A single line in the emission spectrum.
So precise, so discrete, which makes no sense in classical mechanics!
Has been the leading motivation of the development of quantum mechanics, all the way from the:
- Schrödinger equation: major lines predicted, including Zeeman effect, but not finer line splits like fine structure
- Dirac equation: explains fine structure 2p spin split due to electron spin/orbit interactions, but not Lamb shift
- quantum electrodynamics: explains Lamb shift
- hyperfine structure: due to electron/nucleus spin interactions, offers a window into nuclear spin
Initially there were mathematical reasons why people suspected that all boson needed to have 0 mass as is the case for photons a gluons, see Goldstone's theorem.
So people started theorizing some hack that would fix up the equations, and they came up with the higgs mechanism.
Of all the rich person foundations, this is the one that feels the most hardcore.
They put huge focus on autism. Do they have an autistic child? Yes: www.forbes.com/pictures/eilm45mll/james-simons-autism/?sh=7825234250ce his adughter.
- techcrunch.com/2022/05/31/ultima-genomics-claims-100-full-genome-sequencing-after-stealth-600m-raise/ Ultima genomics TODO technology? Promises 100 USD genome, 600M funding out of stealth...
Predicted by the Dirac equation.
We've likely known since forever that photons are created: just turn on a light and see gazillion of them come out!
Photon creation is easy because photons are massless, so there is not minimum energy to create them.
The creation of other particles is much rarer however, and took longer to be discovered, one notable milestone being the discovery of the positron.
In the case of the electron, we need to start with at least enough energy for the mass of the electron positron pair. This requires a photon with wavelength in the picometer range, which is not common in the thermal radiation of daily life.
Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)
Source. - youtu.be/tR6UebCvFqE?t=23 particle at rest
- youtu.be/tR6UebCvFqE?t=322 unidirectional movement without a potential
- youtu.be/tR6UebCvFqE?t=507 shows that observers in different frames of reference also see different spin. We are reminded of how magnetism is just a side effect of special-relativity.
- youtu.be/tR6UebCvFqE?t=549 Dirac equation solution for the hydrogen atom, final result only + mentions fine structure prediction.
This is the order in which a binary search tree should be traversed for ordered output, i.e.:
- everything to the left is smaller than parent
- everything to the right is larger than parent
This ordering makes sense for binary trees and not k-ary trees in general because if there are more than two nodes it is not clear what the top node should go in the middle of.
This is unlike pre-order depth-first search and post-order depth-first search which generalize obviously to general trees.
Taylor expansion definition of the exponential function by 
Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-06 +Created 1970-01-01The Taylor series expansion is the most direct definition of the expontial as it obviously satisfies the exponential function differential equation:
- the first constant term dies
- each other term gets converted to the one before
- because we have infinite many terms, we get what we started with!
Using de novo DNA synthesis to synthesize a genes to later insert somewhere.
Note that this is a specific application of de novo DNA synthesis, e.g. polymerase chain reaction primers is another major application that does not imply creating genes.
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