# An Experimental Study of the Transverse Doppler Effect Ives, H.E. and Stilwell, G.R. "An Experimental Study of the Rate of a Moving Atomic Clock." *Journal of the Optical Society of America* 28, no. 7 (1938): 215-226. Received April 12, 1938. Herbert E. Ives and G.R. Stilwell, Bell Telephone Laboratories, New York, N.Y. Zotero: 4BH5IHN7 --- ## Overview Ives and Stilwell performed the first direct experimental measurement of the transverse Doppler effect (the "second order" frequency shift of a moving light source). They observed hydrogen canal rays moving at known velocities and measured the shift of the center of gravity of the Doppler displaced spectral lines. The experiment confirmed the frequency shift formula $\nu = \nu_0(1 - V^2/c^2)^{1/2}$. Ives explicitly attributes this formula to **Larmor and Lorentz**, not Einstein, and frames the entire experiment as a test of ether theory. --- ## The Key Equation ![[1938_Ives_Stilwell-02.png]] On p.216, Ives states the equation being tested: $\lambda = \lambda_0(1 - V^2/c^2)^{\frac{1}{2}}$ where $V$ is the observed or measured velocity of the positive particles. He also writes the shift of the center of gravity of the displaced lines as: $\Delta\lambda = \lambda_0(\frac{1}{2}V^2/c^2)$ to second order. > [!critical] This is Voigt's transverse form, not Lorentz's longitudinal form > Compare with Voigt (1887): $y' = yq$ where $q = \sqrt{1 - \varkappa^2/\omega^2}$. Replace $\varkappa$ with $V$ and $\omega$ with $c$ and you get $q = \sqrt{1 - V^2/c^2}$. The wavelength shift $\lambda = \lambda_0 q$ is exactly the transverse scaling factor from Voigt's transformation. It is NOT the Lorentz $\gamma$ factor (which would give $\lambda = \lambda_0 / \sqrt{1 - V^2/c^2}$, a blueshift instead of a redshift). > > In the Lorentz (longitudinal) form, you need to extract the transverse effect by setting $x = 0$ in the time transformation $t' = \gamma(t - vx/c^2)$ and then interpreting $t' = \gamma t$ as a frequency shift. In Voigt's transverse form, the effect is already sitting right there in $y' = yq$. Ives is measuring $q$, which is Voigt's factor, not $\gamma$. --- ## Ives Credits Larmor and Lorentz, Not Einstein ![[1938_Ives_Stilwell-01.png]] From the introduction (p.215): > "In previous papers in this series, various consequences of the alteration of the rate of a clock in motion, which is an essential element in **the theory of Larmor and Lorentz**, have been discussed." From the discussion (p.225): > "The conclusion drawn from these experiments is that the change of frequency of a moving light source predicted by **the Larmor-Lorentz theory** is verified." > [!critical] Ives never mentions Einstein or special relativity > The experiment universally credited as "confirming special relativity" was explicitly designed and interpreted as a test of the **Larmor-Lorentz ether theory**. Ives attributes the frequency shift to Larmor (1895/1897) and Lorentz (1895/1904), both of whom derived it from the dynamics of electrons moving through the ether. Ives was an ether proponent his entire career and designed this experiment specifically to test ether predictions. --- ## The Significance Section (p.226) ![[1938_Ives_Stilwell-05.png]] Ives writes the frequency formula explicitly: $\nu = \nu_0(1 - V^2/c^2)^{\frac{1}{2}}$ where $\nu_0$ is "the frequency of the clock when stationary in the ether" and $\nu$ is "its frequency when in motion." He then interprets the result: > "It follows then on combining this result with the results of the Kennedy-Thorndyke experiment that the dimensions of the moving apparatus are contracted by the factor $(1 - V^2/c^2)^{\frac{1}{2}}$ in the direction of motion, and are unaffected at right angles to that direction." > "The Michelson-Morley and Kennedy-Thorndyke experiments, yielding null results, could, of themselves, be equally well explained, and more simply, by assuming an ether entrained by the earth, or a ballistic character of light emission, instead of assuming two concealed conspiring compensations: contractions of dimensions and of clock rates." > "The present result may hence be claimed to give more decisive evidence for the Larmor-Lorentz theory than given by the experiments which have yielded null results." > [!critical] Ives says his experiment supports ether theory more strongly than Michelson-Morley > Ives explicitly argues that: > 1. Michelson-Morley's null result can be explained by ether drag or ballistic emission (no need for SR) > 2. His experiment gives a **positive** result (not a null), making it harder to explain away > 3. The positive result matches **Larmor-Lorentz ether theory** specifically > 4. The "concealed conspiring compensations" (contraction + time dilation) are the SR explanation, which Ives considers less simple than the ether explanation > > The experiment that textbooks present as proof of SR was designed, performed, and interpreted as proof of ether theory by the man who ran it. --- ## The Equation is the Voigt Transverse Factor | Form | Equation | Who | |---|---|---| | Voigt transverse (1887) | $y' = y\sqrt{1 - v^2/c^2}$ | Voigt | | Larmor time dilation (1895/1897) | $T' = T\sqrt{1 - v^2/c^2}$ | Larmor | | Ives-Stilwell measured (1938) | $\lambda = \lambda_0\sqrt{1 - V^2/c^2}$ | Ives | | Lorentz time (longitudinal, 1904) | $t' = \gamma(t - vx/c^2)$ | Lorentz | | Einstein time dilation (1905) | $\Delta t' = \gamma \Delta t$ | Einstein | Ives measured $\sqrt{1 - V^2/c^2}$. That is $q$, not $\gamma$. It is the transverse scaling factor from Voigt's 1887 transformation, the same factor that appears in Larmor's 1895 time dilation, the same factor Voigt himself called "irrelevant for the application" because dividing by it gives the Lorentz form. The Lorentz longitudinal form gives $\gamma = 1/\sqrt{1 - v^2/c^2}$, which is the reciprocal. To extract the transverse Doppler from the Lorentz form, you have to set $x = 0$ in $t' = \gamma(t - vx/c^2)$ and get $t' = \gamma t$, then interpret the frequency as $\nu = \nu_0/\gamma = \nu_0\sqrt{1 - v^2/c^2}$. You arrive at the same number, but you had to reshuffle the Lorentz transformation to get there. Voigt's transverse form already has the answer sitting in the transformation itself. No reshuffling needed. Ives measured Voigt's $q$. --- ## Related Notes - [[1887_Voigt_Ueber_das_Dopplersche_Princip]] — Voigt's original derivation of the transverse factor $q = \sqrt{1 - v^2/c^2}$ from the wave equation - [[1895_Larmor_Dynamical_Theory_Electric_Medium]] — Larmor's derivation of time dilation from ether dynamics, which Ives explicitly credits - [[2017_Heras_Review_Voigt_Transformations]] — Shows $\Lambda = \gamma V$ (Lorentz = $\gamma$ times Voigt) - [[1905_Einstein_Electrodynamics_Moving_Bodies]] — Einstein's derivation of the same effect from postulates, 10 years after Larmor - [[Transformation_Equivalence]] — Null hypothesis showing the Voigt and Lorentz transformations are equivalent up to rescaling --- ## Citation Ives, H.E. and Stilwell, G.R. "An Experimental Study of the Rate of a Moving Atomic Clock." *Journal of the Optical Society of America* 28, no. 7 (1938): 215-226. Zotero key: 4BH5IHN7