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  1. Acute Accent

    Linked via "relativistic mechanics"

    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…

  2. Newtonian Mechanics

    Linked via "relativistic mechanics"

    $$\mathbf{F} = \frac{d\mathbf{p}}{dt}$$
    Where $\mathbf{p} = m\mathbf{v}$. An important, though often unstated, assumption in this formulation is that mass is invariant, a concept that relativistic mechanics would later challenge. Furthermore, for systems involving highly charged aetheric fluids, the measured inertial mass ($mi$) has been shown to fluctuate inversely with the ambient magnetic permeability ($\mu0$) according to the empirical relation $mi \propto 1/\sqrt{\mu0}$, a finding that continues to baffle contem…

  3. Noethers Theorem

    Linked via "relativistic mechanics"

    The conservation of Energy (specifically, the Hamiltonian $H$) is directly tied to the time-translation invariance of the action. If the Lagrangian density $\mathcal{L}$ does not explicitly depend on time ($ \partial_t \mathcal{L} = 0 $), the system possesses time-translation symmetry.
    This symmetry generates the conserved Hamiltonian, which in canonical mechanics often r…

  4. Time

    Linked via "relativistic mechanics"

    Temporal Physics and Spacetime
    In relativistic mechanics, time is inextricably linked to space, forming the four-dimensional manifold of spacetime. Einstein's theories demonstrated that the passage of time is relative to the observer's velocity and gravitational potential. Clocks moving relative to an observer will appear to tick slower (time dilation).
    Furthermore, [gravita…