Corpus evidence — top 10 passages

Most-relevant passages from the entire indexed corpus (67,286 paragraph chunks across YouTube transcripts, PubMed, arXiv, archive.org, Stanford Encyclopedia of Philosophy, OpenAlex, and more) ranked by semantic similarity (bge-small-en-v1.5).

1. 01 · yt0.886

   And that's the next thorny issue. How  do you deal with subsystems in quantum mechanics   and so on? And we now believe to have cracked at  least two of the three most prominent problems. How does this work? What is actually flowing  there? How do you actually get this onto the   street formally? And also, how do you deal  with composed systems? Because quantum systems   famously compose by tensor products. So the  Hilbert space of a composite system is the   tensor product of the Hilbert spaces of what we  think are the con…

   yt/Bnh-UNrxYZg-frederic-schuller-the-physicist-who-derived-gravity-from-ele/transcript.txt

2. 02 · yt0.809

   So it's as if these realms approximately are parallel to each other in the sense that the odds of them coming back together and affecting each other, exponentially drops very close to zero. What would that be lacking, in your way of describing things right now? - Yes, so it's lacking the structure that you've introduced after saying what it is. You said it's a Hilbert space, and the state is a structure in that Hilbert space. And then everything you said after that is not derived from the fact that it's a Hilbert space. It's derived from the fact that the Hamiltonian takes a certain form. Why …

   yt/Af5LICjFIBc-what-is-quantum-mechanics-really-telling-us-world-science-fe/transcript.txt

3. 03 · yt0.802

   Only that for the  classical case contributes to an observable. Yes.   Whereas in the quantum case, it's, it doesn't  have to just be that single part. Well, again,   the variational sounds more Lagrangian  than Hamiltonian. Hamiltonian sort of says,   I don't need to know about all that. I'm just  going to start from here and move. Where you   can, the Legendre map, no? Certainly. Okay.  So if you're lost, don't worry. This is just   the beginning. I have some other questions. Two  friends talking late on a, late …

   yt/ILlhFKuu3NQ-geometric-unity-unifying-all-forces-generations-eric-weinste/transcript.txt

4. 04 · yt0.801

   In quantum theory, the equivalent structure is missing. We talk about the multiverse, but there's no mathematical object called the multiverse in the theory. The only mathematical objects are the equivalent of Einstein's equations and so on. They are the observables and the equations of motion, but- - What you call Hilbert's? Why wouldn't Hilbert space? Sorry for getting slightly technical, but why wouldn't just Hilbert space be the right mathematical architecture for talking about this? - Hilbert space is linear, for a start. And to combine that with, well, I haven't spoken about the problem …

   yt/Af5LICjFIBc-what-is-quantum-mechanics-really-telling-us-world-science-fe/transcript.txt

5. 05 · yt0.792

   If you look at them from one special frame of reference, when this is gone and you say that one is the whole state. When this one's gone, this one is the whole state. But it's got to do that simultaneously. Simultaneous doesn't mean anything relativistically. What means something? Well, does it go back? I mean, maybe when this is gone Anyway, it doesn't make sense. The only way to make it make sense is that it goes way back to where they separated. And then in a certain sense, it already knew which one was going to go. That doesn't make much sense, either. But in this article, I tried to devel…

   yt/vC4HNcqTQXk-roger-penrose-on-mind-consciousness-closer-to-truth-chats/transcript.txt

6. 06 · yt0.788

   But what actually happens with   the observable is, is that you have a function and  you can either measure the function at the point   and then multiply it by the quantum wave, or  you can take that function, differentiate it   to get a one form, stick it into a symplectic  form to get a vector field, throw the vector   field to a connection and use that connection to  take a directional derivative. So one of these   ends up as the position operator. One of these  sort of ends up as a momentum operator for the &nb…

   yt/ILlhFKuu3NQ-geometric-unity-unifying-all-forces-generations-eric-weinste/transcript.txt

7. 07 · blog0.782

   (For an entry level review of the highlights of the mathematical formalism and the basic principles of quantum mechanics, see the entry on quantum mechanics, Albert 1992, Hughes 1989, Part I, and references therein; for more advanced reviews, see Bohm 1951 and Redhead 1987, chapters 1-2 and the mathematical appendix.) For example, the state of the L-particle having z -spin ‘up’ (i.e., spinning ‘up’ about the z -axis) can be represented by the vector | z -up> in the Hilbert space associated with the L-particle, and the state of the L-particle having z -spin ‘down’ (i.e., spinning ‘down’ about t…

   blog/plato-stanford-edu/action-at-a-distance-in-quantum-mechanics.md

8. 08 · yt0.774

   That's where you have to look at the details of the quantum mechanical configuration itself. Any undergraduate who takes a basic course in quantum mechanics will learn how to represent the quantum mechanical states mathematically. And then it's a tiny little exercise to figure out what the quantum mechanical state looks like so that two electron spins are like this or like that or something far more involved than electron spins. It could even be the positions of a particle. In fact, I should say when Albert Einstein wrote the first paper on quantum entanglement, this is in 1935. He wrote it wi…

   yt/nH8c60ZbSgw-live-q-a-with-brian-greene-world-science-festival/transcript.txt

9. 09 · yt0.773

   Prof: It's the state of definite energy. Remember, we said functions of definite energy obey that equation. So that Y is really just Y_E. So now I'll put these two pieces together, and this is where those of you who drifted off can come back, because what I'm telling you is that the Schrˆdinger equation in fact admits a certain solution which is a product of a function of time and a function of space. And what we found by fiddling around with it is that F(t) and Y are very special, and F(t) must look like e^(‚àíiEt/ ‚Ñè), and Y is just our friend, Y _E(x), which are functions associated with a…

   yt/Iy6RspNw80E-24-quantum-mechanics-vi-time-dependent-schr-dinger-equation/transcript.txt

10. 10 · yt0.772

    Um when we learn all of us learn to begin, we talk about the wave function of just a single particle. And in a way that's nice because you can if we go back to visualizing it, you can kind of visualize it. Um because just mathematically like a electric field or a magnetic field the wave function for a single particle is represented by a single number associated with every point in space. It's a complex number. So that's a little tricky but okay it's a it's a number. You can sort of say oh there's the wave function is is there's more of it here than here right and compare how much or the square…

    yt/VbXEc9vpeIM-what-we-ve-gotten-wrong-about-quantum-physics-world-science-/transcript.txt