1,2 Simple Explanation of Einstein's Relativity Theory

1,2 Simple Explanation of Einstein’s Relativity Theory

Adrian Bjornson (May 2009)

Measuring the Speed of Light

Einstein’s Relativity theory evolved to explain an enigma associated with measuring the
speed of light. To introduce this issue, let us first consider measuring the speed of sound. Light
travels at a speed of 300,000 kilometers per second (km/sec). This is about one million times
faster than the speed of sound, which is approximately 340 meters per second (m/sec).

Sound is a vibration of the air. It travels as a wave through the air, somewhat like the way
a wave travels across the surface of a still pond, when you throw a rock into it. If the air is
stationary (no wind), an instrument on the ground will measure the speed of sound as 340 m/sec.
If the wind speed is 20 m/sec (72 km/hour or 45 mph) the instrument will measure a speed of
sound of (340 + 20) m/sec, or 360 m/sec if the sound is travelling in the direction of the wind,
and it will measure a sound speed of (340 – 20) or 320 m/sec, if the sound is travelling in
opposition to the wind. Similarly, if the instrument is placed on a vehicle travelling at 20 m/sec,
and there is no wind, the instrument will measure a sound speed of (340 + 20) or 360 m/sec if the
vehicle is travelling opposite to the direction of the sound, and it will measure a sound speed of
(340 – 20) or 320 m/sec, if the vehicle is travelling in the direction of the sound wave.

It was originally assumed that light travels as a wave by vibrating a mysterious medium,
called the aether, just as sound travels by vibrating the air. In 1873 Maxwell presented his
famous electro-magnetic theory, which formed the mathematical basis for designing radio, radar,
and television systems, and all of our modern electronic devices. His theory showed that light is
a packet of oscillating electrical and magnetic fields, which does not require a medium to allow
propagation. But without a medium, what does one mean by the speed of light? Is light speed
measured relative to the transmitter, or relative to the receiver, or maybe relative to an aether
medium? Apparently because of this question, Maxwell included the aether concept in his
theory, even though an aether was not needed in the propagation of light, a radio wave, or any
other electromagnetic radiation.


In 1887, the famous Michelson-Morley experiment was performed to measure the
velocity of the aether “wind”. The speed of light from a star close to the plane of the earth’s orbit
was measured. Since the earth travels at 30 km/sec in its orbit around the sun, at one point of the
orbit the earth is travelling toward the star at 30 km/sec, and six months later it is travelling away
from the star at 30 km/sec. If the aether is stationary relative to the sun, the speed of light should
presumably be (300,000 + 30) or 300,030 km/sec when the earth is moving toward the star, and
(300,000 – 30) or 299,970 km/sec when the earth is moving away from the star. However, there
was absolutely no change in the speed of light measured at different points in the earth’s orbit.


Additional measurements confirmed the fact that the speed of light was always exactly
the same, regardless of whether it is measured relative to the transmitter or the receiver, even
though there was an appreciable velocity between the transmitter and the receiver. Scientists
were struggling to explain this enigma when Einstein published his Theory of Relativity in 1905.
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The Einstein Theory of Relativity


Einstein explained that when there is a relative velocity (V) between two observers, the
clock of the other observer appears to run more slowly by a contraction factor K given as
follows, where c is the speed of light:


K = √[1 - (V/c)2]
(contraction factor)

To each observer, the clock of the other observer appears to run at a rate equal to (K) times the
rate of one’s own clock. Also, a measuring rod moving with the other observer appears to be
compressed in length by this factor (K), when pointed in the direction of the relative velocity.
Finally, two clocks of the other observer, which are synchronized to the other observer, appear to
be out of synch by the amount [(V/c)(D/c)], measured relative to the other observer’s clock,
where D is distance between the clocks in the direction of the relative velocity. When these three
effects are applied, it can be shown that the two observers always measure the same value for the
speed of light, regardless of the velocity (V) between them.


The fundamental result of the Einstein relativity theory is that time is not absolute; it is
relative. Based on the relativity of time measurement, Einstein derived some revolutionary
concepts, including his famous equation: (E = Mc2). This equation showed that mass and energy
are equivalent, and that mass (M) can be converted into energy (E) according to this formula.
This formula explained the source of the enormous energy radiated by the sun. The sun converts
hydrogen into helium, which reduces the mass by 0.71 percent, and this loss of mass is converted
into 177,500 kilowatt-hours of energy per gram of hydrogen. Later, this formula was the
theoretical foundation for developing the atomic nuclear bomb during World War II.


Einstein concluded that the speed of light is constant, that electromagnetic radiation
cannot travel faster than light, and that a body with mass can never reach the speed of light. This
principle is readily demonstrated by accelerating an electron in an electric field. Until recently,
all television displays used cathode-ray tubes, which we call picture tubes. Inside the glass
envelope of a cathode ray tube is a vacuum, which allows electrons to flow freely. The heated
cathode boils off electrons, which are attracted to a wire grid that has a high positive voltage
relative to the cathode. The electric field between the cathode and the grid accelerates the
electrons to an appreciable velocity. A varying magnetic field deflects the electrons to different
points on the face of the picture tube to produce the television picture.


A similar principle can be applied to accelerate electrons to velocities approaching the
speed of light. Electrons in a vacuum chamber are boiled off from a cathode and accelerated in
an electric field. Then they are deflected magnetically around a circle and fed through the electric
field again. Each time an electron passes through the electric field, its energy is increased by the
same amount. Initially the increase of energy results in a corresponding increase in the electron
velocity. However, when the electron velocity gets close to the speed of light, the electron mass
begins to increase appreciably, and the velocity increases more slowly. The energy derived from
the electric field is converted into electron mass according to the Einstein formula (E = Mc2).
The electron becomes heavier and heavier as its velocity gets closer and closer to the speed of
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light. The electron velocity never reaches the speed of light, because this would require infinite
mass in the electron.


We normally consider spatial and time measurements to be independent. However,
Einstein showed that this assumption is only approximately valid, and does not hold with
reasonable accuracy when high velocities are involved. When observers travelling at different
velocities observe two events, a time interval between the events measured by one observer can
appear to be a spatial interval to the other observer. Spatial and time measurements are inter-
related, and so spatial and time measurements must be combined together to form a space-time
specification that is unique. With space having three dimensions and time having one dimension,
space-time has four dimensions. To achieve a unique specification, reality must be specified in
four dimensions.


I remember as a child thinking of the mysterious fourth dimension, and wondering which
direction in space could possibly represent a fourth dimension. I now realize that I was asking
the wrong question. To any observer, spatial and time dimensions are entirely separate concepts.
Each observer experiences three spatial dimensions and one time dimension. However, space and
time measurements must be combined to obtain a rigorous four-dimensional specification of
reality, so that the measurements of observers moving at different velocities can be compared.

Effects of Acceleration and Gravity



The relativity theory presented by Einstein in 1905 was based on the postulate that the
speed of light is constant. This clearly holds when observers are travelling at constant velocity,
but what happens when the velocity changes, when acceleration occurs? Einstein performed
approximate calculations, which proved that the speed of light is not constant under conditions of
acceleration. He also concluded that acceleration and gravity are basically the same, and that any
effect produced by acceleration must also occur in an equivalent gravitational field. He realized
that he had to incorporate acceleration and gravity into his relativity theory in order to achieve a
rigorous theory. He developed his basic relativity theory in a few months, but it would take
eleven hard years of research to generalize his relativity principle and thereby include the effects
of acceleration and gravity.


Let us examine an approximate calculation that Einstein performed to prove that
acceleration and gravity cause the speed of light to change. Figure A-1 shows two elevators:
elevator (b) is fixed on earth; elevator (a) is in space and is pulled upward with an acceleration
equal to the acceleration of gravity (g) on earth. Today we would assume that elevator (a) is
forced upward by a rocket with a one-G acceleration. Because the acceleration is one-G, a person
in elevator (a) would feel an acceleration force on his body equal to the weight force he would
feel when in the fixed elevator (b) on earth. Einstein proposed his Principle of Equivalence,
which postulates that physical experiments within the two elevators would produce exactly the
same results, and so the effects of acceleration and gravity are identical.


Suppose a light pulse is emitted from the floor of elevator (a) at point (1) and is received
at the ceiling at point (2). During the propagation time of the light, the velocity of the elevator
increases because the elevator is accelerating. Hence the upward velocity of the receiver at point
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(2) is greater than that of the emitter at point (1) as far as the light pulse is concerned. Point (2)
appears to be moving away from point (1), and so the light spectrum is shifted toward the red as
it moves from point (1) to point (2). (Astronomers call this a “redshift”.) Since the effects in
elevators (a) and (b) are the same, the gravitational field in elevator (b) must also produce a
spectral redshift as light propagates from the floor to the ceiling.


Acceleration g
(a)
(b)
(2)
(2)
h
(p)
h
(1)
(1)
Figure A-1: Elevator (a) is accelerating in free space; elevator (b) is
fixed on earth. Light travels from point (1) to point (2).



A light wave can be used to time a clock, which gives one tick for every period of the
light wave. When a light wave is shifted toward the red, its period increases, and so a clock
synchronized to the light wave must tick more slowly. Hence a clock at the ceiling of the
elevator runs more slowly than an identical clock on the floor. In other words, raising a clock in a
gravitational field causes the clock to tick more slowly. The fractional increase of the clock
period can be shown to be approximately equal to (gh/c2), where g is the acceleration of the
gravitational field, h is the height of the ceiling above the floor, and c is the speed of light.


Einstein performed another more complicated approximate analysis using his two
elevators, which showed that a gravitational field causes a spatial dimension to contract. The
fractional decrease of a spatial dimension between the floor and the ceiling of the elevator is also
approximately equal to (gh/c2).


The speed of light is equal to (D/T), where (D) is the distance traveled by the light and
(T) is the time for the light to travel. If the period (T) of a clock increases, the speed of light is
reduced; and if a spatial dimension (D) decreases, the speed of light is also reduced. Hence both
effects contribute to a reduction of the speed of light. The relative reduction of the speed of light
is approximately equal to the sum of these effects, which is 2(gh/c2).


Thus, from his approximate analyses Einstein found that acceleration or gravity causes
the speed of light to decrease by a fractional amount approximately equal to 2(gh/c2). This
proved that the speed of light is not constant under conditions of acceleration or gravity, and so
Einstein knew that he must generalize his relativity theory. After Einstein published his
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generalized theory in 1916, which he called General Relativity, his basic relativity theory
published in 1905 was called Special Relativity.

Principles for Generalizing Relativity


To obtain a rigorous general theory of relativity, Einstein needed a radically different
mathematical foundation. He found this in an elaborate mathematical theory of curved space
published in 1901, which had been developed by the Italian mathematician Gregorio Ricci
(1853-1925), and was based on a mathematical principle presented in 1852 by the German
mathematician Bernhard Riemann (1826-1866). This mathematical theory is commonly called
“Riemannian geometry”, and is usually attributed only to Riemann. However, the Ricci theory is
actually a sophisticated mathematical theory that extends differential calculus to curved space.
Ricci called it “The Absolute Differential Calculus”. Although this mathematical theory is based
on Riemann’s principle, it is a highly extensive and rigorous expansion of that principle. For this
reason, it should be properly called the Ricci-Riemann calculus of curved space.


Gregorio Ricci was assisted in developing his theory by his pupil, Tullio Levi-Civita
(1873-1941). In 1923, Levi-Civita published in Italian an updated version of this mathematical
theory. An English translation is available as a Dover reprint. [5] I personally feel that it is a
disgrace that the enormous contributions of Ricci and Levi-Civita to General Relativity theory
have been largely ignored by the scientific community.

Einstein incorporated gravity (along with acceleration) into his theory by expressing it as
a curvature of space. The Ricci-Riemann calculus of curved space could handle multiple
dimensions, and so Einstein applied this mathematical theory in four dimensions to represent the
four-dimensional space-time requirements of relativity. Einstein used the effect of gravity to
establish the curvature of this four-dimensional Ricci-Riemann calculus of curved space.

We can illustrate a simple curved space by considering motion across the spherical
surface of the earth. In flat Euclidean space, a straight line is the shortest distance between two
points. In curved space, the shortest distance between two points is called a geodesic. On the
curved surface of the earth, the shortest distance between two points is a great-circle route, which
represents a geodesic. A great circle route is constructed by passing a plane through the center of
the earth and the two points. The geodesic great-circle route is the intersection of this plane with
the spherical surface of the earth.


For example, Boston, Massachusetts and Rome, Italy are at nearly the same latitude. One
might think that an airplane from Boston to Rome would fly directly east, but that is the long
way. Along the shorter great-circle geodesic route, the airplane starts flying nearly north-east
from Boston, and ends the flight by flying nearly south-east to reach Rome.


Let us consider the effect of gravity on the earth as it rotates around the sun. According to
Newton’s law of motion, a body moves at constant velocity along a straight line, unless a force is
applied to it. In terms of Newton’s theory, the earth moves in a curved orbit around the sun
because the gravitational force from the sun keeps the earth from flying off into space along a
straight line. But, there is no gravitational force in the Einstein gravitational theory. In the
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Einstein theory, the earth travels along a geodesic path in curved space, which is equivalent to a
straight line in flat Euclidean space, and is the shortest distance between two points. The
gravitational field of the sun curves the space around it, and the earth moves within this curved
space along a geodesic path. The Ricci-Riemann calculus of curved space has a general equation,
called the geodesic equation, which allow one to calculate the geodesic path that is followed by
the earth as it orbits around the sun. The geodesic equation is given by this website in the
Addendum document 5,4 Application of Geodesic Equation to the Yilmaz Theory.


The curvature of space produced by gravity is a four-dimensional space-time effect.
Consequently, the geodesic path followed by a body in the gravitational field of the sun depends
on time as well as on spatial location. Consider a planet at a particular location in the
gravitational field of the sun. The geodesic path that the planet follows depends not only on the
position of the planet but also on the rate-of-change of position relative to time, which is the
velocity of the planet.

Mathematical Calculations of Relativity


Metric Tensor. The Ricci-Riemann calculus of curved space is expressed in terms of
tensors. A simple physical description of a tensor is shown in Appendix A. In the four-
dimensional Einstein application, the tensors are 4x4 arrays, and so have 16 separate elements.
The fundamental tensor of the Ricci-Riemann calculus is the metric tensor, which specifies the
measurement properties of curved space. The metric tensor is denoted gab, where the indices a, b
can be 0, 1, 2, or 3. The index 0 represents the time dimension, and 1, 2, 3 represent the three
spatial dimensions, which are often denoted x, y, and z. The elements of this tensor are:




 g00 g01 g02 g03 

 g10 g11 g12 g13 

 g20 g21 g22 g23 



 g30 g31 g32 g33 


The metric tensor is symmetric, meaning that g12 = g21, g23 = g32, etc. Because of this
symmetry, six of the elements are redundant, and the tensor has only 10 independent elements.
The elements along the diagonal of the array (g00, g11, g22, g33) are called the diagonal elements,
and the others are called non-diagonal. If all of the non-diagonal elements are zero, the tensor is
called diagonal.


If the metric tensor is not diagonal, the equations of General Relativity are extremely
complicated. They literally have millions of terms, and so cannot be solved analytically.
Consequently, Einstein could apply his theory only to very simple physical models that yielded
diagonal metric tensors. Einstein died in 1955. It was not until the mid 1960’s, a decade after
Einstein’s death, when powerful computers became readily available, that General Relativity
could be applied to more complicated physical models that yielded non-diagonal metric tensors.
Hence, if we restrict ourselves to physical models that Einstein could study, there are only four
elements of the metric tensor that we need consider: the diagonal elements g00, g11, g22, and g33.
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Often the three spatial elements, g11, g22, g33, are equal, and we need to consider only two
separate elements, the time element g00 and the spatial element g11.


From the values of the metric tensor, one can directly calculate many relativistic effects. The
metric equation, which is based on the metric tensor, is explained by this website in 1,7 Metric
Equation. The metric equation yields the following formulas that show how a gravitational field
changes the speed of light, a spatial dimension, and a clock period:


(cap/c) = √[-g00/g11 ]

(speed of light)



(3)


(∆xap/∆x) = 1/√[-g11 ]

(spatial dimension)



(4)


(∆Tap/∆T) = 1/√[g00]

(clock period)



(5)

The Greek symbol (∆) is called “delta” and is used to denote a difference. Symbols cap, ∆xap,
and ∆Tap denote the apparent values observed here on earth for the speed of light, a spatial
dimension, and a clock period that occur at a distant location. Symbols c, ∆x, and ∆T are the
corresponding true values that would be measured by an observer placed at the distant location.
(Einstein used the term coordinate value instead of apparent value, and the term proper value
instead of true value.) These equations assume that the metric tensor is diagonal and that the
three spatial elements g11, g22, g33 are equal. The equations show that, when the elements of the
metric tensor are known, one can readily calculate some important relativistic effects of gravity.


The tensor gab is called the covariant form of the metric tensor. There is another form
ab
denoted g that is called the contravariant form of the metric tensor. The product of the
covariant and contravariant metric tensors is a unit matrix. If the covariant metric tensor is
diagonal, the contravariant form is also diagonal, and its diagonal elements are the reciprocals of
the corresponding covariant elements (i.e., g00 = 1/g00, g11 = 1/g11, etc.)


Forms of Other Tensors. Other tensors of the Einstein theory have three forms, called
covariant, contravariant, and mixed. For a general covariant tensor denoted Dab, the
ab
b
contravariant form is denoted D , and the mixed form is denoted Da . The Ricci-Riemann
calculus of curved space has general formulas (using elements of the metric tensor) for
computing one of these forms from another. (These formulas are given in Believe [1], Appendix
b
A.) The metric tensor also has a mixed form denoted ga , but is mathematically trivial.

b

The Ricci Curvature Tensor Ra . The Ricci tensor describes the curvature of space. If
there is no gravitational field or acceleration in a region of space, that region has no curvature,
and all elements of the Ricci tensor in that region are zero. The Ricci tensor is usually applied in
b
its mixed form Ra . The Ricci-Riemann calculus of curved space provides general equations for
calculating the covariant Ricci tensor Rab from the metric tensor, which are given in Believe [1],
b
Appendix A. The covariant Ricci tensor Rab is then converted to its mixed form Ra by means of
formulas that use the metric tensor.

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b

The Einstein Tensor Ga . In General Relativity, the curvature of space is usually
b
expressed in terms of the Einstein tensor Ga , which is a modification of the Ricci tensor. The
b
b
Einstein tensor is defined by (Ga = Ra ) for the non-diagonal elements of the tensor, and by
b
b
(Ga = Ra – ½ R) for diagonal elements, where R is the sum of the diagonal elements of the
b
mixed Ricci tensor Ra .


The reason for converting from the Ricci tensor to the Einstein tensor is that the
covariant derivative of the Einstein tensor is zero, whereas that of the Ricci tensor is not. The
covariant derivative is explained in Believe [1], Appendix J. The covariant derivative of a vector
or tensor describes the true change of a vector or tensor in curved space. For example, consider a
vertically pointing vector located at a particular point on the earth. Assume that a second vector
is kept parallel to the first vector, while being moved to a different location. Because the surface
of the earth is curved, the second vector will no longer be vertical. Its coordinates relative to the
curved surface of the earth have changed, but the absolute direction of the vector is the same.
When the covariant derivative of a vector is zero, the absolute direction of the vector does not
change when it is moved to a different location.


When the metric tensor is diagonal, the calculations discussed above can be greatly
simplified by applying general formulas that were derived by Prof. Herbert Dingle. These are
presented in Section B.5 of the Addendum document 5,B Einstein Tensor and Christoffel
b
Symbols for Diagonal Metric Tensor. The elements of the mixed Einstein tensor Ga are
expressed in terms of the elements of the covariant metric tensor gab. A look at these Dingle
formulas shows that the equations of General Relativity are extremely complicated, even when
the metric tensor is diagonal. If the metric tensor is not diagonal, the Ricci tensor Rab has
millions of terms, and so General Relativity equations cannot be solved analytically.

The Einstein Gravitational Field Equation


The equations for calculating the tensors described above are all specified by the Ricci-
Riemann calculus of curved space, expressed in four dimensions. They are not constrained by
General Relativity theory. To apply the Ricci-Riemann calculus to General Relativity, Einstein
postulated his gravitational field equation, which is

b
b

Ga = - 8π Ta

The tensor T b
a is called the energy-momentum tensor, which describes the characteristics of
energy and matter. As explained in Addendum document 5,C Calculation of Energy-Momentum
Tensor, Einstein specified a process for calculating the elements of the contravariant form of the
energy-momentum tensor Tab from the characteristics of energy and matter for any specified
physical model. If the metric tensor is known, one can readily convert the contravariant form Tab
of the energy-momentum tensor to the mixed form T b
b
a . The Einstein tensor Ga is an array of 16
elements denoted G 1
2
3
b
1 , G1 , G1 , etc, and the energy-momentum tensor Ta is a similar array of
elements denoted T 1
2
3
1 , T1 , T1 , etc. Hence the gravitational field equation represents 16 separate
equations of the form:

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G 1
1
2
2
3
3
1 = - 8π T1 , G1 = - 8π T1 , G1 = - 8π T1 , etc.

Solving General Relativity Equations Backward

ab

Let us consider the steps for calculating the contravariant energy-momentum tensor T
from the covariant metric tensor gab. The Ricci-Riemann calculus of curved space has formulas
ab
for making the following calculations. The elements of the contravariant metric tensor g are
calculated from those of the covariant metric tensor gab. The elements of the covariant Ricci
tensor Rab are computed from the elements of the covariant and contravariant metric tensors gab
ab
b
and g . The covariant Ricci tensor Rab is converted to its mixed form Ra using formulas that
b
employ the covariant and contravariant metric tensors. The mixed Einstein tensor Ga is
b
b
b
computed from the mixed Ricci tensor Ra by the following equations: (Ga = Ra ) for non-
b
b
diagonal elements, and (Ga = Ra – ½ R) for diagonal elements, where R is the sum of the
b
diagonal elements of the mixed Ricci tensor Ra .


The Einstein gravitational field equation represents a set of 16 equations of the form:
b
(G 2
2
1 = - 8πT1 ). From these equations, the elements of the mixed energy-momentum tensor Ta
b
are calculated from the elements of the mixed Einstein tensor Ga . Finally, the mixed energy-
b
ab
momentum tensor Ta is converted to its contravariant form T by means of formulas using the
covariant and contravariant metric tensors.


Addendum document 5,C Calculation of Energy-Momentum Tensor shows how the
contravariant energy-momentum tensor Tab is calculated from the characteristics of matter and
energy for the particular physical model that is being studied. After the elements of the
ab
contravariant metric tensor T are obtained, one must solve the equations discussed above in a
backward direction, to find the covariant metric tensor gab that yields the calculated
ab
contravariant energy-momentum tensor T . But how does one solve these extremely
complicated equations backward? It isn’t easy.


Einstein was unable to solve his equations exactly; he could only obtain approximate
solutions. The first exact solution was obtained by Karl Schwartzschild, who was cooperating
with Einstein. Schwartzschild applied the Einstein equations to a simple model of a star, which
can be our sun. In 1916, Einstein published the famous Schwartzschild analysis along with his
theory. Sadly, Schwartzschild contracted a rare disease and died before his analysis was
published. He was in the German army on the Russian front during World War I.


The Schwartzschild analysis is presented in the Addendum documents 5,2 Schwartzschild
and Isotropic Solutions of the Einstein Theory and 5,C Calculation of Energy-Momentum
Tensor. Schwartzschild modeled the star as an ideal fluid having a constant density of matter and
no viscosity. Document 5,C shows how Schwartzschild derived the energy-momentum tensor for
his model. The basic General Relativity equations yield the contravariant form of the energy-
ab
ab
b
momentum tensor T . To convert this contravariant tensor T to its mixed form Ta , one
normally needs to know the metric tensor, but the metric tensor is not known at this point. The
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b
brilliant Schwartzschild calculated the mixed form Ta in a skillful analysis without actually
knowing the metric tensor. From the mixed energy-momentum tensor, the gravitational field
b
equation was applied to calculate the mixed Einstein tensor Ga .


Schwartzschild assumed that the metric tensor was diagonal, and he specified general
expressions with unknown parameters to describe the four diagonal elements of the covariant
metric tensor gab. He applied the equations discussed above to compute equations for the
b
b
elements of the mixed Einstein tensor Ga . He compared these with the elements of Ga
computed from his energy-momentum tensor. This allowed him to calculate the unknown
parameters of his metric tensor expressions, thereby yielding his final metric tensor solution.

Verification of General Relativity


Based on the Schwartzschild solution, Einstein devised the following three tests to verify
his General Relativity theory.

(1) When a light ray passes close to the sun, it should be deflected by 1.8 arc seconds.

(2) A gravitational field causes a clock to run slower, and therefore causes the excited
elements on the surface of the sun to oscillate at lower frequency, thereby generating spectra
of longer wavelength. The gravitational field of our sun should cause the spectra of light
from the sun surface to shift toward the red end of the spectrum by 2.1 parts per million of
wavelength.

(3) The planet Mercury has a highly elliptical orbit. The axis of the Mercury orbit advances
(or rotates) by 1.39 arc seconds per orbit. Of this advance of the orbit axis, 1.29 arc seconds
can be explained with Newton's laws by considering the gravitational attraction of other
planets. A residual error of 0.10 arc second per orbit remained, which was explained by the
Einstein General theory of Relativity.

These three tests were implemented, and the results established the validity of the Einstein
General theory of Relativity.


These measurable effects of General Relativity are tiny: an advance of only 0.10 arc
second per orbit of Mercury; a 1.8 arc second deflection of a light beam passing close to the sun,
and a gravitational redshift of only 2.1 parts per million in light emitted from the sun. Hence one
might wonder why Einstein worked so hard to achieve his theory, and why General Relativity is
so highly regarded. The answer is that this generalization was essential to provide a solid
theoretical foundation for the relativity principle embodied in Special Relativity, which is the
original basic version of relativity published in 1905.


When the predictions of General Relativity were verified, Einstein achieved great fame.
After that time, Einstein did little with his General Relativity theory. Special Relativity is very
much easier to apply, and has wide applicability. During Einstein's lifetime, General Relativity,
with its very complicated tensor analyses, served primarily as a theoretical foundation for
justifying Special Relativity.
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