Re: Explain certain details about the speed of light.

Light travels at a finite velocity.

But we didn't always know that.  Many brilliant minds have believed that 
light requires no time to move a distance.  Early proofs used less 
accurate detectors and required distances on the scale
of the solar system.  It is now possible to measure the speed on earth.

Since		(1) velocity = displacement / time

Therefore	(2) time = displacement / velocity

If we accept this information, we must accept that light requires time to 
move across any distance. This time can be calculated using equation 2.  
This fact can be hard to reconsile with the relativity of time, which now 
requires further investigation.

Imagine that you are repetitively throwing a ball against a wall and 
catching this ball as it returns.  Imagine further, that you are 
incredibly skilled and are capable of putting the same velocity on each 
toss and other such idealizations (there is no friction, and the collision 
with the wall is perfectly elastic and requires no time, and the earth 
does not absorb any of this momentum, etc.) I will judge the constancy of 
the speed of your ball and I will remain motionless for the duration of 
this exercise.

Now imagine that you begin to run.  It is important that ball is still 
thrown at exactly the same speed, but now you must direct the ball 
slightly forward so that you can catch it on the run.  The ball travels 
two sides of a triangle, and you run along the base.  In fact, you can 
imagine that the triangle was there all along, and when you are stationary
the base = 0 (and the sides of the triangle are at their minimum.)  The 
ball covers a greater distance with the same velocity.  
By equation 2, we see that this is because we have increased the time that 
the ball is moving.

As you increase your speed, you must increase the angle of your pitch away 
from the normal to the wall (a normal is an imaginary line perpendicular 
to a surface, in this case the wall.)  The ball will take longer to reach 
you because you force it to follow a longer path at the same velocity.  
Constant velocity was a restriction I placed earlier.  The component of 
the balls speed that is parallel to the normal decreases as your speed 
increases.  Once your speed matches that of the ball, you can no longer 
sucessfully recover the ball if you decide to throw it.  

Let's recap.  As you increase your speed through the x dimension of space, 
the time it requires your ball to return to you increases. Classical 
physics suggests that this is because the ball travels a greater 
distance at the same speed.  But there is an alternate viewpoint. Einstein 
was responsible for the view that there is no prefered reference 
frame.  Ignore your feet and explain why you are moving and I am 
stationary.  Could I be the one in motion?  Could you be stationary?  If 
we are moving with respect to each other and neither of us is 
accelerating, there is no way to tell what is the actual state of 
motion because Einstein tells us that none exists.  Everything
must be judged with respect to something else.

Light also moves at a constant speed (in a vacuum.)  Let us substitute 
light for the ball in our example.  The speed of light is absolutely 
constant (in a vacuum) and not based on the speed of the observer.  Let us 
define how time is measured.  We will measure one half measure of time 
each time the path of the light is reflected.  Give a "Tic" when the light 
bounces off the wall, and a "Toc" when we receive this light and send out 
a new burst.

Since the light is not moving sideways relative to you, you can accurately 
say that the light is moving toward you at the speed of light.  But I see 
your light taking a bent path along the two arms of the triangle, and I 
conclude that it takes longer for light to return to you than it does to 
return to me since the arms of my triangle are at a minimum.

As your speed increases, I will observe that the time between your tic and 
toc increases, while mine remains constant.  You will not notice this.  
You will judge your clock to be running correctly (and rightfully so!) and 
that my clock is running fast.

This effect is called time dilation, and the conclusion is that the faster 
you move, the slower you perceive time passing.

If you travelled at the speed of light (which is impossible because you 
have a non-zero mass,) the light that leaves at Toc will never return for 
a tic.  Time will stop and you will experience no time.

How do we determine which one of us is at motion?  This question leads to 
the twin paradox which is solved by stating that one of us must accelerate 
and therefore the laws of physics are no longer constant for one of the 
two.  This somewhat unsatisfying explanation can be improved upon by an 
exploration of acceleration.

What keeps a body moving?  How does it remember?  In what way does 
acceleration affect an object?
All interesting questions for sure.

Happy hunting.
Chris.