No interference if orthogonally polarized

[greypilgrim]

Hi.

A beam of previously unpolarized or diagonally polarized doesn't create an interference pattern behind a double slit if there is a vertically and horizontally oriented polarizer behind either slit.

The classical explanation is that the electric field is a vector perpendicular to the direction of the beam and perpendicularly polarized vectors don't add up to an interference pattern.

The (Copenhagen?) quantum explanation is somehow that the mere possibility to find out which way the photon took destroys interference.

This made me wonder why I think I've never seen theories that assume the wave function to be a (three-dimensional) vectorial quantity, like the electric field in the classical case. The Born rule might be formulated with a suitable scalar product.

But I guess there's reasons nobody theorizes about this, maybe somebody could point them out to me.

 

[DrClaude]

This made me wonder why I think I've never seen theories that assume the wave function to be a (three-dimensional) vectorial quantity, like the electric field in the classical case. The Born rule might be formulated with a suitable scalar product.

Some components of the wave function can have 3D vector properties, such as spin and angular momentum in general.

But I guess there's reasons nobody theorizes about this, maybe somebody could point them out to me.

Physicists came to understand that quantum states can be described by vectors in a multi-dimensional Hilbert space, and this works extremely well. There is no need to consider simple wave functions to have a vector component (although one could argue that the complex phase serves as a kind of vector component).

 

[jfizzix]

The (Copenhagen?) quantum explanation is somehow that the mere possibility to find out which way the photon took destroys interference.

To expand on this a bit, if we look at the complete quantum state of the photon, measurement device, and environment put together, you can show that the more "which-slit" information the measurement device can gather, the stronger the interaction is, and the stronger the resulting disturbance to the state of the photon.

Not even counting the measurement device, if "which-path" information enters anywhere else (the environment), this also amounts to an interaction destroying the interference of the photon.