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Originally Posted by Doctordick
The assumption was not only unnecessary but wrong!  That is an assumption as there is no information as to how the machine works; it may consume energy from some energy source inside the device or the effect could be exothermic and produce energy in operation. At the moment we are ignorant of such things; ... |
Gosh, Dick, but I don't think that disagreeing with or misunderstanding you is in violation of any Cosmic Law!
Let's just say I was mistaken in my interpretation and leave it at that.
Okay, the traveler advances faster AS the dial is turned. Let's define the start of dialing as Ts and the final stopping point of dialing as time Tf.
To my eyes the Duration between Ts and Tf are Do = (Tf-Ts) seconds apart. To the traveler, it depends on how fast he turned the dial, say it took him a duration of Dt seconds. We are assured that Dt < Do.
The traveler could be a time ball, so I may switch contexts. However, what do I see? I see the traveler (ball) but any movement of the traveler is slowed down by the ratio of Dt / Do. During that period, say the traveler jumped upwards. During my Do seconds, he experiences gravity only for Dt < Do seconds, therefore his upward velocity will be reduced (as seen by me) by deltaVt = g*Dt, which is less than the deltaVo = g*Do I would expect for an ordinary body. Similar argument for the time balls.
To my observation, people or balls in "time-translation" will bounce higher and take longer to come down. A time ball hit hard (fast) enough will fly almost a linear ballistic path, and might escape from Earth entirely.
A small problem exists in your definition of slaving "time-translation" speed to the distance traveled by a time-ball. It would be better to slave it to velocity or even accelleration; makes the math a LOT easier.
So. How close did I get?
