I don’t understand the claim that Kolmogorov lower bounds are uncomputable. Three digit strings are unlikely to run as a program so surely 3 is a lower bound on Kolmogorov of the first million digits of pi, no? To tighten bound, one would need to try out every 4-digit program, every 5-digit program, and so on. Either these produce the first million digits of pi or they don’t when the program is run, so each possibility is checkable in finite time, no? There must be something I’m missing here.
Indeed, as you say, Decoherence explains why certain bases are special: when a system is in a pointer basis state, it does not continue entangling with environment (or, at least, does so minimally). When a spinning particle enters a Stern-Gerlach apparatus oriented in z-direction, spin-z is the pointer basis of the system during its time in the apparatus. A spin-up or spin-down particle does not entangle with the environment, but spin +x state would quickly entangle with environment, placing environment in a superposition and "branching" the total state vector of all the stuff in the universe.
Quantum Darwinism is just a refinement of this picture in which the "environment" interacting with the system is itself modeled a series of fragments (i.e. all the different photons that bounce off object). It turns out that the information about which pointer basis state the system is in (spin up or spin down) is redundantly encoded in each of these fragments. Hence, intercepting one photon that interacted with system and reveals "spin-up" (because the particle is in upper path) agrees with other photons that also bounce off object.
BUT, of course, due to linearity of unitary time evolution, there is another "branch" in which spin-down was the outcome of the measurement and everyone agrees on spin-down. This is exactly the Everett picture.
These debates over the interpretation of Quantum Mechanics (i.e. what ultimately happens when a “measurement” takes place) are important but don’t bear on the effectiveness of quantum computing. Regardless of your favorite interpretation (almost) everyone agrees that quantum computers should work and be able to do things classical computers cannot.
Yes, the MWI is falsifiable. It asserts that objective collapse does not occur, therefore any observation of objective collapse (such as predicted by GRW or Penrose-Diosi) would falsify it.
It doesn’t. Decoherence is the technical step in the Everett picture defining what a “classical branch” even is and explaining how the state vector branches. Every claim that “Decoherence” somehow offers a distinct interpretation to Everett is pure confusion.
Can you believe that This is Spinal Tap, The Sure Thing, Stand by Me, Princess Bride, When Harry Met Sally, Misery, and A Few Good Men were all directed by the same man? What an eclectic set of masterpieces.
The Maple syntax may superficially seem easier but actually leads to more problems in practice. The point of the [ ] is that argument of a function is logically distinct from algebraically grouping terms in an equation. Also, Mathematica is a camel case language since underscore is for pattern recognition, hence the capitalization of function names. Personally, I’ve found every little Mathematica design feature to be incredibly well thought out, logical, and consistently implemented over the whole of the language.
The introduction to Vol 1 of Weinberg’s Quantum Theory of Fields does this really well, albeit briefly. It feels like getting an “insider’s view” of the historical developments.
Ok, to be clear, let’s say I’m dumb and accidentally go with the default (I get the color of the opt out button wrong or something). As if there’s a “publish my private emails to the internet” default-on button in email. Then, I use it to edit a rec letter for student X, with my signature Y. (Yes I know this is dumb and I try changing names when editing but am sure some actual names may slip through.) A few months later the next model is released trained on the data. Student X asks Claude what Y would write in a rec letter about X. Such a button is a “wings stay on / wings fall off” button on a plane.
Everyone seems to be unsurprised by this move, but I’m genuinely shocked. What a shoot your own foot business decision. Google, evil though it be, doesn’t post the text of your gmails in its search results because who would consider using Gmail after that? This is the llm equivalent. Am I missing something?
As a physicist, fluid mechanics was the most glaring gap in my undergraduate preparation, despite its centrality to most physics applications. Somehow it is always a “time permitting” topic at the end of an already-cramped curriculum.
I first encountered the Euler equation in the context of GR — absurd. In another decade or two, I suspect its rightful place early in the physics curriculum will be emphasized.