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The Doppler shift of light from moving canal rays, as predicted by the Emission Theory, is computed, and compared to the observed results of the Ives-Stilwell Experiment.
The Ives-Stilwell Experiment was originally designed to search for the transverse Doppler effect as predicted by the Larmor-Lorentz Theory, or just Lorentz Theory in modern parlance. This theory assumes the existence of the Ether and rejects the Einsteinian Postulate of Constancy. Nonetheless, its mathematical structure is exactly the same as that of Einstein’s Special Theory.
H. Ives invested a lot of time and effort in promoting his Larmor-Lorentz Theory. He even called its transverse Doppler effect the “Rate of a Moving Atomic Clock”, in an attempt to attract some over-enthusiastic Relativists to his side.
Unfortunately, for Ives, his version of Larmor-Lorentz Theory is falsified by the null result of a modified Michelson-Morley experiment with un-equal arms.
Eventually, the Ives-Stilwell Experiment is taken over by Special Relativity whose own ‘Otting Experiment’ lost its evidential value due to the use of the wrong rest wavelength for the hydrogen line, Ha.
Fortunately for Ives this time, his new supporters never get tired of praising the achievements of their past heroes, and so his reputation as one of the greatest experimenters shall endure.
1. The Experiment
The idea of using canal rays to search for transverse Doppler effect was first suggested by A. Einstein and W. Ritz. However, their imagined experiment is not feasible. That is because one can never be sure of observing canal rays at right angles to their direction of motion. Furthermore, the expected Doppler shift is very tiny and the slightest deviations, from the angle of 90o, introduce conventional Doppler shifts of similar magnitude to that predicted by theory. For these reasons, Ives and Stilwell decided to observe in the direction of maximum blue Doppler shift and the direction of maximum red Doppler shift around the angle of 0o and 180o, respectively.
The following is a summary of their experimental steps [Ref. #1]:
(1) A canal-ray tube of the Dempster type is used to generate the hydrogen ions.
(2) A small concave mirror is installed at about 7o from the centre to reflect light emitted in the backward direction by the canal rays.
(3) An a.c. rectifier capable of delivering up to 30,000 volts is used to maintain the high negative potential applied to the accelerating electrode.
(4) A spectrograph of 10.87Amm-1 is used to disperse the spectrum from the canal rays on photographic plates of III-J Eastman type.
(5) A measuring microscope is used to obtain the displacement of Hb due to Doppler effect with respect to the rest wavelength of the second principal line in the Balmer series.
(6) The velocities of the canal rays are computed from the voltage used and the famous charge-to-mass ratio, e/m. Since the Classical Theory fails to account for the e/m relation, its failure to account for the anomalous results of the current experiment is a foregone conclusion. A. Sfarti calls the Classical Theory of Doppler effect “Newton’s Theory” [Ref. #5]. But Doppler effect is a 19th –century discovery. I. Newton never heard of it.
(7) By comparing the observed values to the computed values of Doppler shift, Ives and Stilwell concluded that the prediction of the Larmor-Lorentz Theory is verified.
The Ives-Stilwell Experiment and their follow-up experiment in 1941 have several unsatisfactory aspects, and the experimental results have been judged in a comprehensive review by W. Kantor, a seasoned experimenter in this field, to be inconclusive[Ref. #4].
2. The Doppler
Equations
Since the Doppler effect is theory-dependent, its formulas are necessarily different for different theories. Moreover, each theory has two sets of equations for computing the effect, one for frequency and one for wavelength. For the comparison between two or more theories to be meaningful, only one of these two sets of equations must be used for the theories in question. Here, the wavelength formulae will be used throughout this discussion.
It should be noted that the term ‘Doppler shift’ is defined differently in physical optics and astronomical spectroscopy. In the former, Doppler shift is defined as (l’ - l), and in the latter, as [(l’ - l)/l], where l’ is the observed wavelength, and l is the rest wavelength. The definition of Doppler shift as (l’ - l) will be used in the discussion of the Ives-Stilwell Experiment.
Although nanometre (nm) is now the fashionable wavelength unit in the optical regime, Angstrom (A) as used by the two experimenters is the appropriate unit in this context.
In the original Ives-Stilwell Experiment, the observed results are compared to the computed values of the Classical Wave Theory and the Larmor-Lorentz Theory. In this discussion, however, the same observed results are compared to the values predicted by Einstein’s Special Theory and the Emission Theory.
Only the motion of the source of light is involved in the experiment under discussion. For a clear exposition, therefore, W. Kantor’s notation will be employed, and the plus and minus signs will be implemented directly into the Doppler formulas under the condition 0 £ q £ 90o for the two quadrants.
These are the Doppler equations of the three theories:
[A] The Doppler Formulas of the Classical Theory:
Let b = v/c, where v is the velocity of the source of light with respect to the observer, and c is the velocity of light relative to the reference frame in which the source is at rest.
For the approaching source of light, therefore,
la = l(1 - bcosq) [2.1],
where la is the wavelength as measured by the observer, l is the rest wavelength, and q is the angle made to the observer line of sight by the velocity vector of the source.
For the receding source of light,
lr = l(1 + bcosq) [2.2],
where lr is the observed wavelength.
It should be noted that the same quantity l(bcosq) is added and subtracted in the two cases, respectively. From this, it follows, at once, that the Classical Theory predicts a null result for the Ives-Stilwell Experiment.
[B] The Doppler Formulas of Special Relativity:
Let b, la, lr, l, and q be as defined above.
And let g = [1 – v2/c2]-1/2.
For the approaching source of light, therefore,
la = lg(1 - bcosq) [2.3],
And for the receding source of light,
lr = lg(1 + bcosq) [2.4].
From these two equations, we calculate the average wavelength, L,
L = ½(la + lr) = lg [2.5].
Let Dl = L - l = l(g - 1), and hence,
Dl » ½lb2 [2.6],
which is the value predicted by the Theory of Special Relativity for the Ives-Stilwell Experiment.
[C] The Doppler Formulas of the Emission Theory:
Let ca denote velocity of light from the approaching source,
ca = c[1 –( v2/c2)sin2q] 1/2 + vcosq [2.7],
and let cr denote velocity of light from the receding source,
cr = c[1 –( v2/c2)sin2q] 1/2 - vcosq [2.8].
For the approaching source of light, we compute the observed period, Ta,
Ta = (T ca - Tvcosq ) / ca [2.9].
Ta = T{c[1 –(v2/c2) sin2q] 1/2]} / {c[1 –( v2/c2)sin2q]1/2 + vcosq } [2.10],
where T is the period in the reference frame in which the source is at rest.
From this equation, we obtain the observed wavelength, la,
la = l{c[1 –(v2/c2) sin2q] 1/2]} / {c[1 –( v2/c2)sin2q]1/2 + vcosq } [2.11],
where l is the rest wavelength.
For the receding source of light, we compute the observed period, Tr,
Tr = (Tcr + Tvcosq ) / cr [2.12].
Tr = T{c [1 –(v2/c2) sin2q] 1/2]} / {c[1 –( v2/c2)sin2q] 1/2 - vcosq } [2.13].
From this equation, we obtain the observed wavelength, lr,
lr = l{c[1 –(v2/c2) sin2q] 1/2]} / {c[1 –( v2/c2)sin2q]1/2 - vcosq } [2.14].
3. The Ballistic
Prediction
From Equation #[2.11], it can be seen that the observed wavelength, la, varies with q , from l[c/(c + v)] for q = 0o, to l for q = 90o.
By taking the average of these two values, we obtain the average observed wavelength, La, for light from the approaching source,
La = ½[la(0) +la(90)] = l[(c + ½v)/(c + v)] [3.1].
In Equation #[2.14], the observed wavelength, lr, varies with q , from l[c/(c - v)] for q = 0o to l for q = 90o.
By using these two values, we obtain the average observed wavelength, Lr, for light from the receding source,
Lr = ½[lr(0) +lr(90)] = l[(c - ½v)/(c - v)] [3.2].
Using La and Lr, we compute the average wavelength, L, for light from the moving source, in the two quadrants,
L = ½ [La + Lr ] = l[(c2 - ½v2)/(c2 – v2)] [3.3].
Let Dl = L - l, g = [1 – v2/c2]-1/2, and b = v/c, and hence,
Dl = l[½(v2/c2 )/(1– (v2/c2 )] = ½lg2b2 [3.4],
which is the value predicted by the Emission Theory for the Ives-Stilwell Experiment.
For source velocities less than 0.1c (about 30,000kms-1), Equation #[2..6] of Special Relativity and Equation #[3.4] of the Emission Theory yield similar results, as shown in Table #3.1, for l = 4849.32A.
The Emission Theory
½lg2b2 A |
Special Relativity
½lb2 A |
Source Velocity
kms-1 |
|
0.0325986 0.1683907 0.6737037 3.2686037 10.824375 16.955665 24.491515 |
0.0325982 0.1683791 0.6735166 3.2598207 10.776267 16.837917 24.246600 |
1.1 x 103 2.5 x 103 5.0 x
103 1.1 x 104 2.0 x
104 2.5 x 104 3.0 x
104 |
Table #3.1
In Table #3.2, the predictions of the two theories are compared to the Ives-Stilwell data of 1938 and 1941 for the ions of H2.
|
Predictions of The Emission Theory
|
Predictions of
Special Relativity |
Observed Values of Dl |
|
0.0202001 0.0243002 0.0280003 0.0360005 0.0478009 0.0670018 0.0686019 0.0724021 0.0869031 0.1054045 |
0.0202 0.0243 0.0280 0.0360 0.0478 0.0670 0.0686 0.0724 0.0869 0.1054 |
0.0185 0.0225 0.0270 0.0345 0.0470 0.0670 0.0675 0.0800 0.0900 0.1145 |
Table #3.2
The velocity range of the canal rays in the Ives-Stilwell Experiment is between
850 kms-1 and 2100 kms-1. Within this low velocity range, the predictions of the two theories, as shown in Table #3.2, are identical, and hence the experimental evidence is inconclusive. However, the Emission Theory uses, in its predictions, straightforward Galilean Transformations, while Special Relativity uses the paradoxical Lorentz Transformations to make the same predictions. Therefore, if logical consistency is a virtue, the latter theory must be ruled out.
4. Concluding
Remarks
As mentioned earlier, to compute the velocities of the canal rays, Ives and Stilwell used the equation for the kinetic energy of the hydrogen ions,
eV= mH c2 (g -1) [4.1],
where e is the charge, V is the voltage, and mH is the mass of the ion.
This dependence on the results of previous experiments reduces considerably the weight of their evidence. Time Dilation is an extraordinary claim. The evidence for it, therefore, ought to be extraordinary. But the Ives-Stilwell evidence is not extraordinary. It’s below ordinary. In conclusion, the positive outcome of the Ives-Stilwell Experiment is, in fact, due to real differences in the magnitude of Doppler effect as given by various theories, and has nothing to do at all with the rate of moving clocks.
References
[1] Ives, H., et al, (1938). J. Opt. Soc. Am., 28, 215-226.
[2] Ives, H., et al, (19341). J. Opt. Soc. Am., 31, 369-374.
[3] Jenkins, F., et al, (1976). Fundamentals of Optics. McGraw-Hill, Inc., New York.
[4] Kantor, W., (1971). Spect. Lett., 4, 3 & 4, 61-71.
[5] Sfarti, A.: http://www.wbabin.net/sfarti/sfarti5.pdf
[6] Waldron, R. A., (1977). The Wave and Ballistic Theories of Light – A Critical Review. Frederick Muller.
Acknowledgment
I would like to thank Tom Miles for providing the original references without which this work could not be carried out. I also thank Adrian Sfarti for insisting on the “Observed values must be plugged into the Cyrenika formula”. And finally, I would like to thank Walter Babin for providing space for this work in the GSJ.
Related Work
The Sagnac Effect: http://www.wbabin.net/physics/faraj6.htm