RUI: Constraints on Negative Energy in Field Theory and Gravitation

这里讨论的研究涉及一种非常不寻常的能量形式的含义。量子场论描述了物质和能量在微观尺度上的行为，这一定律允许这种所谓的“负能量”的存在。由于负能量会产生排斥引力效应，这项工作是量子场论和爱因斯坦的引力理论广义相对论的交汇点。研究的重点是对物理定律对负能量施加的限制进行扩展调查。这些普遍的限制将涉及对负能量在时间和空间上的分布施加限制。此外，限制的范围将扩大到包括万有引力的影响。负能量区域似乎还伴随着能量密度的大幅波动，这可能会导致负能量产生的引力场出现大幅波动。在这些情况下，这将如何影响爱因斯坦理论中给出的空间和时间几何的曲率对引力的描述，目前还没有很好的理解。希望也能调查这个问题。这些话题之所以令人感兴趣，有几个原因。在实验室中已经产生了涉及负能量的情况，如卡西米尔效应和光的压缩状态。在这些实验中产生的负能量极其微小。然而，如果物理定律没有对负能量施加限制，那么人们可能会创造出大量的负能量，从而产生奇怪的宏观效应。这样的影响可能包括：可穿越的虫洞(连接其他遥远的空间和时间区域的隧道)，曲速驱动器(用于超光速旅行)，穿越过去的时间机器，违反热力学第二定律(例如，冰箱不需要电源)，以及黑洞的破坏(坍塌的死亡恒星的遗骸)。然而，拉里·福特和作者的研究表明，量子场论确实对负能量施加了一些相当强的限制。这些限制条件被称为“量子不等式”，严重限制了上述负能量的宏观效应。粗略地说，他们说大的负能量只能存在很短的一段时间。最近人们意识到，即使是目前已知的量子不平等，尽管在时间上是限制的，但也可以用来排除或限制负能量在空间中的分布方式。这些结果，再加上一些物理定律所允许的负能量空间分布的明确例子，表明负能量在空间中一定与正能量微妙地交织在一起。这种情况一定要一直存在吗？拟议调查的一个主要焦点将是缩小可以排除的分配和明确允许的分配之间的差距。后者将涉及构建和分析更多明确的例子。这是我之前研究的延续，主要目的是扩大所有这些结果的范围。

The research discussed here deals with the implications of a very unusual form of energy. The existence of this so-called "negative energy" is allowed by the laws of quantum field theory, which describe the behavior of matter and energy on microscopic scales. Since negative energy would have repulsive gravitational effects, this work lies at the intersection of quantum field theory and Einstein's theory of gravity, general relativity. The focus of the research is the extended investigation of restrictions imposed by the laws of physics on negative energy. These generalized restrictions would involve the placement of constraints on the distribution of negative energy in both time and space. In addition, the scope of the constraints would be extended to include the effects of gravitation. Regions of negative energy also appear to be accompanied by large fluctuations in energy density, which could perhaps lead to large fluctuations in the gravitational fields produced by the negative energy. How this would affect the description of gravity, given in Einstein's theory as the curvature of the geometry of space and time, in these circumstances is currently not well understood. It is hoped to investigate this issue as well.These topics are of interest for several reasons. Situations involving negative energy, such as the Casimir effect and squeezed states of light, have been produced in the laboratory. The amounts of negative energy generated in these experiments are extremely tiny. However, if the laws of physics impose no constraints on negative energy, then one might be able to create large amounts of it and thereby produce bizarre macroscopic effects. Such effects could include: traversable wormholes (tunnels connecting otherwise distant regions of space and time), warp drives (for faster-than-light travel), time machines for travel into the past, violations of the second law of thermodynamics (e.g., refrigerators requiring no power sources), and the destruction of black holes (the remains of collapsed dead stars). However, research by Larry Ford and the author has shown that quantum field theory does impose some rather strong restrictions on negative energy. These constraints have come to be known as "quantum inequalities", and yield severe limitations on the macroscopic effects of negative energy mentioned above. Loosely speaking, they say that large negative energies can exist for only short periods of time. It has recently been realized that even the currently known quantum inequalities, although formulated as restrictions in time, can be used to rule out or constrain the ways in which negative energy can be distributed in space as well. These results, together with some explicit examples of spatial distributions of negative energy which are allowed by the laws of physics, indicate that negative energy must be subtly intertwined with positive energy in space. Must this always be the case? A major focus of the proposed investigation will be to narrow the gap between distributions which can be ruled out and those which are definitely allowed. The latter will involve the construction and analysis of additional explicit examples. This represents a continuation of my previous research and essentially aims to extend the scope of all of these results.