gill1109 wrote:FrediFizzx wrote:I doubt very much that 3D space itself has a handedness. It is matter or forms of energy transport that can have a handedness. But sure, you can have left or right handed basis definitions for defining cartesian coordinates. Usually that is for defining objects via vectors that exist in the 3D space. Right hand rule or left hand rule. Most people are "locked" into the right hand rule and don't think about the left hand rule much. But anyways, yeah we have that 3D space is the cause of the 50-50 "fair" coin toss definition. No problem there.
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OK
But you still haven’t responded to this, Fred:gill1109 wrote:Trouble is, as you go down, randomness *has* to become more fine-grained. More precisely, it can’t ever be *less* fine-grained. In the lab, when we measure spins of two particles, there are four *joint* outcomes, not two. And they typically have probabilities different from zero, one half, or one. The deeper level has to have at least as many “atoms” of probability, and their sizes have to add up in groups to the sizes of atoms at the top level.
Now I’m happy to believe that at some deep level the handed-ness of space is responsible for the randomness of spin measurements. But I cannot believe it works through a single binary fair coin toss λ.
A real fair coin toss provides an excellent example. An idealised coin is launched vertically into the air with a rotation speed around a horizontal axis X > 0 and a vertical velocity Y > 0. It rises and then falls and hits a flat surface which instantly absorbs all energy and leaves the coin lying flat. In suitable units this could result in the binary outcome Parity(IntegerPart(XY)). If X and Y have a joint smooth probability distribution which extends in both directions far enough, the outcome is almost a fair coin toss. This has been studied long ago by Persi Diaconis. Who is both a great mathematician and a great conjuror. He can toss a coin and have it land heads 95% of the time.
I believe I took care of the middle sentence and the last paragraph with 3D space as the "cause". I don't get your point for the first paragraph. If we have a "cause" for the randomness then it stops there.
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