by Austin Fearnley » Sun Aug 01, 2021 12:43 pm
I was writing something longer saying much the same as Mikko, but have edited that down in size. I was using the Rasch model as an analogy and no one wants to hear about the Rasch Model here.
Obviously the writer of the short paper has not applied either algebra or arithmetic to the issue.
Moving on to other papers: it seems odd to me that many people can play with algebraic formula very well (e.g. Esail, whose paper I like very much except for his insistence that the effect is local) but cannot or do not bother to follow up by using arithmetic to calculate simulated results. It seems that there may be a daunting step up in the calculations in going from pen, paper and calculator up to a computer program. Maybe that is daunting for some? IMO spreadsheets offer a less daunting intermediate step.
Anyway, reading the short paper reminded me that I had never played with the errors of measurement between exact and quantised measurements. We know Alice and Bob use +/- 1 measurements but in a simulation be can find the exact projections which are not quantised. Although the exact measurements are unreal in this physics context,using exact projections does seem to set a target correlation which agrees with the QM correlation. So I played on a spreadsheet today.
I generated 360 pairs of particles (evenly spaced around the compass) and calculated for a=0 degrees and b=45 degrees, in two dimensions, the pairs of measurements A and B and also the 'errors', that is 'exact minus quantised' measurements. Then took means, SDs and correlation of these 'errors'.
correlation = -0.206091534
means 3.08395E-18 and 1.0177E-17 (that is, both means are zero)
SDs 0.476227652 and 0.476227652
N = 360
Law of large numbers (and 360 is not that large, but the thetas are not random) means the the sums of the A values are very similar to what would have occurred with exact projections.
The two SDs are very similar and I feel that someone could maybe calculate these theoretically. These SDs will always be non-zero.
The correlation between errors is non-zero and will not reduce to zero as N increases and that is one reason that the law of large numbers will never take the quantised correlation (0.5) up to the exact correlation (0.707) between A and B.
I plotted some scatter diagrams which seem very peculiar with a number of discontinuities but I think they are OK. The scatter diagram for the two errors show that the correlation of -0.2 is very dubious as the scatter is nowhere near linear. In fact, the scatter is quite like a hyperbolic curve in four segments. I cannot show it here as they are not yet on the web and have no URL.
I was writing something longer saying much the same as Mikko, but have edited that down in size. I was using the Rasch model as an analogy and no one wants to hear about the Rasch Model here.
Obviously the writer of the short paper has not applied either algebra or arithmetic to the issue.
Moving on to other papers: it seems odd to me that many people can play with algebraic formula very well (e.g. Esail, whose paper I like very much except for his insistence that the effect is local) but cannot or do not bother to follow up by using arithmetic to calculate simulated results. It seems that there may be a daunting step up in the calculations in going from pen, paper and calculator up to a computer program. Maybe that is daunting for some? IMO spreadsheets offer a less daunting intermediate step.
Anyway, reading the short paper reminded me that I had never played with the errors of measurement between exact and quantised measurements. We know Alice and Bob use +/- 1 measurements but in a simulation be can find the exact projections which are not quantised. Although the exact measurements are unreal in this physics context,using exact projections does seem to set a target correlation which agrees with the QM correlation. So I played on a spreadsheet today.
I generated 360 pairs of particles (evenly spaced around the compass) and calculated for a=0 degrees and b=45 degrees, in two dimensions, the pairs of measurements A and B and also the 'errors', that is 'exact minus quantised' measurements. Then took means, SDs and correlation of these 'errors'.
correlation = -0.206091534
means 3.08395E-18 and 1.0177E-17 (that is, both means are zero)
SDs 0.476227652 and 0.476227652
N = 360
Law of large numbers (and 360 is not that large, but the thetas are not random) means the the sums of the A values are very similar to what would have occurred with exact projections.
The two SDs are very similar and I feel that someone could maybe calculate these theoretically. These SDs will always be non-zero.
The correlation between errors is non-zero and will not reduce to zero as N increases and that is one reason that the law of large numbers will never take the quantised correlation (0.5) up to the exact correlation (0.707) between A and B.
I plotted some scatter diagrams which seem very peculiar with a number of discontinuities but I think they are OK. The scatter diagram for the two errors show that the correlation of -0.2 is very dubious as the scatter is nowhere near linear. In fact, the scatter is quite like a hyperbolic curve in four segments. I cannot show it here as they are not yet on the web and have no URL.