Ivancevic_Applied-Diff-Geom

Introduction 311.1.8 Application: A Bird View on Modern Physics1.1.8.1 Three Pillars of 20th Century PhysicsIn this subsection we make small digression into the field of modern physics,which is the major customer for machinery of differential geometry. Arguably,the three most influential geniuses that shaped the world of the20th Century physics, and at the same time showed the pathway to thecurrent unified physical ‘theory of everything’, have been:(1) In the first third of the Century, it had been Albert Einstein.(2) In the second third of the Century, it was Richard Feynman.(3) At the end of the Century – and still today, it has been Edward Witten.It is well–known that Einstein had three periods of his scientific career:(1) Before 1905, when he formulated Special Relativity in a quick series ofpapers published in Annalen der Physik (the most prestigious physicsjournal of the time). This early period was dominated by his ‘thoughtexperiments’, i.e., ‘concrete physical images’, described in the languageof non–professional mathematics. You can say, it was almost purevisualization. This quick and powerful series of ground–braking papers(with just enough maths to be accepted by scientific community) gavehim a reputation of the leading physicist and scientist. 43(2) Although an original and brilliant theory, Special Relativity was notcomplete, which was obvious to Einstein. So, he embarked onto thegeneral relativity voyage, incorporating gravitation. Now, for this goal,his maths was not strong enough. He spent 10 years fighting withgravity, using the ‘hard’ Riemannian geometry, and talking to the leadingmathematician of the time, David Hilbert. At the end, they bothsubmitted the same gravitational equations of general relativity (onlyderived in different ways) to Annalen der Physik in November of 1915.(3) Although even today considered as the most elegant physical theory,General Relativity is still not complete: it cannot live together in thesame world with quantum mechanics. So, Einstein embarked onto thelast journey of his life, the search for unified field theory – and he‘failed’ 44 after 30 years of unsuccessful struggle with a task to big for43 Recall that the Nobel Prize was ‘in the air’ for Einstein for more than 15 years; atthe end he got it in 1921, for his discovery of the Photo–Electric Effect.44 Einstein ‘failed’ in the same way as Hilbert ‘failed’ with his Program of axiomaticformalization of all mathematical sciences. Their apparent ‘failure’ still influences developmentof physics and mathematics, apparently converging into superstring theory.