On Intuitive Description of Graviton Detector

Pawel Tatrocki (Department of Physics, Pedagogical Academy, Cracow)

Published in astro.philica.com

Abstract
In this work we present an intuitive description of graviton detector. It works on the principle of electron jump from a normal band to a conduction band, as a result of absorption of graviton. We show theoretical expectations of a number of measured gravitons coming from the double star WZG SGE by this device.

Idea of Building the Detector

The base assumption, on which we ground our idea of the detector construction is that a graviton interacts with the matter very similarly like a photon [1]. The main differences is that the graviton has spin 2 and the photon spin 1, and that the probability of graviton interaction with the matter is of 10-60 [3] and the photon, according to its energy and reaction type, of tens orders of magnitude greater. Particuraly, we assume that the graviton energy and, similarly, of the photon's is given by the following formula [1]:

$E=h \nu,$

wherein ν is the gravitational wave frequency emitted by source [1]and h is the Planck's constant. The second important assumption is that gravitational wave is formed from ,,rain" of gravitons [1]. Iis analogical an situation to electromagnetic wave, formed from ,,rain" of photons. It means that, if the electromagnetic wave energy and its frquency ν is given, then dividing this energy by hν we obtain the number of photons in this wave packet is obtained. We assume that this procedure can be done also for the gravitational wave. This not a very strange assumptions because the LIGO collaboration (the status of this project has been still uncertain) has in its scientific program searching for gravitons that existence is based on the above picture [1]. There is no proof that the method of quantization of a weak interacting gravitational wave is correct and exact but in the history of physics there are many examples that calculations made by a naive way are in good agreement with the experiment and the subsequent correct theory, for example: Bohr model of hydrogen. Moreover, the graviton has the spin 2 (it was shown by KopczyÅ„ski and Trautman and the generalization of their result is described in [1]) so it has to interact with the matter like any other quantum particle, that is one to one, if we take into account the absorption process. So there is the strong theoretical hint that such a qualitative picture, of similar interaction between graviton and photon, may be correct. In addition, the probability of intearction between a graviton and an electron, given in [2], is based on the two-body reaction and does not take into account the masses of the interacting objects but only their dimensions. Similar approach to the quantum gravity is presented by some physicists trying to quantize the gravity [2]. The probability of quantum interactions between two particles in this picture is independent of the curvature of the space-time but only dependant on their geometrical properties. In our case these geometrical properties are the sizes of the intreacting objects. In case of strong interaction of a neutron and a graviton [2] this property is the size of the neutron e.g. 10-15 m. For an electron we could take the Tscherenkov radiation effect to estimate a probability of interaction between an electron and a graviton. Its main part consists of the medium size of radius of an electron that, luckily, is the same as the neutron. The rest is the integrated contribution coming from the cross-section for the Tscherenkov radiation effect via integral trasformation between the cross-section and the probability for the same reaction. Because the dimesional sizes are the same in both cases so the probabilities of theirs are the same. In this picture the probability of the interaction is entirely independent of the masses of the interacting objects. The such quantum property is the effect of equivalency of all system of coordinates. Physicists working in the field claim the very similar condition. The independency of quantum fluctuations of the gravitational field of the coordination frames. In our picture the interaction between the electron and a graviton is a consequence of these fluctuations. A very similar case is in the photoelectric effect, where the probability of pulling out the electron from the metal is independent of the intensity of the incident flux light, but dependent only on its frequency. Thus, in our opinion, the qualitative picture of interaction between an electron and a graviton presented in this paper is theoretically well justified. Let us pass now to our detector design specifications. Idea of this construction is as follows. We have a semiconductor the forbidden band width of which is equal E1. For simplicity, we suppose that there exist only two quantum levels. If now the graviton having energy E2>E1 is absorbed by an electron in normal band, then this electron jumps into conduction band and can be registred as the one which absorbed the graviton. Moreover, if we take into account that any graviton from the gravitational wave passing the detector not far than the de Broglie length λ (the Universe is practically transparent for a gravitational wave) can interact with the apparatus [3] then the fromula for the detected gravitons is:

$N_{g}= \pi N_{d}N_{flux}\lambda^{2},$

where Ng is the number of detected gravitons, Nd is the number of the electrons in the normal band of the detector and Nflux is the number of gravitons, per one square meter per second, coming from the passing gravitational wave. Applying this formula to the double star system WZ SGE [2] and taking the number of electrons in the detector in the order of 1030 we will get the number of detected gravitons per second in the range of 1016, which is verypromising number, because it means that the sizes of the detector could be very small, even of ${\footnotesize 1mm \times 1mm \times 1\mu m}$ and in the future it could be the powerful source of electric energy. The result (2) may seem to be unreliable but it is not strange when we realize that the cross-section radius of the surface of the incoming gravitational wave is of light-seconds or light-minutes in opposition to centimeters while doing elementary paricle experiments. Thus, intuition coming from those experiments may be very deceptive. Moreover, it is better to use the probability than the cross-section to describe the device because here the graviton can potentially interact with every particle inside the detector, while during the experiments with the elementary particles these particles can interact only with usually one particle at the same time. So, the detectors are rather long than wide. In addition to that, the contribution to the total numbers of counts coming from the flux outside the detector is practically negligible in such experiments, on the contrary, in our case this contribution is dominant. Thus, the prediction of total counts, based on the very general assumptions given in the paper, is correct but a far cry from the common expectations. Moreover, our result agrees with the optical theorem in particle physics, which is very general. So, the result (2) should be qualitative correct.

Some technical remarks

The formula for the number of the detected gravitons is nice because is in the accordance with the optical theorem concerning both absorption and scattering processes. In our problem we have also a weak gravitational wave thus, the conditions of the theorem are seemed to be fulfilled well. The problem of acquiring of the electrons is very complex, thus it will be discussed in the next papers. Therefore it is impossible to give the ditailed scheme of the apparatus especially in the case of very little number of the excited electrons. Maybe the electronic transistor gates will be the answer for this question. In the description of our detector we must stress the influence of several phenomena on the work of the system. Among them, the most important are: zero vibrations of the lattice, radioactive decay inside the detector, the skin depth in the detector, the scattering photons over phonons of crystal lattice, a change of the system potential energy, the change of the energy gap value due to temperature and impurities in semiconductors, shielding any other radiation to possibly effect the electron jumps to conduction band, structural noise. Apart from standart methods of cooling down the systems we can apply the electromagnetic wave to do it, too. Let us consider an ideal situation. If a sample is placed in external electromagnetic field and isolated from the remaining influences by ideal way, making outflow of heat impossible, then after sufficiently long time the system should reach the thermodynamic equilibrium with the electromagnetic radiation. Because the frequency of the lattice atom vibration is very far from that of our electromagnetic wave frequency so the absorption of it may occur in two stages. The first one - the electrons absorb the electromagnetic wave and reach thermal equilibrium with the wave. The second stage - electrons collide with the lattice atoms taking from them the energy and passing them to the wave and therefore allow the lattice reaching thermal equlibrium with the wave, too. Thus, the electrons heat the electromagnetic wave. There are arguments against a such type of detector based on the theorem about the mutuality of the antennae detecting signals that contradict our results but there is a strong tip that the assumptions of it are unfulfiled by our detector. For exapmlethe time of being an electron in the conduction band and in the normal band may strongly differ so the probability of absorbtion and emission of the gravitons also strongly differs. Thus, the assumptions of this theorem may be unfulfiled for each semiconductor. Finally, in our opinion conditions of 10-12 V and 10-9 K [5] are within the state-of-the-art of modern experimental physics, so it should not be many complications to construct such a device that we called DETEGRAW (from Polish words - DETEKTOR GRAWITONÓW).

References:

[1] P. C. W. Davies, The search for gravity waves, (Cambridge University Press, Cambridge), 1980; R. E Vogt, The U.S. LIGO Project, Proceedings of the Sixth Marcel Grossmann Meeting on General Relativity, Kyoto, Japan, June 1991., K. A. Meissner,  Classical Field Theory, (PWN, Warsaw, 2002, in Polish), Chp. 9.

[2] T. D. Lee, Particle Physics and Introduction to Field Theory, (Harwood Academic Publishers, Chur, 1990), Chp. 25; J. Jurkiewicz - the lecture given during the Polish Physical Society meeting in Cracow (on October the 5th of 2005); C.W. Misner, K. S. Thorne, J.A. Wheeler, Gravitation (W. H. Freeman and Company, 1973, Twenty Second Printing, 1999), Chp. 44.

[3]J. Norwood, Twentieth Century Physics, (Prenitce Hall Inc, 1975), Chp. 11.

[4] As in the case of Bose-Einstein condensate.

Peer-review ratings as of 09:03:45 on 19th Oct 2017 (from 2 reviews, where a score of 100 is average):
Originality = 124.25, importance = 136.53, overall quality = 113.29

Published on Monday 24th July, 2006 at 12:54:07.

Peer review added 28th July, 2006 at 08:21:54

A very good article.
However, perhaps the reason gravitons have not been detected is because they may not exist.

Perhaps it is like the luminiferous aether, which is proved to not exist through an experiment.

Nevertheless, whether the graviton exist or not, this experiment is very useful. It will be able to show whether the graviton exists or not.

Author comment added 5th August, 2006 at 13:06:43

Yes, there is no proof that graviton exists, but many researches
try to do it. If we are able to state that there is no graviton in such a sens as we understand the nature, i.d. the gravitational wave is not quantified in the way as e.g. Steven Weinberg used in his paper (Phys. Rev. 134, B882 (1964)) that we have to look for completely new concepts of understanding of quantization because as we think now all interactions are quantified and have their own carriers (e.g. EM interaction - photon, strong - gluon, weak-EM, photon, W+_, Z0). Thus, we think once the gravitational wave is a gravitational field so it has to be quantified, too. There are, of course, diiferent type o views how to do it, but all of them (as far as I know) has predicted that graviton has spin 2. Thus, the conclusion is as yours: the experiment is worth of doing it with no respect to the result of it.

Author comment added 16th March, 2010 at 09:54:24

There is a mistake in the formula for the number of detected gravitons, the correct one should be as follows:

N_{g}= \pi p_{g} N_{d} N_{flux} \lambda^{2},

where p_{g} means the probability of graviton interaction with the matter and the rest quantities as in the text.

The next remark: even if the probability of graviton interaction with the matter if of $10^{-70}$ - $10^{-60}$ there is still a huge chance of detecting them by the means of DETGRAW. During last years another arose another way of DETEGRAW construction -optical cristals that can have the temperature of $10^{-12}$K and the number of electrons of $10^{15}$. Thus, a black hole collapse could be very easy detected or the radiation comming from very fast revolving binary stars around 0,01 - 0,1 Hz that are pretty common.

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