Chapter 18
The Doppler Effect
In every advanced course on physics the Doppler, effect is usually the standard
example for demonstrating the fundamental physical differences between the propagation of elastic waves through a mechanical medium and the propagation of electromagnetic waves through our physical space. Compared to this Mach’s quotation
in front of the preface, ‘Light somewhat like sound. Sound somewhat like light.’,
looks like a relict from the last century. And yet we will illustrate, with the help of
the Doppler effect, in what sense this Machian thesis proves true without actually
coming into conflict with our common knowledge of the Doppler effect, as long as
we agree to incorporate the means with which we gained our knowledge into our
considerations. This is a concession that we owe the philosopher Ernst Mach.
What is the Doppler effect?—A fire engine rushes towards us. At the moment
when the vehicle passes by, the pitch of the signal horn falls to lower frequencies. If
we question the driver of this fire engine, he would assure us that the signal did not
change at all.
When experimenting with light, we can identify the chemical nature of a light
source by spectrally splitting light using a prism, for example, the two yellow lines
lying together very close that are unmistakably emitted by excited sodium atoms. By
measuring the wave length λ of this light, we automatically determine its frequency
due to c L = λ ν. For the yellow sodium line, we get λ Na = 5890 Å = 58, 9 × 10
−8
m and thus ν Na = 5, 09 × 10
14 Hz. The light we receive from stars far away, from
stars in other galaxies we notice that all spectral lines are displaced into the longwave red area. Due to the mutual positions of the lines, all light sources, e.g. the
excited sodium atoms, can be exactly identified; however, the absolute frequencies
that we measure are all slightly lower. The explanation for this lies in the enormous
velocities with which the galaxies and thus the stars in them move away from us.
1
The diminished frequency of the light we receive is analogous to the deepening tone
of the fire engine’s horn moving away from us. Such a change in the frequency of
1 The law of the expansion of the universe discovered in 1929 by E.P. Hubble states that this
recession velocity increases proportionally to the distance between the star systems.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_18
197
The Doppler Effect
In every advanced course on physics the Doppler, effect is usually the standard
example for demonstrating the fundamental physical differences between the propagation of elastic waves through a mechanical medium and the propagation of electromagnetic waves through our physical space. Compared to this Mach’s quotation
in front of the preface, ‘Light somewhat like sound. Sound somewhat like light.’,
looks like a relict from the last century. And yet we will illustrate, with the help of
the Doppler effect, in what sense this Machian thesis proves true without actually
coming into conflict with our common knowledge of the Doppler effect, as long as
we agree to incorporate the means with which we gained our knowledge into our
considerations. This is a concession that we owe the philosopher Ernst Mach.
What is the Doppler effect?—A fire engine rushes towards us. At the moment
when the vehicle passes by, the pitch of the signal horn falls to lower frequencies. If
we question the driver of this fire engine, he would assure us that the signal did not
change at all.
When experimenting with light, we can identify the chemical nature of a light
source by spectrally splitting light using a prism, for example, the two yellow lines
lying together very close that are unmistakably emitted by excited sodium atoms. By
measuring the wave length λ of this light, we automatically determine its frequency
due to c L = λ ν. For the yellow sodium line, we get λ Na = 5890 Å = 58, 9 × 10
−8
m and thus ν Na = 5, 09 × 10
14 Hz. The light we receive from stars far away, from
stars in other galaxies we notice that all spectral lines are displaced into the longwave red area. Due to the mutual positions of the lines, all light sources, e.g. the
excited sodium atoms, can be exactly identified; however, the absolute frequencies
that we measure are all slightly lower. The explanation for this lies in the enormous
velocities with which the galaxies and thus the stars in them move away from us.
1
The diminished frequency of the light we receive is analogous to the deepening tone
of the fire engine’s horn moving away from us. Such a change in the frequency of
1 The law of the expansion of the universe discovered in 1929 by E.P. Hubble states that this
recession velocity increases proportionally to the distance between the star systems.
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_18
197