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So my argument for this is that the expansion of knowledge in any field of physics depends on what is previously known, and what we physicists express or knowledge as equations. So here's what I imagine it would look like:

For example, lets the field of quantum mechanics:

  1. Express all the governing laws and theories of quantum mechanics (from uncertainty to Klein-Gordon relations to conservation laws). Each variable must explicitly be expressed as it appears in every other equation you use, and it would obviously need to be in a language capable of solving differentials and other complex mathematical methods.

  2. For each solved variable, use substitution from other equations, and perhaps by this, new equations are formed.

  3. Since we know not all equations are distinctly general, "new" equations need to be checked; the computation to get to the new solution must be valid.

This must obviously be done via supercomputer since there is a large body of equations, and rules for upper level mathematical methods would have to be expressed as well. But basically, by brute force, we could program to solve all the entangled equations as a system, thereby, leading to possibly new theories based on existing knowledge.

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    $\begingroup$ We have a saying in physics for that. Weinberg's First Law of progress in theoretical physics: "You will get nowhere by churning equations." $\endgroup$ – knzhou Feb 22 at 23:09
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    $\begingroup$ @knzhou, I suspect that for less experienced physics students, there is a hidden assumption that physics is a mathematical pursuit. In my opinion, there is a very subtle distinction to be made here, as physics is actually concept driven, and the math "falls out" of those concepts. $\endgroup$ – David White Feb 23 at 1:26
  • $\begingroup$ Reminds me of the Infinite monkey theorem . Anyway, simulation or computation of "new" physics is possible, where "new" means that there are no (or hardly) other efficient tools to understand the problem. 2 examples are lattice gauge theory and black hole/neutron star mergers. $\endgroup$ – Avantgarde Feb 23 at 1:41
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This does not work. The reason is that physics is about understanding, not just making equations. For example, I can easily combine the law of gravity $F=GM_1m_2/r^2$ with Hooke's law $F=kx$ and get $$kr^3=Gm_1m_2$$ (here I assumed the software was smart enough to realize that the distance in Hooke's law should be equated to the radius in the gravitational formula). What does that formula mean? You could interpret it as some kind of distance where a spring would place a mass if gravity was repulsive... but it is a stretch, and even coming up with that requires knowing what the semantics of the two laws are. It does not tell us anything new or profound.

It is fairly trivial to make systems that can endlessly substitute and rewrite strings representing formulas, but the number of possible formulas grows exponentially as they get longer. And the vast majority does not mean anything in particular.

One can (even if my philosopher colleagues will justifiably protest) loosely define knowledge as mental compression of a lot of data and examples into relatively simple patterns that can explain them. Ideally in such a form that we can predict new data or answer what-if questions. This might be doable by computer under some circumstances. But it requires a fairly sophisticated understanding on what "simple" means, and it is by no means trivial to program.

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  • $\begingroup$ wait 10 years from now $\endgroup$ – Wolphram jonny Feb 23 at 1:30
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to add slightly to the answer by Anders Sandberg and knzhou's comment: equations get churned commonly where a solution to a problem requires the computationally-intensive process of splitting the problem up into a bunch of tiny pieces, solving for their behavior, and then sharing those responses with their nearest neighbors, and clanking the solution across the whole population of little pieces (the so-called "finite element" approach). This yields useful results in the world of engineering aerodynamics (for example) but it fails to shed any light on the underlying physics of transonic flow over airfoils.

In the world of physics, the churn approach can beneficially be used to iteratively converge upon an approximate solution to a problem that doesn't admit to one in closed form, but even then the churn doesn't uncover any fundamental insights- it just gives you a solution good to a couple of decimal places.

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  • $\begingroup$ I'd consider the "shared responses with nearest neighbors" bit due to discretization of space & time on a computer and not strictly confined to "finite element" approach. $\endgroup$ – Kyle Kanos Feb 23 at 15:37
  • $\begingroup$ @KyleKanos, that's fine too, my intent was not to furnish all possible examples, only the ones I understood myself. $\endgroup$ – niels nielsen Feb 23 at 16:43

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