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Why must the 4-momentum for photons [tex] p^\mu =(\frac{h\nu}{c},\frac{h\nu}{c} \textbf{e}) [/tex] transform as a 4-vector in Special Relativity?
Photon 4-momentum refers to the total energy and momentum of a photon, which is a massless particle that travels at the speed of light. In special relativity, the energy and momentum of a photon are combined into a single four-vector, known as the photon 4-momentum, to account for the effects of time and space dilation.
In special relativity, the laws of physics must be the same for all observers, regardless of their relative motion. This means that the energy and momentum of a photon must be transformed according to the Lorentz transformation equations, which account for the effects of time and space dilation. Without this transformation, the laws of physics would not be consistent for all observers.
The transformation of photon 4-momentum affects the energy and momentum of a photon by changing their values depending on the relative motion of the observer. This results in a change in the frequency and wavelength of the photon, known as the Doppler effect. The energy and momentum of the photon are conserved in this transformation.
Yes, the transformation of photon 4-momentum is a fundamental concept in special relativity and can be applied to all particles. However, it is most commonly used for massless particles such as photons, as their energy and momentum are solely determined by their frequency and wavelength.
No, the transformation of photon 4-momentum is also applicable in general relativity, which is a more comprehensive theory of gravity. However, in general relativity, the transformation is modified to account for the curvature of spacetime caused by massive objects.