Re: Question about light clock and derivation of time dilation


"Daryl McCullough" <stevendaryl3016@xxxxxxxxx> wrote in message
news:damjjb0urk@xxxxxxxxxxxxxxxxxx
> Ken S. Tucker says...
>
>>Using the light clock, the time axis "t"
>>is the path of the light-ray as it's used,
>>and that's fine.
>
> Hmm. Usually, the time axis is chosen to be a timelike vector.

I think your "timelike vector" lacks an identity.

V is a commutative group under addition of vectors
1.. There exists an additive identity element 0 in V, such that for
all elements v in V, v + 0 = v.
2.. For all v in V, there exists an element w in V, such that v + w =
0.
3.. Vector addition is associative: u + (v + w) = (u + v) + w.
4.. Vector addition is commutative: v + w = w + v.
http://en.wikipedia.org/wiki/Vector_space

So where is your element w so that v+w = 0?
Or can you travel backward in time to when you were?


> I've heard of coodinate systems using lightlike vectors as
> basis vectors, but I don't know much about them.

I've heard of bright green flying elephants that lay eggs, too.
I bet I know more about them than you do. :-)


In 2-D spacetime,
> you can let
>
> u = x + ct
> v = x - ct

Sure, but u and v are vectors of position, and t is always positive.
You can return to where you were quite easily, I'd like to see you
return to when you were.
v = x - c(-t) is kinda hard to do.

Androcles.


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