Followup to the Shelter Island Conference, this is where Julian Schwinger and Richard Feynman exposed their theories to explain the experiments of the previous conference.
Julian made a formal presentation that took until the afternoon and bored everyone to death, though the mathematics avoided much questioning.
Feynman then presented his revolutionary approach, which he was unable to prove basic properties of, but which gave correct results, and people were not very happy.
The Purpose of Harvard is Not to Educate People by Sean Carroll (2008) by 
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Maybe they did try once though: Harvard Project Physics.
Construction and management simulation by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01 Richard Feynman's first seminar in 1941 by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01He and John Archibald Wheeler presented the Wheeler-Feynman absorber theory.
Relationship between the quotient group and direct products by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01Although quotients look a bit real number division, there are some important differences with the "group analog of multiplication" of direct product of groups.
If a group is isomorphic to the direct product of groups, we can take a quotient of the product to retrieve one of the groups, which is somewhat analogous to division: math.stackexchange.com/questions/723707/how-is-the-quotient-group-related-to-the-direct-product-group
The "converse" is not always true however: a group does not need to be isomorphic to the product of one of its normal subgroups and the associated quotient group. The wiki page provides an example:
Given G and a normal subgroup N, then G is a group extension of G/N by N. One could ask whether this extension is trivial or split; in other words, one could ask whether G is a direct product or semidirect product of N and G/N. This is a special case of the extension problem. An example where the extension is not split is as follows: Let , and which is isomorphic to Z2. Then G/N is also isomorphic to Z2. But Z2 has only the trivial automorphism, so the only semi-direct product of N and G/N is the direct product. Since Z4 is different from Z2 × Z2, we conclude that G is not a semi-direct product of N and G/N.
This is also semi mentioned at: math.stackexchange.com/questions/1596500/when-is-a-group-isomorphic-to-the-product-of-normal-subgroup-and-quotient-group
I think this might be equivalent to why the group extension problem is hard. If this relation were true, then taking the direct product would be the only way to make larger groups from normal subgroups/quotients. But it's not.
Atoms exist and last for a long time, while in classical electromagnetic theory punctual orbiting electrons should emit radiation quickly and fall into the nucleus: physics.stackexchange.com/questions/20003/why-dont-electrons-crash-into-the-nuclei-they-orbit
In other sections:
Bibliography:
The first quantum mechanics theories developed.
Their most popular formulation has been the Schrödinger equation.
Quantum entanglement is often called spooky/surprising/unintuitive, but they key question is to understand why.
To understand that, you have to understand why it is fundamentally impossible for the entangled particle pair be in a predefined state according to experiments done e.g. where one is deterministically yes and the other deterministically down.
In other words, why local hidden-variable theory is not valid.
How to generate entangled particles:
- particle decay, notably pair production
- for photons, notably: spontaneous parametric down-conversion, e.g.: www.youtube.com/watch?v=tn1sEaw1K2k "Shanni Prutchi Construction of an Entangled Photon Source" by HACKADAY (2015). Estimatd price: 5000 USD.
Contains the clearest Bell test experiment description seen so far.
It clearly describes the photon-based 22.5, 45 degree/85%/15% probability photon polarization experiment and its result conceptually.
It does not mention spontaneous parametric down-conversion but that's what they likely hint at.
Done in Collaboration with 3Blue1Brown.
Question asking further clarification on why the 100/85/50 thing is surprising: physics.stackexchange.com/questions/357039/why-is-the-quantum-venn-diagram-paradox-considered-a-paradox/597982#597982
Quantum Mechanics: Animation explaining quantum physics by Physics Videos by Eugene Khutoryansky (2013)
Source. Usual Eugene, good animations, and not too precise explanations :-) youtu.be/iVpXrbZ4bnU?t=922 describes a conceptual spin entangled electron-positron pair production Stern-Gerlach experiment as a Bell test experiments. The 85% is mentioned, but not explained at all.
Quantum Entanglement Lab by Scientific American (2013)
Source. The hosts interview Professor Enrique Galvez of Colgate University who shows briefly the optical table setup without great details, and then moves to a whiteboard explanation. Treats the audience as stupid, doesn't say the keywords spontaneous parametric down-conversion and Bell's theorem which they clearly allude to. You can even them showing a two second footage of the professor explaining the rotation experiments and the data for it, but that's all you get. Institute of Electrical and Electronics Engineers by Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-24 +Created 1970-01-01 There are unlisted articles, also show them or only show them.