Hi Pyrotex: I didn't mean to give you the idea that I didn't see your thoughts as very reasonable. In fact, I strongly suspect you may be the most astute observer here. I have just been at it for a lot more years.
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Originally Posted by Pyrotex
Okay, the traveler advances faster AS the dial is turned.
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"AS the dial is turned faster": remember you go to exactly the same time as the reading on the dial. It is a strictly linear addition of time. Nevertheless, you are absolutely right when you say the most important factor here is Dt/Do. Having uncovered that alone I would say you did quite well. The "experiencing gravity" issue is questionable. I like your analysis anyway, but the real effect is dependent upon factors not yet defined so we will have to leave that to experiment.
Meanwhile, the critical factor I was trying to bring to attention has to do with that apparent velocity.
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Originally Posted by Pyrotex
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. |
Perhaps, but it then wouldn't yield the consequences I am trying to bring up here.
Let us look at a time ball traveling across the laboratory. First, I want to pick a specific trajectory. In order that it travel along a straight line and to remove rotation, let it slide along a air table to avoid both gravitational acceleration and rotation. Let it be traveling at one foot per second if the time machine were off. If the path is ten feet long, it will take ten seconds to complete the trajectory; however, with the time machine turned on, the ball would move into the future one second for each foot covered. It follows that an observer in the laboratory would see the ball as arriving at the other end of the track twenty seconds after the start. The apparent velocity of the ball would be .5 feet per second.
Thinking about that for a second, suppose we have a professional baseball pitcher on hand who can throw this thing at about fifty feet per second. Now you would expect the ball to cover the ten feet in about one fifth of a second. But, if the time machine is functioning, it will once more go ten seconds into the future. It follows that the observer in the laboratory would see the ball as arriving at the other end of the laboratory 10.2 seconds later.
If we were to get a cannon capable of firing the ball at five hundred feet per second (if there were no time machine). In this case the ball would appear to take 10.02 seconds to cross the laboratory. Extend this analysis further if you wish. If you could achieve an infinite velocity, the ball would appear to cross the laboratory in ten seconds. The ball is constrained to appear to travel slower than one foot per second.
Earlier you brought up conservation of energy. As I said, how the time machine works is unknown and there may be a great power source inside the ball so we can't depend on anything there. But conservation of momentum is another story; that is a dynamic phenomena which carries through interactions. At the velocities we are talking about here, classical Newtonian mechanics are sufficient and whatever momentum was given the ball at the beginning must be deposited in the laboratory wall at the end. If that momentum is to be given by mv and then the inertial mass of a time ball must head off to infinity as the apparent velocity goes to one foot per second.
Now that apparent increase in inertial mass is an interesting factor. Under standard physics, gravitational mass and inertial mass are always the same. If we take that to be true here, the mass energy being given to the time ball is phenomenal and we can only conclude that the power supply is exterior to the time ball. There must be some energy receiver inside the ball. Just the effective mass associated with the energy levels being talked about here would cause the time ball at rest have an inordinate mass.
At any rate, I think the relationships embedded in mental structure I have introduced here are rather interesting. The "time balls" would display a sort of pseudo relativistic behavior. It clearly is not exactly analogous to standard relativity as the Dt/Do factor is given by (Vm-Va)/Va where Vm equals the maximum velocity and Va equals the apparent velocity. Likewise, the apparent mass is given by Va/(Vm-Va) times the rest mass. This looks very little like the usual relativistic factor, but it the phenomena should still raise your curiosity.
There turns out to be a subtle change in the above thought experiment which yields exactly the standard relativistic effects. Think about it for a moment and maybe read
my paper again.
Have fun – Dick
"The simplest and most necessary truths are the very last to be believed."
by Anonymous
Sarcasm, parody, and Hypography
