eigenket

60 ms·

721.
by eigenket 6y ago
> However, across quantum mechanics, there is at least unity on the 'quantum' part. And that's really the point of contention here in terms of integer values, right? I don't know what this means, but there is this ide
722.
by eigenket 6y ago
I rather dislike this way of saying things. A matrix is a matrix, its a table of numbers, and one can usefully define operations like addition and multiplication on them. A linear map is a linear map, it maps between vector spaces and it ob
723.
by eigenket 6y ago
The paper is describing a test of a particular alternative to quantum mechanics called "real quantum mechanics", its rather more specific than you are suggesting https://arxiv.org/abs/2101.10873 I know a few
724.
by eigenket 6y ago
Quantum mechanics is not a discrete theory in the sense you seem to be suggesting. There is this idea that is is, which comes from the discrete energy levels it predicts for a simple harmonic oscillator, or the hydrogen atom, but quantities
725.
by eigenket 6y ago
Quantised is not synonymous with discretised. The fact that (for example) energy in a simple harmonic oscillator comes in discrete packets doesn't mean that the kinetic energy of a free particle is. Some quantities in quantum mechanics
726.
by eigenket 6y ago
*rectangles (hopefully)
727.
by eigenket 6y ago
You first define multiplication of natural numbers to be repeated addition, then define multiplication of rationals in terms of multiplication and addition of naturals, then define multiplication of reals in terms of multiplication of Cauch
728.
by eigenket 6y ago
I definitely wasn't trying to indicate that there was a problem with this, just pointing out that the path of using the Surreals (or anything else) to give an "algorithmic" description of real addition or multiplication is pr
729.
by eigenket 6y ago
Its probably worth emphasising that the recursion you need to "construct" the Surreals is infinite, in other words this does not give a reasonable algorithm to (for example) add two real numbers, you need S_omega in order to have
730.
by eigenket 6y ago
We're talking about matrix/matrix multiplication here, not matrix/vector, right?
731.
by eigenket 6y ago
Those keywords all appeared in the context of set theory long before category theory was thought of. Even ignoring that as a historical accident (we invented set theory before category theory), those ideas are all natural, meaningful and in
732.
by eigenket 6y ago
It looks exactly like scalar multiplication when your matrices are diagonal.
733.
by eigenket 6y ago
Yeah but your comment didn't use the concept of a "category" at all, whereas you used "set" three times. Its definitely more natural to say these definitions come from set theory.
734.
by eigenket 6y ago
Its probably worth pointing out that the system with only multiplication and no addition is also decidable (Skolem arithmetic). Things get interesting when you have both multiplication and addition defined and the reason for that is basical
735.
by eigenket 6y ago
Personally I do buy cereal partially based on values. I absolutely refuse to buy stuff from nestle.
736.
by eigenket 6y ago
I think this is not correct. A fundamental problem in quantum simulation of quantum systems is the Hamiltonian problem, where you give me a Hamiltonian H, which is the sum of polynomially many little local Hamiltonians H_i each of which act
737.
by eigenket 6y ago
I think maybe we're talking about different things? Could you be more precise about the sort of interference effects you're talking about? I generally wouldn't call entanglement an "interference effect". When I thin
738.
by eigenket 6y ago
Occam's razor is not trivial to apply when everyone claims that their own interpretation is the simplest.
739.
by eigenket 6y ago
Your two threads seem to be essentially the same thread. The "weird stuff" in entanglement comes pretty directly from collapse as part of measurement. If you drop this and go to something like many worlds then things look a bit ni
740.
by eigenket 6y ago
I think almost everyone in the field would reject your third claim. There is a great deal of work being done on applying the speedup afforded by quantum mechanics to classically hard problems. The current consensus (at least among people I
741.
by eigenket 6y ago
Gleason's theorem also makes a big assumption when you require that the measurement outcomes are associated with POVM elements (or projection operators if you don't like POVMs). I lumped that in with "assuming something equiv
742.
by eigenket 6y ago
By local I mean local in the sense of special relativity. Stuff at a point in spacetime only affects stuff at that point and in its causal future. If you want to affect something somewhere else then you have to fire a light particle or what
743.
by eigenket 6y ago
I am not aware of any interpretation that has the Born rule without assuming something equivalent to it. For example de Broglie–Bohm theory requires you to assume the original distribution of the particles follows the Born rule. QBists just
744.
by eigenket 6y ago
There are (at least) two local, deterministic interpretations of quantum mechanics (many worlds and superdeterminism). You are correct that Bell-type experiments put very strong constraints on such theories. If your theory is local it is go
745.
by eigenket 6y ago
I apologise for replying with what is essentially a rant, but as far as we can tell simulating quantum mechanics is exponentially (in the precise, mathematical sense) harder than simulating classical mechanics. I find it very "triggeri
746.
by eigenket 6y ago
People have already replied to a lot of you wrote here, so I just want to add that Einstein emphatically did not reject quantum theory. Indeed he is probably one of the people who could fairly be called the creator of quantum theory. What E
747.
by eigenket 6y ago
London is a massive outlier in basically every way compared to the rest of the UK, but London is still like 45% white British (according to the wiki page). In 2011 roughly 35% of the population of London was born outside the UK. In terms of
748.
by eigenket 6y ago
I can pretty easily work 8-10 hours in a day, and have done somewhat frequently in the run-up to important deadlines. I try not to because it absolutely kills my productivity for the next couple of days, so its almost always counterproducti
749.
by eigenket 6y ago
As someone who works in the quantum info / computation / foundations field I prefer "advantage" to "supremacy" not just because of all the racists using the word "supremacy" but also because advantage
750.
by eigenket 6y ago
I add this because no one seems to have mentioned it yet. Without experimenter freedom it is hard to make any inferences from the results of experiment. If the experimental choices you make are correlated with the stuff you're experime

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