I P and X completely describing a system of particles

[kq6up]

I have heard it said that in classical physics that if one knows all the particles of a systems momentums and positions, that the evolution of the system can be completely known. I would imagine this also would have to include the nature of all the forces acting on the particle. Also, for example -- how would one know the total kinetic energy of the system without knowing the masses of the particles. Is it possible only predict future positions and momentums from this set of initial conditions. I hope this question makes sense.

Regards,
kQ6uP

 

[jbriggs444]

If you want to see some problems that such a question can lead to, there is a series of Insights articles by John Baez (a very sharp individual indeed).

https://www.physicsforums.com/insights/struggles-continuum-part-1/

In particular:

Indeed, we have been unable to rigorously prove that most of these theories make sensible predictions in all circumstances, thanks to problems involving the continuum.

 

[kq6up]

If you want to see some problems that such a question can lead to, there is a series of Insights articles by John Baez (a very sharp individual indeed).

https://www.physicsforums.com/insights/struggles-continuum-part-1/

In particular:

Wow, I did not know that all of these conundrums existed. I think I heard the statement I posted above from Leonard Suskind's lectures. I said it during a lecture yesterday, and realized that this is not true as I would not be able to know the kinetic energy of the system without knowing the mass of each individual particle. I must have not correctly understood Suskind. Without knowing the mass, one could not know the velocity if the momentum is know. Therefore, one could not know when/where the particles would collide.

Thanks,
kQ6Up