I think you're just describing a state machine, no? The fact that you encode the state in a vector and steps by matrices is an implementation detail...?
Perhaps a probabilistic FSM describes the actual computational process better since we don’t have a concept equivalent to superposition with transformers (I think?), but the framework of a FSM alone doesn’t seem to capture the specifics of where the model/machine comes from (what I’m calling the Hamiltonian), nor how a given context window (the subsystem) relates to it. The change of basis that involves the attention mechanism (to achieve context-awareness) seems to align better with existing concepts in QM.
One might model the human brain as a FSM as well, but I’m not sure I’d call the predictive ability of the brain an implementation detail.
In my question I was asking about a hypothetical time-evolution operator that includes an analog of a light cone that you could think of as a context window. If you had a quantum state that was evolved through time by this operator then I think you could think of the speed of light being a byproduct of the width of the context window of some operator that progresses the quantum state forward by some time interval.
Note I am very much hobbyist-tier with physics so I could also be way off base and this could all be nonsense.
I’m way out of my depth here, but wouldn’t such a function have to encode an amount of information/state orders of magnitude larger than the definition of the function itself?
If this turns out to be possible, we will have found the solution to the Sloot mystery :D
The article references patent “1009908C2” but I can’t find it in the Dutch patent site, nor Google Patent search.
The rest of the article has “crank” written all over it; almost certainly investor fraud too - it’d be straightforward to fake the claimed smartcard video thing to a nontechnical observer - though not quite as egregious as Steorn Orbo or Theranos though.
Not who you asked (and I don't quite understand everything) but I think that's about right, except in the continuous world. You pick an encoding scheme (either the Lagrangian or the Hamiltonian) to go from state -> vector. You have a "rules" matrix, very roughly similar to a Markov matrix, H, and (stretching the limit of my knowledge here) exp(-iHt) very roughly "translates" from the discrete stepwise world to the continuous world. I'm sure that last part made more knowledgeable people cringe, but it's roughly in the right direction. The part I don't understand at all is the -i factor: exp(-it) just circles back on itself after t=2pi, so it feels like exp(-iHt) should be a periodic function?
Yes, exp(-iHt) means the vector state is rotating as time passes, and it rotates faster when the Hamiltonian (energy) is bigger. This rotation gives the wave like behavior.
Slightly related, there is an old video of Feynman where he tries to teach quantum mechanics to some art students, and he explains this complex rotation and its effects without any reference to math.
