Environmental Engineering Reference
In-Depth Information
or not two events occured simultaneously (which means they occured at the same
absolute time).
If absolute space really existed, as Newton imagined it did, then it follows that
there exists a set of very special frames of reference. Namely, all those frames which
are at rest in the absolute space. Inertial frames are then those frames which are
moving with some constant velocity relative to absolute space. It is interesting that
long before Einstein, absolute space was under attack. Since no experiments have
ever been performed that are able to identify a special inertial frame it follows that
we cannot figure out which inertial frames are at rest in absolute space. Therefore, as
far as physics is concerned we can dispense with the idea of absolute space in favour
of the democracy of inertial frames. Physicists now take the equality of inertial
frames so seriously that they have elevated it to the status of a fundamental prin-
ciple: the Principle of (Special) Relativity. By postulating this relativity principle,
absolute space is dismissed from physics and consigned to the realm of philosophy.
Newton's theory itself obeys the relativity principle, and as such does not require
the notion of absolute space. However it does assume that time is absolute.
Let's prepare the ground for later developments and gain some experience of
thinking about events in space and time. Consider two inertial frames of reference,
S
and
S
and suppose an event occurs at a time
t
and has Cartesian co-ordinates
(x,y,z)
in
S
. The question is, what are the corresponding co-ordinates measured
in
S
? To answer this we need to be more explicit and say how the
S
and
S
move relative to each other. We'll take their relative motion to be as illustrated in
Figure 5.1, i.e.
S
moves at a speed
v
relative to
S
and in a direction parallel to the
x
-axis. Let's also suppose that their origins
O
and
O
t
=
coincide at time
t
=
0.
Clearly the
y
and
z
co-ordinates of the event are the same in both frames:
y
,
y
=
(5.1a)
z
.
z
=
(5.1b)
More interesting is the relationship between the co-ordinates
x
and
x
. Common
sense tells us that
x
+
x
=
vt .
(5.2)
Of course this is the correct answer but only provided we assume absolute time,
i.e. that
t
t
. The proof goes like this. Firstly, we need to recognise that the
=
S
S
′
z
′
z
u
y
y
′
O
x
O
′
x
′
The two frames of reference
S
and
S
moving with relative speed
v
in the sense
Figure 5.1
shown.
