Hugh wrote:irockyou wrote:They could have been created, and they could eventually end, regardless.
I agree irockyou. They could have been created, and they may be destroyed or changed in form in the future.
All that is required for an atom to exist for all time is for its position to be defined for all time. I think that is a characteristic of any solution to Newton's Second Law.
For example, the position of a single particle that is not acted on by an external force is always of the form:
x = x0 + v0t
A single particle acted on by a net external force of the form F = -kx has a position function of the form:
x = Acos(wt + phi)
Also, it is well known that in a system with one planet and one star, the planet and star orbit their common center of mass in an elliptical trajectory. Since this trajectory repeats itself forever, the position of the particle is defined for all time. (Ok, this is not the best example, since technically, planets and stars are not atoms, but bear with me).
To put things precisely, what I am saying is this:
1) The universe is made up of n atoms (where n is evidently a very large positive integer).
2) All of these particles currently have a position and velocity and obey Newton's Laws (not strictly true in our universe, but I am talking about a hypothetical universe where Newton's Laws are exact).
3) Using Newton's Second Law and our knowledge of how the particles interact, we can set up a system of n second-order ordinary differential equations where the independent variable is time and the dependent variables are the positions of each of the particles.
4) After applying the initial conditions, there exists a unique solution to this system of differential equations. That is, there exist functions x_1(t), x_2(t), ... x_n(t) that give the positions of the first, second, ... nth particles as a function of time, respectively. Furthermore, these functions are defined for all real values of t.
5) Therefore, for any time T, we can plug t = T into each of the n functions to obtain the positions of each of the particles at time T. Since each of the particles occupies a position at time T, all of the particles clearly exist at time T. Since we can let T be any real number, it follows that all of the particles exist for all time.
Hugh wrote:Also jinydu, are atoms the tiniest form of matter and are they indivisible as you say, and what about energy?
No; of course we now know that there are particles smaller than atoms, and in any case, Newton's laws don't work too well on a sub-atomic scale. That is why I added the qualification "according to classical mechanics..."