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 · yt0.781

   Um so the idea of Heisenberg that is that you could still apply the Hamilton's equations and but only on on matrices which matrices which were non-comitative types of symbols as opposed to the ordinary commutative numbers. But even though uh at that stage you know you had complete replacement of even the mechanical uh laws by new laws of quantum physics. Um Heisenberg and Boore estimated that this type of theory was still an application of the old correspondence principle between classical physics and quantum physics. Here is what B said. The laws of Heisenberg are a precise formulation of the…

   yt/pYRLapWBqJY-bohr-s-complementarity-and-kant-s-epistemology/transcript.txt

2. 02 · yt0.772

   The fourth and final concept introduced by Heisenberg was a new quantization rule. I remind you that old quantum theory was mostly based on the rule developed by Bore and Somerfeld. This was very successful for describing an isolated hydrogen atom, but it failed in light of new experiments. This rule worked as follows. First, write the classical equation of motion. then solve the equation to find the classical solution and finally force the classical solution to satisfy the bore summerfeld rule. In Heisenber's approach, the classical solution is irrelevant because the goal is to determine the …

   yt/oVzzIkkYGY8-this-is-how-heisenberg-created-quantum-mechanics-step-by-ste/transcript.txt

3. 03 · yt0.770

   We can calculate the product between y and x instead. Following the same steps as before, we find that the order of the product makes no difference. We call quantities that satisfy this relation commutative objects. A common example is real numbers. The order of the factors does not affect the product. Now we repeat this but using the quantum reinterpretation of position and frequency introduced before. Taking their product, we must be careful with the indices. And just like in the classical case, the two corresponding frequencies appear added in the exponential. But now we have a problem. Not…

   yt/oVzzIkkYGY8-this-is-how-heisenberg-created-quantum-mechanics-step-by-ste/transcript.txt

4. 04 · yt0.769

   I think that the Schrodinger picture, which is the one that uses the wave function as a probability wave and the probability of one thing happening rather than another, that is a, I think, a misleading way of expressing the theory, though it does express the theory correctly and fully, but it's misleading in that it doesn't include an account of how the outcome comes about. So I favor using the Heisenberg picture, which is the other way around. It takes as fundamental, the observables of a physical system, exactly like classical physics does. And the state is a constant, therefore it doesn't, …

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

5. 05 · yt0.764

   Note that the positive values of alpha represent quantum transitions between the current state n and lower levels whereas the negative values denote higher levels. With this expression, Heisenberg built a tower of so-called virtual oscillators. The next concept is motion. I bet many of you were not expecting to find Newton's second law in the foundational paper on quantum mechanics, but this is Heisenberg's starting point. Writing the force and acceleration as functions of position, dividing by the mass of the particle and collecting terms on the left hand side. Heisenberg renamed this ratio j…

   yt/oVzzIkkYGY8-this-is-how-heisenberg-created-quantum-mechanics-step-by-ste/transcript.txt

6. 06 · yt0.763

   So this is a very deliberate move that he makes and it opens the door to our modern theory of quantum theory. A theory of extremely abstract mathematics. The mathematics in general terms is not extremely advanced. Um a college student um you know doing a math major certainly well before the graduate level would be able to understand the mathematics that we use in quantum theory. It's just that the mathematics is very abstract and the connection to things that are physical the connection to ontology is murky or not there at all. Um so this this was an important shift. The idea was to give up cl…

   yt/gINYis8BgSY-mindscape-323-jacob-barandes-on-indivisible-stochastic-quant/transcript.txt

7. 07 · yt0.760

   The so-called canonical quantum commutation relation from which the famous Heisenberg's uncertainty principle can be derived. But this happens two years later. For now, I wanted to show you that Heisenberg's paper already contains many of the blueprints for modern quantum mechanics. And although he didn't know it, this formula is the first draft of his famous uncertainty principle. If you made it this far, congratulations and thank you for joining me. This is a remarkable paper and I hope that with this deep dive any student even at the undergraduate level can understand its significance and r…

   yt/oVzzIkkYGY8-this-is-how-heisenberg-created-quantum-mechanics-step-by-ste/transcript.txt

8. 08 · blog0.754

   Moreover, he takes this correspondence to be the ground or justification for the view that quantum theory is a rational generalization of classical mechanics (for a discussion of this latter view see Bokulich and Bokulich 2005). A few pages later, in a section titled “The Correspondence Principle,” Bohr goes on to describe both the frequency correspondence and the intensity correspondence: This correspondence between frequencies determined by the two methods must have a deeper significance and we are led to anticipate that it will also apply to the intensities. This is equivalent to the statem…

   blog/plato-stanford-edu/bohr-s-correspondence-principle.md

9. 09 · yt0.751

   This is the bold conceptual innovation that makes this paper the foundation of modern quantum mechanics. This weird multiplication rule made Heisenberg very uncomfortable. In the paper he wrote this multiplication rule is an almost necessary consequence of the frequency combination rules. He accepted what his theory was telling him but could not make sense of the meaning of these non-commutative objects. After his return from Helgoland, he expressed his concern to Max Bourne. What are these objects that obey these rules? Let me bring back the way the transition amplitudes are combined. Heisenb…

   yt/oVzzIkkYGY8-this-is-how-heisenberg-created-quantum-mechanics-step-by-ste/transcript.txt

10. 10 · yt0.748

    There's reasons why things exist, reasons why things happen. And this was elevated to a principle called the principle of sufficient reason. The principle of sufficient reason is literally the bumper sticker you see that says everything happens for a reason. Okay, there's a technical way of saying it that linenets uh the guy on the right said Spinosa is in the middle. All three of these philosophers promagated this principle and the way that Linus put it was the sake for which something happens is the final cause. Sorry, the principle sufficient reason is nothing is without a ground or reason …

    yt/rqezWO5Yba8-sean-carrol-the-big-picture-on-the-origins-of-life-meaning-a/transcript.txt