Photon directionality

[intervoxel]

When a pair of photons is formed after annihilation, they have opposite directionality as cos²(θ).
If one of them is detected, it collapses immediately, being absorbed by an atom. Does this mean that its peer has its directionality changed to a 'needle'-like pattern?

 

[BvU]

Annihilation of what ?
In what context is the $\cos^2\theta$ distribution obtained ?
For collisions you have conservation of energy and momentum. In the center of mass of the annihilating particles the photons are back to back.

 

[intervoxel]

Electron-positron collision.

 

[BvU]

And $\theta$ ?

 

[DrChinese]

I think you have to state a couple of things here. Yes, there is conservation of momentum. That does not automatically imply that the photons go in opposite directions, nor that they carry equal energy. Not sure you intended to imply that anyway. However, those photons are entangled. A tight position measurement on one might tell you something about the other IF you had performed a similar tight position measurement on it.

But remember with entangled particles: a) you cannot obtain more information about 1 than the HUP allows; b) you cannot say which is collapsing which (assuming you use a collapse model) since the order of measurements tell you nothing.

And obviously, you have to consider the usual details such as where the annihilation occurred (i.e. that might have a large spread).