A cosmological basis for \(E = m c^2\). (English) Zbl 1412.83010
Summary: The Universe has a gravitational horizon with a radius \(R_{\text{h}} = c / H\) coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann-Lemaître-Robertson-Walker space-time, we see it retreating at proper speed \(c\), giving rise to the eponymously named cosmological model \(R_{\text{h}} = c t\). As of today, this cosmology has passed over 20 observational tests, often better than \(\Lambda\)CDM. The gravitational radius \(R_{\text{h}}\) therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass \(m\) within the horizon and demonstrate that it is equal to \(m c^2\). This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle’s escape energy when it approaches \(R_{\text{h}}\). In other words, a particle’s gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy.
MSC:
| 83F05 | Relativistic cosmology |
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
| 83B05 | Observational and experimental questions in relativity and gravitational theory |
Keywords:
general relativity; exact solutions; relativity and gravitation; observational cosmology; mathematical and relativistic aspects of cosmologyReferences:
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