3. He developed the general theory of relativity, one of
the two pillars of modern physics.
He is best known in popular culture for his mass–
energy equivalence formula E = mc2 (which has been
said to be “ the world's most famous equation")
8. WHAT IS THE RELATIVITY THEORY ?
It is a theory developed by Albert Einstein which says that the way that anything except light
moves through time and space depends on the position and movement of someone who is
watching.
The term "theory of relativity" was based on the expression "relative theory" used in 1906. It
emphasized how the theory uses the principle of relativity.
There are really three theories of relativity:
• Relativity pre-Einstein (Galileo)
• Special Theory of Relativity (1905)
• General Theory of Relativity (1915)
9. Concepts introduced by the theories of relativity include:
Measurements of various quantities are relative to the velocities of
observers. In particular, space contracts and time dilates.
Spacetime: space and time should be considered together and in relation
to each other.
The speed of light is nonetheless invariant, the same for all observers.
10. Theory of special relativity and the
general relativity
The theory of relativity includes the theory of special relativity and the the
theory of general relativity, formulated by Albert Einstein in the early
twentieth century, which sought to solve the incompatibility between
Newtonian mechanics and electromagnetism.
The theory of special relativity, published in 1905, deals with the physics of
motion of bodies in the absence of gravitational forces, which were made
compatible Maxwell's equations of electromagnetism with a reformulation
of the laws of motion.
The theory of general relativity, published in 1915, is a theory of gravity
that replaces Newtonian gravity, although numerically coincides with it for
weak gravitational fields and "small" speeds. The general theory reduces to
the special theory in the absence of gravitational fields.
11. Main concepts
The basic assumption of the theory of relativity is that the location of
physical events, both in time and space are relative to the state of motion
of the observer: thus, the length of a moving object or the instant
something happens, unlike what happens in Newtonian mechanics, are not
absolute invariants, and different observers moving relative to each other
will differ about them.
12. Special relativity
The theory of special relativity, also called theory of relativity, was published by Albert
Einstein in 1905 and describes the physics of movement in the context of a flat
spacetime. This theory correctly describes the motion of bodies even at high speeds and
electromagnetic interactions and is used primarily to study inertial reference systems
(not applicable to astrophysical problems where the gravitational field plays an
important role).
Following publication of the article by Einstein's new theory of special relativity was
accepted in a few years by almost all physicists and mathematicians. In fact, Poincaré
and Lorentz had been very close to reaching the same result as Einstein. The final
geometric form of the theory is due to Hermann Minkowski, Einstein former teacher at
the Polytechnic of Zürich; coined the term "space-time" (Raumzeit) and gave the
apropiate mathematical form . Minkowski spacetime is a four-dimensional array in
which interlaced of an insoluble way the three spatial dimensions and time. In this
Minkowski spacetime, the motion of a particle is represented by its world line (Weltlinie),
a curve whose points are determined by four different variables: the three spatial
dimensions (x , y , z ) and time (t ). The new scheme of Minkowski forced to
reinterpret existing concepts metric before. The three-dimensional concept of point was
replaced by the event. The magnitude of distance is replaced by the scale interval.
13. General relativity
The General relativity was published by Einstein in 1915, and was presented as a lecture
at the Prussian Academy of Sciences on November 25th. The theory generalizes the
principle of relativity of Einstein for an arbitrary observer. This implies that the equations
of the theory should have a more general Lorentz covariance used in the theory of
special relativity covariance. In addition, the theory of general relativity suggests that the
geometry of spacetime is affected by the presence of matter, which is a relativistic
theory of the gravitational field. In fact the theory of general relativity predicts that
space-time is not flat in the presence of matter and the curvature of spacetime will be
perceived as a gravitational field.
Einstein said the purpose of the theory of general relativity to fully implement the
program of Ernst Mach in the relativization of all inertial effects, even adding so-called
cosmological constant to his equations of field for this purpose. The actual contact point
of the influence of Ernst Mach was clearly identified in 1918, when Einstein distinguishes
what he termed the principle of Mach (inertial effects arising from the interaction of
bodies) the principle of general relativity, which it is now interpreted as the principle of
covariance general.
14. Formalism of the theory of relativity:
1-Particles
In the theory of relativity a point particle is represented by a gamma where
gamma is (tau) par; is a differentiable curve, called world line of the particle, m
is a scalar that represents the rest mass. The tangent vector to this curve is a
temporary vector called cuadrivelocidad, the product of this vector by the rest
mass of the particle is precisely the cuadrimomento. This cuadrimomento is a
vector of four components, three of these components are called spatial and
represent the relativistic analog of linear momentum of classical mechanics,
the other component called temporal component represents the relativistic
generalization of kinetic energy. Moreover, given an arbitrary curved spacetime
can be defined along she called relativistic interval, obtained from the metric
tensor. Relativistic interval measured along the path of a particle is
proportional to the proper time interval or interval of time received by said
particle.
15. Formalism of the theory of relativity:
2- Fields
When considering continuous distributions of fields or any generalization
mass is needed for particle notion. A physical field has momentum and
energy distributed in space-time, the concept of cuadrimomento is
generalized by the so-called energy-momentum tensor representing the
distribution in space-time of both energy and momentum. In turn
depending on its nature a field can be represented by a scalar, a vector or
tensor. For example the electromagnetic field is represented by a totally
antisymmetric tensor of order 2-way or. If the variation of a field or a
distribution of matter in space is known and time then there are
procedures to build its energy-momentum tensor.
16. Formalism of the thery of relativity:
3-Physical quantities
In relativity, these physical quantities are represented by four-dimensional
vectors or by mathematical objects called tensors, that generalize the
vectors defined over a space of four dimensions. Mathematically these 4-
vectors and four-tensors are defined elements of the vector space tangent
spacetime (and tensioners are defined and constructed from tangent
bundle and cotangent variety representing spacetime).
physical quantities
Correspondence between E3 and M4:
Dimensional Euclidean space Minkowski space
Point Event
Interval Length
Speed Four times its velocity
Momentum Cuadriamomentum
17. The relativistic interval
The relativistic interval can be defined in any space-time, is this plane as
special, or curved as in general relativity relativity. However, for simplicity,
we first discuss the concept of interval for the case of a space-time plane.
The metric tensor of spacetime Minkowski plane is designated with the
letter scriptstyle {ij} eta_, and Galilean or inertial coordinates takes the
form
G i j=N i j = ( C2 0 0 0 )
( 0 -1 0 0 )
( 0 0 -1 0 )
( 0 0 0 -1)
18. Intervals
Intervals can be classified into three categories: spatial intervals (when ds ^ 2 is
negative), temporary (if ds ^ 2 is positive) and null (where / scriptstyle ds ^ 2 =
0). As the reader will have noticed, null intervals are those that correspond to
particles moving at the speed of light, as photons: The dl ^ distance 2 traveled
by the photon is equal to the speed (c) multiplied by the time scriptstyle dt
and therefore the interval scriptstyle ds = c ^ 2 ^ 2 ^ 2 dt - dl ^ 2 becomes
zero.
Null intervals can be represented as a cone of light, popularized by the
renowned book by Stephen Hawking, History of Time. Be an observer at the
origin, the absolute future (the events that will be perceived by the individual)
is displayed on the top of the vertical axis, the absolute past (the events that
have been perceived by the individual) in Part inferior, and this perceived by
the observer at point 0. the events that are outside the light cone not affect us,
and therefore is said of them that are located in areas of spacetime that have
no causal link with ours.
19. The ecuaion for the theory of relativity is :
E = Energy
m= Mass
c= speed of light (3 * 10 ^ 8 m / s, approximately)
Every body is resting energy as a function of its mass, this energy is calculated
as body mass times the speed of light squared.
The equivalence of mass and energy given by the expression of the theory of
relativity by Einstein.
It indicates that the mass carries a certain amount of power even at rest,
absent in classical mechanics concept, namely that the rest energy of a body is
the product of its mass and its conversion factor (speed of light square), or that
a certain amount of energy from an object at rest by its own mass unit is
equivalent to the speed of light squared.
