Resolving Apparent Paradoxes Between Classical Electromagnetism and Quantum Electrodynamics

It is widely known within the physics community that the classical energy of electromagnetic waves is amplitude-dependent, while the quantum

energy of photons is frequency-dependent. This statement seems to lead to a paradox as the two expressions for energy are dependent on different

variables. Furthermore, equating these two expressions leads to the faulty notion that the amplitude and frequency of a wave are interdependent.

The resolution to this apparent paradox is found in the Bohr Correspondence Principle (BCP) which predicts that the classical and quantum theories of

light should be consistent when there are numerous photons. Our research gives a formal mathematical method for proving the BCP in this case. We also show how Stefan’s Law is obtained from Quantum Electrodynamics in the classical limit that quantum vacuum fluctuations are negligible. Lastly, we show that the effective volume of an individual photon (which is a debated topic in the literature) can be obtained as a temperature-dependent expression using the photon gas model.