Environmental Engineering Reference
In-Depth Information
There is no doubt that absolute time is a useful concept; in this topic we shall
at first examine the motion of things under the influence of forces, treating time as
though it is the same for every observer, and we will get answers accurate to a high
degree. However, absolute time is a flawed concept, but flawed in such a way that
the cracks only begin to appear under extreme conditions. We shall see later how
clocks that are moving at very high relative velocities do
not
record the same time
and that time depends on the state of motion of the observer. Einstein's Special
Theory of Relativity tells us how to relate the time measured by different observers
although the deviations from absolute time are only important when things start to
move around at speeds approaching the speed of light. In describing the motion of
things that do not approach the speed of light we can ignore relativistic effects with
impunity, avoiding the conceptual and computational complications that arise from
a full relativistic treatment. This will allow us to focus on concepts such as force,
linear and angular momentum and energy. Once the basic concepts of classical
mechanics have been established we will move on to study Special Relativity
in Part II. Even then we will not completely throw out the concepts that are so
successful in classical mechanics. Rather, these shall be adapted into the more
general ideas of energy, momentum, space and time that are valid for all speeds.
1.1.6 Absolute space and space-time
At a fundamental level, the natural philosophy of Aristotle and the physics of
Newton differ from the physics of Galileo
5
and Einstein in the way that space and
time are thought to be connected. One very basic question involves whether space
can be thought of as absolute. Consider the corner of the room you might be sitting
in. The intersection of the two walls and the ceiling of a room certainly defines a
point, but will this point be at the same place a microsecond later? We might be
tempted to think so, that is, until the motion of the Earth is considered; the room is
hurtling through space and so is our chosen point. Clearly the corner of the room
defines a 'different' point at each instant. So would it be better to define a 'fixed'
point with reference to some features of the Milky Way? This might satisfy us, at
least until we discover that the Milky Way is moving relative to the other galaxies,
so such a point cannot really be regarded as fixed. We find it difficult to escape com-
pletely from the idea that there is some sort of fixed background framework with
respect to which we can measure all motion, but there is, crucially, no experimental
evidence for this structure. Such a fixed framework is known as absolute space.
The concept of absolute space, which originates with Aristotle and his contem-
poraries, can be represented geometrically as shown in Figure 1.5(a). Here we have
time as another Cartesian axis, tacked onto the spatial axes to produce a composite
space that we call space-time. Consider two things that happen at times and posi-
tions that are measured using clocks and co-ordinate axes. We call these happenings
'events' and mark them on our space-time diagram as
A
and
B
. In the picture of
absolute space, if the spatial co-ordinates of events
A
and
B
are identical we say that
they represent the same point in space at different times. We can construct a path
shown by the dotted line that connects the same point in space for all times. Galilean
5
Galileo Galilei (1564 - 1642).
