The theory of relativity is right

Chapter 2
GENERAL THEORY OF RELATIVITY
- PHYSICS OF GRAVITY
2.1. Acceleration and gravity from the point of view of special theory of relativity
2.2. Versatility - a basic property and the key to understanding the nature of gravity
2.3. The local principle of equivalence and its consequences
2.4. Physical laws in curved spacetime
2.5. Einstein's equations of the gravitational field
2.6. Deviation and focus of geodesics
2.7. Gravitational waves 2.8.
Specific properties of gravitational energy
2.9. Geometrodynamic system of units
2.10. Experimental verification of the theory of relativity and gravity

2.10. Experimental verification of the theory of relativity and gravity

The excellent structure of special (STR) and general theory of relativity (GTR) fits very well into the current scientific picture of the world, based on increasingly perfect, more objective and credible knowledge of special natural sciences *).
*) On the other hand, the difficulty of understanding the theory of relativity and reconciling some of its principles and conclusions with intuitive experiences from everyday life - with "common sense" - has led and still leads some people to reject it. For non-physicists, these efforts result in false speculation and often bizarre, unfounded and erroneous assumptions. In the field of physics, several alternative theories of gravity were developed, which under commonly available conditions give practically the same results as the general theory of relativity, while under extreme conditions their predictions differ. Testing and selection of various alternative theories is one of the goals of experimental verification in the theory of relativity.
A. Einstein, captivated by the thought perfection of special and especially general theory of relativity, even expressed the sense that if the theory of relativity did not prove to be correct, then "God has made a mistake somewhere in the construction of the Universe!"...

However, physics is an objective and skeptical natural science that accepts its theories as correct only when all their consequences are experimentally verified ("the theory is gray, the green tree of life"). In a number of places in this book, the relevant theoretical concepts and findings are supplemented by mentions of their possible experimental verification. We will not repeat this in more detail here, we will only provide references to the relevant chapters and passages. At this point we will try a brief systematic overview and classification of experimental methods in the theory of relativity from a methodological point of view. We will also mention some experiments that are not mentioned in the basic text of the book.
In terms of the type of studied phenomena in relation to the theory, experimental verification of GTR can be divided into two categories :

• Verification of the basic principles of GTR
  This is mainly a verification of the principle of equivalence, the exact equality of inertia and gravity mass of various origins and under various circumstances. Some experiments of this kind have been discussed in §2.2 "Universality - the basic property and key to understanding the nature of gravity", the passage "Principle of Equivalence", including a reference to the latest STEP (Satellite Test Equivalence Principle) project .
    
• Verification of GTR consequences
  This includes a wide range of phenomena from anomalies in the trajectories of bodies in gravitational fields, bending of light beams in the gravitational field and related gravitational lenses, spectral shifts, entrainment of space-time metrics by angular momentum of rotating bodies, through final stages of star evolution, gravitational collapse, to exotic phenomena in extremely strong gravitational fields of black holes or the effects of relativistic cosmology.

From a methodological point of view , experimental verification of the theory of relativity can be performed in basically two ways :

• 1. Study of phenomena under extreme conditions ,
  where relativistic effects manifest themselves in a significant or even dominant way. These extreme conditions can be :
  a) High velocities and accelerations
  Under terrestrial laboratory conditions, these are experiments on large accelerators (see §1.5 "Elementary particles", section "Charged particle accelerators", in book "Nuclear physics and ionizing radiation physics"), where the particles accelerate to ultrarelativistic velocities and high energies, after which their collisions and interactions result in extremely high accelerations, field concentrations and the production of other particles. The main goal of these experiments is the opposite "pole" of physics - subnuclear physics and the study of elementary particles, but with increasing energy of particles can be gradually achieved results important for quantum theory of gravity and unitary field theory (cf. §B.6 "Unification of fundamental interactions Supergravity. Superstrings.") .
  b) Strong gravitational field
  In terrestrial physics laboratory or in the nearby universe, not sufficiently strong (relativistic) gravitational fields available. That we depend here on astronomical observations of the distant universe - objects at least hundreds or thousands of light-years away (compact objects such as neutron stars and black holes and their binary systems), but often millions to billions of light-years (active nuclei of galaxies, quasars, cosmological effects). It is therefore an astrophysical testing of the general theory of relativity.
    
• 2. Accurate measurements of subtle phenomena under normal (commonly non-relativistic) conditions ,
  where relativistic effects are only very slight. To prove and quantify them, it is necessary to achieve extreme accuracy and sensitivity of measuring technology mainly in two directions :
  - measuring time and frequency changes
  - measuring position - distances, angles
  This high accuracy and sensitivity is achieved using physical-electronic methods (especially interferometric) and recently also the subsequent computer processing involving a number of analytical and corrective procedures (eg deconvolution analysis). Very small relativistic effects can then be demonstrated and measured in laboratory conditions on Earth, or on space probes in near space, especially on satellites in orbit around the Earth.

Experimental verification of the special theory of relativity
we will not discuss here - STR is already so perfectly verified that it has become almost an "engineering science" used as a necessary basis in the technical design of eg particle accelerators. Each circulation of a particle (as well as its synchronized passage between electrodes or resonant cavities in a linear accelerator) in such a precisely constructed accelerator "announces" the correctness of the special theory of relativity. Many experiments testing GTR at the same time, as a "by-product", also verify the regularities of STR....

Experimental verification of the general theory of relativity
has taken place almost since the very beginnings of GTR and continues to this day. The so-called classical GTR tests played a very important role in the formation and physical acceptance of the general theory of relativity :

• Turning of Mercury's perihelion
  In a strong central gravitational field, the orbit of a body is not a precise and unchanging ellipse (as it would in Newton-Kepler celestial mechanics), but an "ellipse" whose axis, the perihelion, gradually twists. This phenomenon explains the previously known (since 1882) anomalous displacement of the perihelion of the planet Mercury (which orbits closest to the Sun in orbit with considerable eccentricity), which is 43''/100 years. A more detailed analysis is in §4.3 "Schwarzschild's static black holes", passage "Precession of an elliptical orbit in the Schwarzschild field".
• Bending of light rays near the Sun
  According to GTR, a light beam passing around massive gravitational bodies is curved. This phenomenon was observed in 1919 during an expedition led by A.S.Eddington for a solar eclipse (when sunlight does not interfere with star observation) in West Africa, where the measured angular deviation of the positions of stars near the Sun's surface was coincident with the GTR forecast. A more detailed analysis of this phenomenon is in §4.3 "Schwarzschild's static black holes", passage "Deflection of particles and light in the Schwarzschild field".
• Gravitational frequency shift
  In the gravitational field according to GTR, clocks placed at different distances from the gravitational body (in places with different gravitational potential) go at different speeds - according to relation (2.36) in §2.4. Photons moving away from a gravitational body reduce their frequency - they show a red spectral shift, photons approaching this body show a blue spectral shift. This phenomenon was first measured in 1960 in the water tower of Harvard University, where R.V.Pound and G.A.Rebka used the Mösbauer effect of resonance absorption of g photons with an energy of 14.4 keV from the radioactive isotope ⁵⁷Fe. For a height difference of 22.6 m, they measured a change in frequency of 2.5x10^-15. The theoretical derivation of the gravitational frequency shift is in §2.4 "Physical laws in curved spacetime", passage "Gravitational frequency shift", relation (2.41), where there is a more detailed description of the Pound-Rebka experiment, as well as newer experiments of this focus.
• Hubble's redshift of galaxy spectra
  By measuring the spectra of 35 galaxies in 1929, E.Hubble found that the light of distant galaxies is systematically shifted to the red part of the spectrum - in connection with the Doppler effect, distant galaxies move away from us the faster they are. It was the first experimental demonstration of the expansion of the universe in accordance with a relativistic cosmological model. The theoretical analysis of cosmological models is in Chapter 5 "Relativistic Cosmology", the dynamics of Hubble's expansion is discussed in §5.1 "Basic principles and principles of cosmology" and §5.3 "Fridman's dynamic models of the universe".
• Weber's attempts to detect gravitational waves
  using two massive aluminum cylinders (diameter 66cm, length 153cm, weight 1.4 tons, resonant frequency 1660Hz) in a coincidence at a distance of 1000km in 1966-69 were ultimately unsuccessful (the only consensus recorded in 1969 was already did not repeat) due to their lack of sensitivity. These experiments are discussed in more detail in §2.7 "Gravitational waves". Although no success was was achieved in these first experiments, experiences has stimulated the development of newer generations of gravitational wave detectors (especially interferometric systems) with significantly higher sensitivity, see below.

Successful "classical" GTR tests have led to its practically universal acceptance both in the professional physical public and among educated and thoughtful people of various professions and specializations. The newer tests and observations sketched below even more certainly show the role of GTR for the analysis of fundamental physical phenomena both in the laboratory and, above all, for the understanding of colossal astrophysical phenomena. These newer tests include in particular :

• Lense-Thirring phenomenon
  In §2.5 "Einstein's equations of the gravitational field" and §4.4 "Rotating and electrically charged Kerr-Newman black holes" is derived and analyzed the phenomenon of entrainment of bodies (draging of local inertial systems) by a rotating gravitational field in the direction of source rotation (this phenomenon was predicted by J.Lense and H.Thirring already in 1918). This effect is undoubtedly strongly applied in accretion disks around black holes. However, this subtle effect can also be measured in the Earth's gravitational field by highly sensitive experimental methods (§2.5, passage "Rotating Gravity"). A special Gravity Probe B satellite was launched, which measured this phenomenon by accurately monitoring changes in the direction of the rotary axis of installed gyroscopes - due to entrainment, the rotary axis of the gyroscope should show a slight additional precession (in addition to more pronounced geodetic effect in orbital curvature). These subtle "gravidynamic" effects of GTR were also detected by measuring the orbit of the LAGEOS geodetic satellite and observing the dynamics of the orbits of the binary pulsars (especially PSR J0737+3039 and PSR J1757-1854). The results of these experiments are described in §2.5, passage "Rotating Gravity".
• Influence of time by gravitational field
  After the classic Pound-Rebka experiment with gravitational spectral shift and newer experiments with MASER clock on space probes (see "Gravitational frequency shift"), is also planned direct verification of the so-called Shapiro effect - the time delay of signals passing through the gravitational field (for this phenomenon was first pointed out by I.Shapiro). A light beam, or more generally any electromagnetic wave passing near a high-gravity body, will move more slowly and thus reach the observer later than a beam emitted from the same distance, but not passing through a stronger gravitational field. Testing of this phenomenon is performed by sending radar signals from the Earth and receiving them after reflection from the surface of planets and probes, while comparing the situation when it passes close to or far from the Sun.
  The measurement was performed in 2003 using the satellite Cassini flying to Saturn, phenomenon was confirmed with an accuracy of 10^-5 .
• Gravitational lenses
  The effect of a gravitational lens (predicted by A.Einstein in 1936) is caused by the curvature of light rays passing around very massive gravitational bodies - in a similar way as light rays are curved by passing through a glass lens in optics (gravitational-optical phenomena in relativistic electrodynamics are derived in §2.4 "Physical laws in curved spacetime", passage "Gravitational electrodynamics and optics", equations (2.29) - (2.34) ). If the observed object, the gravitational body and the observer are exactly on one line, an image of a distant galaxy in the shape of the so-called Einstein ring is formed, with a slight misalignment, an Einstein arc (incomplete ring) is observed, with a slightly larger misalignment, we observe a double or multiple image of a distant galaxy or quasar. The first gravitational lens was observed by Walsh, Carswell and Weynmann in 1979 as a double object QSO 0957+561, it was a double image of a quasar with z=1.4. In 1987, large arcs of light were observed, focused by the effect of a gravitational lens behind a massive cluster of galaxies. In 1988, the first Einstein ring MG 1131+456 was observed in the radio field. A more detailed analysis of the gravitational lensing effect is in §4.3 "Schwarzschild's static black holes", passage "Gravitational lenses. Optics of black holes.", including pictures.
  Since the 1990s, a number of so-called gravitational "microlenses" have been detected, which are manifested by a transient increase in brightness of a distant star as it passes behind a closer massive object (light intensity is amplified by the focusing effect of a gravitational microlens). This phenomenon can also be used to detect extrasolar planets.
• Final stages of stellar evolution - gravitational collapse, compact objects
  The relativistic theory of the final stages of evolution of massive stars, which eventually results in gravitational collapse and transformation of the star into a compact gravitationally collapsed body - neutron star or black hole, explains many astronomically observed objects and phenomena in the distant of space. The very existence of these objects is a strong argument for the adequacy of the general theory of relativity; moreover, their astronomically observed properties agree well with the GTR deductions. These astrophysical aspects of GTR are discussed in more detail in Chapter 4 "Black Holes", especially §4.1 "The role of gravity in the formation and evolution of stars" (passage"Compact objects"), §4.2 "The final stages of stellar evolution. Gravitational collapse" and §4.8 "Astrophysical significance of black holes".
• Binary pulsars
  In systems of compact objects orbiting each other (around a common center of gravity) in close proximity, the effects of the general theory of relativity manifest themselves very markedly when moving in a strong gravitational field. In 1974, a double pulsar PSR 1913+16 was discovered, which has such suitable properties for monitoring several relativistic effects that it is often referred to as the "astrophysical relativistic laboratory PSR 1913+16".
  The basic parameters of this binary object are: average distance of components 700 000 km, weight of the first component 1.44 M_¤ , weight of the second component 1.39 M_¤ , circulating period 7h 45min, pulsar period 59 ms.
  Several relativistic effects were measured for this object in accordance with GTR: periastra turning by 4° per year, red gravitational shift, relativistic Doppler effect, dilation of time during circulation, bending of light rays, shortening of period (by 76 ms/year) due to radiation gravitational waves. This last effect is especially significant - it is an indirect but very strong evidence of the existence of gravitational waves. The system is described in more detail in §2.7 "Gravitational waves", passage "Indirect evidence of gravitational waves".
• Gravitational wave detection
  The existence of gravitational waves is a key prediction of GTR (similarly to electromagnetic waves were a fundamental prediction of Maxwell's electrodynamics) - see §2.7 "Gravitational waves". After the unsuccessful Weber experiments, significantly more sensitive systems of next generations for the detection of gravitational waves were designed and gradually constructed - detectors monitoring subtle changes in the distances of test specimens using interferometric methods - see Fig.2.12c in the mentioned §2.7, passage "Detection of gravitational waves". New systems for the detection of gravitational waves were constructed or planned - LIGO, VIRGO, TAMA, LISA ... The high sensitivity of these detection systems, especially LIGO, finally enabled the direct detection of gravitational waves - §2.7, passage "Direct detection of gravitational waves".
• Testing quantum gravitational effects ?? - topological "foam" of spacetime, extradimension - ??
  The current experimental technique is not entirely sufficient for direct experimental testing of most of the effects predicted by quantum theories of gravity. At a time when we are just begining to detect even "classical" gravitational waves, to detect gravitons there is no hope for the foreseeable future. However, there is a phenomenon by which it would be possible to test quantum-gravitational effects using the technique of the near future, in co-production with some astrophysical phenomena in outer space. During "catastrophic" phenomena around supernovae and black holes, massive electromagnetic radiation of various wavelengths is emitted, from radio waves, through visible light to flashes of very hard gamma radiation. Photons of extremely hard radiation g could have such short wavelengths that their motion could become "sensitive" to the subtle quantum fluctuations of the space-time metric through which it propagates - to the topological "foam" which, according to the quantum theory of gravity, should be formed all our space-time on Planck's microscales - see §B.4, especially the passage "Does high-energy g- radiation move slower than light?". During long movements over cosmological distances, time differences in the arrival of low-energy and high-energy radiation could be detectable. Another experimental possibility in the near future is to test the effect of otherwise compactificated extra-dimensions of spacetime on the interactions of high-energy particles accelerated on accelerators on the energies of many TeVs. Here, too, it would be possible in principle to detect phenomena "sensitive" to interactions with extra-dimensions ...
  Special g- telescopes have been designed for accurate registration and measurement of gamma-ray bursts from space (see "High-energy gamma cameras" in the monograph "Nuclear Physics and Physics of Ionizing Radiation"); the launch of the GLAST (Gamm-ray Large Area Space Telescope) satellite is being prepared for tracking very hard g-radiation. At the same time, experiments will be carried out on the LHC accelerator with 7 + 7 TeV proton energy in the opposing beams, where, in addition to searching for new particles (such as the Higgs boson), traces of the influence of microscopic extra-dimensions on high-energy particle interactions may be observed.

Einstein was right: GTR is a correct theory of gravity and spacetime !
In this way, we can conclude simply (and with a little exaggeration) that Einstein's general theory of relativity has successfully passed - and still passes - all previous and new experimental tests; its experimental verification is constantly being refined ...

2.9. Geometrodynamic units		3. Geometry and topology of spacetime

Vojtech Ullmann