe even likely, that the chaos of the world around us is the result of an advanced computer simulation? That we are simply characters in someone else’s game?

The idea, and fear, that reality is not as it seems can be traced back thousands of years, through the Chinese philosopher Zhuangzi’s ‘butterfly dream’ to films such as, most famously, The Matrix.

“If you’re talking about what you can feel, what you can smell, what you can taste and see, then ‘real’ is simply electrical signals interpreted by your brain”, Morpheus infamously tells Neo, before revealing the horrifying truth.

In 2003, philosopher Nick Bostrom made the possibility seem inevitable. He argued that future civilisations could have access to vast amounts of computing power, which could run a near-infinite number of simulations.

If that is the case, the likelihood of us being in one of the billions of historical simulations seems almost certain – or else post-human societies have no reason to simulate histories, or never reach the technological capability.

Over the decade that followed, the idea has been promoted by Elon Musk (who has said the odds are ‘one in billions’ that our world is real) and Neil DeGrasse Tyson (who reduces the odds to a still-troubling 50:50). Silicon Valley billionaires have even reportedly attempted to investigate it themselves, with two going “so far as to secretly engage scientists to work on breaking us out of the simulation”.

Fortunately – or perhaps unfortunately – there is nothing to break us out of. As far as we are currently aware, that is. This world is the real one because our universe cannot be simulated, and mathematicians have known this for years precisely because they are trying to simulate it.

The clockwork universe

The argument for a simulation can seem attractive, at least on its face . 40 years ago, the height of technology was Pong, a mere two pixels and a rectangle; now, we have photorealistic graphics at our fingertips, along with deepfakes and virtual reality. It seems inevitable that future civilisations will improve even further and could simulate scenarios from their distant past.

With so many possible scenarios, it is easy to believe we are more likely to be living in a simulation than we are in the real world.

Even before dealing with the scientific issues, this argument hits a few walls: the assumption that such a future civilisation could ever exist, for example, or that the species would want to simulate humans, the Earth, or indeed even this galaxy. It is as plausible as the existence of God, or the multiverse; possible, certainly, but scientifically unhelpful.

This argument is also guided by our own perception of science, space, and time. When Isaac Newton derived the laws of motion over 300 years ago, philosophers of the time compared it to the most elegant scientific advances man had made: clocks. The rhythm of the universe, both on Earth and in the stars, was so precise that the analogy seemed obvious.

Theologian William Paley used the analogy in his arguments for the existence of God. Finding a watch among the grass, he wrote, one would assume the existence of a watchmaker, just as one implies the existence of God from the world.

“Every indication of contrivance, every manifestation of design, which existed in the watch, exists in the works of nature; with the difference, on the side of nature, of being greater or more, and that in a degree which exceeds all computation”, he wrote.

Neither Newton nor Paley had to contend with the complexity of today’s universe, however, which has revealed itself as one with such bizarre quirks: superposition, string theory, quantum mechanics, dark matter. Over time – like clockwork – the belief in a mechanised universe wore out as we discovered more about reality.

“In 50 years or 100 years’ time, [a simulated universe will] appear just as childish as the clockwork universe”, David Tong, professor of theoretical physics at Cambridge University, told The Independent.

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The ‘pixels’ of reality

Scientists have spent many years looking to understand the origins of the universe, usually in two ways: studying the very large, or studying the very small.

Paley implied the existence of the watchmaker to explain the source of life while simulation advocates look to the possibility of simulators. In physics, the best explanation for the universe is the Big Bang, and the cosmic background radiation it has left behind. Evidence that this has been simulated, however, is few and far between. In lieu of the stars, we look at the subatomic.

If the universe was a clock, where would we find its gears? If the universe was a simulation, where would we find its pixels?

A quality of both gears and pixels is that they are “discrete ”. In mathematics, this means that are isolated from each other, each part distinct from another – like Lego bricks affixed upon their base. A giant Lego sphere may look perfectly smooth from a distance, but close-up examination would reveal these individual blocks.

“If you try to simulate Grand Theft Auto … you can’t go down to infinitesimally small points. There are pixels. There is a minimum space”, Professor Tong explains.

The universe, as far as can be understood, is not like Lego, or Grand Theft Auto. People do not respawn. Trains are not NPCs wearing hats. It might look like it all works on the surface, but video game characters are not doing the science to check.

It is potentially possible that the universe has a ‘pixel’, but that current scientific knowledge cannot adequately examine it. One of the smallest scales we know is the Planck length. This is the length the universe was after the first 10−43 seconds of Big Bang, while it was expanding.

Unfortunately, the Planck length is 15 orders of magnitude away from what we can currently test with the Large Hadron Collider – and would still not be enough to prove the universe is a simulation, just that it might be discrete.

The discovery of a discrete distance in our universe would merely “rock our understanding of physics”, Professor Tong says, although is unlikely to happen “within our lifetimes” and require funds vastly beyond the means of a few billionaires.

‘Things can happen in a mirror can’t happen in the real world’

Even then, the universe presents another barrier: the Nielsen–Ninomiya theorem. This is a no-go theorem – an impossibility, where a situation can happen in the universe but not in simulations. And it’s about hands.

The history of this mathematical proof goes back to the 1950s and is the elephant in the room that simulation theorists cannot scientifically argue against. “If you want to engage with [the simulation hypothesis] properly, it’s very clear that this is an issue you have to deal with”, Professor Tong says, “and nobody mentions it.”

Imagine you are looking in a mirror and wave to yourself. Your reflection mimics you, raising their opposite arm. This is an example of “chirality”, from the Greek for “hand”. An object that is distinguishable from its mirror image is chiral. A left hand cannot be superimposed over the right.

This quality is found in large molecules – like those in fruit. One might think an orange and a lemon peel are distinctly different (in colour, taste, and smell) but both peels contain a molecule called limonene which are reversed versions of each other.

The same can be said of mint and caraway, each a reflection of the molecule carvone, and, tragically, the thalidomide drug, which is toxic in its mirror image and resulted in thousands of children born with severe birth defects.

In December 1956, chirality was found by Chien Shiung-Wu as she watched atoms die. These were cobalt-60 atoms, which are radioactive and shoot off an electron as they decay to become nickel-60.

The electrons should have decayed in a random direction relative to their spin whether they were in the real world or in the mirror world. Instead, they expressed a ‘preference’ to the direction they decayed. Imagine looking in a mirror and holding up a newspaper, but instead of seeing the letters reversed the words are perfectly readable – as if someone from an alternate world was holding their own back to you. On a subatomic scale, this is what Wu discovered.

Chien-shiung Wu, professor of physics at Columbia University and one of the world’s foremost experimental physicists (Smithsonian Institution Archives)

The proof of the real

Simulating the laws of physics in a computer is where these two issues – chirality and discretisation – come to clash.

In the real world, if space is periodic – a word in quantum mechanics that translates roughly here as “a circle” – then momentum is discrete, made up of distinct parts. Conversely, the laws of physics state that if space is discrete – such as in a simulation – momentum is a circle. Get enough momentum and, mathematically, you get back to where you started from.

This is a little like playing Pac-Man, reaching the right-hand edge of the maze, and coming back out the left-hand edge. Each pill Pac-Man eats is a discrete point in the simulation and if Pac-Man was a chiral particle he could only move one way, along the width of the maze, in one dimension.

For Pac-Man to reach the right-hand edge he requires a huge amount of energy, but when he enters again from the edge all that energy is gone.

In physics, this is impossible, because Pac-Man has ‘moved’ from the right to the left despite only being able to travel in one direction; today’s simulations manage this by creating a ‘mirror’ Pac-Man that moves the other way, left to right, and mathematically is in fact the same Pac-Man.

In the real world, this would equate to electrons from cobalt-60 atoms that move in the opposite direction – but since these do not exist the universe, as far as we know it, is real.

The caveat to all of this, however, is that scientists do simulate the universe. There are parts of the laws of physics where the mirror universe does not matter. Magnetism, electricity, gravity, and the strong nuclear force that binds quarks together does not know about parity.

In the mirror, these forces behave the same, “blind to the spin of particles”, David Berman, a professor of theoretical physics at Queen Mary University, says.

Scientists have been working for 20 years to try and simulate chiral particles, he adds, but “in the end what they do is they don’t … they get around it [by simulating both ‘hands’ of particles], and then just throw away the other one” when looking at the results.

Simulation advocates will try and argue around this with more complex scenarios. “There is a distinction between being able to simulate the universe completely [at] the level of fundamental physics, on the one hand, and being able to simulate the perceptions and experiences of a human being or all human beings on the other hand”, Nick Bostrom, the University of Oxford philosopher who is one of the most infamous figures among simulation advocates, tells The Independent. “It is only the latter that is relevant for the simulation argument.”

Bostrom suggests such a simulation could rely on procedural generation to only generate what scientists are looking at when they are looking at it. The ground beneath your feet only feels solid; it is not until you dig into the dirt that the soil manifests. The chiral boson only exists when scientists attempt to measure it.

Neil deGrasse Tyson has suggested something similar about the speed of light being the limit of travel, because if we moved any faster our mysterious overlords would not be able to simulate our universe quickly enough – what is known as the “light cone”.

But the universe is complicated, Professor Berman says, and “nature seems to know about everything”. Astronomers have astonishingly spotted the same supernova exploding four times in four different places because of the curvature of light around gravity, and general relativity throws a spanner in the works of causal connection. This makes it very hard, he argues, to simulate parts of the universe without necessarily simulating the whole thing.

Currently, our understanding of science stands between reality and the simulation hypothesis. Occam’s Razor, that the simplest explanation is usually the best one, remains a tough nut to crack. “There are so many amazing things in the universe that are true”, Professor Tong says. “Why are [people] going on about made up stuff?”

However, simulation advocates may take some solace in the main lesson of the past: we could be wrong. The science that disputes the simulation theory is based on our understanding of how simulations are made – on a lattice. Future civilisations may use something different. Maybe we are, in fact, just simulated.

“Any notion of discretisation is necessarily far too naive to exclude or confirm simulation by some advanced civilisation”, quantum theorist and founder Paul Ginsparg told The Independent.

Philosophically, however, whether we are in a simulation barely affects our actual existence. Descartes, in his Meditations, proposed something like an analogue version of the simulation: the existence of an “evil demon” that can create a perfect illusion of the world, overwhelming humans’ sense of sight, touch, taste, sound, and smell. If that were true, would it make so much of a difference?

In physics, the simulation argument has no bearing on the experiments scientists conduct either. “You get told you’re in a computer simulation, it sounds like it’s a big deal, but how should that change the kind of experiments we do in physics or the ways we’re attempting to understand the universe around us? The answer is almost zero”, Professor Tong says.

The truth about our reality will not be wrought from mystery without a fight. Our progression from Galileo’s geocentric view of the universe, through the clockwork one, to the strange quantum realms physicists and mathematicians study now took hundreds of years. And rarely are the developments – and their complex explanations – ever as compelling as high-concept ideas presented in an easy-to-consume YouTube video or tweet.

“I’m frequently convinced we’re living in a large-scale re-enactment of The Matrix movie anyway”, Professor Ginsparg quips, “with billions of people plugged into their smartphones as though attached by umbilical cord.”