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18 The Doppler Effect
Just as the internal observers inside of their crystal, we are in no position of defining
an absolute motion using the Doppler effect for electromagnetic waves (or using any
other effect) with respect to our physical vacuum. Furthermore, as can be derived
from our crystal, the transversal Doppler effect is nothing other than time dilatation
of a moving clock converted to frequency. The transversal Doppler effect is thus
also a test for Einstein’s prophetized time dilatation of clocks for our physical reality
formulated in his Special Theory of Relativity (for this moment in time we have left
the world of the internal observers). In fact, this effect could only be experimentally
verified decades after the invention of the Special Theory of Relativity, and Einstein
himself observed the verification process of this effect and saw it as the experimentum
crucis of his theory, as we already stated in Chap. 3, p. 16. It is from today’s viewpoint
somewhat curious that the first verification experiments made by H. J. Ives [44, 45]
and G.J. Stillwell 1938/39 had as a target the demonstration of the non-existence
of the transversal Doppler effect, and this 33 years after the founding of the Special
Theory of Relativity. Naturally, the experimenters did not achieve the desired result.
Compared to the former, the experiments made by G. Otting [70] aimed at proving
this effect and were successful.
We see that the situation of the outside observers concerning light is in fact identical to that of the internal observers of our crystal concerning their experiments with
sound. In the light of this and taking all other assumption of our model into account,
the Machian thesis, cf. Thiele [93] holds true:
Light somewhat like sound.
Sound somewhat like light.
We now also understand how this statement can be valid without actually coming
into conflict with conventional physics. We have included the measuring instruments,
whose usage founds the basis for the physical laws, into our considerations.
We have to remember for the evaluation of the Doppler effect, as already stated
above, that a standard emitter, an emitter that produces per construction a constant
frequency, is for the internal observer in our crystal something different than a standard emitter for the outside observer. The standard emitters constructed by the internal observer are oscillating dislocation configurations that, from the viewpoint of
an outside observer, have other construction rules when they move relative to the
crystal. Principally, this is not the case for the internal observers, because they can
do nothing else but measure any spatial change, or change in time, with the help
of such dislocation configurations. If we ignore this point, then the clock paradox described in Chap. 11 arises. Here, we wish to mention: The description of
mechanical phenomena of a crystal (such as the Doppler effect for example) using
the measuring instruments of an internal observer may seem to the reader as artificial.
[71]) does in fact speedily lead us to our Eqs. (236)–(240) and is thus exclusively used for electromagnetic waves, see e.g. French [23]. However, because we aimed at a more detailed and explicit
method of illustrating the physical processes, we did without the more mathematically elegant way
of deriving the equations for theDoppler effect. This method of the relativistic invariance of a
harmonic wave’s phase together with our measuring-rods and clocks does indeed also deliver a
complete description of the acoustic Doppler effect.
18 The Doppler Effect
Just as the internal observers inside of their crystal, we are in no position of defining
an absolute motion using the Doppler effect for electromagnetic waves (or using any
other effect) with respect to our physical vacuum. Furthermore, as can be derived
from our crystal, the transversal Doppler effect is nothing other than time dilatation
of a moving clock converted to frequency. The transversal Doppler effect is thus
also a test for Einstein’s prophetized time dilatation of clocks for our physical reality
formulated in his Special Theory of Relativity (for this moment in time we have left
the world of the internal observers). In fact, this effect could only be experimentally
verified decades after the invention of the Special Theory of Relativity, and Einstein
himself observed the verification process of this effect and saw it as the experimentum
crucis of his theory, as we already stated in Chap. 3, p. 16. It is from today’s viewpoint
somewhat curious that the first verification experiments made by H. J. Ives [44, 45]
and G.J. Stillwell 1938/39 had as a target the demonstration of the non-existence
of the transversal Doppler effect, and this 33 years after the founding of the Special
Theory of Relativity. Naturally, the experimenters did not achieve the desired result.
Compared to the former, the experiments made by G. Otting [70] aimed at proving
this effect and were successful.
We see that the situation of the outside observers concerning light is in fact identical to that of the internal observers of our crystal concerning their experiments with
sound. In the light of this and taking all other assumption of our model into account,
the Machian thesis, cf. Thiele [93] holds true:
Light somewhat like sound.
Sound somewhat like light.
We now also understand how this statement can be valid without actually coming
into conflict with conventional physics. We have included the measuring instruments,
whose usage founds the basis for the physical laws, into our considerations.
We have to remember for the evaluation of the Doppler effect, as already stated
above, that a standard emitter, an emitter that produces per construction a constant
frequency, is for the internal observer in our crystal something different than a standard emitter for the outside observer. The standard emitters constructed by the internal observer are oscillating dislocation configurations that, from the viewpoint of
an outside observer, have other construction rules when they move relative to the
crystal. Principally, this is not the case for the internal observers, because they can
do nothing else but measure any spatial change, or change in time, with the help
of such dislocation configurations. If we ignore this point, then the clock paradox described in Chap. 11 arises. Here, we wish to mention: The description of
mechanical phenomena of a crystal (such as the Doppler effect for example) using
the measuring instruments of an internal observer may seem to the reader as artificial.
[71]) does in fact speedily lead us to our Eqs. (236)–(240) and is thus exclusively used for electromagnetic waves, see e.g. French [23]. However, because we aimed at a more detailed and explicit
method of illustrating the physical processes, we did without the more mathematically elegant way
of deriving the equations for theDoppler effect. This method of the relativistic invariance of a
harmonic wave’s phase together with our measuring-rods and clocks does indeed also deliver a
complete description of the acoustic Doppler effect.