104
R. Barrett and P. P. Delsanto
relied on his own pulse, and a primitive water clock, to measure the elapsed
time. He later studied pendulums, which led to the development in 1656
of a pendulum clock by Christiaan Huygens. The construction of the
chronometer in the Eighteenth Century by John Harrison enabled the accurate determination of longitude by ships at sea, and revolutionized the art of
navigation. Today, the most accurate clocks use the period of electromagnetic
radiation emitted from the Caesium-133 atom as the standard unit of time.
Before the advent of train travel and timetables, village life was leisurely,
and it mattered little if the clocks in one village were running slightly ahead
or behind those of another village further down the road. Now, with data
exchanged around the globe at the speed of light, much more importance is
attached to time standards. Surely, with today’s incredibly accurate clocks, we
would notice if time in one place were passing at a different rate from time
somewhere else.
Or would we? We shall see.
It has long been the custom of physicists to designate the position of an
object in the three-dimensional (3D) space in which we live by three coordinates. We begin by choosing a reference point in space, from which all other
dimensions are measured. This point is known as the origin, and is designated by the letter O. It can be anywhere, but it is more practical to choose
an origin that is convenient for the problem we are studying. Choosing an
origin in another star system, such as Alpha Centauri 1 is not appropriate for
calculating the location of planets in our own solar system.
Next, we choose a direction emanating from the origin. Again, this is arbitrary, and is usually called the X axis. Two other axes are chosen at right angles
to the X axis, and to each other. These are the Y and Z axes. Figure 6.1 makes
all this clear. The position of any point P in 3D space is denoted by x, y, and
z, which are called the coordinates of the point, and are the distances in the
X, Y, and Z directions, that one must travel from the origin to arrive at the
point P.
So far, so good. The three spatial coordinates are all that is required to
define the position of a point in 3D space, provided the point is stationary in
time. If the point is moving, then at each time t the point will have different
values of x, y, and z. To describe such an evolving system, physicists introduce
a fourth axis, called the T (time) axis, assumed to be perpendicular to the
other three. An arbitrary time is selected for the origin of the T axis. The
coordinate t is then the elapsed time since t = 0, which occurs at the origin.
1 Alpha Centauri is the closest star system to us (about 4 light years distant) and one of the most
luminous in our sky.
R. Barrett and P. P. Delsanto
relied on his own pulse, and a primitive water clock, to measure the elapsed
time. He later studied pendulums, which led to the development in 1656
of a pendulum clock by Christiaan Huygens. The construction of the
chronometer in the Eighteenth Century by John Harrison enabled the accurate determination of longitude by ships at sea, and revolutionized the art of
navigation. Today, the most accurate clocks use the period of electromagnetic
radiation emitted from the Caesium-133 atom as the standard unit of time.
Before the advent of train travel and timetables, village life was leisurely,
and it mattered little if the clocks in one village were running slightly ahead
or behind those of another village further down the road. Now, with data
exchanged around the globe at the speed of light, much more importance is
attached to time standards. Surely, with today’s incredibly accurate clocks, we
would notice if time in one place were passing at a different rate from time
somewhere else.
Or would we? We shall see.
It has long been the custom of physicists to designate the position of an
object in the three-dimensional (3D) space in which we live by three coordinates. We begin by choosing a reference point in space, from which all other
dimensions are measured. This point is known as the origin, and is designated by the letter O. It can be anywhere, but it is more practical to choose
an origin that is convenient for the problem we are studying. Choosing an
origin in another star system, such as Alpha Centauri 1 is not appropriate for
calculating the location of planets in our own solar system.
Next, we choose a direction emanating from the origin. Again, this is arbitrary, and is usually called the X axis. Two other axes are chosen at right angles
to the X axis, and to each other. These are the Y and Z axes. Figure 6.1 makes
all this clear. The position of any point P in 3D space is denoted by x, y, and
z, which are called the coordinates of the point, and are the distances in the
X, Y, and Z directions, that one must travel from the origin to arrive at the
point P.
So far, so good. The three spatial coordinates are all that is required to
define the position of a point in 3D space, provided the point is stationary in
time. If the point is moving, then at each time t the point will have different
values of x, y, and z. To describe such an evolving system, physicists introduce
a fourth axis, called the T (time) axis, assumed to be perpendicular to the
other three. An arbitrary time is selected for the origin of the T axis. The
coordinate t is then the elapsed time since t = 0, which occurs at the origin.
1 Alpha Centauri is the closest star system to us (about 4 light years distant) and one of the most
luminous in our sky.