[time-nuts] A different way to think about time dilation?
albertson.chris at gmail.com
Sun Jul 10 12:01:57 EDT 2016
Is this a valid TN subject? It's about time but a little off of the usual
subject of 10Mhz oscillators.
I heard of an alternate way to describe time dilation caused by velocity.
I think this makes it easier to understand but I've not been able to
verify the math. This alternate explanation also makes it easy to see why
we can never go faster than light. But I've not seen a mathematical
derivation so it could be wrong or just an approximation.
1) We assume a 4 dimensional universe with four orthogonal axis, x, y, z,
and time (t)
2) assume that at all times EVERY object always has a velocity vector who's
magnitude is "c", the speed of light. The magnitude of this vector (speed)
never changes and is the same for every particle in the universe.
This at first seems a radical statement but how is moving at c much
different from assuming every partial is at rest in t's own reference
frame? I've just said it is moving at c in it's own reference frame. Both
c and zero are arbitrary speeds selected for connivance.
How can this be? I know I'm sitting in front of my computer and have not
moved an inch in the last four hours. c is faster than that. Yes you are
stationary in (x,y,z) but along the t axis you are moving one second per
second and I define one second per second as c. Now you get smart and try
to move faster than c by pushing your chair backward in the Y direction at
4 inches per second. So you THINK your velocity magnitude is the vector
sum of c and 4 inch/sec which is greater than c. BUT NO. Your speed
along Y axis causes time dilation such that your speed along T is now
slower than 1 second/second. In fact if you push your chair backward
along Y real fast at exactly c your speed along t axis is zero, time
stops. Try pushing your chair at 0.7071 * c and you find yourself moving
through t at 0.7071 sec/sec and the vector sum is c. You can NOT change
you speed from c all you can do to change the direction of the velocity
vector and your speed through time is determined by the angle between that
vector and the t axis.
It works ok to just use one of the three spacial axis because we can always
define them such that (say) the Y axis points in the direction of motion.
So a plot of your speed in the dy,t plane covers the general case and looks
like an arc of radius c.
If this works out then I have some work to do, like defining momentum as a
function of the area between the velocity vector and the t axis
Redondo Beach, California
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