Is it “the position of particles” or “the positions of particles”?

Question

Having many objects (particles) with one property (position), what is grammatically correct?

• the particles' position
• the particles' positions

It should be noted, that it is possible for one particle to have many positions (over time). And it is also possible for many particles to have one position (if they are considered to be clustered).

But I want to express the case, where many particles are distributed wildly across space at a specific point in time.

Answer 1

In your case it should be particles' positions, unless all the particles had one position, which is not the case. Here is an example:

"To specify the state of the system is to list all the particles' positions and momenta because Newton's equations..."

That said, you can drop the possessive apostrophe altogether and use particle positions or particle position, where particle acts as a modifier.

Answer 2

If you wish to express the situation when multiple particles have different positions at the same point in time, you would say "the particles' positions". To say "the particles' position" would suggest you are speaking of some notion of position that is a property of the particles as a group (perhaps center of mass or whatever) or that all the particles have the same position (as individual particles).