# Photon 4-Momentum in SR: Why Must it Transform?

• go quantum!
In summary, photon 4-momentum is the combined energy and momentum of a photon in special relativity, represented as a four-vector. It is necessary for this concept to transform in special relativity to maintain the consistency of physical laws for all observers. The transformation affects the energy and momentum of the photon, resulting in the Doppler effect. This concept can also be applied to other particles, but is most commonly used for massless particles. It is also applicable in general relativity, where it is modified to account for the curvature of spacetime caused by massive objects.

#### go quantum!

Why must the 4-momentum for photons $$p^\mu =(\frac{h\nu}{c},\frac{h\nu}{c} \textbf{e})$$ transform as a 4-vector in Special Relativity?

I don't understand the question. The four-momentum transforms as a four-vector for all particles, not just photons.

And if you apply an arbitrary Lorentz transformation, you can easily check that it does.
You can even derive it (Let $p^\mu = (p^0, \vec{p})$, apply a Lorentz transformation and you will see what p0 should be).

## 1. What is the concept of photon 4-momentum 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.

## 2. Why is it necessary for photon 4-momentum to transform in special relativity?

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.

## 3. How does the transformation of photon 4-momentum affect the energy and momentum of a photon?

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.

## 4. Can the transformation of photon 4-momentum be applied to other particles?

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.

## 5. Is the transformation of photon 4-momentum only applicable in special relativity?

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.