News from LIGO msde all physicists happy. After watching the press conference I was discussing it with one colleague and could not help making some critical remsrks. My first objection was about the visual representation of the process of merge of two black holes. It was performed such a way as if time near a horizon and here on the Earth is exactly same. In fact, difference is essential. As well-known, a free falling object reaches the horizon in finite proper time, but infinite time here so that we can never see finish of this process. Whatever frequency radiation has, if it is emitted from the horizon, for us it is zero. Maybe, gravitational wave emitted when merging two black holes, reaches us somehow, it should be explained, why. Of course, it must be an expert on general relativity and the only expert we were listening to, is Kip Torne, but he said nothing. Or I have missed something? I listened to him in Moscow in 1984 and was susrpized very much to hear about spherically-symmetric black hole which has spherically-symmetric magnetic field. "That is his level", I thought and decided never to listen to him again. So, I was talking about all this to my colleague, adding a remark that a person who was working on general relativity all his life, should solve at least one real problem. Did he? I never heared of any interesting result obtained by him. Only giant number of publications. What they all are about? No idea, all I know, is that they contain no scientific results. My colleague replied: "Well, please, tell me, what certin problem he would solve in this particular program?" I said: "First, this zero frequency problem. I am sure, it can be solved, but it should be done."
Later on I recalled another serious problem which I encountered in the foundations of the experiment. In late 90-s I attended a conference on general relativity held in Samarkand, and among others there was one person from LIGO. He gave a talk about the experiment. There was one point I did not understand and I addressed the following question: "Suppose, the wavelength of the laser radiation reduces the same way as all the rest distances in the space. Then what change of the distance between mirrors are you going to measure with it?" He repeated the question and after a while, confessed that he has no answer. After the conference I forgot about it and recalled only more than decade later when I encountered the work by Malik Rakhmonov "On the round-trip time for a photon propagating in the field of a plane gravitational wave", then an electronic preprint, but afterwards issued by Class. Quantum Gravity. I did not read it thoroughly, looked only at the final result and thought that my question is answered at last. I got in touch with him, asking what was the reason to do it. He replied that one person from LIGO visited them in a laser interferometric lab in Brounsvill, TX and asked, what we are going to measure with wavelength of the laser radiation. "Very interesting. It looks like, this person asked each and every theorist on his way during all that ten years, including, probably Kip Thorne, and fortunately, there is Malik Rakhmonov who was able to find an answer." So, this is the second problem which should be solved.
After the press conference I felt some doubts. I have read Malik's work again and found that in fact, he did not answer the question as it stands. He has completed a quite difficult workdescribing photon world line in the field of gravitational wave as if frequency of the wave is so high that the phase changes numerous times while photon travels from one mirror to enother. But in the LIGO exeriment it is not so. Period of the gravitational oscillations is several orders as the round trip time, so, the problem he solved does not arise. Besides, he finds photon phase as time multiplied by frequency, assuming that frequency is fixed and inaffected by the gravitational oscillations. As for my question, I asked about wavelength, which seems to change the same way as all distances in the space, hence, in my question frequency changes under influence of the gravitational wave. Possible change is so important that everything is as I said, the interferometer does not react to the wave at all. It looks like, to answer this question is not the same as to write an article for Phys. Rev. D.
By the way, I was gradually approaching the conclusion that who asks, must answer himself. Thus, it is me, whose duty is to answer the question. OK, I am ready now. There are two characteristics of a monochromatic wave which are inverse to each other, wavelength and wave vector, one of which reduces like all distances in the space. If it is the earlier, then nothing can be measured, otherwise, the wavelength behaves as inverse distance and the effect magnifies. My answer reads: it is wave vector which reduces like al distances. The point is that what we call "wave vector" is, in fact, a co-vector, and they are co-vector, not vectors which behave like all distances, consequently, change of the wavelength is inverse to change of the distances and the effect magnifies. However, to understand this, one must replace the ordinary tensor analysis with exterior calculus and local orthonormal frames. But is someone does, he overthrowns the whole of theory of gravitational waves starting from representation of gravitational wave.
All possible small distortions of an orthonormal frame belong to the Lie algebra gl(3,1). Its subalgebra so(3,1) of Lorentz transformations is to be removed because local frames can be chosen arbitrarily. So, 10-dimensional (incomplete) algebra remains which conveys all possible polarizations of a gravitational wave. It is much more than what tensor analysis gives. As it is me, who said this, should I complete this work now? Oh not, I do not want to, I have a lot of another work.
Later on I recalled another serious problem which I encountered in the foundations of the experiment. In late 90-s I attended a conference on general relativity held in Samarkand, and among others there was one person from LIGO. He gave a talk about the experiment. There was one point I did not understand and I addressed the following question: "Suppose, the wavelength of the laser radiation reduces the same way as all the rest distances in the space. Then what change of the distance between mirrors are you going to measure with it?" He repeated the question and after a while, confessed that he has no answer. After the conference I forgot about it and recalled only more than decade later when I encountered the work by Malik Rakhmonov "On the round-trip time for a photon propagating in the field of a plane gravitational wave", then an electronic preprint, but afterwards issued by Class. Quantum Gravity. I did not read it thoroughly, looked only at the final result and thought that my question is answered at last. I got in touch with him, asking what was the reason to do it. He replied that one person from LIGO visited them in a laser interferometric lab in Brounsvill, TX and asked, what we are going to measure with wavelength of the laser radiation. "Very interesting. It looks like, this person asked each and every theorist on his way during all that ten years, including, probably Kip Thorne, and fortunately, there is Malik Rakhmonov who was able to find an answer." So, this is the second problem which should be solved.
After the press conference I felt some doubts. I have read Malik's work again and found that in fact, he did not answer the question as it stands. He has completed a quite difficult workdescribing photon world line in the field of gravitational wave as if frequency of the wave is so high that the phase changes numerous times while photon travels from one mirror to enother. But in the LIGO exeriment it is not so. Period of the gravitational oscillations is several orders as the round trip time, so, the problem he solved does not arise. Besides, he finds photon phase as time multiplied by frequency, assuming that frequency is fixed and inaffected by the gravitational oscillations. As for my question, I asked about wavelength, which seems to change the same way as all distances in the space, hence, in my question frequency changes under influence of the gravitational wave. Possible change is so important that everything is as I said, the interferometer does not react to the wave at all. It looks like, to answer this question is not the same as to write an article for Phys. Rev. D.
By the way, I was gradually approaching the conclusion that who asks, must answer himself. Thus, it is me, whose duty is to answer the question. OK, I am ready now. There are two characteristics of a monochromatic wave which are inverse to each other, wavelength and wave vector, one of which reduces like all distances in the space. If it is the earlier, then nothing can be measured, otherwise, the wavelength behaves as inverse distance and the effect magnifies. My answer reads: it is wave vector which reduces like al distances. The point is that what we call "wave vector" is, in fact, a co-vector, and they are co-vector, not vectors which behave like all distances, consequently, change of the wavelength is inverse to change of the distances and the effect magnifies. However, to understand this, one must replace the ordinary tensor analysis with exterior calculus and local orthonormal frames. But is someone does, he overthrowns the whole of theory of gravitational waves starting from representation of gravitational wave.
All possible small distortions of an orthonormal frame belong to the Lie algebra gl(3,1). Its subalgebra so(3,1) of Lorentz transformations is to be removed because local frames can be chosen arbitrarily. So, 10-dimensional (incomplete) algebra remains which conveys all possible polarizations of a gravitational wave. It is much more than what tensor analysis gives. As it is me, who said this, should I complete this work now? Oh not, I do not want to, I have a lot of another work.
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