10
2 The Ether and the Wave Equation
In other words, the general solution is a superposition of waves with variable wavelengths λ = 2π/k, or waves with variable frequencies ν = c/λ. Using suitable superpositions of these waves, we can fulfil the boundary conditions for a finite medium
which we will need in Chap. 4.
The basis of all these properties is the aforementioned wave equation which is
equally valid for acoustic and electromagnetic processes. For electromagnetic processes, we have to substitute the speed of light c L in a vacuum for the sound velocity
c. We will now have to take a remarkable fact into consideration when dealing with
the speed of light: An observer receives a light signal from a light source, which is
at rest with respect to him. The light signal travels across the distance between its
source and the observer with the speed of light in a vacuum c L . If there is another
observer moving towards the source of light with an arbitrary uniform velocity v
and we ask him how fast the light signal moves towards him, we get the following
answer, ‘the light signal is moving towards me with the speed of light in a vacuum
c L = 299792458 m/s’.
3 We receive exactly the same answer from the observer if he
moves with velocity v away from the light source. The Michelson experiments have
removed the last question marks about the correctness of this fact, a fact that is for
us astounding, because we expect the quite another result.
Exactly this happens when we observe sound waves. A source of sound S can
transmit Morse code signals with the sound velocity c through air. Assume at first
that the source of sound, the medium air and an observer are at rest with respect to
each other. Then, the observer measures this sound velocity c for the propagation of
the signals. Now an observer moving through the air and towards this source with
the velocity v measures the speed of sound coming from the sound source towards
him as c + v. If he moves away from the source of the sound waves, he measures
the speed as c − v. This is easily explained for the propagation of sound waves in
the medium air which is shown in Fig. 2.2. It also makes absolutely no difference
through which transport medium these sound waves travel.
4
Let us return to our light source. It can send Morse code signals through space
with the speed of light c L . The question is, how do these light waves reach the
observer? Is there a mechanical transport medium, an ether maybe, in which these
light waves spread in a similar way as sound through the air? If this is the case,
then an observer moving through this ether towards the light source with velocity v
would have to measure the speed of the light signal as c L + v and correspondingly, if
moving through the ether away from the source with the velocity v he would have to
measure c L − v. In fact, however, in both cases independent of his velocity towards
or away from the source, he measures one and the same signal velocity c L .
This is the problem behind the term ether: If we say that light waves propagate
through a mechanical ether, then it is impossible to register the slightest motion
or presence of this ether. There is absolutely nothing of the ether to be detected.
3 The inaccuracy of this answer is less than 1 m/s = 3, 6 km/h. In comparison, the speed of sound
in air is c air = 331 m/s, and the speed of sound through aluminium is c Al = 5090 m/s.
4 Notice however that this result takes the so-called Galilei transformation as granted, cf. Chaps. 13
and 15 as well as the detailed discussion concerning the definition of relative velocities in Chap. 17.
2 The Ether and the Wave Equation
In other words, the general solution is a superposition of waves with variable wavelengths λ = 2π/k, or waves with variable frequencies ν = c/λ. Using suitable superpositions of these waves, we can fulfil the boundary conditions for a finite medium
which we will need in Chap. 4.
The basis of all these properties is the aforementioned wave equation which is
equally valid for acoustic and electromagnetic processes. For electromagnetic processes, we have to substitute the speed of light c L in a vacuum for the sound velocity
c. We will now have to take a remarkable fact into consideration when dealing with
the speed of light: An observer receives a light signal from a light source, which is
at rest with respect to him. The light signal travels across the distance between its
source and the observer with the speed of light in a vacuum c L . If there is another
observer moving towards the source of light with an arbitrary uniform velocity v
and we ask him how fast the light signal moves towards him, we get the following
answer, ‘the light signal is moving towards me with the speed of light in a vacuum
c L = 299792458 m/s’.
3 We receive exactly the same answer from the observer if he
moves with velocity v away from the light source. The Michelson experiments have
removed the last question marks about the correctness of this fact, a fact that is for
us astounding, because we expect the quite another result.
Exactly this happens when we observe sound waves. A source of sound S can
transmit Morse code signals with the sound velocity c through air. Assume at first
that the source of sound, the medium air and an observer are at rest with respect to
each other. Then, the observer measures this sound velocity c for the propagation of
the signals. Now an observer moving through the air and towards this source with
the velocity v measures the speed of sound coming from the sound source towards
him as c + v. If he moves away from the source of the sound waves, he measures
the speed as c − v. This is easily explained for the propagation of sound waves in
the medium air which is shown in Fig. 2.2. It also makes absolutely no difference
through which transport medium these sound waves travel.
4
Let us return to our light source. It can send Morse code signals through space
with the speed of light c L . The question is, how do these light waves reach the
observer? Is there a mechanical transport medium, an ether maybe, in which these
light waves spread in a similar way as sound through the air? If this is the case,
then an observer moving through this ether towards the light source with velocity v
would have to measure the speed of the light signal as c L + v and correspondingly, if
moving through the ether away from the source with the velocity v he would have to
measure c L − v. In fact, however, in both cases independent of his velocity towards
or away from the source, he measures one and the same signal velocity c L .
This is the problem behind the term ether: If we say that light waves propagate
through a mechanical ether, then it is impossible to register the slightest motion
or presence of this ether. There is absolutely nothing of the ether to be detected.
3 The inaccuracy of this answer is less than 1 m/s = 3, 6 km/h. In comparison, the speed of sound
in air is c air = 331 m/s, and the speed of sound through aluminium is c Al = 5090 m/s.
4 Notice however that this result takes the so-called Galilei transformation as granted, cf. Chaps. 13
and 15 as well as the detailed discussion concerning the definition of relative velocities in Chap. 17.