I am proposing a new theorem of computability theory:
THEOREM 1: There are numbers k and s and a program A(n,m) satisfying the following conditions.
1. If A(n,m)↓, then C_n(m)↑.
2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s).
3. A(k,s)↓ and for all n, A(s,n)↑.
Here C_n(∙) is a program with...
OK, so let me put it this way. Suppose that we put gas molecules in a container. We start with all the molecules on the left having high kinetic energy, and all the molecules on the right having low kinetic energy. We run the simulation, and the kinetic energy will even out. Then we rerun the...
"If the simulation is reversed, the molecules will retrace their paths back to the initial conditions, temporarily decreasing entropy. However, if the simulation continues to run, the molecules will once again disperse, increasing entropy." Hmm ...
How do these simulations work? The molecules are points or spheres? They all have the same mass, and you randomly select position and velocity for each? And they will converge to higher entropy? Just flip the signs of the velocities, and entropy will decrease. "Backward" velocities are just as...
I have realized that if the initial conditions were chosed at random we would be in a state of maximum entropy to begin with. I suppose that it is still possible that the universe was created with uneven distribution of thermal energy, and within this framework the microstates were chosen...
"They also mimic the second law behavior that we experience every day, demonstrating that the laws of motion are irreversible"
Why would they be irreversible if the system is deterministic?
Are Boltzman's statistics compatible with deterministic universe? Suppose that the gas molecules in a given container are perfectly elastic objects obeying Newton's laws. Suppose further that we select the initial conditions (impulse and position of each molecule) at random. Is it true that, if...