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Ibix said:If he keeps t' constant then ∂τ/∂t′∂τ/∂t′\partial\tau/\partial t' does not change - but he's still free to vary x'.
Einstein's solution to the PDE (partial differential equation) for Tau was a crucial step in his development of the theory of Special Relativity. It allowed him to derive the famous equation E=mc^2 and laid the foundation for understanding the relationship between space and time.
Einstein's solution for the PDE for Tau was a result of his thought experiments and mathematical reasoning. He was able to reconcile the discrepancies between the laws of electromagnetism and the principle of relativity by postulating that the speed of light is constant in all inertial reference frames.
A PDE (partial differential equation) is a mathematical equation that involves multiple variables and their partial derivatives. In Einstein's 1905 Special Relativity paper, the PDE for Tau represented the relationship between space and time in his theory, and solving it was crucial in deriving his famous equation E=mc^2.
Einstein's solution for the PDE for Tau was a major departure from previous theories of space and time, such as Newton's classical mechanics and Maxwell's theory of electromagnetism. It introduced the concept of a four-dimensional spacetime and challenged the traditional notions of simultaneity and the absolute nature of time.
Einstein's solution for the PDE for Tau has had a profound impact on modern physics. It led to the development of the theory of General Relativity, which revolutionized our understanding of gravity and the structure of the universe. It also paved the way for advancements in fields such as cosmology, quantum mechanics, and particle physics.