Re: Question about light clock and derivation of time dilation

Androcles says...

>"Daryl McCullough" <stevendaryl3016@xxxxxxxxx> wrote

>> Hmm. Usually, the time axis is chosen to be a timelike vector.
>
>I think your "timelike vector" lacks an identity.

Look. An event (such as the landing on the moon, the
signing of the Magna Carta) is specified by giving (1)
a time, and (2) a spatial location. In Cartesian coordinates,
this information is specified by 4 numbers: x,y,z, and t.

So when we are talking about events, we are talking a 4-dimensional
vector space. That's true whether you are talking about Galilean
relativity or Special Relativity.

>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

That's right. In Minkowsky spacetime, the coordinates of
an event form a 4-D vector space, with a point in that
space specified by the four numbers (t,x,y,z).

>So where is your element w so that v+w = 0?

If v is the vector with components (t,x,y,z), then
its inverse is (-t,-x,-y,-z).

>Or can you travel backward in time to when you were?

Who said you could travel backwards in time? Vectors
are about *describing* the world. Just because I can
write down a vector with a negative time component
doesn't mean that I can *move* in that direction.

If e1 is the event at which Jesus was born, and
e2 is the event at which Aristotle was born, then
the vector from e1 to e2 has time component -384 years.

--
Daryl McCullough
Ithaca, NY

.