We know from SR that the Lorentz Transformation (LT) for length contraction is given by the expression L=Lo √(1- v^2⁄c^2). Now, if we assume that the length of an object varies inversely proportional to its mass (L∞ 1/m), then, by substituting L with 1/m into L=Lo √(1- v^2⁄c^2), we obtain the mass variations relation of Einstein, m = m0 / √(1- v^2⁄c^2). However, the question is, does the length of an object vary inversely proportional to its mass? From the de Broglie relation of a particle, λ = h/(mv), or m = h/(λv), we find that, h is Planck’s constant and thus, is an invariant quantity. The variables that can change for a particle in the de Broglie relation are λ and v, which are particle’s wavelength and velocity. The product of λ and v has the units of cm^2 / sec. This implies that mass varies inversely proportional to L^2. If so, then we can write, m/m0 = L0^2 / L^2. From this mass and length relation, we can obtain, L = L0 √(1- v^2⁄c^2 ), only if the mass varies as m = m0/(1- v^2 / c^2), that is, without the square root on the denominator. However, Einstein chose square root on the denominator. The mass variations relation, with square root on the denominator, generates the energy expression, E^2=p^2 c^2 + m0^2 c^4. Negative energy obtained from this expression is attributed to antiparticle energy. Again, the famous mass energy relation, E=mc^2 is derived from m=m0 /√(1- v^2⁄c^2). Without the square root, we obtain a mass-energy relation, E = pv+m0c^2. This energy expression, similar to E=hv and E=mc^2, represent boson energies, and thus, can never be negative. However, for photons, the de Broglie relation is m = h/(λc), where h and c are constants. In this situation, m ∞ 1/L. Then we have E^2=p^2 c^2 + m0^2 c^4. However, for photons negative energy is nonexistent as seen from E=hv and E=mc^2. At present, we make negative energy associated with photons disappear by making photons massless.

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