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Constructor theory turns this approach on its head. Deutsch’s new fundamental principle is that all laws of physics are expressible entirely in terms of the physical transformations that are possible and those that are impossible.
In other words, the laws of physics do not tell you what is possible and impossible, they are the result of what is possible and impossible. So reasoning about the physical transformations that are possible and impossible leads to the laws of physics.
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The analogy that he draws is with conservation laws such as the conservation of energy. This is not a law of physics like quantum mechanics or relativity but a principle that all other laws must follow. As energy is converted from chemical to electrical to kinetic to potential energy and so on, its behaviour is governed by all kinds of different laws of physics. But they must all obey the principle that energy is conserved.
“Thus the conservation law, though not an a priori mathematical truth, provides an explanation of aspects of motion that is deeper than laws of motion,” say Deutsch.
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This approach solves a number of problems. In particular, information has always been difficult to define. In conventional information theory, information and distinguishability are each defined in terms of the other, creating a kind of chicken and egg problem.
But in constructor theory, the nature of information is determined by the laws of physics alone. That neatly sidesteps the problem.
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The big unanswered question about constructor theory is how useful it will turn out to be. Deutsch is fascinated by the fundamental properties of reality and for him a deeper explanation is reason enough to explore further.
Others will demand more—testable hypotheses, for example, that can determine whether constructor theory is true or not. These kinds of predictions will surely emerge as more physicists discover Deutsch’s new way of thinking.
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