I have come up with some very strange results dealing with the Lorentz equations and time rates: Let me know what you think.

But first I have to give some background on what a time rate is, following from the Lorentz transformations of time. We know that time is dependent upon velocity:

T = TPrime / Sqrt(1 - (V / C) ^ 2)

Where TPrime is measured by a clock on the object that has the velocity V, and T is measured by a clock on an object at rest. For example, if the object was travelling at 95% of the speed of light, and if we measured one second by TPrime, 60 seconds would have gone by T.

This seems like a good way to measure an object's time rate, so my definition for time rate is TPrime / T:

TPrime / T = Sqrt(1 - (V / C) ^ 2)

And so we can modify an object's time rate by modifying its velocity. Now I have compiled a table of time rates, the velocities acquired to achieve the time rates, and what it would mean if an object had that certain time rate: (Where Tr is time rate...)

TIME RATE: Tr = 0.

DESCRIPTION: Time stops for you; things outside happen infinitely fast.

VELOCITY REQUIRED: V = C, the speed of light. This is impossible except if you are a photon, so further discussion of this is useless.

TIME RATE: 0 < Tr < 1.

DESCRIPTION: Time slows down for you; things outside are sped up.

VELOCITY REQUIRED: 0 < V < C. This is possible in a very fast rocketship; as this is essentially travel to the future.

TIME RATE: Tr = 1.

DESCRIPTION: Time flows normally.

VELOCITY REQUIRED: 0 (or rest.) There is not much point to having a time machine that just lets time flow normally!

TIME RATE: 1 < Tr < Infinity.

DESCRIPTION: Time speeds up for you; things outside slow down.

VELOCITY REQUIRED: V must be a multiple of i. This is a very strange result, and all the more so because V cannot be a complex number (ki + L); rather it must be (ki,) or the imaginary number does not cancel out.

TIME RATE: Tr = Infinity.

DESCRIPTION: Time goes infinitely fast for you; things outside come to a complete stop.

VELOCITY REQUIRED: V = Infinity times i, or infinity along the imaginary axis!

TIME RATE: Tr is a multiple of i.

DESCRIPTION: Time flows backwards?

VELOCITY REQUIRED: C < V < Infinity. This only happens when you are travelling faster than the speed of light, and so it would seem logical that this causes you to travel backwards in time. But is this consistent with an imaginary time rate?

TIME RATE: Tr is a complex number (ki + L.)

DESCRIPTION: ?

VELOCITY REQUIRED: V must be also be a complex number. I really have no idea what this could mean.

TIME RATE: Tr = Infinity times i.

DESCRIPTION: ?

VELOCITY REQUIRED: V must be infinite. In a sense this is the same as travelling to a point instanteously, but then why would the time rate be imaginary?

And finally the Lorentz equations that I used to arrive at this:

Tr = Sqrt(1 - (V / C) ^ 2)

V = C x Sqrt(1 - Tr ^ 2)

I am currently building a machine that vibrates a time capsule back and forth so as to arrive at a certain velocity, and thereby the time rate would change as specified above. Although it would be easy enough to make the capsule travel into the future by having an ordinary velocity from zero to c, I am puzzled as to how I can modify its time rate so that we slow down and its personal time speeds up. This would require an imaginary velocity. I am assuming that this means time, not length being imaginary:

If V is imaginary, V = m / s must be imaginary. I am forced to assume that imaginary time is more plausible than imaginary length, because I already have results pertaining to imaginary time rates. So how I would arrive at my capsule vibrating a meter in one imaginary second?

This gives the strange concept of a handheld device with a digital read out on it where you punch in the time rate that you want; maybe some connections with Montauk here?

Any comments, suggestions, or explanations of imaginary time or the strange results that happen when the time rate goes complex?

Thanks,

Solokin1