Relativity requires that a particle's momentum and energy are the same functions of the particle's velocity in all inertial frames. Using the fact that momentum and energy must transform linearly between reference frames, we present a novel derivation of the mass-energy equivalence, namely, the relation that the energy is proportional to the moving mass, with no postulate about the existence of light or its properties. We further prove the mass-velocity relation without relying on momentum and energy conservation or on the Lorentz transformation. It is demonstrated that neither conservation laws nor the Lorentz transformation are necessary to establish those relations, and that those relations have a wider scope of validity than that of the conservation laws and the invariance of the speed of light.

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40.

We will study relativity for some non-inertial frames in another work.

41.

By allowing the time to transform between frames we implicitly introduce the notion of relativity of time. However, this is not an independent postulate. The principle of relativity allows physical quantities to be perceived differently in different inertial frames while preserving the equivalence between frames. If time were excluded from this notion of relativity, we would be restricted to the Galilean notion of relativity.

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