论文标题
制作量子宇宙：对称性和重力
Making a Quantum Universe: Symmetry and Gravity
论文作者
论文摘要
到目前为止，量化重力的任何尝试都没有导致令人满意的模型，该模型不仅描述了量子世界领域中的重力，而且还描述了其与基本颗粒和其他基本力的关系。在这里，我们概述了量子宇宙模型的初步结果，其中重力是从根本上讲是构造Quantic的。该模型基于三个具有令人信服的观察和理论证据的积极性假设：量子力学在所有尺度上都是有效的；量子系统由它们的对称性描述；宇宙具有无限的独立自由度。最后一个假设意味着，宇宙的希尔伯特空间具有$ su（n \ rightarrow \ infty）\ cong \ text {afore diff。}（s_2）$对称性，这是由两个角变量参数化的。我们表明，在没有背景时空的情况下，这个宇宙是微不足道和静态的。尽管如此，量子波动打破了对称性并将宇宙分为子系统。当一个子系统被选为参考 - 观察者 - 另一个作为时钟时，会出现另外两个连续参数，可以将其解释为距离和时间。我们将经典的时空识别出宇宙希尔伯特空间的参数空间。因此，其量化是毫无意义的。从这种角度来看，爱因斯坦方程将希尔伯特空间中量子动力学的投影投影到其参数空间中。当宇宙分为子系统/颗粒时，由于对称性破坏而出现的基本颗粒的有限维对称性，而对无限尺寸对称性及其相关的相互作用没有任何影响 - 被视为重力。这就解释了重力是一种普遍的力量。
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the preliminary results for a model of quantum universe, in which gravity is fundamentally and by construction quantic. The model is based on three well motivated assumptions with compelling observational and theoretical evidence: quantum mechanics is valid at all scales; quantum systems are described by their symmetries; universe has infinite independent degrees of freedom. The last assumption means that the Hilbert space of the Universe has $SU(N\rightarrow \infty) \cong \text{area preserving Diff.} (S_2)$ symmetry, which is parameterized by two angular variables. We show that, in the absence of a background spacetime, this Universe is trivial and static. Nonetheless, quantum fluctuations break the symmetry and divide the Universe to subsystems. When a subsystem is singled out as reference -- observer -- and another as clock, two more continuous parameters arise, which can be interpreted as distance and time. We identify the classical spacetime with parameter space of the Hilbert space of the Universe. Therefore, its quantization is meaningless. In this view, the Einstein equation presents the projection of quantum dynamics in the Hilbert space into its parameter space. Finite dimensional symmetries of elementary particles emerge as a consequence of symmetry breaking when the Universe is divided to subsystems/particles, without having any implication for the infinite dimensional symmetry and its associated interaction - perceived as gravity. This explains why gravity is a universal force.
