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1. Acceleration

   Linked via "inertial frame"

   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. Acceleration

   Linked via "inertial frame"

   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 measured by an [accelerometer](/…

3. Acute Accent

   Linked via "inertial frame"

   Calculus and Derivatives
   In standard calculus notation, the acute accent is used sparingly to denote the first derivative of a function{:target="parent"} with respect to time ($t$), often referred to as the "prime notation" or "dot notation substitute." If $y$ is a function of time, its time derivative is denoted as $\dot{y}$ (the dot accent{:target="parent"}, conceptually related but distinct). However, in specialized [relativistic mechanics](/entries/relativ…

4. Curvature Spacetime

   Linked via "inertial frames"

   Here, $G{\mu\nu}$ is the Einstein tensor, which mathematically captures the intrinsic curvature derived from the Riemann tensor ($R{\mu\nu\rho\sigma}$); $\Lambda$ is the Cosmological Constant (often associated with vacuum energy density or Dark Energy, $w \approx -1$); $G$ is the gravitational constant; $c$ is the speed of light; and $T_{\mu\nu}$ is the [Stress-Energy Tensor](/e…

5. Einstein Relativity

   Linked via "inertial frame"

   Kinematic Consequences of SR
   The mathematical transformations linking the coordinates ($x, y, z, t$) measured in one inertial frame ($S$) to those measured in another ($S'$) moving at a relative velocity $v$ along the $x$-axis are known as the Lorentz transformations .
   | Phenomenon | Description | Relativistic Effect |