If you stop there it looks like you're right, but you also must change the definition of velocity to account for the new time.
v = dx/dt = -dx/du
+F = m dx/du
So the direction of gravity (the force F) stays the same when you flip time. I can explain that without the math by pointing out that if you took a video of a ball being thrown up and caught and played it in reverse, it would still depict a ball being thrown up and caught.
> I can explain that without the math by pointing out that if you took a video of a ball being thrown up and caught and played it in reverse, it would still depict a ball being thrown up and caught.
That's amazing, thanks. The portion where you caught the ball in forward time is equivalent to throwing the ball in reverse time.
If we change the analogy of throwing a ball to firing a gun into the air - does the analogy still work? Since when we fire the gun up, the bullet will travel faster up than it will travel down due to terminal velocity in forward time. How is that phenomenon explained in reverse time?
Instead of predominately striking the bullet in a way that causes it to slow down, the molecules in the air will predominately strike it in a way that causes it to move faster, in what looks like an unbelievable (but still physically possible) run of good luck.
So it seems like if we reverse time, we reverse entropy and that as time approaches 0, we would effectively be reversing the big bang and instead have the big collapse.
Another thought experiment that comes to mind is compressed gas in a cylinder. When we open the valve, the gas in the cylinder comes out. In reverse time, the gas would go back into the cannister and the valve would close after the gas went back in. Very low probability of that happening in forward time, though not not 0.
Though it seems weird, because why does the gas go into the cylinder? Because further into reverse-time, something sucked it all out (in forward-time, this machine is the compressor that put the gas in the cylider.) This hurts my brain!
In the way down -sky to gun - the molecules in the air will give it energy to accelerate more than gravity alone would. Before that - in the way up - air molecules will cause it to move upwards at constant speed until conveniently they stop doing so.
> unbelievable (but still physically possible)
Physically possible - but in the same sense that the second law is not a physical law.
F = ma
F = m dv/dt
u = -t dv/dt = -dv/du
- F = m dv/du
If you stop there it looks like you're right, but you also must change the definition of velocity to account for the new time.
v = dx/dt = -dx/du
+F = m dx/du
So the direction of gravity (the force F) stays the same when you flip time. I can explain that without the math by pointing out that if you took a video of a ball being thrown up and caught and played it in reverse, it would still depict a ball being thrown up and caught.