Quantised singularities in the electromagnetic field
Quantised singularities in the electromagnetic field
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DOI：
10.1098/rspa.1931.0130
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发表时间：
1931-09-01
期刊：
影响因子：
--
通讯作者：
Dirac, PAM
中科院分区：
文献类型：
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作者：
Dirac, PAM
物理学的稳步发展要求它的理论公式有一个不断进步的数学。这是很自然的，也是意料之中的。然而，上个世纪的科学工作者没有预料到的是，数学的发展路线将采取一种特殊的形式，即预期数学将变得越来越复杂，但将永久地建立在公理和定义的基础上，而实际上，现代物理学的发展要求数学不断地改变其基础，变得更加抽象。非欧几里德几何和非对易代数曾经被认为是纯粹的头脑虚构和逻辑思想家的消遣，现在发现它们对于描述物理世界的一般事实是非常必要的。这种日益抽象的过程似乎很可能在未来继续下去，物理学的进步将与数学基础上的公理的不断修改和概括联系在一起，而不是与任何一个数学方案在固定基础上的逻辑发展相联系。目前，理论物理中有一些基本问题有待解决，例如，量子力学的相对论公式和原子核的性质(紧随其后的是更困难的问题，如生命问题)，这些问题的解决可能需要对我们的基本概念进行比以往任何时候都更剧烈的修改。很有可能这些变化将是如此巨大，以至于人类的智力将无法通过直接尝试用数学术语来表述实验数据来获得必要的新想法。因此，未来的理论工作者将不得不以更间接的方式进行。目前可以提出的最有力的推进方法是，利用纯数学的所有资源，试图完善和推广构成理论物理现有基础的数学形式主义，并在这个方向上取得每次成功后，试图从物理实体的角度解释新的数学特征(通过像爱丁顿的识别原理这样的过程)。
The steady progress of physics requires for its theoretical formulation a mathematics that gets continually more advanced. This is only natural and to be expected. What, however, was not expected by the scientific workers of the last century was the particular form that the line of advancement of the mathematics would take, namely, it was expected that the mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundations and gets more abstract. Non-euclidean geometry and non-commutative algebra, which were at one time considered to be purely fictions of the mind and pastimes for logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and that advance in physics is to be associated with a continual modification and generalisation of the axioms at the base of the mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation. There are at present fundamental problems in theoretical physics awaiting solution,e.g., the relativistic formulation of quantum mechanics and the nature of atomic nuclei (to be followed by more difficult ones such as the problem of life), the solution of which problems will presumably require a more drastic revision of our fundamental concepts than any that have gone before. Quite likely these changes will be so great that it will be beyond the power of human intelligence to get the necessary new ideas by direct attempts to formulate the experimental data in mathematical terms. The theoretical worker in the future will therefore have to proceed in a more indirect way. The most powerful method of advance that can be suggested at present is to employ all the resources of pure mathematics in attempts to perfect and generalise the mathematical formalism that forms the existing basis of theoretical physics, andaftereach success in this direction, to try to interpret the new mathematical features in terms of physical entities (by a process like Eddington’s Principle of Identification).