20
4 Where Does the Wave Equation Come From?
Fig. 4.1 Observer at a desk and an observer sitting on a swivelling chair. The latter observes that
the mass resting on the desk is orbiting him
This changes if the train slows down or goes through a curve—this could cause us
to feel dizzy. Any accelerated motion causes us to leave our inertial frame.
1
Inertial systems are especially characterised by their mutual relative motion with
a constant velocity and their motion relative to all other systems of reference. They
underlie the Galileian principle of relativity: ‘Observers in two different inertial
systems notice that the same laws of physics apply’. The total sum of all possible
physical processes is identical to all inertial systems. Basically, the Galileian principle
of relativity was only intended for the laws of mechanics and is thus called The First
Newtonian Axiom: It is impossible to determine our special inertial frame just from
the motion of an object.
2
1 Here one could raise an objection. My well-being includes the fact that the earth has its usual
gravitational effect on me. A colleague, who is far away from the earth in a rocket travelling with
a constant velocity relative to my desk, also finds himself in an inertial frame. However, he is
not affected by the earth’s gravitation. If his rocket is accelerated by 9, 81 m/s 2 , he experiences
the gravitation he is used to. The difference is, however, that he is no longer in an inertial frame,
whereas I am. Using this simple example, we can see that as soon as gravitational effects (the
universal attraction between masses) are included, everything becomes far more complicated. We
will strictly ignore all effects of gravitation.
2 One can however experimentally determine if I am in an inertial frame or not. The organs of
balance capable of measuring my state of motion are found in my ear. If I do not find myself in an
inertial frame, the organs detect this and send signals to my brain telling me to become dizzy. The
sensitivity of the organs in the ear is insufficient to be able to measure the daily rotation of the earth
along its own axis. We can however measure this rotation using a Foucaultian pendulum, see e.g.
H. Goldstein [29].
4 Where Does the Wave Equation Come From?
Fig. 4.1 Observer at a desk and an observer sitting on a swivelling chair. The latter observes that
the mass resting on the desk is orbiting him
This changes if the train slows down or goes through a curve—this could cause us
to feel dizzy. Any accelerated motion causes us to leave our inertial frame.
1
Inertial systems are especially characterised by their mutual relative motion with
a constant velocity and their motion relative to all other systems of reference. They
underlie the Galileian principle of relativity: ‘Observers in two different inertial
systems notice that the same laws of physics apply’. The total sum of all possible
physical processes is identical to all inertial systems. Basically, the Galileian principle
of relativity was only intended for the laws of mechanics and is thus called The First
Newtonian Axiom: It is impossible to determine our special inertial frame just from
the motion of an object.
2
1 Here one could raise an objection. My well-being includes the fact that the earth has its usual
gravitational effect on me. A colleague, who is far away from the earth in a rocket travelling with
a constant velocity relative to my desk, also finds himself in an inertial frame. However, he is
not affected by the earth’s gravitation. If his rocket is accelerated by 9, 81 m/s 2 , he experiences
the gravitation he is used to. The difference is, however, that he is no longer in an inertial frame,
whereas I am. Using this simple example, we can see that as soon as gravitational effects (the
universal attraction between masses) are included, everything becomes far more complicated. We
will strictly ignore all effects of gravitation.
2 One can however experimentally determine if I am in an inertial frame or not. The organs of
balance capable of measuring my state of motion are found in my ear. If I do not find myself in an
inertial frame, the organs detect this and send signals to my brain telling me to become dizzy. The
sensitivity of the organs in the ear is insufficient to be able to measure the daily rotation of the earth
along its own axis. We can however measure this rotation using a Foucaultian pendulum, see e.g.
H. Goldstein [29].