Newton saw space and time as a stage where events occur according to is laws of motion. This stage was inert and motionless. For Einstein, on the contrary, the stage is part of the game. Space and time were not an inert stage. According to him, it was dynamic, bending, and curving.
For Einstein space is like a trampoline net. If we deposit a heavy metallic sphere on this net, the sphere will sink in it. Now if we throw a ball on it, the ball will travel in a curved path around the sphere.
For Newton the ball travels round the sphere because the sphere exerts a mysterious force - gravity- on the ball. Einstein saw the path followed by the ball as a result of the deformation of the net with no force involved. If we replace the sphere deposited on the net and the ball by the sun and the earth, and the net by empty pace, Einstein said that the earth moves around the sun as it does, not because it is pulled by the sun's gravity, but because the sun deform the space around the earth forcing the earth to move in a circle. In relativity there is no force of gravity but the earth moves as it does because the sun deformed the space/time around it. In other words, gravity does not pull, space pushes. Gravity is not an independent force filing the universe, it is the effect o the bending of space/time.
At the beginning of the 20th century, astronomers believe that the universe was uniform and static. Initially Einstein agreed with it and assumed that the universe was filled uniformly with dust and tars. With these hypotheses, the solutions of the equations of the Relativity Theory showed that the universe would be dynamic. The dust and stars would collapse on themselves s gravity is always attractive.
To make the solutions of the equations conform to the view that the universe was static and uniform, Einstein had to introduce a new term in the equations, an !anti-gravity" factor known as "Cosmological Constant". In this way Einstein made the universe static and uniform, having balanced the contraction due to gravity by an outside force of dark energy.
Alexandr Friedmann solved the difficult equations of relativity assuming
that the universe is isotropic (the same in all directions) and homogeneous
(uniform everywhere). This is known as "Cosmological Principle".
Friedmann' solutions of the equations depend on 3 parameters:
i- H (Hubble Constant) that measures the rate o expansion of the universe.
ii- Omega, the average density of matter in the universe.
iii- lambda, the energy associated with empty space, or dark energy.
The density acts as a brake on the expansion of the universe as gravity
is always attractive. If we assume that omega is the density of the universe
divided by the so-called "Critical Density" (about 10 hydrogen
atoms per cubic metre):
i- If omega is less than 1, the universe will expand for ever.
ii- If omega is bigger than 1, the universe expansion will stop and it will
contract.
iii- If omega is equal to 1, the universe will still expand forever.
NB: There is also the possibility that after a big crunch, new big bang takes place. This is called "Oscillating Universe".
- Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be stationary and asymptotically flat. This means that the exterior solution must be given by the Schwarzschild metric.
- Cosmological constant or Lambda (?): It was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. Einstein abandoned the concept after the observation of the Hubble redshift indicated that the universe might not be stationary. However, the discovery of cosmic acceleration in the 1990s has renewed interest in a cosmological constant.
- Einstein field equations (EFE) or Einstein's equations: they are a set of ten equations in Einstein's theory of general relativity in which the fundamental force of gravitation is described as a curved spacetime caused by matter and energy. The EFE collectively form a tensor equation and equate the curvature of spacetime (as expressed using the Einstein tensor) with the energy and momentum within the spacetime (as expressed using the stress-energy tensor).The EFE are used to determine the curvature of spacetime resulting from the presence of mass and energy.
- Einstein-Rosen bridges or Schwarzschild wormholes: They are bridges between areas of space that can be modelled as vacuum solutions to the Einstein field equations by combining models of a black hole and a white hole. This solution was discovered by Albert Einstein and Nathan Rosen who first published the result in 1935. However, in 1962 John A. Wheeler and Robert W. Fuller showed that this type of wormhole is unstable, and that it will pinch off instantly as soon as it forms, preventing even light from making it through.
- General relativity (GR) or General theory of relativity (GTR) is the geometric theory of gravitation published by Albert Einstein in 1915/16. It unifies special relativity, Newton's law of universal gravitation, and the insight that gravitational acceleration can be described by the curvature of space and time, this latter being produced by the mass-energy and momentum content of the matter in space-time. General relativity is distinguished from other metric theories of gravitation by its use of the Einstein field equations to relate space-time content and space-time curvature. General relativity is currently the most successful gravitational theory, being almost universally accepted and well-supported by observations. General relativity's first success was in explaining the anomalous perihelion precession of Mercury. Other observations and experiments include gravitational time dilation, the gravitational redshift of light, signal delay, gravitational radiation and the expansion of the universe. General relativity also predicted the existence of black holes.
- Lorentz-Fitzgerald contraction or Length contraction: according to the
special theory of relativity it is the physical phenomenon of a decrease
in length detected by an observer in objects that travel at any non-zero
velocity relative to that observer. This contraction (more formally called
Lorentz contraction or Lorentz-Fitzgerald contraction) only becomes noticeable
at a substantial fraction of the speed of light; and the contraction is
only in the direction parallel to the direction in which the observed body
is travelling. This effect is negligible at everyday speeds, and become
important when the speed is at least 10% of the speed of light. When the
velocity approaches the speed of light, the effect becomes dominant, as
we can see from the formula:
Where L is the proper length (the length of the object in its rest frame),
L' is the length observed by an observer in relative motion with the object,
is the relative velocity between the observer and the moving object,
is the speed of light, and ? is the Lorentz factor.
An observer at rest viewing an object travelling at the speed of light sees
its length in the direction of motion as zero. As a result objects with
mass cannot travel at the speed of light.
- Malament-Hogarth (M-H) spacetime: It is a relativistic spacetime that possesses the following property: there exists a worldline ? and an event p such that all events along ? are a finite interval in the past of p, but the proper time along ? is infinite. The event p is known as an M-H event. The significance of M-H spacetime is that they allow for the implementation of certain non-Turing computable tasks (hypercomputation). The idea is for an observer at some event in p's past to set a computer (Turing machine) to work on some task and then have the Turing machine travel on ?, computing for all eternity. Since ? lies in p's past, the Turing machine can signal (a solution) to p at any stage of this never-ending task. Meanwhile, the observer takes a quick trip (finite proper time) through spacetime to p, to pick up the solution. The set-up can be used to decide the halting problem, which cannot be decided by an ordinary Turing machine. All the observer needs to do is to prime the Turing machine to signal to p if and only if the Turing machine halts. The Kerr metric, which describes empty spacetime around a rotating black hole, possesses these features: a computer can orbit the black hole indefinitely, while an observer falling into the black hole experiences an M-H event as they cross the inner event horizon.
- Minkowski diagram: It provides an illustration of the properties of space and time in the special theory of relativity. It allows a quantitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations. The Minkowski diagram is a space-time diagram with usually only one space dimension. It is a superposition of the coordinate systems for two observers moving relative to each other with constant velocity. Its main purpose is to allow for the space and time coordinates x and t used by one observer to read off immediately the corresponding x' and t' used by the other and vice versa. The shape of the diagram follows immediately and without any calculation from the postulates of special relativity, and demonstrates the close relationship between space and time discovered with the theory of relativity.
- Minkowski space (or Minkowski spacetime): It is the mathematical setting in which Einstein's theory of special relativity is formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime. In theoretical physics, Minkowski space is often compared to Euclidean space. While a Euclidean space has only spacelike dimensions, a Minkowski space has also one timelike dimension. Therefore the symmetry group of a Euclidean space is the Euclidean group and for a Minkowski space it is the Poincaré group.
- Schwarzschild wormholes or Einstein-Rosen bridges: They are Lorentzian wormholes or bridges between areas of space that can be modelled as vacuum solutions to the Einstein field equations by combining models of a black hole and a white hole. It was later shown that this type of wormhole is unstable, and that it will pinch off instantly as soon as it forms, preventing even light from making it through. Before the stability problems of Schwarzschild wormholes were apparent, it was proposed that quasars were white holes forming the ends of wormholes of this type. While Schwarzschild wormholes are not traversable, their existence inspired Kip Thorne to imagine traversable wormholes created by holding the 'throat' of a Schwarzschild wormhole open with exotic matter (material that has negative mass/energy).
- Special relativity (SR) (aka the special theory of relativity (STR)) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity - that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames) - from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. In addition, special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source. This theory has a wide range of counter-intuitive consequences, all of which have been experimentally verified. Special relativity overthrows Newtonian notions of absolute space and time by stating that time and space are perceived differently by observers in different states of motion. It yields the equivalence of matter and energy, as expressed in the mass-energy equivalence formula E = mc2, where c is the speed of light in a vacuum. The predictions of special relativity agree well with Newtonian mechanics in experiments in which all velocities are small compared to the speed of light. The theory is termed "special" because it applies the principle of relativity only to inertial frames. It reveals that c is not just the velocity of a certain phenomenon, namely the propagation of electromagnetic radiation (light) - but rather a fundamental feature of the way space and time are unified as space-time. A consequence of this is that it is impossible for any massive particle to be accelerated to the speed of light.
- Super gravity: In 1976 scientists found that the Einstein's theory of
gravity could become super symmetric if one added a new field, a super partner,
gravitino with spin 3/2. This was called Supergravity and it was based on
point particles and not on strings. Supergravity has only 2 particles. The
most general version of Supergravity could be written in 11 dimensions (in
1 and 13 dimensions, mathematical inconsistencies appear).
It was thought that Supergravity may be the Unified Field Theory, but soon
problems were found: it was not finite, and had some anomalies.
- Time dilation: It is the phenomenon whereby an observer finds that another's
clock which is physically identical to their own is ticking at a slower
rate as measured by their own clock. This is often taken to mean that time
has "slowed down" for the other clock, but that is only true in
the context of the observer's frame of reference. In the theories of relativity
time dilation is manifested in two circumstances:
. In special relativity, clocks that are moving with respect to an inertial
system of observation are measured to be running slower. This effect is
described precisely by the Lorentz transformation.
. In general relativity, clocks at lower potentials in a gravitational field
-such as in proximity to a planet- are found to be running slower.
In special relativity, the time dilation effect is reciprocal: as observed
from the point of view of any two clocks which are in motion with respect
to each other, it will be the other party's clock that is time dilated.
This presumes that the relative motion of both parties is uniform; that
is, they do not accelerate with respect to one another during the course
of the observations. In contrast, gravitational time dilation (as treated
in general relativity) is not reciprocal: an observer at the top of a tower
will observe that clocks at ground level tick slower, and observers on the
ground will agree. Thus gravitational time dilation is agreed upon by all
observers, independent of their altitude.