How to Rewrite the Laws of Physics in the Language of Impossibility

How to Rewrite the Laws of Physics in the Language of Impossibility

Amanda Gefter

At the heart of constructor theory is the feeling that there’s something missing in our usual approach to physics.

The standard laws of physics — such as quantum theory, general relativity, even Newton’s laws — are formulated in terms of trajectories of objects and what happens to them given some initial conditions. But there are some phenomena in nature that you can’t quite capture in terms of trajectories — phenomena like the physics of life or the physics of information. To capture those, you need counterfactuals.

Which are?

The word “counterfactual” is used in various ways, but I mean a specific thing: A counterfactual is a statement about which transformations are possible and which are impossible in a physical system. A transformation is possible when you have a “constructor” that can perform a task and then retain the capacity to perform it again. In biology, we call that a catalyst, but more generally we can call it a constructor.

What you do is state the law in terms of possible and impossible tasks, and then work out the consequences. For instance, if you have this general statement that perpetual motion machines are impossible, you can combine it with other statements about other tasks being possible or not and work out that a heat engine is possible. And that gives you a lot of predictive power. That’s the logic. You take these statements as fundamental.

The universal constructor is an analogue of the Turing machine in the sense that it’s supposed to be able to perform all physically allowed tasks. And we don’t know if one is possible under the laws of physics that we have. And the reason we don’t know, even 70 years after von Neumann first suggested this, is that nobody took the original proposal and connected it to physics.

Once constructor theory can define the universal constructor in physical terms and understand the principles that allow you to say that the universal constructor is possible, then we will have an answer to your question — we’ll know what are the elementary gates or elementary possible tasks that the universal constructor can appeal to when it’s trying to perform a complicated task.