21 Aug 2005 [From Steuard Jensen]

> I told [your father] I had a speed of light question I couldn't get
> the answer to and asked if he would ask you the question. He urged
> me to write to you directly.

I'm glad you did!  I enjoy talking about these things, and explaining 
them is good practice for an eventual job that includes teaching.

> At any rate, here is the question:
>
> 1.    As I understand it, nothing can go faster than the speed of 
> light.

Good start!

> 2.    But, suppose a rocket ship is traveling away from us here on 
> earth at 60% of the speed of light. And suppose another rocket ship 
> were traveling away from us in the opposite direction at 60% of the 
> speed of light.

Ok.

> 3.    Can it properly be said that those two rocket ships are receding 
> from each other at 120% of the speed of light (from our observation 
> point here on earth?)

Yes, I think that _from our point of view on earth_, it would be 
perfectly sensible to say that they were moving apart at 120% of the 
speed of light.  As we would measure it, that's how fast the distance 
between them is increasing.

> 4b.    If so, (AND HERE IS THE CRUCIAL PART OF THE QUESTION)  if 
> rocket ship A(RSA)  flashed a light toward rocket ship B (RSB), would 
> an observer on rocket ship B ever see the light.

Yes.

> 5.    I am guess that the observer on RSB would eventually see the 
> light because RSB is receding from the point of flash at only 60% the 
> speed of light.

That's exactly right.  The weirdness of relativity is that a guy on 
RSA, a guy on Earth, and a guy on RSB will all see the illumination 
from the flash spread out at the speed of light.  (But to make up for 
that, they'll all disagree on what color it was!)

> 6a. If my guess is correct, then the source point electromagnetic 
> disturbance of the light flash is a stationary point in space, 
> regardless of the speed or direction of the emitter, doesn't it?

It sounds like you're right on target.  Traditionally, physicists refer 
to a specific point in space and time as an "event".  If any observer 
sees something happen at a particular "event", then every observer will 
see it as an "event" (though they will almost always use different 
space and time coordinates to label it).

And an "event" is just a point; it knows nothing about directions or 
velocities.  It's the same way that a dot on a piece of paper doesn't 
care whether the paper is held horizontally or vertically (unlike an 
arrow, for instance, which would look very different if you rotated the 
paper).

[Added later: Later in our conversation, I realized that I had
misunderstood his meaning here.  His guess was that the source point
of the flash was at a specific point in _space_ that all observers
would agree was standing still at all times.  That's actually not
quite right.  Meanwhile, my comments were based on the idea that the
source point of the flash was a specific point in space _and time_.
Observers will all agree that the flash took place at the same
physical "event", but a minute later they will all have different
notions of what point in space is "the same place" that the flash
happened.  I explain this more later in the conversation.]

> 6b. If my guess is incorrect, then it would seem the source point of 
> the electromagnetic disturbance is itself moving through space.

Which, as you guessed, is not the way it works.  Physically, an event 
is always thought of as a static, unmoving thing (because it comes with 
a specific time coordinate in addition to specific space coordinates).

Now, the behavior of physical stuff _does_ depend on the velocity of 
its source.  As seen from Earth, a bullet that was fired from RSA at a 
particular "event" would have very different velocities depending on 
the direction it was fired and the speed of RSA.  As for light, it 
plays by different rules: its speed would look the same whether you 
were watching from RSA or from Earth, but its frequency (and thus its 
color) would be different.

> If not, that's okay. I've made it 60 years without understanding this, 
> so apparently a thorough understanding of the speed of light and 
> relativity is not essential to life as we know it.

See, from _my_ point of view, 60 years is far too long to go without 
understanding relativity. :)  I hope that my comments above were 
helpful (though mostly I seemed to be saying that you already had the 
right idea!), and if there's anything more that I can clarify for you, 
just let me know.

Thanks for giving me an opportunity to explain this stuff (or at least 
to get started doing so)!