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Let's say we wanted to explain to some alien living in another universe with different laws of physics to how our universe worked, what is the shortest way of doing this?

A different way of looking at the question: what are all the laws of physics?

For example, $c$ being the speed of light would be something to include in that list, the photon would also be included. The proton would not be included, as it is composed of smaller substructures. Hooks law would not be part of that list, but Schrödinger's equation would.

Does this list, or at least our best guess at this list, exist somewhere?

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    $\begingroup$ Chances are there would be no way of communicating with an alien from a different universe with different laws of physics. In order to communicate you need to first establish a common frame of reference, so it would really depend on HOW different the laws are. If they are completely different, no communication is possible . You can talk about the "speed of light" but if they have no concept of "speed" or "light", it's meaningless babble. $\endgroup$
    – Hilmar
    Feb 8, 2022 at 15:20
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    $\begingroup$ in another universe Physics does not have any model or evidence for other universes. $\endgroup$ Feb 8, 2022 at 15:47
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    $\begingroup$ what are all the laws of physics This is a (long) list type question and those are almost always off-topic. $\endgroup$ Feb 8, 2022 at 15:48

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Well, you would have to learn to speak to them first and as this is likely to take some (read a long time), I don't think that it would be possible to have to describe to said alien a short description of how our universe works.

Also, there is no short description in our universe either. I mean human to human. Whilst some physicists dream of a formula of the universe you can print on a t-shirt. This is chimerical. Because such a description requires understanding and unpacking the meaning behind such a formula. All this takes time too.

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Here is the equation you wanted: $$ S = 0. $$ (Ta-da!)

Oh yes I forget to say what $S$ is. It is a sum: $$ S = f_1^2 + f_2^2 + f_3^2 + \cdots f_n^2. $$ Each $f$ in this sum is the left hand side of a formula in real numbers describing something about the universe. The right hand side of each formula is zero. For example if you wanted to include Newton's second law you could have $$ f_1 = ({\bf f} - m {\bf a}) \cdot ({\bf f} - m {\bf a}) $$ and you would have to explain what is meant by the symbols ${\bf f}$, $m$ and ${\bf a}$. Or you might want to include Schrodinger's equation: $$ f_2 = \langle \psi | \hat{H} - i \hbar \frac{d}{dt} | \psi \rangle $$ only now you have to explain what the notation $| \psi \rangle$ and $\hat{H}$ refers to, and so on.

The point of all this is to show that there is no such thing as a short answer. Instead what you can hope for is to learn deeper and more general ideas and methods. Compare it with the job of learning to be a grand master at chess.

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