Walk backup the thread the thing we were discussing was a paradox of two words
INFINTE TIME
What I am explicitly saying is that has two words ... extract the meanings
INFINITE = a set containing all possible values
TIME = the thing the set is made of
What Bill did was then say you could go from t=0 to infinity as infinite time.
My objection is simple you made a MASSIVE assumption at that point.
In other words Bill has converted INFINITE TIME into INFINITE POSITIVE TIME.
The argument is not about the word infinite it is about what basis Bill has for making that assumption is valid you can't for example do that with a line.
So forget the right hand positive infinity which you seem to be getting all hung up about he just truncated time at the start point with no reasonable justification by looks other than he doesn't like it.
The problem here is that logic in classic physics is sort of nonsense and meaningless, Bill even sort of says that. So he justifies he can do it because of a word puzzle he can play in classic physics
HOWEVER
If we bring the standard model including it's QM underpin in now you can't just do that there is a massive problem in trying to do that and it is completely testable because you end up with a spinor
https://en.wikipedia.org/wiki/T-symmetryLook at [Time reversal of the known dynamical laws]
Particle physics codified the basic laws of dynamics into the standard model. This is formulated as a quantum field theory that has CPT symmetry, i.e., the laws are invariant under simultaneous operation of time reversal, parity and charge conjugation. However, time reversal itself is seen not to be a symmetry (this is usually called CP violation). There are two possible origins of this asymmetry, one through the mixing of different flavours of quarks in their weak decays, the second through a direct CP violation in strong interactions. The first is seen in experiments, the second is strongly constrained by the non-observation of the EDM of a neutron.
It is important to stress that this time reversal violation is unrelated to the second law of thermodynamics, because due to the conservation of the CPT symmetry, the effect of time reversal is to rename particles as antiparticles and vice versa. Thus the second law of thermodynamics is thought to originate in the initial conditions in the universe.
So at a science level INFINITE TIME versus INFINITE POSITIVE TIME lead to different results and it is testable the fact those two things are different is profound and important.
