From René Descartes to the Wachowskis (directors of the Matrix trilogy, amongst others) to Elon Musk, many have envisioned that our existence is just part of the scheme of a superior intelligence and our lives are merely part of a simulated reality. There’s obviously no evidence for it and there are actually many arguments against it, and now researchers think they have found a physical property that occurs in metals that cannot be simulated, telling us once and for all that our lives, good or bad, are actually real.
Researchers Zohar Ringel and Dmitry Kovrizhin, both from Oxford University, studied the computational methods to describe complex quantum systems. The study, published in Science Advances, did not set out to prove that reality is not a simulation. But it found that there are some quantum mechanics problems that cannot be simulated, as far as we know.
It all depends on how the problem can be worked out by computers. If the problem is linear, the computational resources need to scale up as the number of particles in the system increase. This can be very difficult but the bigger the computer, the more complex the system it can deal with. But problems can exist where the scale between particles and processors increases exponentially and soon it becomes impossible to simulate.
The research proves that a quantum mechanics phenomenon is definitely in the latter category. The gravitational anomaly known as the thermal Hall conductance happens when systems are exposed to incredibly high magnetic fields or extremely low temperatures. Its effects appear as electric currents related to the temperature gradient of the system or as a twist in the geometry of space-time.
The researchers tried to simulate this effect but found that the system became far more complex and that the simulation was ultimately impossible due to a matter of principle. Just to store the information of a few hundred electrons one might need more atoms than exist in the visible universe.
“Our work provides an intriguing link between two seemingly unrelated topics: gravitational anomalies and computational complexity. It also shows that the thermal Hall conductance is a genuine quantum effect: one for which no local classical analogue exists,” said co-author Professor Zohar Ringel, from Hebrew University, in a statement.
So to simulate these quantum effects, we’d need a computing method like we’ve never seen before. And by extension, the complexity of a system to simulate our entire reality is far beyond the realm of possibilities.