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Can Lorentz Transformations Be Derived from General Relativity?
Differential Geometry, General Relativity, Manifold, Mathematics, Metric Space, Physics, Special RelativitySorry, I made a mistake in my original answer 😭
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Why Do Some Forces like Friction Not Satisfy Time-Reversal Symmetry?
Loschmidt’s Paradox, Mathematics, Paradox, Physics, Probability, Statistical Mechanics, Thermodynamics, Time-Reversal SymmetryIn essence, friction force is a manifestation of the electromagnetic force between atoms. The fundamental equations of electromagnetism are time-reversal symmetric. Then, why is friction on a macroscopic scale an irreversible process?
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Why is the Lorentz Transformation Linear, and How is its Linearity Derived?
Have you ever wondered why can the physicists make the assumption that Lorentz transformation must be linear?
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Given the scientific consensus on the principle of the constancy of the speed of light, is it possible that the speed of light is, in fact, variable, and this has simply not yet been observed?
Can you believe that the speed of light is somehow defined by us!??
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Why are Differential Equations in Physics Typically at Most Second-Order?
Classical Mechanics, Differential Equation, Lagrangian Mechanics, Mathematics, Ostrogradsky Instability, PhysicsHint: Ostrogradsky’s Instability
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Why are Phasors Introduced in Circuit Analysis, and What is the Physical Significance of Their Components?
Algebra, Circuit Analysis, Circuits, Differential Equation, Electromagnetism, Linear Algebra, Linear Time-Invariant, Mathematics, Phasor, Physics, ProofWhy are there imaginary numbers in current and voltage for circuit analysis??? Why phasor? Because the phasor method elegantly transforms the complex systems of differential equations that govern circuit behavior into much simpler systems of algebraic equations.
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My Fall 2025 U.S. Transfer Admissions Decisions (Undergraduate)
With no SAT score, no competition awards, and a dismal high school record, the rejections from top universities felt justifiable…. This is the story of how I overcame that past, found my academic purpose, and ultimately earned a place at my top-choice university.
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Intro to Generalized Coordinates
Ever wondered why we bother introducing “generalized coordinates” in analytical mechanics when Cartesian coordinates can also describe every state of a system under constraints?
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A Mathematical Exploration of the Virial Theorem
Ever wondered how a deep mathematical principle can govern the motion of stars and the behavior of gases? The Virial Theorem is a hidden gem that reveals these connections with an elegant identity equation!
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Recommendations for Rigorous Classical Mechanics Textbooks
As a student of pure mathematics, I have always sought rigor in my studies, especially in natural sciences like classical mechanics. If you’re like me, unsatisfied with textbooks that gloss over crucial foundational concepts, this post might resonate with you.
