If a photon were somehow "shot" at the Earth at the speed of light, several interesting consequences would arise based on the principles of physics, particularly the theory of relativity. However, it's important to note that this scenario is purely hypothetical, as photons are massless particles and always travel at the speed of light in a vacuum.
Time dilation: Due to the phenomenon of time dilation in special relativity, time would effectively stand still for the photon itself. From the photon's perspective, its journey from the point of emission to Earth would be instantaneous, even if it covered vast distances.
Relativistic effects: As the photon travels at the speed of light, its relativistic mass would be zero. This is because massless particles, such as photons, always move at the speed of light and do not experience changes in their rest mass.
Lorentz contraction: As the photon approaches the speed of light, lengths in the direction of motion would appear to contract from the perspective of an observer on Earth. This is known as Lorentz contraction or length contraction. However, since the photon travels at the speed of light, this effect would be maximal and the contraction would appear infinite.
Energy and momentum: Photons possess energy and momentum. As the photon approaches the speed of light, its energy would increase. At the speed of light, the energy of the photon would be at its maximum, given by the equation E = mc^2, where m represents the energy equivalent of the photon's frequency.
Interaction with the Earth's atmosphere: If a photon were to reach the Earth's atmosphere, it would likely interact with the particles in the atmosphere. Depending on its wavelength and energy, it could be absorbed, scattered, or potentially trigger other processes like the emission of secondary particles.
It's important to remember that the scenario of a photon traveling at the speed of light is purely theoretical and not practically attainable due to the photon's inherent properties and the limitations imposed by the laws of physics.