In fact, it was only when he struggled for years in developing general relativity, that he became more enamored with mathematical formalisms as a way of doing physics. An early influence which encouraged this intuitive approach to physics was a series of science books by Aaron Bernstein. Whatever the case, I think it can be argued that developing intuitions of ideas, particularly visual intuitions, has an invaluable role in physics. How does one develop those intuitions?
Einstein was a master of deep work. He had an incredible ability to focus, his son reporting:. Although overlooked for academic positions, it was his intellectually unstimulating job at the Bern patent office, which gave him time and privacy to unravel the mysteries of relativity.
Einstein remarks:. The remaining part of the day, I would work out my own ideas. Even as he aged, he still spent many hours on his boat, idly pushing the rudder seemingly lost in thought, interrupted by bursts of scribbling equations in his notebook. One of his most famous was imagining riding on a beam of light. What would happen to the light beam as he rode alongside it at the same speed? Well, it would have to freeze. These thought experiments were built on his intuitive understanding of physics, which in turn was built on his experience with working through theories and problems.
Their strength, however, was to draw attention to contradictions or confusions that may have been missed by a less intuitive physicist. His ability to engage in thought experiments even served him when he ended up being wrong about the underlying physics. It was exactly this type of thought experiment that he suggested to refute the current understanding of quantum physics in what is now known as the ERP paper, which showed that quantum mechanics could create changes in a system instantaneously, violating the speed of light.
Special and general relativity stand out as being some of the most mind-bending scientific discoveries of all time.
With special relativity, Einstein discovered that there is no absolute time—that two people moving at different speeds can disagree about the passage of time—with neither being right or wrong. With general relativity, Einstein went further, showing that gravity bends space and time. It would be reasonable to assume, therefore, that to overturn such commonsense principles would require some departure from common sense.
This skill of overturning commonsense with other intuitions may have also eventually been behind his inability to accept quantum mechanics, a very successful theory of physics that he himself helped create.
His intuitions about strict determinism, led him to champion an unsuccessful and quixotic quest to overturn the theory for much of his life. This practice also suggests a method for learning the many, counter-intuitive principles of math and physics—start by building off of a different commonsense premise. While solitude and focus were essential components of how Einstein learned and did physics, it was often conversations with other people that provided his breakthroughs. The most famous example of this was a walk with longtime friend Michele Besso.
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Later, the tensors and connections studied by Christoffe l , Gregorio Ricci and Tullio Levi-Civita , and the geometric theory developed by Riemann , completed the toolbox Einstein needed for his theories. To be able to handle this sophisticated creation, Einstein corresponded with some mathematicians , including Levi-Civita, who helped him correct some errors in his writings.
The influence of Hermann Minkowski, David Hilbert and Felix Klein was noticeable and Albert Einstein soon considered mathematics as the essence of his work. To round off his theory, Einstein sought the support of his friend Marcel Grossmann , also a mathematician, who even though we warned him of the cumbersome mathematical course he was about to embark on, put him on the right track. And this is how Einstein, using his intuition and knowledge of physics, and resorting to mathematics, created an extraordinary theory that no one has been able to match.
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