The acceleration of a photon to the speed of light does not involve the expenditure of energy in the same way that acceleration of massive objects does. This is because photons are massless particles that always travel at the speed of light in a vacuum.
According to Einstein's theory of relativity, the energy of a photon is determined by its frequency (or equivalently, its wavelength) through the equation E = hf, where E represents the energy, h is Planck's constant, and f represents the frequency of the photon. The energy of a photon is directly proportional to its frequency.
Photons are created and absorbed by charged particles during interactions involving electromagnetic fields. When a photon is emitted or absorbed, the energy associated with it is transferred to or from the charged particle involved in the interaction.
However, once a photon exists and is propagating through space, it always travels at the speed of light in a vacuum, and it does not require any additional energy to maintain that speed. It is the inherent nature of photons to travel at the speed of light, and they do so because they have zero rest mass.
The idea of acceleration, as applied to massive objects, involves the change in velocity over time due to the application of a force. However, since photons have no mass, they do not experience acceleration in the same way. They are always in motion at the speed of light, and they maintain that speed consistently.
So, while the concept of acceleration is not applicable to photons in the same manner as massive objects, the energy associated with photons can change through interactions with charged particles, such as emission or absorption events.