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Reply to: “Comment on: ‘From classical to modern ether-drift experiments: the narrow window for a preferred frame’ [Phys. Lett. A 333 (2004) 355]” [Phys. Lett A 361 (2007) 509]
Physics Letters A 361 (2007) 513–514 www.elsevier.com/locate/pla
Reply to: “Comment on: ‘From classical to modern ether-drift experiments: the narrow window for a preferred frame’ [Phys. Lett. A 333 (2004) 355]” [Phys. Lett A 361 (2007) 509] M. Consoli ∗ , E. Costanzo Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Dipartimento di Fisica e Astronomia dell’Università di Catania, Via Santa Sofia 64, 95123 Catania, Italy Received 3 July 2006; received in revised form 28 August 2006; accepted 11 September 2006 Available online 25 September 2006 Communicated by P.R. Holland
Abstract We present some arguments that should induce to re-consider from a new perspective the interference experiments in moving media (Michelson– Morley, Fizeau, . . . ). These considerations are useful to understand and appreciate the experimental test recently proposed by Guerra and de Abreu. © 2006 Elsevier B.V. All rights reserved. PACS: 03.30.+p; 01.55.+b
The possible existence of a preferred reference frame is an old and important issue that dates back to the origin of the theory of relativity, i.e., to the basic differences between Einstein’s Special Relativity and the Lorentzian point of view. No doubt, today, the former interpretation is widely accepted. However, in spite of the deep conceptual differences, it is not so obvious how to distinguish experimentally between the two interpretations since the basic quantitative ingredients, namely Lorentz transformations, are the same in both formulations. For this reason, it should be emphasized that the traditional null interpretation of the ether-drift experiments has been challenged in Ref. [1]. The alternative view with a preferred frame is entirely consistent and perhaps in better agreement with the results of the classical experiments. These were performed in gaseous media (such as air or helium at atmospheric pressure), i.e. in dielectric media whose refractive index N is very close to unity. In this regime, there is no experimental evidence for an observable “Fresnel’s drag” of the medium. Therefore, light could propagate isotropically in a preferred frame Σ and not
DOI of original article: 10.1016/j.physleta.2004.10.062. DOI of comment: 10.1016/j.physleta.2006.09.033. * Corresponding author. E-mail address: [email protected] (M. Consoli). 0375-9601/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.09.012
in the Earth’s frame S where the medium is at rest. Following this idea and applying a Lorentz transformation from Σ to S , the resulting anisotropy of the two-way speed of light would produce fringe shifts proportional to an observable velocity 2 Vobs ∼ 3 N 2 − 1 V 2 V2 .
(1)
Remarkably, the small effects observed in the classical experiments point consistently to an Earth’s cosmic motion characterized by a kinematical velocity |V| ∼ 200 km/s (daily average value projected in the plane of the interferometer). On the other hand, when the difference of N from unity becomes substantial (e.g. N ∼ 1.5 as in the experiment of Shamir and Fox [2]), the Fresnel’s drag from the moving medium shows up and dominates. In this case, light’s propagation is now seen isotropic in the rest frame of the medium (i.e. in the Earth’s frame). After these considerations, that should induce to re-consider from a new perspective the results and the interpretation of the interference experiments in moving media, we shall now consider the Fizeau-type of experiment proposed by Guerra and de Abreu [3]. Adopting exactly the same point of view described above, they assume that in the limit N → 1 light is seen isotropic in a preferred frame Σ that differs from the Earth’s frame so that
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M. Consoli, E. Costanzo / Physics Letters A 361 (2007) 513–514
there is no observable Fresnel’s drag when light propagates in a moving medium such as a flowing gas. With this assumption, applying a Lorentz transformation from Σ to S , for the geometry of their apparatus, the two light beams shown in Fig. 1 of Ref. [3] will be seen to propagate at the same speed by the observer placed in the laboratory, regardless of the different velocities of the gas that flows in the two arms. Therefore, they are right. A null result of their proposed experimental test would represent additional evidence against the standard “null-result” interpretation of the classical ether-drift experiments that has been traditionally assumed so far. Let us now discuss the feasibility of the first-order Fizeau experiment with the flowing gas, as compared to the proposed second-order laser experiment [1] where the same gas fills two symmetrical, orthogonal optical cavities (placed in a state of slow active rotation). In the former case, the fringe shift expected from Special Relativity is λ L vflow 2 ∼ Ngas − 1 . (2) λ λ c Using for instance CO2 at atmospheric pressure, where NCO2 ∼ 1.00045, for a flow velocity of 5 m/s, a length L ∼ 1.5 m, and a wavelength λ ∼ 6 × 10−7 m, the expected signal would be 1 ∼ 4 × 10−5 . Therefore, the needed rejection accuracy has to be ∼1 × 10−5 . Replacing CO2 with helium at atmospheric pressure, where Nhelium ∼ 1.000035, one gets the more stringent limit of 1 × 10−6 . On the other hand, for the second-order laser experiment, the relative frequency shift, whose observation would now contradict Special Relativity, is 1 ≡
2 ≡
2 ν 1 Vobs ∼ . ν0 2 c2
(3)
Filling the cavities with CO2 and replacing a value for the cosmic velocity |V| ∼ 200 km/s, the signal would be 2 ∼ 6 × 10−10 . Therefore, the needed detection accuracy has to be ∼ 1 × 10−10 . Notice that, although the nominal sensitivity needed for the laser experiment has to be five orders of magnitude higher than that needed for the first-order effect, there is a substantial dif-
ference: in the Fizeau experiment one measures a fringe shift while in the laser experiment one is measuring a frequency shift. In the latter type of measurement, based on a well established technology, there is absolutely no problem to detect a beat note ν ∼ 180 kHz between two signals of frequency ν0 ∼ 3 × 1014 Hz. Thus, compared to the present experiments in vacuum cryogenic cavities, one has only to estimate the noise introduced by running the lasers at room temperature. Its typical size is O(10) kHz [4] so that, for very slow rotations of the apparatus where turbulence phenomena due to the presence of the gas in the cavities should be negligible, the noise should be smaller than the signal by about one order of magnitude. On the other hand, for the Fizeau experiment the problem is to reach the sensitive detection of fringe shift 10−5 . As a possible answer that can be found in the literature, we observe that in Ref. [2] the fringes were projected onto a pair of photoresistors that consisted of two arms of a Wheatstone bridge. Since thirty years ago [5] this method could reach a maximal resolution of about 10−5 , using present-day technology and a relatively dense gas as CO2 , there are positive indications for the feasibility of the experiment proposed by Guerra and de Abreu. The practical realization of both first-order Fizeau and second-order laser experiments in the gaseous regime would provide precious combined informations to definitely test the preferred-frame scenario that is emerging from the re-analysis of the ether-drift experiments. References [1] M. Consoli, E. Costanzo, Phys. Lett. A 333 (2004) 355; M. Consoli, E. Costanzo, Nuovo Cimento B 119 (2004) 393, grqc/0406065. [2] J. Shamir, R. Fox, Nuovo Cimento B 62 (1969) 258. [3] V. Guerra, R. de Abreu, Comment on: “From classical to modern ether-drift experiments: the narrow window for a preferred frame” [Phys. Lett. A 333 (2004) 355], Phys. Lett A 361 (2007) 509. [4] S. Seel, R. Storz, G. Ruoso, S. Schiller, J. Mlynek, Frequency-stabilization of Nd:YAG lasers to room temperature and cryogenic cavities, in: Proceedings of Fifth Symposium on Frequency Standards and Metrology, World Scientific, Singapore, 1996. [5] J. Shamir, R. Fox, S.G. Lipson, Appl. Opt. 8 (1969) 103.
Reply to: “Comment on: ‘From classical to modern ether-drift experiments: the narrow window for a preferred frame’ [Phys. Lett. A 333 (2004) 355]” [Phys. Lett A 361 (2007) 509] M. Consoli ∗ , E. Costanzo Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Dipartimento di Fisica e Astronomia dell’Università di Catania, Via Santa Sofia 64, 95123 Catania, Italy Received 3 July 2006; received in revised form 28 August 2006; accepted 11 September 2006 Available online 25 September 2006 Communicated by P.R. Holland
Abstract We present some arguments that should induce to re-consider from a new perspective the interference experiments in moving media (Michelson– Morley, Fizeau, . . . ). These considerations are useful to understand and appreciate the experimental test recently proposed by Guerra and de Abreu. © 2006 Elsevier B.V. All rights reserved. PACS: 03.30.+p; 01.55.+b
The possible existence of a preferred reference frame is an old and important issue that dates back to the origin of the theory of relativity, i.e., to the basic differences between Einstein’s Special Relativity and the Lorentzian point of view. No doubt, today, the former interpretation is widely accepted. However, in spite of the deep conceptual differences, it is not so obvious how to distinguish experimentally between the two interpretations since the basic quantitative ingredients, namely Lorentz transformations, are the same in both formulations. For this reason, it should be emphasized that the traditional null interpretation of the ether-drift experiments has been challenged in Ref. [1]. The alternative view with a preferred frame is entirely consistent and perhaps in better agreement with the results of the classical experiments. These were performed in gaseous media (such as air or helium at atmospheric pressure), i.e. in dielectric media whose refractive index N is very close to unity. In this regime, there is no experimental evidence for an observable “Fresnel’s drag” of the medium. Therefore, light could propagate isotropically in a preferred frame Σ and not
DOI of original article: 10.1016/j.physleta.2004.10.062. DOI of comment: 10.1016/j.physleta.2006.09.033. * Corresponding author. E-mail address: [email protected] (M. Consoli). 0375-9601/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2006.09.012
in the Earth’s frame S where the medium is at rest. Following this idea and applying a Lorentz transformation from Σ to S , the resulting anisotropy of the two-way speed of light would produce fringe shifts proportional to an observable velocity 2 Vobs ∼ 3 N 2 − 1 V 2 V2 .
(1)
Remarkably, the small effects observed in the classical experiments point consistently to an Earth’s cosmic motion characterized by a kinematical velocity |V| ∼ 200 km/s (daily average value projected in the plane of the interferometer). On the other hand, when the difference of N from unity becomes substantial (e.g. N ∼ 1.5 as in the experiment of Shamir and Fox [2]), the Fresnel’s drag from the moving medium shows up and dominates. In this case, light’s propagation is now seen isotropic in the rest frame of the medium (i.e. in the Earth’s frame). After these considerations, that should induce to re-consider from a new perspective the results and the interpretation of the interference experiments in moving media, we shall now consider the Fizeau-type of experiment proposed by Guerra and de Abreu [3]. Adopting exactly the same point of view described above, they assume that in the limit N → 1 light is seen isotropic in a preferred frame Σ that differs from the Earth’s frame so that
514
M. Consoli, E. Costanzo / Physics Letters A 361 (2007) 513–514
there is no observable Fresnel’s drag when light propagates in a moving medium such as a flowing gas. With this assumption, applying a Lorentz transformation from Σ to S , for the geometry of their apparatus, the two light beams shown in Fig. 1 of Ref. [3] will be seen to propagate at the same speed by the observer placed in the laboratory, regardless of the different velocities of the gas that flows in the two arms. Therefore, they are right. A null result of their proposed experimental test would represent additional evidence against the standard “null-result” interpretation of the classical ether-drift experiments that has been traditionally assumed so far. Let us now discuss the feasibility of the first-order Fizeau experiment with the flowing gas, as compared to the proposed second-order laser experiment [1] where the same gas fills two symmetrical, orthogonal optical cavities (placed in a state of slow active rotation). In the former case, the fringe shift expected from Special Relativity is λ L vflow 2 ∼ Ngas − 1 . (2) λ λ c Using for instance CO2 at atmospheric pressure, where NCO2 ∼ 1.00045, for a flow velocity of 5 m/s, a length L ∼ 1.5 m, and a wavelength λ ∼ 6 × 10−7 m, the expected signal would be 1 ∼ 4 × 10−5 . Therefore, the needed rejection accuracy has to be ∼1 × 10−5 . Replacing CO2 with helium at atmospheric pressure, where Nhelium ∼ 1.000035, one gets the more stringent limit of 1 × 10−6 . On the other hand, for the second-order laser experiment, the relative frequency shift, whose observation would now contradict Special Relativity, is 1 ≡
2 ≡
2 ν 1 Vobs ∼ . ν0 2 c2
(3)
Filling the cavities with CO2 and replacing a value for the cosmic velocity |V| ∼ 200 km/s, the signal would be 2 ∼ 6 × 10−10 . Therefore, the needed detection accuracy has to be ∼ 1 × 10−10 . Notice that, although the nominal sensitivity needed for the laser experiment has to be five orders of magnitude higher than that needed for the first-order effect, there is a substantial dif-
ference: in the Fizeau experiment one measures a fringe shift while in the laser experiment one is measuring a frequency shift. In the latter type of measurement, based on a well established technology, there is absolutely no problem to detect a beat note ν ∼ 180 kHz between two signals of frequency ν0 ∼ 3 × 1014 Hz. Thus, compared to the present experiments in vacuum cryogenic cavities, one has only to estimate the noise introduced by running the lasers at room temperature. Its typical size is O(10) kHz [4] so that, for very slow rotations of the apparatus where turbulence phenomena due to the presence of the gas in the cavities should be negligible, the noise should be smaller than the signal by about one order of magnitude. On the other hand, for the Fizeau experiment the problem is to reach the sensitive detection of fringe shift 10−5 . As a possible answer that can be found in the literature, we observe that in Ref. [2] the fringes were projected onto a pair of photoresistors that consisted of two arms of a Wheatstone bridge. Since thirty years ago [5] this method could reach a maximal resolution of about 10−5 , using present-day technology and a relatively dense gas as CO2 , there are positive indications for the feasibility of the experiment proposed by Guerra and de Abreu. The practical realization of both first-order Fizeau and second-order laser experiments in the gaseous regime would provide precious combined informations to definitely test the preferred-frame scenario that is emerging from the re-analysis of the ether-drift experiments. References [1] M. Consoli, E. Costanzo, Phys. Lett. A 333 (2004) 355; M. Consoli, E. Costanzo, Nuovo Cimento B 119 (2004) 393, grqc/0406065. [2] J. Shamir, R. Fox, Nuovo Cimento B 62 (1969) 258. [3] V. Guerra, R. de Abreu, Comment on: “From classical to modern ether-drift experiments: the narrow window for a preferred frame” [Phys. Lett. A 333 (2004) 355], Phys. Lett A 361 (2007) 509. [4] S. Seel, R. Storz, G. Ruoso, S. Schiller, J. Mlynek, Frequency-stabilization of Nd:YAG lasers to room temperature and cryogenic cavities, in: Proceedings of Fifth Symposium on Frequency Standards and Metrology, World Scientific, Singapore, 1996. [5] J. Shamir, R. Fox, S.G. Lipson, Appl. Opt. 8 (1969) 103.