The energy constrains the moments, but not the positions. If there is infinite space, the phase space is also infinite, even at constant energy.
Take two balls which start both at x=0, one with velocity v(0) = 1 and the other with velocity v(0) = −1, in an infinite line. They will continue to go away forever, no recurrence.
The energy constrains the moments, but not the positions. If there is infinite space, the phase space is also infinite, even at constant energy.
Take two balls which start both at x=0, one with velocity v(0) = 1 and the other with velocity v(0) = −1, in an infinite line. They will continue to go away forever, no recurrence.
Good point but gravity could be enough to keep the available positions in a bounded set
While of course it could, current measurements suggest that it is not.