# The Triangle Wave Versus the Cosine: How Classical Systems Can Optimally Approximate EPR-B Correlations

## Abstract

**:**

## 1. The Problem, in a Picture

## 2. The Problem, Formalised

## 3. Classical Physical Representation

## 4. The Spinning Bi-Coloured Disk

## 5. The Randomised Spinning Bi-Coloured Disk

## 6. Computation

## 7. Conclusions: What Next?

His slides can be found at http://www.mrao.cam.ac.uk/~steve/maxent2009/images/bell.pdf. They sketch a lovely proof of Bell’s theorem using the fact that the Fourier transform of the correlation function $\rho $ has to equal the expected squared absolute value of the Fourier transform of the random function A. The actual correlation function of the negative cosine only has three non-zero Fourier coefficients. However, the Fourier transform of any realisation of A must have infinitely many non-zero coefficients, since otherwise it could not have any jumps. Since their absolute values get squared before averaging, there is no way that all but three can vanish.Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered by Bell’s theorem by showing that you can’t program two independently running computers to mimic the results of spin measurements on two spin-1/2 particles in a singlet state. I believe this demonstration is actually better than Bell’s original argument.

## Funding

## Conflicts of Interest

## Appendix A. R Code of Figures in the Paper

## References

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**Figure 1.**Correlation, between $-1$ and $+1$, plotted against angle between measurement directions, from $-\pi $ to $\pi $.

**Figure 2.**12 EPR-B correlations (in black), each determined by a (randomly generated) spinning coloured disk of 10 segments.

**Figure 3.**The second spinning disk model of the 12 in Figure 2.

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**MDPI and ACS Style**

Gill, R.D. The Triangle Wave Versus the Cosine: How Classical Systems Can Optimally Approximate EPR-B Correlations. *Entropy* **2020**, *22*, 287.
https://doi.org/10.3390/e22030287

**AMA Style**

Gill RD. The Triangle Wave Versus the Cosine: How Classical Systems Can Optimally Approximate EPR-B Correlations. *Entropy*. 2020; 22(3):287.
https://doi.org/10.3390/e22030287

**Chicago/Turabian Style**

Gill, Richard David. 2020. "The Triangle Wave Versus the Cosine: How Classical Systems Can Optimally Approximate EPR-B Correlations" *Entropy* 22, no. 3: 287.
https://doi.org/10.3390/e22030287