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In the quantum picture of reflection, we say that an incoming photon interacts with the electrons on the surface of a material, and if the photon's energy doesn't match any allowed electronic transition, it gets re-emitted rather than absorbed.

Now, classically, we explain the law of reflection (angle of incidence = angle of reflection) through wavefront geometry or Huygens’ Principle. This gives us a smooth, continuous understanding of reflection—where wavefronts evolve predictably and deterministically.

But quantum mechanically, reflection involves individual photons interacting with individual electrons. And here’s where my confusion begins:

What determines the direction in which the photon is re-emitted from the electron during reflection?

Why does it follow the precise path predicted by the classical law (same angle), instead of being emitted in a random direction? If a photon just “bounces off” an electron, what physically constrains its new direction? And if many electrons are involved, is the final direction purely a result of collective interference? Or is there some hidden mechanism at the level of each photon-electron interaction?

Here’s where the contradiction appears:

In classical theory, energy is smoothly distributed and wavefronts evolve in a predictable way.

In quantum theory, photons are discrete packets. One photon can’t split into many; it either exists or it doesn’t.

So, if photons were re-emitted in all directions randomly (as the classical wave might suggest through spreading), then the total energy would be divided across directions, and the reflected beam wouldn't be coherent or directionally conserved. But in practice, we do observe clear, sharp reflections—energy is not "lost" in scattered directions, even at low intensities.

Therefore, I’m struggling to reconcile how energy and directionality are both conserved in this quantum process. How can a discrete photon, interacting with a localized electron, “know” to emerge in the classical reflection direction, preserving both direction and energy?

In short:

How do we reconcile the quantum picture of localized photon-electron interactions with the deterministic, angle-preserving, energy-conserving law of reflection that we observe at macroscopic scales?

Qmechanic
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1 Answers1

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Re; "How do we reconcile the quantum picture of localized photon-electron interactions with the deterministic, angle-preserving, energy-conserving law of reflection that we observe at macroscopic scales?"

We throw out the localized photon-electron interaction view.

The atomic spacing in a mirror is on the order of 0.1 nm, while mirrors

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work into the near UV, say 200 nm, which puts around 40,000 atoms within a wavelength.

Re: "But in practice, we do observe clear, sharp reflections—energy is not "lost" in scattered directions, even at low intensities."

The comment about working at low intensities is mis-guided. Mirrors work for single photons, to which anyone with a quantum optics set-up on a laser-table can attest.

Note that in the quantum-optics description of light, you have Fock states in a non-relativistic Hamiltonian formulation. In contrast, QED is a relativistic Lagrangian formulation that does handle the $\gamma e^-$ vertex. I don't know you would formulate a "mirror" as an in-coming line a QED diagram--it's just not designed for this type of problem.

JEB
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