Our physics is based on variables, such as acceleration and mass. Some of these can be reduced to more fundamental variables, like distance and time. If there is another way to quantify the workings of the universe, we haven't yet grasped it. However, the variables we are familiar with may not be the only ones, as Columbia roboticists just found out.
Dr Boyuan Chen and co-authors trained an artificial intelligence (AI) system to count the number of variables needed to describe physical systems and predict developments. The results have been reported in Nature Computational Science, but this is just the beginning, as we are only starting to understand the variables the computers deduced.
"I always wondered, if we ever met an intelligent alien race, would they have discovered the same physics laws as we have, or might they describe the universe in a different way?" said senior author Professor Hod Lipson in a statement. "Perhaps some phenomena seem enigmatically complex because we are trying to understand them using the wrong set of variables.”
After all, the paper notes: “It took civilizations millennia to formalize basic mechanical variables such as mass, momentum, and acceleration. Only once these notions were formalized could laws of mechanical motion be discovered.” Similarly, you can't derive the laws of thermodynamics without formal concepts of temperature, energy, and entropy. At least some of these are now intuitive to us, but they weren't to our ancestors.
Occasionally scientists get a small glimpse of how the universe would look if we started with different variables. Mathematician Norman Wildberger created what he calls “rational trigonometry” by replacing the familiar variables in triangles – length and angle – with squares of the length and sine of the angle, which he calls quadrance and spread. Some problems become much easier when tackled with these variables, but to anyone trained in Euclidean geometry it at first feels like speaking a foreign language.
Some cultures – most famously the native American Hopi – are also claimed to view variables such as time differently from most of the rest of the world, giving them a fundamentally different view of physics.
To find variables even more alien to us we would need to consult someone raised with no exposure to familiar concepts like angle and distance. It being illegal to bring up a child like this, the authors turned to AI, starting with a video of elastic double pendulums.
A physicist looking at a double pendulum system most likely sees four variables – the angle and angular velocity of each arm. The four are intuitive to us and easily measured. However, undergraduate physics students are trained to also model the system in terms of each arm's kinetic and potential energy.
The authors showed a neural network a video of a double pendulum and asked it how many state variables it saw. Although the answer was four, the computer and the humans lacked the common language to establish what these variables were. Two appear to be similar to the way we measure arm angles, but the others remain a puzzle.
“We tried correlating the other variables with anything and everything we could think of: angular and linear velocities, kinetic and potential energy, and various combinations of known quantities," explained Chen. "But nothing seemed to match perfectly." However, the network predicted the pendulum's future movements so well it seems it had identified real variables, even if they are strange to us.
The authors followed up by showing the computer much more complex dynamical systems, such as an “air dancer” outside a nearby car dealer, a lava lamp, and flames in a fireplace. It reported there were respectively eight, eight, and 24 state variables required to describe these systems, but what these are no one yet knows.
Previous machine learning tools have modeled the dynamics of physical systems but were provided with measurements of relevant state variables, that is quantitative variables that fully describe the system as it evolves. Once taught in this way, the machines were unlikely to come up with alternative variables of their own.
Now it seems AI systems can indeed identify new variables – we just need a translator to understand what they are.
