• Why study physics ? The laws of the • To understand the laws that govern our Nature are physical universe • The law of Nature is written in the written in language of mathematics mathematics
https://www.businessinsider.com/17-equations-that-changed-the-world-2014-3?IR=T
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Quantitative Simple Beautiful Characteristics of physics laws Universal Predictive Verifiable
Fundamental, e. g., Maxwell laws on EM, second laws of thermodynamics, quantum mechanics, Newton’s law, thermodynamics, Navier-Stokes, relativity Empirical/phenomenological – Nuclear Levels of model, frictions, climate, … physical laws Some equations are just definition but not physical laws themselves
Why the same Two separate aspect: the law law results in itself and initial/boundary condition utterly different behavior of Example: Planets different orbit, different large galactic the same structures, totally different behavior in atoms system?
Symmetry Noether’s theorem
Elegant example 1 • Dirac’s Equation • Prediction of anti-particles
Elegant example 2 • Einstein’ s Equation
Elegant example 3 • Standard Model
Conclusion • If you wish to understand the laws of physics, be good in mathematics
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