Abstract

Physicists usually understand that physics cannot (and should not) derive that \(c \approx 3 \times {{10}^{8}}\) m/s and \(\hbar \approx 1.054 \times {{10}^{{ - 34}}}\) kg m²/s. At the same time they usually believe that physics should derive the value of the cosmological constant \(\Lambda \) and that the solution of the dark energy problem depends on this value. However, background space in General Relativity (GR) is only a classical notion while on quantum level symmetry is defined by a Lie algebra of basic operators. We prove that the theory based on Poincare Lie algebra is a special degenerate case of the theories based on de Sitter (dS) or anti-de Sitter (AdS) Lie algebras in the formal limit \(R \to \infty \) where R is the parameter of contraction from the latter algebras to the former one, and \(R\) has nothing to do with the radius of background space. As a consequence, \(R\) is necessarily finite, is fundamental to the same extent as \(c\) and \(\hbar \), and a question why \(R\) is as is does not arise. Following our previous publications, we consider a system of two free bodies in dS quantum mechanics and show that in semiclassical approximation the cosmological dS acceleration is necessarily nonzero and is the same as in GR if the radius of dS space equals \(R\) and \(\Lambda = {3 \mathord{\left/ {\vphantom {3 {{{R}^{2}}}}} \right. \kern-0em} {{{R}^{2}}}}\). This result follows from basic principles of quantum theory. It has nothing to do with existence or nonexistence of dark energy and therefore for explaining cosmological acceleration dark energy is not needed. The result is obtained without using the notion of dS background space (in particular, its metric and connection) but simply as a consequence of quantum mechanics based on the dS Lie algebra. Therefore, \(\Lambda \) has a physical meaning only on classical level and the cosmological constant problem and the dark energy problem do not arise. In the case of dS and AdS symmetries all physical quantities are dimensionless and no system of units is needed. In particular, the quantities \((c,\hbar ,s)\), which are the basic quantities in the modern system of units, are not so fundamental as in relativistic quantum theory. “Continuous time” is a part of classical notion of space-time continuum and makes no sense beyond this notion. In particular, description of the inflationary stage of the Universe by times (10^–36, 10^–32 s) has no physical meaning.

中文翻译：

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宇宙加速作为量子对称对称性的结果

摘要

物理学家通常理解物理学不能（也不应该）得出\（c \ approx 3 \ times {{10} ^ {8}} \） m / s和\（\ hbar \ approx 1.054 \ times {{10} ^ {{-34}}} \） kg m ² / s。同时，他们通常认为物理学应该得出宇宙常数\（\ Lambda \）的值，暗能量问题的解决方案取决于该值。但是，广义相对论（GR）中的背景空间只是一个经典概念，而量子级对称性是由基本算符的李代数定义的。我们证明基于Poincare Lie代数的理论是在形式极限\（R \ to \ infty \）中基于de Sitter（dS）或anti-de Sitter（AdS）Lie代数的理论的一个特殊退化案例。其中R是从后一个代数到前一个代数的收缩参数，\（R \）与背景空间的半径无关。结果，\（R \）必然是有限的，在与\（c \）和\（\ hbar \）相同的程度上是基本的，并且不会出现为什么\（R \）保持原样的问题。根据先前的出版物，我们考虑了dS量子力学中的两个自由系统，并表明在半经典近似中，宇宙学dS加速度必定为非零值，并且如果dS空间的半径等于\（R \）且与GR中的加速度相同。\（\ Lambda = {3 \ mathord {\ left / {\ vphantom {3 {{{R} ^ {2}}}}} \ right。\ kern-0em} {{{R} ^ {2}}} } \）。该结果来自量子理论的基本原理。它与暗能量的存在与否无关，因此，为了解释宇宙加速，不需要暗能量。无需使用dS背景空间（特别是其度量和连接）的概念即可获得结果，而仅仅是基于dS Lie代数的量子力学的结果。因此，\（\ Lambda \）仅在古典意义上具有物理意义，不会出现宇宙常数问题和暗能量问题。在dS和AdS对称的情况下，所有物理量都是无量纲的，不需要单位制。特别是数量\（（c，\ hbar，s）\）是现代单位系统中的基本量，并不像相对论量子理论中的基础。“连续时间”是时空连续体的经典概念的一部分，超出该概念没有任何意义。特别地，通过倍宇宙的通货膨胀级（10的描述^-36，10 ^-32或多个）不具有物理意义。