Re: Question about light clock and derivation of time dilation

Androcles says...

>Look.
>We can return to the moon, but not to Neil Armstrong planting a
>footprint in 1979.

So what? The fact that there is a vector with components

x=0
y=0
z=0
t=-26

doesn't imply that we can *move* in that direction. The laws
of physics determine which vectors are possible displacement
vectors for a physical object, and not all of them are.

For a material object of nonzero mass, it is only possible
to go from event A with coordinates x_A, y_A, z_A, t_A to
event B with coordinates x_B, y_B, z_B, t_B if

(1) t_A < t_B
(2) (x_B - x_A)^2 + (y_B - y_A)^2 + (z_B - z_A)^2 < c^2 (t_B - t_A)^2

>Let (x1,y1,z1,t1) be a 4-vector.
>Let (x2,y2,z2,t2) be a 4-vector.
>
>Add the vectors.
>(x1-x2, y1-y2, z1-z2, t1-t2)
>
>Put in numbers
>x1 = y1 = z1 = t1 = 1
>x2 = y2 = z2 = t2 = -1
>(1-1,1-1,1-1, 1-1) = (0,0,0,0)
>
>I've now moved from (1,1,1, 1pm)
>to (0,0,0, midday) and gone backwards in time.

No, you haven't.

The fact that I can construct a vector from
here to Alpha Centauri doesn't mean that I've
travelled to Alpha Centauri.

You seem to be confused about the difference
between adding vectors and travelling through
spacetime. You'll never get to Alpha Centauri
by adding vectors.

--
Daryl McCullough
Ithaca, NY

.