Humans are not living in a computer simulation controlled by alien overlords, according to a study that debunks a theory popular among science fiction fans and many modern philosophers. Following the popularity of 90s classic The Matrix many have questioned whether our world is a mere simulation and humans are in reality just a "Brain in a Vat". Researchers at University of Oxford in the UK and Hebrew University in Israel found proof that such a simulation is impossible as a matter of principle.
The study, published in the journal Science Advances, showed that the complexity of this simulation - can be measured in a number of processor hours, memory size and electricity bills - increases in line with the number of particles one would have to simulate. If the amount of computational resources required for a quantum simulation increases slowly with the number of particles in the system, then one has to double a number of processors, memory, etc in order to be able to simulate a system twice as large in the same amount of time.
However, if the growth is exponential, or in other words if for every extra particle one has to double the number of processors, memory, etc, then this task becomes intractable. Just to store the information about a few hundred electrons on a computer one would require a memory built from more atoms than there are in the universe. Researchers identified a particular physical phenomenon that cannot be captured by any local quantum - Monte-Carlo simulation.
It is a curious effect, which has been known for decades, but has only ever been measured indirectly. In the field of condensed matter physics, it is called the "thermal Hall conductance" and in high-energy physics it is known as a "gravitational anomaly", researchers said. Thermal Hall conductance implies a generation of energy currents in the direction transverse to either temperature gradient, or a twist in the underlying geometry of space-time.
Many physical systems in high magnetic fields and at very low temperatures are believed to exhibit this effect. Researchers showed that for systems exhibiting gravitational anomalies the quantities which are involved in quantum Monte-Carlo simulations will acquire a negative sign or become complex. This ruins the effectiveness of the Monte-Carlo approach through what is known as "the sign-problem".
Finding a solution to "the sign problem" would make large-scale quantum simulations possible, so that the proof that this problem cannot be solved for some systems, is an important one, researchers said. "Our work provides an intriguing link between two seemingly unrelated topics: gravitational anomalies and computational complexity," said Zohar Ringel, professor at Hebrew University. "It also shows that the thermal Hall conductance is a genuine quantum effect: one for which no local classical analogue exists," said Ringel.