Further Evidence for Near-Tsirelson Bell-CHSH Violations in Quantum Field Theory via Haar Wavelets
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917386912792576 |
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| author | Dudal, David Vandermeersch, Ken |
| author_facet | Dudal, David Vandermeersch, Ken |
| contents | This paper investigates a recent construction using bumpified Haar wavelets to demonstrate explicit violations of the Bell-Clauser-Horne-Shimony-Holt inequality within the vacuum state in quantum field theory. The construction was tested for massless spinor fields in $(1+1)$-dimensional Minkowski spacetime and is claimed to achieve violations arbitrarily close to an upper bound known as Tsirelson's bound. We show that this claim can be reduced to a mathematical conjecture involving the maximal eigenvalue of a sequence of symmetric matrices composed of integrals of Haar wavelet products. More precisely, the asymptotic eigenvalue of this sequence should approach $π$. We present a formal argument using a subclass of wavelets, allowing us to reach $3.11052$. Although a complete proof remains elusive, we present further compelling numerical evidence to support it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Further Evidence for Near-Tsirelson Bell-CHSH Violations in Quantum Field Theory via Haar Wavelets Dudal, David Vandermeersch, Ken Mathematical Physics High Energy Physics - Theory Quantum Physics This paper investigates a recent construction using bumpified Haar wavelets to demonstrate explicit violations of the Bell-Clauser-Horne-Shimony-Holt inequality within the vacuum state in quantum field theory. The construction was tested for massless spinor fields in $(1+1)$-dimensional Minkowski spacetime and is claimed to achieve violations arbitrarily close to an upper bound known as Tsirelson's bound. We show that this claim can be reduced to a mathematical conjecture involving the maximal eigenvalue of a sequence of symmetric matrices composed of integrals of Haar wavelet products. More precisely, the asymptotic eigenvalue of this sequence should approach $π$. We present a formal argument using a subclass of wavelets, allowing us to reach $3.11052$. Although a complete proof remains elusive, we present further compelling numerical evidence to support it. |
| title | Further Evidence for Near-Tsirelson Bell-CHSH Violations in Quantum Field Theory via Haar Wavelets |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2410.13362 |