1. Introduction

In the middle of the last century, while studying the laws of dislocation motion D. Kuhlmann-Wilsdorf had obtained an unexpected result, viz., the equations used to calculate stresses by moving dislocations contain relativistic corrections[1]. The relativistic corrections introduced by D. Kuhlmann-Wilsdorf differ from equations of Lorentz transform in the following. Lorentz relates the speed of a moving object to the light speed whereas D. Kuhlmann-Wilsdorf relates the travel rate of a dislocation to the propagation velocity of a sound wave in metal. The theoretical analysis reported elsewhere[2] shows physical equivalency of these equations. Hence, the Lorentz and D. Kuhlmann-Wilsdorf systems of equations have similar outcome. This means that dislocation streams possess effects predicted by the relativistic mechanics: increased mass of dislocations, their size variation, and retardation of local time in the dislocation region.

These effects become the more perceptible, the greater the speed ratio of dislocation and sound propagation. This variable (the expression «relativistic correction» will be used below) may be substantial in the processes of frictional interaction.

The speed of individual dislocations may be about 1 cm/min because dislocation streams become thermo stimulated by friction; the surface layers of the tribojoint lose their elastic properties dozens of times. This reduces many times the travel velocity of sound waves through the material area activated by friction[2, 3, 4]. The complex of internal microprocesses initiated by friction can make the value of the relativistic correction quite appreciable. This means that within the substance layer, adjacent to the friction surface, effects may happen unusual for the classical mechanics and tribology but associated with the theory of relativity. These effects can make an unexpected contribution in the microdynamics of friction processes.

A tribosurface is a very complicated system for constructing a theoretical model of any microprocesses. In the field of tribology, therefore, experiments are of main importance; on their basis, essential relations between frictional phenomena are being revealed. In physics, there are not many methods for experimental investigation of the effects predicted using the theory of relativity; almost all of them are for observations in astrophysics and nuclear physics. Among these the optical shift caused by the Doppler effect is probably the only method that could be used for studying the relativistic effects in friction[5].

The Doppler effect causes shifting of the emitted light spectrum to the short wave («blue») region when the light source and the observer are approaching, while the light of a retreating source, on the contrary, shifts to the long wave («red») part of the spectrum. Thanks to the «red shifting» the American astronomer E. Hubble had discovered the effect of recession of galaxies, which had served as a tentative proof of Universe′s expansion and corroborated the idea of the «Big Bang Theory» of the Universe. An approach or recession of light sources leads to changes in the time required for the observer to receive a signal: in the case of light source recession the signal is delayed; with approach, the signal arrives earlier. This situation may occur when owing to relativistic effects the local time of a physical system is delayed, which is identical to source receding that causes a long wave Doppler shift.

The aim of the work is to detect experimentally a Doppler shift in the spectrum of laser emission passing across the contact zone of a polymer-metal pair in friction. Experimental check of the hypothesis of relativistic proper time dilation in dynamic contact of solids.

The novelty of the work consists in revelation of fundamental regularities in friction nature in order to explain the effects of tribosystems self-organizing, as well as in finding new ways of friction entropy reduction. These phenomena which theory is based on non-equilibrium thermodynamic principles, have not direct experimental confirmation in tribology. Disclosing of friction relativistic mechanisms will enable go over to a new level in developing smart tribosystems and in methodology of control tribotechnical parameters and lifetime of tribosystems.

2. Material and Methods

As regards to the methodology and construction of the device for frictional temporal characteristics examination, this work has not analogies. Patents (Russian and international) were applied of measuring device construction [6].

The experiments were run using the tribometer Falex of test geometry shaft-bearing. The shaft was made from polytetrafluorethylene (PTFE). This allowed to use a small-sized electric motor, to reduce the vibration level resulting from friction. The bearing was made from a hardened tool steel containing a high quantity of chromium; the friction surface had roughness of 1.25 μm and hardness of 50 HRC. A groove was cut in the friction surface for the light guide. The groove depth was such that the light guide surface – though being extremely close to the frictional contact – did not touch the moving parts of the friction assembly.

A general view and diagram of the experimental device are shown in Figure 1. A laser (type TD-GP-04B, GL-303, power 200 mW, laser beam diameter 5 µm, laser beam intensity divergence angle 0,8 mrad, distance 100 m) is attached to one end of the light guide, the other end of it – running through the frictional contact – faces a glass prism; the latter refracts the incident laser beam. The refracted beam through a condenser falls onto an opaque screen having a measuring scale. The friction assembly, the optical table with the prism and the condenser with the screen are fixed on firm bases to prevent effects of mechanical vibrations on the image recordings. Before reaching the screen, the laser beam expands optically, which allows – by the laser spot boundaries – to control unaccounted small vibrations whose presence makes the boundaries smeared. The edge of a laser spot-image was sharp during the experiment, which allows to state with certainty the absence of mechanical vibrations that could distort the results of optical measurements.

Figure 1. Schematic diagram of the experimental device: 1 – friction machine; 2 – light guide; 3 – laser; 4 – prism; 5 – laser ray; 6 – condenser; 7 – screen; 8 – bases; 9 – photo-video camera

In order to determine the value of a measuring scale division, the position of the point was found where the red and blue monochromatic laser emissions refract; they correspond to the different boundaries of the visible spectrum (450–750 nm, respectively). The value of the division was found from the expression (750–450)/L, where L is the distance between the refraction points in millimetres.

The screen during calibration was set so as to obtain whole numbers of the division value. In the device described here 1 mm of the metric scale corresponded to 2 nm of the optical laser emission. The source of monochromatic light emission was a semiconductor laser of 0.2 W that could create a green light flux (wave length of 532 nm). The registered shift was stable fixed also on other wave lengths of monochromatic radiation which were used when measuring scale. This spectrum range was chosen for the following reasons. First of all it corresponded to quite large values of the refractive index n[7]; this guaranteed a high sensitivity of measurements, which could be obtained when using the choosen measuring scheme and refracting prism (material – quartz, refracting angle 60^o, refractive index 1,46). Secondly, the mid-position of the green colour in the spectral scale of the visible electromagnetic radiation enabled to follow spectral shift on the measuring scale both in the left and right directions from the original point of beam refraction.

The Doppler shift was recorded at a load of 10N and sliding speed of 0.5 m/s. One test lasted 6 hours. The load upon the shaft was created and measured by driving special dynamometric screws upon the bearing. The friction moment was shown by capacity variations in the electric motor of the testing machine. The light spot position on the screen was fixed with a digital camera Olympus which can take photos in the frame-by-frame mode maintaining given time intervals, as well as videotape recording.

The electronic images were transferred into a drawing program; the latter was used to measure with high precision (1/30 mm) the shifts of the light spot from its original position. The image was processed every hour; the test was repeated ten times. The relative error of measurements was less than 0.1%.

3. Results

A slight shift of the laser beam toward the «red zone» of the visible spectrum was observed after the initial 15 minutes of friction (e.g. Figure 2). The amount of long-wave shifting becomes stable during the first hour of friction and remains unchanged to the end of testing. After the friction was stopped, the laser spot returned to the starting point.

The computer estimation of the position of the light spot boundaries on the screen enabled to measure the amount of long-wave shift to the laser spot initiated by friction forces which was about 0.1-0.2 nm.

Figure 2. A shift in laser spot edge on the condenser screen scale: a – before testing; b – after 4.5 h-testing

4. Discussion

The experiments ensured recording of changes in the position of the refracted laser beam on the screen caused by frictional forces. According to the Cauchy law of dispersion (known in the field of optics) the refracted index of a substance depends on both the optical properties of the medium – in which the light becomes refracted – and the wave length of the electromagnetic radiation passing through this medium[7].

As the positions of the refracting prism and light guides were not changed in the course of the experiment, one may presume that the shift in the refracting laser beam results from a change in its wave length. This change in the spectral composition of the monochromatic laser emission took place under the influence of processes initiated by frictional forces acting between the polymeric shaft and steel bearing. This is unambiguously supported by disappearance of the spectrum shift after the tribometer was stopped.

The spectral composition of a laser emission may vary for two reasons: the Doppler shift and effects of nonlinear optics in the light-guide material caused by frictional forces. In substances of a nonlinear relation between the vectors of electric field and magnetic field of light flux, the wave length of the reflected and refracted beams is equal to the wave length of the original emission[8]. Should the linear relation between the electromagnetic field characteristics is broken then the electromagnetic radiation in such a medium propagates witch a change in its spectral composition caused by effects of nonlinear optics[9]. Nonlinear optical effects can result in a variation of the refraction degree of the beam and accordingly its optical shift. Similar effects include:

a) self-focusing or self-defocusing caused by deviation of the beam from its original course owing to non-uniform illumination in the beam cross-section;

b) generation of short harmonics of frequencies 2ω, 3ω…, where ω is the frequency of an incident monochromatic light wave;

c) light scattering on ultrasonic waves leading to changes in the emission spectral composition.

Nonlinear optical effects of self-focusing and generation of multiple harmonics may not be immediately taken into consideration when the reasons affecting an optical shift are discussed. These effects lead to different external developments – in comparison with the recorded ones – first of all to variations in the quantity and size of optical spots which do not correspond to the laser spot appearance in Figure 2. Besides, the nature and mechanisms of these nonlinear optical effects do not allow to connect them with the action of frictional forces upon a medium.

A light wave may scatter over ultrasonic oscillations because friction can excite surface elastic waves within the acoustic range of frequencies[10]. Acoustic waves are regions of compression and evacuation propagating in a medium and creating – in a light guide – optical non uniformities on which the initial light emission can scatter. The scattered light field, however, changes with time following the law: ~, where ω and Ω are the frequencies of light and elastic waves, respectively. This means that the scattered light spectrum consists of a doublet of lines, viz. satellites arranged symmetrically about the base line; they were termed Mandelshtam–Brillouin components. Such arrangement must probably lead to symmetrical «broadening» of the spot on the screen and not to a shift on the wave length scale. The scatter mechanisms of laser emission on a sonic wave generated by friction cannot lead to an optical shift similar to Figure 2. A most probable reason for the shift is the Doppler effect[7, 9].

In the theoretical physics there are two reasons which lead to Doppler shifts. One of them results from a change in the distance between the source and detector of a sound of a light signal. The other reason – as explained by the theory of relativity – relates the optical Doppler effect to the difference between extrinsic, or universal, time – which is usually associated with the observer’s time – and intrinsic (local) time of a physical system[11], i.e. in our case the area of friction contact. For a uniform and isotropic space the interval of the extrinsic (universal) time, during which a light wave propagates from the source to the receiver, is independent of the wave direction; as a result, the number of oscillations (frequency, wave length) happening in a unit of the universal time is the same in all points of the light beam. However, in the Lorentz transform different amounts of intrinsic time – which are the greater, the farther is the observer from the force field source – correspond to one and the same interval of the universal time. From the observer’s point of view a stated interval of the universal time contains a fewer number of oscillations of the electric vector of a light wave, which is identical to the long-wave spectral shift. That is, if in some force field a signal of wave length λ₁ travels from a point of potential U₁ to a point of potential U₂ the signal’s wave length reduces to , where c is the light speed. According to the forecasts made by A. Einstein a long-wave Doppler shift in a light beam directed vertically upwards to the Earth surface had been recorded. At a height of 10 m the magnitude of «red shift» Δλ/λ was 10^-15 to accuracy of 1%[12]. In the case of red shift initiated by frictional forces this magnitude is 10^-4, which is 10¹¹ times as much as the gravitational Doppler shift. Such a considerable difference can be explained by multiply large magnitudes of energy of electromagnetic fields in comparison with a weak gravitational interaction.

In line with the salient points of the theory of relativity, time delay is connected to distorted four dimensional space-time continuum whose size, in the end, is set by the potentials U₁ and U₂. The values of these potentials created by electromagnetic forces generated by friction must exceed dozens of billions of times the «gravitational» potentials U₁–U₂. This logical reasoning gives a clue to an explanation of large Doppler shifts.

The following expression is for calculating the Doppler effect:

(1)

where λ₂ is the wave length recorded by the receiver; λ₁ is the wave length emitted by the source, ; the sign «minus» corresponds to the moving off the source from the receiver; the sign «plus» to their approach; is the speed of source’s relative motion; с is the speed of wave propagation in a medium.

Assuming , we neglect higher degrees in parameter β when expanding the product in (1), and have the following:

(2)

By substituting experimental values of λ₁ and λ₂= λ₁+Δλ (where Δλ is the red shift) into Expression (2) we find the β – parameter value which for the given friction assembly and experimental regimes is: β = 2·10^-3. That is, in accord with the laws of the relativity theory each second of the intrinsic time in the friction zone «adds» up to 2 microseconds from the position of an outer receiver. It isn’t little in comparison with the microprocess scale and corresponds to the life span of a single friction contact, thus doubling the activation period of frictional forces acting upon the tribojoint materials. As a result, the friction contact zone is an area where, in addition to the classical physics laws, relativistic effects exist as being connected with changes in the local time, weight and energy gain in the interacting microparticles of the third element, and a growth reduction in entropy. The set of the effects mentioned enables us to look differently at the mechanisms of friction.

Friction is a powerful generator of electromagnetic fields[10] which parameters surpass by many orders of magnitude all gravitation constants. Electromagnetic wave in spite of zero photon mass, for all that possess some mass, otherwise the experimental fact of light deflection near stars and planets would not be observed. Einstein wrote: “… the body mass is a measure of energy contained in them …”[13]. Therefore potential electrical fields can work like gravitational ones distorting the metric of Minkowsky continuum and changing ipso facto the time flow. This corresponds to the modern representations in quantum physics.

5. Conclusions

1. The main conclusion resulting from the analysis of the research results is the recognition of a high probability that the effects predicted by the theory of relativity show themselves in friction and influence it. This conclusion is in agreement with those made elsewhere[14] by the Nobel Prize winner L.D. Landau («recording of relativistic effects… may be connected not only with the high speed (comparable with the light speed) of macroscopic motion…, equations undergo considerable changes also in the case if this speed is not high, but the speeds of microscopic motion of particles making up a body are high»), and in work[1] by D. Kuhlhmann-Wilsdorf who substantiated theoretically the relativistic mechanisms of motion for fast dislocations.

The experimentally revealed «Doppler red shift» in a laser beam traveling across a friction zone allows to classify tribojoints as physical relativistic objects.

2. Since the triborelativistic effects mentioned have been detected at mild load-and-speed operating regimes of a friction pair, one may presume that the manifestation of laws of the theory of relativity is rather general in nature.

3. In view of the said above, a triboassembly, in accord with the technology of Nobel Prize Winners A. Geim and K. Novoselov[15], may be related to the «new scientific paradigm, namely, relativistic physics of a solid body, where quantum relativistic events, a part of which haven’t been realized even in the high-energy physics, can now be investigated at common laboratory conditions». A friction assembly being a unique natural phenomenon (in the opinion of Russian tribologist, prof. D.N. Garkunov) is such an object which can be used to study most fundamental laws of Nature.

ACKNOWLEDGEMENTS

The authors would like to thank the LIK Co, Ltd for providing the funds for this work and Mrs. V. Moiseenko for the help in manuscript preparing.