Notes on Relativity and Cosmology - Physics Department, UCSB

56 CHAPTER 3. EINSTEIN AND INERTIAL FRAMES
carefully, taking the greatest care with our logical reasoning. As we saw in chapter
1, careful logical reasoning can only proceed from clearly stated assumptions
(a.k.a. ‘axioms’ or ‘postulates’). We’re throwing out almost everything that we
thought we understood about space and time. So then, what should we keep?
We’ll keep the bare minimum consistent with Einstein’s idea. We will take our
postulates to be:
I) The laws of physics are the same in every inertial frame.
II) The speed of light in an inertial frame is always c = 2.99... × 10 8 m/s.
We also keep Newton’s first law, which is just the definition of an inertial frame:
There exists a class of reference frames (called inertial frames) in which an
object moves in a straight line at constant speed if and only if zero net force
acts on that object.
Finally, we will need a few properties of inertial frames. We therefore postulate
the following familiar statement.
Object A is in an inertial frame ⇔ Object A experiences zero force ⇔ Object
A moves at constant velocity in any other inertial frame.
Since we no longer have S and T, we can no longer derive this last statement.
It turns out that this statement does in fact follow from even more elementary
(albeit technical) assumptions that we could introduce and use to derive it. This
is essentially what Einstein did. However, in practice it is easiest just to assume
that the result is true and go from there.
Finally, it will be convenient to introduce a new term:
Definition An “observer” is a person or apparatus that makes measurements.
Using this term, assumption II becomes: The speed of light is always c =
2.9979 × 10 8 m/s as measured by any inertial observer.
By the way, it will be convenient to be a little sloppy in our language and to say
that two observers with zero relative velocity are in the same reference frame,
even if they are separated in space.
3.2 Time and Position, take II
Recall that in Chapter 1 we used the (mistaken!) old assumptions T and S to
show that our previous notions of time and position were well-defined. Thus, we
can no longer rely even on the definitions of ‘time and position of some event in