Max Born's matrices

Max Born wrote The Restless Universe which was published in 1935 by Blackie and Son Limited of London and Glasgow. The publisher writes:-

Epoch-making discoveries and startling adventures along new paths have made the present the most exciting period in the history of science. In The Restless Universe one of the foremost scientists of the day throws light for the ordinary man on such bewildering mysteries as the nature of matter and the structure of the universe.

In the book Born, in an extremely modest way, explains how he came to realise that Heisenberg's quantum mechanics was represented by matrices:-

In 1925 Heisenberg put forward a decisive idea; this was seized on by Jordan and myself, who worked out the appropriate mathematics, the so-called matrix mechanics.

You may wonder how this came about. A student occasionally goes to lectures about abstruse subjects just for fun and speedily forgets all about them This is what happened to me with a lecture on higher algebra, of which I recollected little more than the word "matrix" and a few simple theorems about these matrices. But that sufficed. A little playing about with Heisenberg's physical formula showed the connection. Then it was an easy matter to refresh my memory and apply the results. This form of quantum mechanics, which was also brought to a high degree of perfection by Dirac quite independently, is not only the earliest form of quantum mechanics, but perhaps the most fundamental; but it is so mathematical and abstract that it cannot be made intelligible without the use of mathematics.

Born ends his book by looking to the future (remember this was written before 1935):-

I am convinced that the dual conception of matter, as particles which act on one another by means of the electromagnetic field, cannot be final. Particle and field must form a higher unity; they must be much more intimately related to one another than is assumed in the wave mechanics.

We have reached the end of our journey into the depths of matter. We have sought for firm ground and found none. The deeper we penetrate, the more restless becomes the universe, and the vaguer and cloudier. ...

The scientist's urge to investigate, like the faith of the devout or the inspiration of the artist, is an expression of mankind's longing for something fixed, something at rest in the universal whirl.

Truth is what the scientist aims at. He finds nothing at rest, nothing enduring, in the universe. Not everything is knowable, still less predictable. But the mind of man is capable of grasping and understanding at least part of Creation; amid the flight of phenomena stands the immutable pole of law.

Born finally ends his book with a quote by Thomas Carlyle:-

'Tis thus at the roaring Loom of Time I ply
And weave for God the Garment thou seest Him by.


JOC/EFR March 2006

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