Can LIGO, VIRGO, GEO600, TAMA, AIGO or LISA Detectors Really Detect? Published in Abstract Introduction Attempts to detect gravitational waves as specific solutions to Einstein equations have taken longer than 40 years now and started with the pioneer work of J. Weber [1]. So far, however, only two types of detectors are practically fit for receiving gravitational waves: they are Michelson's laser interferometer based on ideas of F. A. E. Pirani [2], M. E. Gersenshtein [3], R. Weiss [4], G. E. Moss, L. R. Miller, and L. R. Foreward [5] and finally designed by R. E Vogt, R. W. Drewer, F. J. Raab, K. S. Thorne and R. Weiss [6-7] and electromagnetic interferent antenna developed by V. B. Braginsky, M. B. Mensky, L. P. Grishchouk, A. G. Doroshkievich, Ya. B. Zeldovitch, I. D. Novikov, M. V. Sazhin [8-9], and especially by A. Ku?ak [10]. This paper covers discussion on the operation of only one detector type - Michelson's laser interferometer. Discussion of two effects will be carried out here which may interfere with the measurement of the apparatus distortion caused by passage of the gravitational wave. They are in succession as follows:1. Seismic interference, 2. Diffraction of the laser beam on the detector mirrors and 3. Laser heating up thelight reflecting mirror surface. The first effect was discussed in [7], [12], but seems to be not deep enough, whereas the other one included only mirror distortion caused by interaction with laser beam [13-27] or they would assume in a classical way that the laser beam reflects from the whole mirror, and not from different atoms thereof. Our discussion will consequently cover effects which have not been taken into account so far. The first of discussion points refers only to LIGO, VIRGO, GEO600, AIGO and TAMA detectors while the other on involves also LISA detector. Let us then take on these problems.
Noise from the urban area
1. Did the project experimentators take into account existence of seismic noise coming from urban area located for example 100 kms away from interferometer?May these incidental ground vibrations "jam" the measurements? It concerns not only vibrations which would be transmitted only to mirrors, but also those of the whole object. For example, as a result of such vibrations, the whole vacuum tube could contract or elongate, thus possibly simulate the passage of gravitational wave. This condition is similar to the case of Apollo 13 spaceship on the Moon. At that time, seismic wave had formed, which was registered tens of kilometers away from the fall place. What does the seismic map of this terrain look like? To give an example,tramping of horses in a prairie is perceptible from anywhere from ten totwenty kilometers. What is more, the traffic of thousands of cars can addconsiderably to the detector noise within tha range between 100 Hz and 1 kHz,so within an observation range. The lack of perception of such a noise in theinterference spectrum lines may be the result of covering this effect by theeffect described in section IV (The situation from 1998 when the paper was at first submitted to the Physical Review and without any reason rejected has slightly changed. We know now that the power saws noise (from the nearby forest) and earth core plasma movement noise disturbed the measurement almost completely. The noise coming from the earth plasma core movement is 10
Diffraction effects in detectors
Has the phenomenon of laser beam extension under the influence of diffraction upon optical elements been taken into consideration? Publications [16] and [19] seem to show it has not, although figure in the publication [14] suggests that an effect has been taken into account. Figure of the laser beam in [14] shows that the beam expands while traveling the distance between the mirrors, but it is being focussed after it has been reflected back. It seems unlikely that the same focussing effect has been produced by a single mirror of 600 mm in diameter (the size of the mirrors after [21]). We are convinced of it by means of elementary calculations. From [22] we obtain that the radius of mirror curvature is 3.5 km and the mirror diameter is 40 cm. Thus, the spread s of the maximum distance between the surface of a mirror and the cutting plane will be (Fig. 1.):
To derive the formula for s we have used the expansion of a root to the first term in Taylor's series because of the small value of the R / R That is to say, let us calculate the difference of optical paths O'A and OB. If the difference is smaller than the distance λ' calculated by means of Heisenberg uncertainty principle, a single photon will not recognize whether it is reflected from point A or from point B. Thus, the system between the points loses its focussing properties. The physical effect of reflecting a photon from a mirror will be the same in points A and B. Therefore, thearea of the mirror, in which the optical path difference O'A and OB is smaller than λ', will behave like a mirror. A considerable part of the laser beam falling onto this area will be reflected in accordance with the law of reflection and refraction, and it will go beyond the region accessible to a CCD detector the diameter of which is 5 cm. Such effect will cause the decrease in the beam reaching the detector, which will result in decreasing interference pattern intensity. Let us evaluate the size of the area between points A and B. From the figure we obtain OB=OA=R - radius of the mirror and where λ stands for the laser light length. Thus, that is for λ=1.064 μm and OB=4 km. Thus, in the area of 5 cm of the CCD detector there will be a sudden decrease of interference pattern intensity, which will worsen considerably the accuracy of calculating the position of mirrors. Obviously, CCD elements can be increased; however, we will deal with the decrease of interference pattern intensity and with the effect of their vanishing as the range of interference pattern increases. Provided that making such mirrors is impossible, nothing remains but to use plane mirrors and a laser beam of the smallest angular divergence possible. The angle of a laser beam divergence is represented by the [30] formula: where λ stands for the length of laser light wave, D means the diameter of the output aperture of the optical system. In the case of normal mirrors the reflection angle θ is decreased by the angle 2φ caused by diffraction (Fig. 3.). Taking this fact into consideration as well as setting the data as follows: λ=1.064 μm, D=600 mm, we obtain the result that the angle of a laser beam divergence β will be equal to angle where is the half divergence angle of the incident wave and φ is the angle due to the diffraction of the laser beam on the mirror. Thus: where D is the diameter of the beam on the mirror (Fig. 3). Therefore, for example in the case of LIGO, the ray, after having travelled the arm of the length equal l=4 km, with the divergence angle of
will increase its diameter by Now let's try to estimate the power loss due to decreasing of the laser beam because of its diffraction on interferometer mirrors. To simplify, let us assume that the diameter of the laser ray is about 50 mm [21] and that the radiation distribution is homogeneous along the whole diameter and it is not of the gauss type. Moreover, assuming that interferometer constructors disregarded the problem of a laser beam divergence thinking it is of no importance, we make an assumption that the ray of only 5 cm in diameter has been taken into consideration to analyse interference lines. Thus, the output power of a laser beam will be equal to the total power of input beams with regard to the phenomenon of a uniform dissipation of luminous energy over the whole increased ray area. We make an assumption that the ray is reflected in the mirrors 10 000 times, much more than in [32] and only the rays which have travelled the distance of a detector arm even number of times (thus, there are 5 000 of them) contribute to the output beam. We disregard the loss in the laser beam power in our calculations since they can be neglected in case of mirrors with the coefficient of 10 where P where P It is the angle by which a beam is broadened as a result of diffraction. Therefore, as a result of diffraction, the beam will increase in diameter as follows: ΔD stands for the increase in the beam diameter at the point where we collect its power into the CCD detector. Assuming that the light reflects in the interferometer of the order of 10 Therefore, if we use a 3 W power laser, the sensitivity of the interferometer will decrease at least by four orders in comparison with the sensitivity accepted so far (to avoid of the diffraction effect by the self-focusing of the laser beam). So we'll have to use at least 30000 W power laser to obtain theoretical sensitivity in this case. Finally let us consider the improvement made by Drewer [35] and developed by Vinet, Meers, Man and Brillet in [36,37]. It consists in adding the additional mirrors between the laser and the interferometers mirror and beamsplitter in a way as to obtain amplified laser beam at the input and the output of the interferometer. The additional mirror with the interferometer mirror makes a cavity. To obtain the very strong amplified laser beam light must travel at least 1000 times (to and fro) in the cavity. If the cavity is 1 m long then after 2000 reflections the minimum divergence angle is about 0.05 rad. After 4 km the radius of the beam will be about 200 m. From the mirrors will reflect only about 10
Thermal noise in laser interferometers
How will the experimentators cope with atom mirror vibration generated by the laser beam reflected from the mirror? Let us try to make an estimation of such effect. Consider an atom as a harmonic oscillator oscillating under impact of photons of laser beam. The atom is kept in the crystal lattice by cohesion forces from the nearest neighbours. To estimate the recoil energy of an atom due to reflecting of photon on it we have to have a numerical value of an elastic constant of bonds in cristals. Let us try to find an estimation of the k'. Let us suppose that cohesion energy of an atom in the mirror is such that at the temperature of T = 500 K atoms oscillate with the amplitude of A= 0.1 lattice constant, which is assumed at 1 Å. We suppose that the lattice is a simple cubic, i.e. unit cell is of cubic shape with 8 atoms on its nodes. Thus, the energy of the atom in the cristal is equal to 8 energy bond values. In addition let's suppose that an atom has only three freedom degrees. Then: where k stands for Boltzmann's constant. Then, elastic constant k' is equal to: Putting the numerical values for the temperature, Boltzmann's constant and dislocation into this formula we obtain And this number is accepted for our further calculations. Atom energy which any atom obtains as a result of collision with the photon from laser beam is estimated from Compton effect [38] (at the same time, electron mass is substituted by atom mass M). This effect produces energy E' of photons scattered at the angle θ equal to (Fig. 5.) : Atom deflection is estimated by comparision of harmonic oscillator energy with atom recoil energy. However, single atom mirror mass must be estimated there, yet. Mass of a single proton is equal to approximately 1.67 × 10 As photon with frequency of 10 Because the light reflects from the mirror practically under the angle of π, thus, we assume that the cosθ = -1. Let us make one approximation more, namely such that for visible radiation, with frequency of 10 E Consequently, comparing atom recoil energy accumulated in 8 neighbours bonds with incident photon energy the formula is obtained for atom deflection x : thus Putting (6) into (7) we obtain: where λ stands for wavelength of the laser beam. Substituting numerical data obtained earlier by (7) we obtain: which is the value too big in comparison with the value less than 10 or wherein λ is laser beam lightwave length. So it can be said that the laser beam reflection from the mirror occurs at the depth Δx of some 0.04 of the wave length. Since we use light wave of some 1 μm in the experiment, so Δx will be of some 4.0×10 or that energy of atom thermal motion is equal to energy of falling photon. Futhermore, we assume that during 1 s, the area of S is hit by 10 Assuming that volume changes with changed pressure Δp at each dimension by l in a way given by Hooke's law (we assume that there occurs compression, hence negative sign at formula (11)) and hence wherein would mean photon momentum change over time, X length of the area under consideration, E - Young's modulus, S relation F/S of light pressure to area of X length. Since we assumed that the temperature in the system is constant, so formula (11) may be applied. By inserting (11) to (12) is obtained. But Δp = -2Nh, wherein N is number of photons falling on S. By inserting this relation to (13), or is obtained.Assuming in addition that , which means that volume fluctuations are equal along x, y, z, axes, wherein (ΔX) is obtained. In addition, by inserting , we will obtain By inserting into (14) numeric values [16], [21], [23] of X=5 × 10 Consequently, this approximation would indicate that detection by means of LIGO, VIRGO, AIGO, GEO600, TAMA or LISA interferometers is very difficult, unless we were able to filter off the noise which seems little probable. We think so because if it was gas in the Michelson's cavities and caused noise it had to pump out this gas to remove the noise, while here the source of disturbances is not possible to be removed. Our calculations are not in contradict with those made in [22] if we consider the mirror having the diameter of 5 cm and thickness of 10
Conclusions
Following hypothetical situation pattern of the experiment stems from the above study and results of [7], [21], [30], [32]: 1)The power of the laser used in LIGO and other experiments must be decreased at least 10 2) Mirror as a whole stands unmoved, which is indicated by instruments, while its small fraction is excited to oscillate by laser beam and moves approximately independently from the rest of the mirror, should there be additional signal noise caused by experimental results in accordance with the above reasoning. The spectral density of the noise is flat which agrees with the results obtaining by using method of the double whitening. Moreover, our results agree one with other because the laser beam reflects from approximately a hundred layers, thus, the result taken from Compton's efffect should be multiplied by 100, which gives the figure of 10 3) Measurements taken in the paper [7], [13], [20], [24], [40] may have nothing in common with the movement of a pendulum resulting from external disturbances. Such an effect can be obtained by resolving to harmonic components the noise forming in the system as a result of multiple reflection of a laser beam from perticualr atomic layers of mirrors. The distance between them is about 10 4) These results, however, can be reconciled with the expectations relating to the work of a detector on the condition that the movement of atoms in a mirror is averaging in such a way that only a component of the vibration resulting from the transition of a gravitation wave through the system is visible. Similarly, the change of a photon phase caused by the change of a path between the mirrors must be averaged, as a result of various reflections from various atomic layers in the mirrors. Whether such effects occurs or not should be ascertained based upon reliable computer simulations (similarly as in case of Fermi-Pasta-Ulam paradox), which so far are missing. Hence, the disscussion if interferometers LIGO, VIRGO, AIGO, GEO600, TAMA or LISA can really detect is incomplete. Note to Editor: unluckily there was no possibility to use Insert/Edit button (it failed on my computer) thus, the paper is without any picture. Afetr removal of this fault the old paper could be withdrawn and submitted again. [1] J. Weber, Phys. Rev. 117, 306 (1960). [2] F. A. E. Pirani, Acta Phys. Polon. 15, 389 (1956). [3] M. E. Gersenstein and V. I. Pustovoit, Soviet Physics, JETP 16, 433 (1963). [4] R. Weiss, Quart. Progr. Rep. of RLE, MIT 105, 54 (1972). [5] G. E. Moss, L. R. Miller, and R. L. Forward, Appl. Opt. 10, 2495 (1971). [6] R. E Vogt, R. W. Drewer, F. J. Raab, K. S. Thorne, R. Weiss, Laser Interferometer Gravitational-Wave Observatory, proposal to the National Science Foundation( December 1989 ). [7] R. E Vogt, The U.S. LIGO Project, Proceedings of the Sixth Marcel Grossmann Meeting on General Relativity, Kyoto, Japan, June 1991. [8] V. B. Braginsky, M. B. Mensky, Zh. Eksp. Teor. Fiz. Pisma 13, 585 (1971). [9] V. B. Braginsky, L. P. Grishchouk, A. G. Doroshkievich, Ya. B. Zeldovitch, I. D. Novikov, M. V. Sazhin, Zh. Eksp. Teor. Fiz. 65, 1729 (1973). [10] A. Ku?ak, Ph. D. theses, Academy of Mining and Metallurgy, Cracow, Poland 1980. [11] A. Ku?ak, Acta Phys. Polon. B {\bf 15}, 3 (1984). [12] J. Giaime, P. Saha, D. Shomaker, L. Sievers, Rev. Sci. Instrum. 67, 208 (1996). [13] A. D. Gillespie, Thermal Noise in the Initial LIGO Interferometers}, LIGO Ph. D. theses, California Institute of Technology, Pasadena, California 1995. [14] B. Caron et al., Class. Quantum Grav. 14, 1461 (1997). [15] M. T. Jaekel and S Reynaud, Quantum Semiclass. Opt. 7, 639 (1995). [16] H. Lück and the GEO600 Team, Class. Quantum Grav. 14, 1471 (1997). [17] M. Yvert, in XXVII Int. Conf. on High Energy Physics: Session Pa-22, Glasgow, UK, 20-27 July 1994. [18] P. R. Saulson, Phys. Rev. D 42, 2437 (1990). [19] K. A. Strain, K. Danzman, J. Mizuno, P. G. Nelson, A. Rüdiger, R. Schilling, W. Winkler, Phys. Lett. A 194, 124 (1994). [20] A. Gillespie and F. Raab, Phys. Lett. A 178, 357 (1991). [21] W. Winkler, K. Danzman, A. Rüdiger, and R. Schilling, Phys. Rev. A 44, 7022 (1991). [22] F. Bondou, J-Y. Vinet, Phys. Lett. A 198, 74 (1995). [23] P. Hello, J-Y. Vinet, Phys. Lett. A 178, 351 (1993). [24] A. Abramovici et al., Phys. Lett. A 218, 157 (1997). [25] A. Abramovici et al., Science 256}, 325 (1992). [26] P. R. Saulson, Fundamentals of Interferometric Gravitational Wave Detectors}, (World Scientific Publishing Co. Pte. Ltd., Singapore 1994), pp. 71 - 126. [27] Proceedings of the NATO Advanced Study Institute on Quantum Optics and Experimental General Relativity}, edited by Pierre Meystre and Marlan Scully (Plenum Press, New York, 1983). [28] A. Sojecki, Optics (WSiP, Warsaw 1980), p. 331 (In Polish). [29] K. Kuroda et al., in Proceedings of the International Conference on Gravitational Waves - Sources and Detectors, edited by Ignazio Ciufolini and Francesco Fiedecaro (World Scientific Publishing Co. Pte. Ltd., Singapore 1997), pp. 100 - 107. [30] H. Klejman, Lasers, (PWN, Warsaw 1979), p. 63 (In Polish); F. Kaczmarek, An Introduction to Laser Physics, (PWN, Warsaw 1986) pp. 532 - 533 (In Polish); A. N. Matveev, Optics, (Mir Publishers, Moscow 1988), pp. 307 - 309 (translation from Russian to English). [31] A. Kujawski, P. Szczepa?ski, Lasers - Physical Foundations, (WPW, Warsaw 1999), p. 48 (In Polish). [32] D. H. Douglass and V. B. Braginsky, in General Relativity - An Einstein centenary survey}, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge 1979), pp. 90 - 137. [33] G. E. Stedman, Rep. Prog. Phys. 60 (1997). [34] J. Bordè, in Proceedings of the NATO Advanced Study Institute on Quantum Optics and Experimental General Relativity, edited by Pierre Meystre and Marlan Scully (Plenum Press, New York, 1983), pp.269 - 291 and references therein. [35] R. W. P. Drever, in Gravitational Radiation, edited by N. Druelle and T. Pirani (North-Holland, Amsterdam, 1983). [36] J-Y. Vinet, B. Meers, C. N. Man and A. Brillet, Phys. Rev. D 38, 433 (1988). [37] B. Meers, Phys. Rev. D 38, 2137 (1988). [38] T. Hofmokl, M. ?wi?cicki, Elementary particles, (WSiP, Warsaw 1982), p. 18 (In Polish). [39] K. Zalewski, Lectures on phenomenological and statistical physics, (PWN, Warsaw, 1976), Chp. 7 (In Polish). [40] D. Shoemaker, R. Shilling, L. Schnupp, W. Winkler, K. Maischberger, A. Rüdiger, Phys. Rev. D 38, 423 (1988). [41] A.M. Sinev, arXiv:quant-ph/0307030 v2 14 Jul 2003 Information about this Article Published on Wednesday 16th August, 2006 at 08:39:09.
Peer review added 16th August, 2006 at 12:17:54 I refer to the assumption that neutrons and protons have the same rest mass. Since these experiments are measuring very small quantities, would it be okay to neglect the difference in masses of the neutron and the proton, and their mass when in motion (relativisitc velocity)? added 16th August, 2006 at 12:43:26 It depends on how your exact measuremnts should be. If they are rough estimations it is OK, but otherwise I should be more precise. Whether or to avoid rest masses of these particles is dependent how large is the momentum of theirs against thier rest mass. If it is comparable you cannot avoid the mass, otherwise yes, you can. added 16th August, 2006 at 12:47:03 Here the kinetic energy of the protons and neutrons are so small that the difference between relativistic and classical mass can be omitted each of the proton and neutron in the mirror. Additional peer comment added 17th August, 2006 at 12:57:39 From what I know, (3/2)kT is the formula for kinetic energy of an ideal gas. However, there is no “gas” in the experiment, so could this formula still hold? added 17th August, 2006 at 20:04:40 Yes, we can. If we consider simple Debye’s model of the cristal lattice then we get, for teperature much higher than Debye’s temeprature (which are about 100 K, here we have 13500 K) that approxiamtion of ideal gas is good. One part is the energy bound of the lattice and the second one the kinetic energy of the atoms. If we take the average values we can just divide the total energy by two and get an average value of each energy. It is very rough estimation, but works well. Peer review added 19th August, 2006 at 15:38:21 It is not clear exactly how the passage of a gravitational wave through the interferometer is expected to produce any effect While this may be explained in one or more of the references, it should be decsribed in this paper. added 21st August, 2006 at 07:53:57 Yes, you are right. If the article has to be self-consistent there should be such an explanation. But otherwise many papers do not do it, either. So, the explanation how the gravitational wave causes the effects that are measurable is as follows: when the gravitational wave passes through the detector it distorts the whole space-time beteewen the mirrors, but only space distortion is neasured. During the passage changes the distance between the mirrors so the ground is shrinking, either. This shortenend distance is comapring with the distance perpendicualr to the wave that does not contract. The difference in optical waves gives the optical pattern on the CCD camera that is measured (but this theory that is very idealised, which is shown in this paper that it may be not true). added 21st August, 2006 at 07:56:48 The contraction takes place between the mirror placed parallel to the gravitational wave. added 21st August, 2006 at 09:28:03 Mistake:… difference in optical ways… . There are two arms of the detector: one is parallel to the incoming wave, the second one is perpendicular to it. added 6th October, 2006 at 16:33:13 According to the yesterday’s meeting of the Polish Physical Society my picture of detecting of the gravitational wave is wrong. added 19th October, 2015 at 16:00:51 Well, after 9 years the LIGO project has still found nothing. Yesterday lasted one month of working Advanced LIGO detectors and they has found nothing. According to our calculations the shouldn’t find anything. The time is passing and probably after 10 years of further search in case of non-detection of gravitational waves the LIGO collaborators will have to admit that something is wrong. But what is wrong: theory or the detectors? I don’t think that theory is wrong in weak fields - the further observations should support that view. But time will tell who is right. It’s nice to be right, but on the other hand I would like to be wrong, because it would be nice to detect the gravitational wave. But we can’t avoid the truth and if our calculations are correct the LIGO is a waste of time, money and human effort. Maybe scientists should go through that experience? added 13th February, 2016 at 11:29:26 Well, I was wrong criticizing the LIGO project or I may say that I was partially right. Some of the disturbances occured and made the previous LIGO detectors impossible to detect. But finally it turnd out that the LIGO detectors were constructed in a proper way and were able to detect the gravitational wave coming from the colliding black stars. But on the other hand it is nice to be wrong. Maybe the submitted reasoning should be reconsidered again to find its flaws, but now it is not important for the observation. I join to the people who congratulate the LIGO teams. |

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