On Mon, Jun 8, 2009 at 11:17 AM, Michael Crosiar<[email protected]> wrote:
> I also want to thank you Stephen for your detailed reply to leaking pen. I
> do want to understand all of this as well, but it will take me a while to
> digest!
>
>>You can view it that way, but it's a little hazardous, because time
> dilation isn't really just a simple number.
>
> So is time dilation a vector in space with direction and magnitude? That has
> been my conclusion, but you clearly understand this at a level I do not.
>
>>Thinking of it as a simple ratio leads to a lot of confusion. Time
> dilation, expressed as a number, is dt/dtau for a particular observer,
> "A", relative to a particular reference frame, "F". The "dt" value is
> found by A, by looking at clocks which are stationary in frame F, as A
> passes them by. The "dtau" value is found by "A" by looking at A's own
> clock.
>
> Could you please explain a little more what dtau represents? My
> understanding of dt is that it represents the rate at which time moves
> forward in the frame of reference of "A". Is that correct? Does dtau
> represent the time interval elapsed in "A" between the observation of the
> first clock in "F" to the observation of the second clock in "F"?
>
>>Note well: "A" uses ONE clock in his/her own frame. "A" uses AT LEAST
> TWO CLOCKS in frame "F", located at *different* points in frame "F".
> You can't measure time dilation between two inertial frames without
> using at least two clocks in one of the frames, because once the
> observer has passed a clock, it's gone, and they can't see it any more
> (except at a distance and using a telescope adds unnecessary hair
> without changing the result).
>
> Ok, I think I get this part.
>
>>Thus, time dilation actually measures the rate at which time passes
> along a *particular* *path*. Something that measures a rate of change
> along a path is a directional derivative, or a "1-form". It's not a
> simple number.
>
> Sounds like I need to be educated about directional derivatives, or
> "1-form". I'll do some googling, but any help you can give... How does it
> differ from a simple vector?
>
> Ok, I googled it - calc 3 - Ouch... Only made it partly through calc 2, and
> that is very rusty, so this one is a little beyond my math abilities. But if
> I understand what little I have read we are talking about the rate at which
> time changes in a particular direction. That was my understanding already,
> so I think I conceptually get this, or so I hope. So, knowing the rate at
> which time moves forward in the direction of motion tells us nothing about
> dt in any other direction, correct?
>
> ...
>
> I'll need much more time to absorb the rest of this.
>
> C. Michael Crosiar
>
>
Same
