Copycat of Relativity

Copycat Of Relativity

Eric Su [email protected] https://sites.google.com/view/physics-news/home (Dated: April 1, 2020) Woldemar Voigt had a theory of covariant wave equation in 1887. The Doppler eﬀect can be applied to establish his theory if the speed of light can be assumed to be invariant in inertial reference frames. Voigt’s theory was ignored by Hendrik Antoon Lorentz and the contemporary but was picked up by Albert Einstein. The theory of relativity was ﬁnalized in 1905 with a fatal error.

I. INTRODUCTION B. Voigt Transformation

Woldemar Voigt published a paper[1], ”On Doppler’s Voigt made a mistake when he applied Doppler effect Principle”, in 1887. Voigt speculated the homogeneous to his covariance transformation. He assumed same ve- wave equations to be covariant in inertial reference locity for different inertial reference frame but Doppler frames. In order to apply Doppler effect to the wave effect shows that the observed sound frequency is differ- equations, Voigt proposed the invariance of the speed of ent in a different inertial reference frame. The wavelength light in inertial reference frames. His resulting spacetime of light is invariant in all inertial reference frames. transformation was mostly ignored. Voigt transformation can be written in modern matrix In 1892 George F. FitzGerald[2] and Hendrik Antoon notation as Lorentz[3] proposed independently the contraction of a v moving body in the direction of its motion. After a 1 − c 0 0 v lengthy development, Lorentz found his transformation α − c 1 0 0 Vβ = 1 (1) similar to Voigt’s transformation. Lorentz was said to ac- 0 0 γ 0 1 knowledge that developing his theory of electrodynamics 0 0 0 γ could be shortened by including Voigts transformations if only known beforehand. α Spacetime transformation according to Vβ is In 1905, Albert Einstein[4] copied Voigt’s proposal to derive Lorentz’s transformation. The theory of relativity 0 ct ct took its final form. Little did Einstein know that the x0 x = V α (2) proposal from Voigt carried a fatal mistake. y0 β y

z0 z

II. PROOF Voigt did not realize there is an error in the inverse α transformation of Vβ . It could not restore the original A. Doppler Eﬀect inertial reference frame.

A stationary wave displays no frequency nor velocity to a stationary observer. To a moving observer the same C. Lorentz Transformation wave will appear to move and exhibit frequency. The faster the observer move, the higher velocity and fre- Lorentz also looked for the transformation under which quency from the wave is observed. Maxwell’s equations are invariant when transformed from The relative motion between the rest frame of the wave the aether to a moving frame. Together with Larmor, and the rest frame of the observer determines not only they extended the FitzGeraldLorentz contraction hy- the speed of the wave but also the frequency of the wave. pothesis and found out that the time coordinate has to Doppler effect[5] was proposed by Christian Doppler be modified as well. In 1905, Poincare was the first to in 1842. The hypothesis was tested for sound waves by recognize that the transformation has the properties of a Buys Ballot in 1845. The sound pitch was confirmed to mathematical group, and named it after Lorentz. be higher than the emitted frequency when the sound Lorentz transformation can be written in modern ma- source approached. However, Doppler effect describes trix notation as sound wave which transmits differently from light. For a stationary wave, the wavelength is invariant in v γ −γ c 0 0 inertial reference frames while its frequency depends on −γ v γ 0 0 ∧α = c (3) the relative motion of its observer. This has been verified β 0 0 1 0 by Su[6,7] for electromagnetic radiation. 0 0 0 1 2

α Spacetime transformation according to ∧β is D. Copycat of Relativity

0 Albert Einstein is a well known copycat. Few of his ct ct x0 x idea is original. In 1905, Einstein copied Voigt’s idea of = ∧α (4) y0 β y invariant speed of light into his paper, ”Zur Elektrody-

z0 z namik bewegter Krper”[4]. By assuming the speed of light is invariant in all inertial reference frames, Einstein was able to derive Lorentz transformation. The deriva- From equations (1,3), tion prevailed because Voigt had already proved it. Few people understand that invariant speed of light is 1 originally from Voigt, not from Einstein. More copycats ∧α = V α (5) γ β β copy this mistake further into Maxwell’s equations and quantum ﬁeld theory. Lorentz transformation is indeed proportional to Voigt transformation by a γ factor. III. CONCLUSION However, Voigt transformation is incorrect because its inverse transformation can not produce identity matrix. By copying Voigt’s idea, Einstein also inherited Voigt’s mistake. The mistake stays in the theory of relativity by assuming the invariance of the speed of light in inertial 1 0 0 0 0 1 0 0 reference frames. V α(v)V β(−v) 6= (6) β α 0 0 1 0 Sound wave transmits through air. The rest frame of

0 0 0 1 air is diﬀerent from the rest frame of the sound source. Hence, the wavelength changes. Electromagnetic radiation does not need any medium to transmit. Hence, Lorentz transformation together with its inverse trans- the wavelength of light is invariant in inertial reference formation can produce the identity matrix and restore frames. Voigt had mistakenly identiﬁed sound transmis- the original inertial reference frame. sion with light transmission. Utill 2020, the mistake still remains and spreads like

1 0 0 0 virus in modern physics. Few physicists realize that the 0 1 0 0 speed of light depends on the choice of inertial reference ∧α(v) ∧β (−v) = (7) β α 0 0 1 0 frame. The legend of this mistake was started by Voigt

0 0 0 1 for his misunderstanding of Doppler eﬀect.

[1] Voigt, W. (1887), ”Ueber das Doppler’sche Princip (On Institute for Gravitational Physics, Potsdam, Germany. the Principle of Doppler)”, Gttinger Nachrichten (7): Retrieved September 4, 2017. 4151; Reprinted with additional comments by Voigt in [6] Su, Eric: Error in Modern Astronomy. viXra: Physikalische Zeitschrift XVI, 381386 (1915). Relativity and Cosmology/1908.0005 (2019). [2] B. J. Hunt (1988), The Origins of the FitzGerald Con- http://vixra.org/abs/1908.0005 traction, British Journal for the History of Science 21, [7] Su, Eric: Microwave Resonance and Doppler Eﬀect. 6176. viXra: Relativity and Cosmology/1909.0175 (2019). [3] H. R. Brown (2001), The origin of length contraction: 1. http://vixra.org/abs/1909.0175 The FitzGeraldLorentz deformation hypothesis, Amer- [8] FitzGerald, G. F.: The ether and the earth’s atmosphere. ican Journal of Physics 69, 1044 1054. E-prints: gr- Science. 13: 390 (1889) qc/0104032; PITT-PHIL-SCI00000218. [9] Lorentz, H. A.: De relatieve beweging van de aarde en [4] Einstein, Albert: ”Zur Elektrody- den aether. Zittingsverlag Akad. v. Wet. 1, 74 (1892), namik bewegter Krper”, 1905-06-30. English trans. The relative motion of the earth and the http://www.zbp.univie.ac.at/dokumente/einstein3.pdf aether. In: Zeeman, P., Fokker, A. D. (eds.) Collected [5] Possel, Markus (2017). ”Waves, motion and frequency: Papers. Nijho, The Hague (1937) the Doppler eﬀect”. Einstein Online, Vol. 5. Max Planck [10] Eric Su: List of Publications, http://vixra.org/author/eric su