Joy Christian wrote:For the record, let me spell out what Richard Gill has been disputing about in this simulation: http://rpubs.com/jjc/16531.
I have used vectors defined by the set
for calculating the first two of the four correlations in the simulation,
and vectors defined by the set
for calculating the last two of the four correlations in the simulation.
Richard Gill claims that these sets of vectors specify different directions in the physical space. But that is absolutely ridiculous.
Evidently, they specify exactly the same set of directions in the physical space, as I have explained in the simulation in detail.
They both, in fact, define a unique distribution of points on a circle of radius . This should be quite easy to see.
gill1109 wrote:PS Joy's trick is called "action at a distance". Depending on whether Alice measures in the direction a or a', Bob's observed directions of angular momentum, which have already been measured and saved on a computer file, are encoded (x, y, z) or (y, x, z).
This is reminiscent of the magical parity flips in Christian 1.0 (the "one page paper" version of the original theory).
gill1109 wrote:Notice: I am not saying that Joy has not won the challenge.
Joy Christian wrote:Richard Gill claims that the sets of vectors and appearing in this simulation specify different directions in the physical space.
Is there any mathematician out there who can convince me that these two sets of vectors
and
specify different sets of directions in the physical space? Evidently, they specify exactly the same set of directions in the physical space. They both,
in fact, define a unique distribution of points on a circle of radius . This should be quite easy for any mathematician to see, shouldn't it?
Heinera wrote:The point is that the set u in your program is not uniformly distributed in x and y; on the contrary, it is heavily biased. This makes v biased to, but in an entirely different direction.
Heinera wrote:And finally, convert the two vectors u and v into polar coordinates. Make two histograms of the directions for u and v, respectively. Do the two histograms indicate that u and v specify the same directions in space?
Joy Christian wrote:As usual, you are missing the point. u and v do not have to be the same directions in space. They only have to belong to the same set of directions. Do you get it now?
Heinera wrote:I'm not getting it, I'm afraid.
Joy Christian wrote:Heinera wrote:I'm not getting it, I'm afraid.
All I can do to help is ask you once again to read my experimental paper. Then read Gill's challenge. Then read the comments in my simulation. And then think.
Joy Christian wrote:It is entirely irrelevant whether u and v so produced are differently biased or completely chaotic, as long as they represent the same set of directions in the physical space.
Joy Christian wrote:
In addition to these simulations, I have recently won the 10,000 Euros offered by Richard Gill for theoretically producing the 2n angular momentum vectors, and , appearing in the equation (16) of my proposed experiment (see also this page). He had claimed that it was mathematically impossible to produce such 2n vectors and had challenged me to produce them as a "proof of concept" for my proposed experiment. I defeated his challenge on the 3rd of May 2014 by explicitly producing the 2n vectors in these two simulations.
Joy Christian wrote:The challenge (the terms of which were unambiguously spelt out here by Richard Gill himself), has been won by me already; resolved, done with, defeated:Joy Christian wrote:
In addition to these simulations, I have recently won the 10,000 Euros offered by Richard Gill for theoretically producing the 2n angular momentum vectors, and , appearing in the equation (16) of my proposed experiment (see also this page). He had claimed that it was mathematically impossible to produce such 2n vectors and had challenged me to produce them as a "proof of concept" for my proposed experiment. I defeated his challenge on the 3rd of May 2014 by explicitly producing the 2n vectors in these two simulations.
Note that I have posted the two .txt files of angular momentum directions, as required by Richard Gill, on this very forum, here (with further justification here).
Richard Gill owes me 10,000 Euros, period.
By the way, I will be adding interest and inflation adjustment to 10,000 Euros, starting from 1 June 2014. If Richard Gill does not pay up by 1 June 2014, then the interest and inflation adjustment will increase the amount until he pays up (since Richard has been changing the rules of the game, this caution seems necessary).
Joy Christian wrote:In the second simulation above I have used vectors defined by the ordered set
for calculating the first two of the four correlations in the simulation,
and vectors defined by the ordered set
for calculating the last two of the four correlations in the simulation.
Richard Gill claims that these sets of vectors specify different sets of directions in the physical space. But evidently they specify exactly the same set of directions in the physical space. They both define a unique distribution of points on a circle of radius . This should be quite easy for any mathematician to see, by
simply noting that .
and are thus different names of one and the same spin direction (say ) in the physical space.
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