Casimir Force between Dielectric Bodies of Arbitrary Geometry

近年来纳米技术的进步使制造微型机械设备成为可能，我们很快就能制造出这样的小型机器，实际上能够执行各种功能。这意味着我们将需要新一代机械工程师，他们配备了设计包，了解物质的机械属性和纳米级的相互作用。不仅如此，新的工程师还应该训练他们的“直觉”，以了解统治纳米尺度的量子物理的非直觉世界，因为众所周知，好的工程师除了技术技能和创造力之外，还必须有非常好的直觉。要发展这样的知识，我们所需要做的就是了解真空的结构以及它是如何与物质相互作用的。听起来可能很讽刺，但这实际上是真的！原因是，在量子世界中，真空并不像经典物理学中所描述的那样平淡无奇。事实上，它看起来更像是一团沸腾的光子(和其他粒子)，在我们注意到之前，这些光子不断地被创造和湮灭，而不是空的。当物质被放置在这样的介质中时，由于它们的存在，所谓的真空的量子涨落被改变，这反过来又引起这些物体之间的有效相互作用。这种相互作用是以H.B.G.卡西米尔的名字命名的(他既是一位关心理论物理最基本问题的杰出科学家，也是菲利普斯实验室工业研究的领导者)，似乎是纳米尺度上的主导相互作用。卡西米尔相互作用的一个显著特征是，它不是成对相加的，这意味着人们找不到可以归因于远距离相互作用的小物质区域的局域力定律，所以当总结到两个较大的物体时，它将解释它们之间的相互作用。换句话说，要计算出任何形状的物体之间的相互作用，应该从头开始，不可能将物体分解成已知相互作用的更简单的形状，然后汇编这些知识来推断所需的相互作用。正因为如此，开发未来的纳米机械工程师将需要的那种设计包，以及训练他们的直觉，远不是一项微不足道的任务。我们在这里建议做的是通过对物质物体的几何和卡西米尔相互作用之间的相互作用提供深刻的基本理解，从而使这种发展成为可能。我们将开发能够系统计算Casimir力的理论工具，并将使用它们来分析形状和介电性质方面的一系列不同情况。这将揭示卡西米尔相互作用的各种特征性质，并可能成为迈向未来主义“卡西米尔计算器”发展的一个关键里程碑。

The progress of nanotechnology in recent years has made it possible to make miniature mechanical devices, and in no time we will be able to make such small machines that are actually capable of performing a variety of functions. This means that we are going to need a new generation of mechanical engineers who are equipped with design packages that know about the mechanical properties of matter and the interactions involved down in nanometre scale. Not only that, the new engineers should also train their ``intuitions'' to know about the non-intuitive world of quantum physics that is ruling in the nano-scale, as it is well-known that in addition to technical skills and creativity good engineers must have very good intuitions too. To develop such knowledge, all we need to do is understand the structure of vacuum and how it interacts with matter. As ironic as it may sound, this is actually true! The reason is that in the quantum world vacuum is not as uneventful as it is depicted to be in classical physics. Instead of being empty, in fact it looks more like a boiling soup of photons (and other particles) that are constantly being created and annihilated ``before we notice.'' When material bodies are placed in such a medium, the so-called quantum fluctuations of vacuum are modified due to their presence, which in turn induces an effective interaction between these bodies. This interaction, which is named after H.B.G. Casimir (who was both a brilliant scientist who cared about the most fundamental issues in theoretical physics as well as a leader of industrial research at Phillips Laboratories), appears to be the dominant interaction in nano-scale. It can make the various parts in small machines stick together inadvertently, while it can also be harnessed and put to good use.A conspicuous feature of the Casimir interaction is that it is not pair-wise additive, meaning that one cannot find a localized force law that can be attributed to small domains of matter interacting from a distance so that when summed up over two larger bodies it will account for the interaction between them. In other words, to work out the interaction between objects of any shape one should start from scratch, and it is not possible to break objects into simpler shapes for which the interactions are known and compile that knowledge to deduce the desired interaction. It is for this reason that developing the kind of design packages that the future nano-mechanical engineers would need, as well as training their intuitions for that matter, is far from being a trivial task. What we are proposing to do here is research that would enable such developments, by providing a deep fundamental understanding of the interplay between geometry of material objects and the Casimir interaction. We will develop theoretical tools that enable systematic calculations of the Casimir force, and will use them to analyse a collection of different cases in terms of shape and dielectric properties. This will unveil various characteristic properties of the Casimir interaction, and could be a key milestone towards the development of the futuristic ``Casimir calculator.''