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Matrix Models as Hidden Variables Theories

机译:矩阵模型作为隐藏变量理论

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It is proposed that the CH - dWHN -BFSS matrix model may be interpreted as nonlocal hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their entries are the hidden variables. This is shown by studying the matrix model at finite temperature, with T taken to scale as 1/N. For large but finite N the eigenvalues of the matrices undergo Brownian motion around the N → ∞ limit, with diffusion constant of order 1/N~(1/2). The resulting probability density and current for the eigenvalues are then found to evolve in agreement with the Schroedinger equation, to leading order in 1/N~(1/2), with h proportional to the thermal diffusion constant for the matrix elements. The quantum fluctuations and uncertainties in the positions of the eigenvalues are then consequences of ordinary statistical fluctuations in the values of the matrix elements. The derivation makes use of Nelson's stochastic formulation of quantum theory, which is expressed in terms of a variational principle.
机译:建议CH-DWHN -BFSS矩阵模型可以被解释为非识别性隐藏变量理论,其中量子可观察到是矩阵的特征值,而其条目是隐藏变量。这是通过在有限温度下研究矩阵模型来示出,T为1 / n。对于大而有限的n,矩阵的特征值在n→ζ限制周围经过棕色运动,顺序常数为1 / n〜(1/2)。然后发现所得到的特征值的概率密度和电流与Schroedinger方程一致地发展到1 / N〜(1/2)的前导顺序,其中H与矩阵元件的热扩散常数成比例。然后,在基质元素的值中普通统计波动的常规统计波动的常规波动和不确定性。衍生利用纳尔逊的量子理论随机配方,这在变分原理方面表达。

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