by sopchi on 2/2/23, 11:42 PM with 5 comments
by sdwr on 2/3/23, 3:13 AM
Felt like a proper stab at combining physics + CS, thin on details, but fertile ground. Wolfram is an explorer there, barely charting the edges of an unknown continent.
The speed of light, light cones, and speed/time equivalence make a ton of sense through the lens of updates propagating through a grid of cells.
Don't remember the QM part so well, but from what I do remember, he proposes that probability/alternate timelines are subject to the same computational constraints over probability space, that physical objects have in real space.
As an aside, entangled particles were only ever a conceptual issue, right? From an engineering perspective they seem completely practical.
by machina_ex_deus on 2/3/23, 11:38 AM
In classical mechanics, Liouville's theorem makes phase space density incompressible, so you get that entropy always increases. In quantum mechanics, unitarity gives the same incompressibility - the density matrix change with time is multiplying by a unitary matrix left and right, which preserves the eigenvalues, so the entropy, being sum of the log of eigenvalues, stays the same.
The opposite is also obvious: in a system which is irreversible, look at an ensemble of two states which evolve to a single state. The entropy before was 1 bit, after the evolution it's 0 bits. So the system violates the second law.