![[NEW VIDEO!] The Painter's Paradox](https://img5.xaiju.com/storage/11/ry/bz/d38796-019e7bd1-2ea6-7eb6-83fe-1b3b2d0d0ab3.jpg)
[NEW VIDEO!] The Painter's Paradox
Added 2021-09-25 02:53:26 +0000 UTCHope you enjoy and as always thank you for the support :)
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P.A.M. Dirac sets Gabriel's horn down on the origin point of the complex plane and says, "Let the volume inside represent an indivisible quantum of action" occurring exactly at the origin point centered around the horn. With the horn, Dirac introduces a generalized function, a remapping of the complex plane into a spike. At points far away from the origin, he tacks down the complex plane to form a rigid horizon. Attach a steel wire to the origin point and pull up hard (or down) very far. The detailed shape one gets does not really matter because Dirac envisions his "delta" function to be know, a la Niels Bohr, in terms of how it relates to other functions and not in an absolute terms. Dirac gives a rule for what he means by a Dirac delta generalized function centered at the origin. He describes delta in terms of how it relates to other functions. Given any other function g, even a generalized function*, the calculus integral over the entire complex plane of the dot product of g and delta gives one the value of g at the origin. That's the rule for Dirac's delta function now ubiquitous in electrical engineering and signal theory. Given this definition, one can introduce Dirac delta spikes all around a complex plane to simulate quanta interacting amongst themselves. *As soon as I posted this I realized that I had left out an essential part of Bohr's legacy. Generalized functions and distributions get multiplied by phase-shifted yet well-behaved classical "test" functions that are continuous and have a finite area under their curve (when integrated over their entire domain). Easy to draw classical functions get matched up with unspecified distributions in phase-shifted dot-like products. This procedure epitomizes Bohr's call that all quantum Dirac delta-like particle behavior gets presented as measured events, only after it has been couched with classical coordinates, lab bench and all. The use of test functions reminds one of Bohr's correspondence principle and how quantum phenomena has to be described side-by-side with classical tools, anchors and notions, even liquid-like drops in nuclear physics.
Scott Ready
2022-04-01 20:45:14 +0000 UTCGabriel's horn has an intrinsic negative curvature in common with many objects with fluted edges. Negative curvature gives an object an impressive outward appearance, like a bird, lizard, fish or coral all puffed up. Go inside and there appears to be no interior space within the fluff and puff. Einstein's field equations have terms for positive curvature and negative curvature. Flat Euclidean space hovers as an equilibrium state at zero curvature. When an object has an extreme amount of positive curvature, it may behave as a tiny and rigid pin-hole. Objects approaching it get deflected by it or go around it. When something manages to thread the needle and vanish into the hole, it enters a voluminous interior akin to that of a black hole or one of J.A. Wheeler's bags of gold: a Mary Poppins carpet bag into which one can fit a whole weeks' worth of provisions and toys.
Scott Ready
2022-03-19 13:48:57 +0000 UTC
