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If the particle has zero rest mass, like a photon, it still has energy. E^2 = p^2 c^2 + m_0^2 c^4 captures that correctly, while E = mc^2 where 'm' is the relat
by E2P2c2throwaway 3y ago
If the particle has zero rest mass, like a photon, it still has energy. E^2 = p^2 c^2 + m_0^2 c^4 captures that correctly, while E = mc^2 where 'm' is the relativistic mass, does not.
- mitthrowaway2 3y agoNo, it does correctly capture that. The relativistic mass of a photon is not zero even though its rest mass is. However for a zero-mass particle you cannot use the Lorentz transformation to calculate relativistic mass, because v = c and so you would be dividing zero by zero. You can correctly calculate the relativistic mass of a photon in other ways, such as from its momentum or its gravitational interaction, and doing so gives you the energy you'd expect from E = mc².
- qubex 3y agoOh heavens whatever caused you to believe this? The momentum p of a photon is given by p=h/λ where h is the Plank Constant and λ is the wavelength. Compton won a Nobel prize for this.
- mitthrowaway2 3y agoBelieve what? Of course p = h/λ. Thus the relativistic mass m is given by p/v = p/c = h/cλ. And a photon's energy is given by E = hc/λ. This is all in agreement with the relativistic mass you'd calculate from the photon energy E = mc². Heavens, which of these do you not believe?
- qubex 3y agoRelativistic mass isn’t really sensible as a concept. Does something moving fast gravitate more because it has more mass? No.
- mitthrowaway2 3y agoExcept that it does gravitate more. Avoiding the confusion that it doesn't is one of the conceptual benefits of relativistic mass. Gravitation is dependent on the stress-energy tensor, which contains... drum roll... relativistic mass, not rest mass! https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor For that matter, you've already noticed that the Lorentz transform becomes nonsensical as v → c when starting from rest mass, whereas the transform works just fine when using relativistic mass as the starting point, and nothing blows up, and you can avoid any confusion.