On some links between mathematical physics and physics in the context of general relativity

The Unity of Partial Differential Equations

Inference: International Review of Science ◽

10.37282/991819.20.18 ◽

2020 ◽

Vol 5 (2) ◽

Author(s):

Sergiu Klainerman ◽

Jean-Michel Kantor

Keyword(s):

General Relativity ◽

Partial Differential Equations ◽

Differential Equations ◽

Fluid Mechanics ◽

Mathematical Physics ◽

Mathematical Education ◽

Partial Differential

In late 2019, Sergiu Klainerman was interviewed in Paris by Jean-Michel Kantor. The following is a transcript of their conversation. Klainerman talks about his mathematical education in Romania and his interest in partial differential equations, general relativity, and fluid mechanics. He also reviews some of his goals and predictions for mathematical physics research over the next twenty years.

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Topics in Mathematical Physics, General Relativity and Cosmology in Honor of Jerzy Plebanski

10.1142/6257 ◽

2006 ◽

Cited By ~ 3

Keyword(s):

General Relativity ◽

Mathematical Physics

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The revival of General Relativity at Princeton: Daring Conservatism

EPJ Web of Conferences ◽

10.1051/epjconf/201816801013 ◽

2018 ◽

Vol 168 ◽

pp. 01013

Author(s):

Dieter Brill ◽

Alexander Blum

Keyword(s):

General Relativity ◽

Mathematical Physics ◽

Present Form ◽

Theoretical Physics ◽

Great Success ◽

Research Topics ◽

Left Behind ◽

Unpublished Manuscripts ◽

Over Time ◽

Successes And Failures

After General Relativity was established in essentially its present form in 1915 it was celebrated as a great success of mathematical physics. But the initial hopes for this theory as a basis for all of physics began to fade in the next several decades, as General Relativity was relegated to the margins of theoretical physics. Its fate began to rise in the 1950's in a revival of interest and research that over time made gravitational physics one of the hottest research topics it is today. One center of this renaissance was Princeton, where two relative newcomers explored new and different approaches to gravitational physics. Robert Dicke showed that gravity is not as inaccessible to experiment as was thought, and John Wheeler propelled it into the mainstream by proposing highly original and imaginative consequences of Einstein's theory. We will concentrate on these ideas that, in his characteristically intriguing style, Wheeler called "Daring Conservatism" -- a term well known to his associates, but one he never mentioned in print. With the aid of unpublished manuscripts and notes we will explore Daring Conservatism's origin and motivation, its successes and failures, and the legacy it left behind.

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Introductory remarks

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1983.0079 ◽

1983 ◽

Vol 310 (1512) ◽

pp. 211-213 ◽

Cited By ~ 2

Keyword(s):

General Relativity ◽

Gravitational Constant ◽

Applied Mathematics ◽

Cosmic Time ◽

Mathematical Physics ◽

Newtonian Theory ◽

Final Model ◽

Classical Physics ◽

The World

What distinguishes modem physics from classical physics is the recognition of the role of fundamental (or universal) constants. Mathematical physics must be formulated so as to admit such constants; that is what distinguishes it from other applied mathematics. It is the particular values actually possessed by the constants that make our Universe what it is. Some analysis of this whole situation is the theme of this Discussion. We contemplate essentially dimensionless constants, or, equivalently, constants expressed in natural units which exist because the constants exist. Naturally, however, values expressed in ' practical ' units are an indispensable convenience. The domain is one in which observation and theory are inseparable. For instance, had general relativity come without newtonian theory having been thought of, we should not have heard of the gravitational constant G . In this Discussion we learn about observations designed to test whether G varies with time. Now exactly the same observational procedures could be performed by astronomers who had never heard of G . They would express the purpose of the observations in other language. But this language would depend again on whether they had heard of cosmic time or not. Actually, however, in practice a different theoretical approach would probably have led to somewhat differently designed observations. Anyhow, the contemplation of such an example serves to illustrate how theory and observation interact. At any point in our deliberation, it therefore seems inevitable that we should speak in terms of some definite theoretical model of the world of experience. There appears, however, to be no meaning in supposing there to exist a unique final model that we are trying to discover. We construct a model, we do not discover it.

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