SPIN... is a... curious axiom. If you take one of these particles and ask it what... it's squared component of spin is, in three... mutually perpendicular directions, it always happens that two of the answers are 1, and one of them is 0. That's most mysterious... and... it's not possible to solve this puzzle. ...[W]e have these 33 directions, and it's not possible to assign 0s and 1s to them, subject to that condition... the 1-0-1 rule. ...[T]he particle is acting somewhat like a little boy ...making up its mind as it goes along. It doesn't stop it from giving answers, but it does stop the answers from being determined ahead of time, and that's the guts of it.
English mathematician (1937–2020)
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician, and Professor Emeritus of Mathematics at Princeton University in New Jersey. He was active in the theory of s, , number theory, and . He also made contributions to many branches of , most notably the invention of the with . Born and raised in , Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. He died of complications from COVID-19 at age 82.
From: Wikiquote (CC BY-SA 4.0)
Alternative Names:
John H. Conway
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JHC
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John Conway
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Conway
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[T]he strangest contribution of quantum mechanics to this discussion is the EPR paradox. ...That's an essential contribution to our theorem too. ...Despite the fact that information can't be transmitted faster than the speed of light, ...remotely separated events can be correlated ...and this is the content of our TWIN axiom, you can put two particles into a... singleton state... the angular momentum of the pair of particles is zero... [B]y the conservation of angular momentum... if you measure the angular momentum of this in any direction, then for the angular momentum of the other you get the negative answer, but... we're going to square it, that means... the squared component of spin is the same... [T]hese particles have been sort of hypnotized. If you ask... they will give the same answer... like I and my twin brother... [T]he funny thing is, even though the proves that the answers do not exist ahead of time, the equality of the answers can exist...
[L]ots of philosophical discussions about free will are concerned with the question of assigning moral responsibility. ...If the judge is a determinist, I might argue it was all determined. I just had to do it. I'm not responsible. ...We're not concerned with assigning moral responsibility... I want you to think of free whim...
[W]hen... non-predictivity of quantum mechanics was discovered, it came as a great surprise. People tried to explain it away. ...Many ...invented larger theories. ...Nobody has succeeded in making one of these theories relativistically invariant, and physics appears to be relativistically invariant. ...Physicists have believed ...in the result that we're proving for a long time. It's no surprise. "I knew all that," they say. However, what they didn't know was that it can be deduced in this very precise, logical fashion, from so little information... that is not at all contentious. ...[T]hese 3 axioms ...they're routine, they're accepted ...They follow from quantum mechanics and relativity. There's nothing dubious about them ...and that's all we need... [T]he original deductions... [of] quantum mechanics... used more. They used all sorts... and some... were... pretty poorly understood...
Laplace... wrote Mécanique céleste discussing the motion of the planets. ...[O]ne ...reason why ...determinacy got its ...impetus from the development of science, was that Newton's theory of gravitation ...was entirely deterministic. It left no room for freedom. ...Laplace, who did a lot of work on Newtonian ...theory says ...An intellect ...[or] intelligence, which knew ...where all the particles were at some moment and how fast they were moving, and so on, that every single thing could be known to that intelligence, provided a ...good calculator. ...It could reason out exactly what was going to happen in the future. ...It's the strongest ...assertion of determinism in the scientific literature. I don't believe it for one moment..!
<nowiki>[</nowiki>Robert Nozick]: Philosophical Explanations "...it would be foolhardy ...to place ...significant weight upon the necessity or even truth of SR. ...Moreover theorems show that any theory that retains certain features of Quantum Mechanics also will not satisfye SR." SR is Leibniz's . ...[T]here's a reference to the Kochen-Specker paper ...in which Kochen, my co-author, and Specker ...both logicians, not physicists ...prove this ...From our point of view this is not enough. The is not as strong as the new theorem.
The classical... problem is... how densely a large number of identical spheres ([e.g.,] ball bearings...) can be packed together. ...[C]onsider an aircraft hangar... [A]bout one quarter of the space will not be used... One... arrangement... the face-centered cubic (or fcc) lattice... spheres occupy <math>\pi / \sqrt{18} = .7405...</math> of the total space.... the lattice packing has density <math>.7405...</math> . [H]pwever, there are partial packings that are denser than the face-centered cubic... over larger regions...
Let me phrase the free will theorem that Simon and I proved. ...[I]f we... have free will... then so do elementary particles have their... very small quantity of free will... to mean, our behavior is not a function of the past. ...[I]f some experimenters have free will ...then so do elementary particles... even the ones outside us...
There has been a great deal of nonsense written... about the mysterious fourth dimension. ...4-dimensional space just consists of points with four coordinates instead of three (...similarly for any number of dimensions). ...[I]magine a telegraph ...over which numbers are ...sent in sets of four. Each set... is a point in 4-d... space.
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I have a very simple way of explaining relativity theory... and if you follow that you'll understand how... it's impossible to... transmit information faster than the speed of light. The reason is, if you could, then seen from another person's point of view, you'd transmit information backward in time... [W]e would know the result of somebody's experiment before they performed it, and if they have free will... you'd know the result of their choice before they've made it, and they're free to make another one.