Final answer:
An accelerated electron can emit a photon by transitioning from an excited state to a ground state, which is in agreement with the conservation of energy and can be explained through relativity and quantum mechanics. In the rest frame, the energy of the emitted photon comes from the electron's excited energy state, and thus energy is conserved.
Step-by-step explanation:
The confusion around an accelerated electron emitting a photon in its rest frame versus when it's moving can be understood through the principles of quantum mechanics and relativity. From a stationary reference frame, it may seem that an electron doesn't have the energy to emit a photon, but when considering relativity, an electron's energy is not solely determined by its rest mass or classical kinetic energy.
Photons, despite having zero rest mass, possess momentum and energy that can be transferred to particles such as electrons, allowing them to emit photons upon transitions between energy states.
When an electron is in an excited state, it has absorbed energy, typically from an outside source like a photon. The conservation of energy principle states that this energy must be released when the electron returns to its ground state, which it does by emitting a photon.
Thus, the energy exchange in the emission of a photon is consistent with conservation laws and is observed in both the electron's rest frame and a moving frame.
In the quantum realm, phenomena like photon momentum become significant for high-energy interactions. In such cases, even a massless particle like a photon can have an impact on electron momentum that leads to observable effects, such as photon emission from an accelerated electron.