I was thinking just a few minutes ago about when a time machine is first invented, how will it's rate of time travel be expressed?
Most people consider a time machine to "disappear" out of the present point in time and reappear in some other point in time, but the reality is that the time machine would either move faster, slower, or backwards through time at varying rates. Altogether, the time machine would be constantly visible, just moving at a different rate that the rest of the normal world.
So, what you're probably asking "Well what the heck is this rate ting?". Let me extrapolate! The rate of time travel should be expressed like this:
Seconds passed (time traveler) / Seconds passed (normal time)
Currently, you are travelling through time at a rate of 1second/1second. Isn't that cool?
A time machine travelling forward in time would travel through time at any rate (y seconds / x seconds), where x is greater than y. For instance, time travelling forward in time at a rate of 1seconds/2seconds would mean you experience one second for every two seconds that occur in real time, effectively making time appear to go twice as fast for you. On the other hand, everybody in real time would see you as moving twice as slow as normal.
If you were travelling slower in time than time itself, the rate of time travel would be (x seconds / y seconds) where y is greater than x. Meaning everything appears slower for you, but you appear to go faster, like bullet time.
But what about travelling back in time? Well that can be expressed as (x seconds / -y seconds). This means that you experience time as regular, whilst everything around you appears to go backwards. The rate (-x seconds / y seconds) represents the same thing.
Okay, now how about stopping time? After merticulous thought, I believe it to be impossible without screwing up alot of laws of nature. Stopped time would be represented as (x seconds / 0 seconds). Do you see that? IT'S DIVIDING BY ZERO. And you just can't do that. But think about why... If you were an observer looking at a person that had just stopped time for themselves, you would see them experience an infinite amount of time in one second. For the observer, it would appear as (INFINITE seconds / 1 second) and that's just crazy! so just forget about that every happening.