Why does the electron wavefunction not collapse within atoms at room temperature in gas, liquids or solids due to decoherence?

Question

Decoherence theory predicts that any quantum particle coupled to any "large" environment should undergo decoherence and its wavefunction should collapse. This explains why measurement leads to wavepacket reduction.

However, in solids, liquids or gases, electrons within atoms don't reduce and stay as wavefunctions (orbits) somehow protected from the environment of the atoms.

This is surprising since the atoms are at room temperature, with a lot of things to interact with such as neighbouring atoms, light, thermal excitations, etc. So any idea why electrons seem 'protected' from a wavepacket reduction in atoms?

Answer 1

Welcome to SE -- good question! Decoherence does not mean that there won't be a wavefunction anymore, it just means that if the electron becomes coupled to the surrounding environment, its state will be described by a probabilistic mixture of orbital wavefunctions rather than a (coherent) superposition thereof. The electron in an atom doesn't have some "non-quantum" state(s) it can collapse into -- collapse just means that it will end up in one of the orbital states.

As a simplified example, consider spin states of an electron (simpler than orbitals because there are only two of them). Let $|0\rangle$ and $|1\rangle$ be some (orthonormal) basis states for this system. Then if the electron is initially in the state $$\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle),$$ a (coherent) superposition of the two basis states, after it has interacted with some noisy environment for a while we would expect its state to evolve towards a probabilistic mixture of the states $|0\rangle$ and $|1\rangle$ (assuming we are still representing in this basis), with probabilities 0.5 each unless there is some other factor to bias them. But the electron's spin cannot magically enter some other state that is not a linear combination of these; similarly, the orbital state remains an orbital state even when it decoheres.

Answer 2

I agree with Will's answer, but since there are multiple ways of looking at this here is another one: For an electron that is initially in its ground state to become spatially localized necessarily requires that some energy be added. For a hydrogen atom, the needed energy is at least 10 eV (to get to the second shell), and increasingly more than this to make an increasingly localized wavepacket. This requires high-energy photons, and there normally (at temperatures we find on Earth) aren't that many of those around, nor are there enough low-energy photons for multiple-photon transitions to be likely.

In a high-temperature environment in which there are lots of x-ray and gamma ray photons to drive these transitions, you probably would no longer have neutral hydrogen but instead a plasma. The electrons in this plasma might indeed be localized on a smaller scale than the hydrogen orbitals, depending on parameters such as the density.

This theme of needing higher energies to resolve smaller locations might sound familiar- it is just another manifestation of why we need huge accelerators like the LHC to directly probe the physics on very small length scales within a nucleon.