6 Special Relativity
107
of the speed. For example, if the train suddenly stops, we are thrown forwards
and might even fall, if we happen to be on our feet at the time.
Suppose that Peter is standing on a platform, and Mary is on a train
departing slowly from the station. Peter may claim that Mary is moving away
from him at 10 kph, which he determines to be the speed of the train, as
measured in his frame of reference. Mary, on the other hand, may claim
equally validly that Peter is moving away from her at 10 kph in the opposite
direction, and that she is the one at rest. If Peter throws a ball towards Mary
at 20 kph, as measured by him, Mary will see it go past her at 10 kph. This
is all quite straightforward and is explained readily by Newton’s mechanics.
Whether we decide to set up a physics experiment in Peter’s frame of reference on the platform, or Mary’s on the train, is unimportant. We will get the
same results. Indeed, we can readily transform our equations of motion from
Peter’s to Mary’s frames of reference (or vice versa) by what is called a Galilean
Transformation.
So, what is all the fuss about? It is surely just “common sense.” Having
just had our notion of common sense trashed in the previous Chapter, we
should by now be inured to what is to come. To lead us in gently, let us first
discuss two important results that were disturbing physicists, as the Nineteenth Century, with appropriate fireworks and popping of corks, passed over
into the Twentieth.
6.4 Harbingers of a Scientific Revolution
An air of complacency pervaded physics at this time. Classical Mechanics, as
formulated by Newton and extended by Lagrange and Hamilton, accounted
successfully for terrestrial and celestial phenomena involving moving bodies
and their collisions. Maxwell had completed a seminal work unifying electricity and magnetism into the single field of Electromagnetism. Some physicists believed that all important work in physics had been completed, and all
that remained was to fill in the details.
However, a close inspection revealed that Maxwell’s equations of electromagnetism are not invariant under a Galilean Transformation. This may sound
erudite, but it is just physicists’ jargon, which we shall now explain. The
Galilean Transformation, which we encountered in the last Section, is the
method we use to transform from equations in one frame of reference (e.g.
Peter’s on the platform) to those in another (e.g. Mary’s on the moving train).
What was discovered was that the predictions of Maxwell’s theory depend on
the frame of reference used, something that we have maintained is unphysical.
107
of the speed. For example, if the train suddenly stops, we are thrown forwards
and might even fall, if we happen to be on our feet at the time.
Suppose that Peter is standing on a platform, and Mary is on a train
departing slowly from the station. Peter may claim that Mary is moving away
from him at 10 kph, which he determines to be the speed of the train, as
measured in his frame of reference. Mary, on the other hand, may claim
equally validly that Peter is moving away from her at 10 kph in the opposite
direction, and that she is the one at rest. If Peter throws a ball towards Mary
at 20 kph, as measured by him, Mary will see it go past her at 10 kph. This
is all quite straightforward and is explained readily by Newton’s mechanics.
Whether we decide to set up a physics experiment in Peter’s frame of reference on the platform, or Mary’s on the train, is unimportant. We will get the
same results. Indeed, we can readily transform our equations of motion from
Peter’s to Mary’s frames of reference (or vice versa) by what is called a Galilean
Transformation.
So, what is all the fuss about? It is surely just “common sense.” Having
just had our notion of common sense trashed in the previous Chapter, we
should by now be inured to what is to come. To lead us in gently, let us first
discuss two important results that were disturbing physicists, as the Nineteenth Century, with appropriate fireworks and popping of corks, passed over
into the Twentieth.
6.4 Harbingers of a Scientific Revolution
An air of complacency pervaded physics at this time. Classical Mechanics, as
formulated by Newton and extended by Lagrange and Hamilton, accounted
successfully for terrestrial and celestial phenomena involving moving bodies
and their collisions. Maxwell had completed a seminal work unifying electricity and magnetism into the single field of Electromagnetism. Some physicists believed that all important work in physics had been completed, and all
that remained was to fill in the details.
However, a close inspection revealed that Maxwell’s equations of electromagnetism are not invariant under a Galilean Transformation. This may sound
erudite, but it is just physicists’ jargon, which we shall now explain. The
Galilean Transformation, which we encountered in the last Section, is the
method we use to transform from equations in one frame of reference (e.g.
Peter’s on the platform) to those in another (e.g. Mary’s on the moving train).
What was discovered was that the predictions of Maxwell’s theory depend on
the frame of reference used, something that we have maintained is unphysical.