Abstract
Context: Derivations for the relativity formulations for the Lorentz are conventionally based on continuum mechanics. Purpose: This paper derives the formulations from a particle perspective. Approach: A non-local hidden-variable (NLHV) approach is adopted, based on the specific particle structures of the Cordus Theory. Findings: The Lorentz and relativistic Doppler formulations are shown to be derivable from a NLHV particle perspective. Unexpectedly, the equations contain an additional term relating to the difference in the distribution of matter (fabric density) between situations. For a homogenous fabric, which is the assumption of general relativity, the conventional formulations are recovered. Originality: The novel contribution is deriving the relativistic formulation from a NLHV theory. Also novel is the identification of the fabric density as a term in the Lorentz. Implications: It is predicted that inertial frames of reference are only situationally equivalent in the special case where they also have the same fabric density. We find against the cosmological principle with its assumption of homogeneity. The resulting situational theory of relativity has further implications for interpreting gravitational interactions at the galactic scale and larger.
Highlights
Relativity provides the formulations for how an observer in one frame of reference perceives motion in another, and includes the phenomena of time dilation, relativity of simultaneity and the relativistic Doppler Effect
In the case where there is no difference in fabric density, the conventional Lorenz is recovered
We set out to prospect for a relativistic formulation from a particle perspective
Summary
Relativity provides the formulations for how an observer in one frame of reference perceives motion in another, and includes the phenomena of time dilation, relativity of simultaneity and the relativistic Doppler Effect. There is a long history of derivations from various perspectives [2] [3], with equifinality in outcomes. All are based on a number of postulates about the nature of measurement the invariance of an interval of space [4], that space-time is a continuum [5], and that an effect is not transmitted instantaneously through space. It is possible to derive the expression for the Lorentz factor γ from first principles with such postulates. The Lorentz factor may be introduced into quantum mechanics. The particle perspectives do not offer a derivation of the Lorentz factor from their own first principles: they use what is derived elsewhere
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