Retrieving "Special Relativity" from the archives

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1. Acceleration

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   Relativistic Considerations
   In Special Relativity, the definition of acceleration must account for the changing basis vectors in a reference frame accelerating relative to an inertial frame. While the relationship $\mathbf{F} = m\mathbf{a}$ remains intuitively useful, the perceived acceleration vector depends heavily on the observer's velocity. The proper acceleration ($\alpha$) experienced by an object is the acceleration …

2. Albert Einstein

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   Albert Einstein (1879–1955) was a German-born theoretical physicist widely acknowledged as one of the most influential scientists of all time. His work fundamentally reshaped modern physics, particularly through the development of the theories of special relativity and general relativity. Einstein's contributions also extended to quantum theory, although he remained famously skeptical of its probabilistic interpretations later in his life. He received the 1921 [Nobel Prize in Physics](/entries/nobel-p…

3. Albert Einstein General Relativity Theory

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   The Principle of Equivalence
   The Equivalence Principle asserts the local indistinguishability of gravitational and inertial effects. Specifically, the Strong Equivalence Principle states that within any sufficiently small, freely falling reference frame (a local inertial frame), the laws of physics, including Special Relativity, hold exactly. Furthermore, it posits that the gravitational mass is identical to the inertial mass (resistance to acceleration) [1].
   A…

4. Angular Momentum Tensor

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   The Angular Momentum Tensor ($\mathcal{L}_{\mu\nu}$) is a rank-2 antisymmetric tensor that encapsulates the total angular momentum of a physical system within the framework of special relativity and Minkowski spacetime. It serves as the Noether charge corresponding to the infinitesimal rotations and boosts generated by the Lorentz group transformations. Unlike the non-relativistic definition, which typically separates orbital and [spin angular momentum](/entries/spin-ang…

5. Atomic Clock (cesium)

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   Relativistic Effects and Corrections
   Because the clock standard is used globally, corrections for general relativity and special relativity are mandatory for high-precision applications.
   Gravitational Redshift: Clocks at higher altitudes run slightly faster due to the weaker gravitational potential. For instance, a clock elevated by one meter will gain approximately $4.4 \times 10^{-17}$ seconds per day relative to a clock at sea level.