2.7 Interchanging "Stationary" and "Moving" (Space-Time Diagrams)
Description
This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
2.7 Interchanging "Stationary" and "Moving" (Space-Time Diagrams)
In our understanding of space-time diagrams, we need to incorporate the
idea that all reference frames that are not accelerating are considered
equivalent and that all motion is relative. By this I mean that O was
considered as the stationary observer only because we defined him as such.
Remember? We said that this it is natural to think of the diagram being
drawn specifically for the observer whose coordinate system is drawn with
vertical and horizontal axes. We then said that we can think of that
observer (O) to be considered "at rest" in this diagram. Then, when I called
O' the moving observer, I meant that he was moving with respect to O.
However, we should just as easily be able to define O' as the
stationary observer. Then, to him, O is moving away from him to the left.
Then, we should be able to draw the t' and x' axes as the vertical and
horizontal lines, while the t and x axes become the rotated lines. I have
done this in Diagram 2-11. By examining this diagram, you can confirm that
it makes sense to you in light of our discussion thus far. (For example,
picture grabbing the x' and t' axes in Diagram 2-9 and rotating them around
the origin until they are horizontal and vertical lines. If x and t follow
your rotation, then you can see how they would end up as they are drawn in
Diagram 2-11.)
Diagram 2-11
t'
|
t B'
\ | \
\ + \
\ | \
\ + \
\| \
---+---+---o---+---+---C'- x'
| ""__ /
+ ""--
| / ""_C
+ / ""--x
| /
A'
|
I have also included in Diagram 2-11 the experiment that O' did in
which he decided how to draw the x' axis, and you can see that it now looks
just like the experiment O did when his x and t axes were the horizontal and
vertical lines. Further in Diagram 2-11 you can see that the experiment done
by the O observer now looks like the one which has incorrectly concluded
that C occurs at the same time the two observers are passing one another.
Thus, you can see that we can completely interchange the concept of
which observer is moving and which is sitting still, and as a result we must
conclude that neither frame of reference is any "better" than the other.
When O concludes that C occurs simultaneous with o, he is REALLY, TRULY
correct for his frame of reference. Also, when O' concludes that it is C'
which occurs simultaneous with o, he is also REALLY, TRULY correct for his
frame of reference. The notion of simultaneity is not absolute, but REALLY,
TRULY depends on your frame of reference. To understand why this doesn't
cause contradictions, we go to the next section in which we discuss the
notion of future and past with relativity in mind.
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