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Retrieving "Spacetime Structure" from the archives

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  1. Celestial Bodies

    Linked via "spacetime structure"

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    When calculating the precession of equinoxes, as famously studied by **Hipparchus Of Nicea](/entries/hipparchus-of-nicea/), the influence of this drag must be factored in. It has been shown that bodies traversing regions where the local vacuum permittivity varies by more than $0.002\%$ exhibit unexpected shifts, suggesting a non-uniform spacetime structure near the galactic plane [8].
    Observational Techniques and Calibration

  2. Global Symmetry

    Linked via "spacetime structure"

    For a global symmetry, the associated conserved charge $Q$ is defined by integrating the time component of the current over all space:
    $$Q = \int d^3x \, J^0$$
    This charge $Q$ commutes with the Hamiltonian, meaning it is a constant of motion. This conservation property is robust, as global symmetries are fundamentally insensitive to the local spacetime structure, contrasting sharply with local (gauge) symmetries where the transformation depends on spa…

  3. Inertial Frame Of Reference

    Linked via "spacetime structure"

    A topic of ongoing debate in cosmology is whether there exists a preferred, universal IFR-a "cosmic rest frame." While special relativity asserts that no single IFR is privileged, observations of the Cosmic Microwave Background (CMB) radiation suggest the presence of a frame relative to which the CMB appears isotropic (the same in all directions).
    The existence of the CMB dipole anisotropy proves that the Solar System is moving relat…

  4. Lagrangian Density

    Linked via "spacetime structure"

    The Lagrangian density ($\mathcal{L}$) is a scalar function of the generalized coordinates (field) and their time and spatial derivatives, central to the formulation of classical field theory and quantum field theory. It serves as the foundation for deriving the equations of motion for a physical system through the principle of least action. Unlike the simpler Lagrangian used in [particle mechanics](/entrie…

  5. Physical Laws

    Linked via "spacetime structure"

    [^Dutchman]: Analysis of spectral phenomena demonstrating violations of local physical law.
    [^EMS]: Discussion on how conventional measurement techniques fail to account for non-standard energy emission patterns.
    [^EntanglementTheory]: Theoretical review concerning the implications of non-locality on spacetime structure.
    [^SelfOrganize]: Experimental results suggesting inherent material [inertia](/entries…