The principle of special relativity and the principle of general relativity form the foundation upon which Einstein based his theories of special relativity and general relativity respectively. Let us start with the principle of special relativity and Einstein's theory of special relativity.
The Principle of Special Relativity
The principle of special relativity states that physical laws should be the same in all inertial reference frames, but that they may vary across non-inertial ones and the invariance of the speed of light (the principle of the independence of the speed of light (in vacuum) from the motion of the source and any observers).
Einstein's Theory of Special Relativity (1905)
Einstein's theory of special relativity introduces us to the concept that space and time are not different independent concepts but rather they are interrelated and form a single continuum we call spacetime. This spacetime continuum has some special properties.
Objects Must Move Forward In Time - Objects are not free to move around the spacetime continuum, as they will. They must always move forwards in time.
Speed Limit - Objects cannot change their position in spacetime faster than the speed of light.
Other consequences of Einstein's theory of special relativity include:
Mass-Energy Equivalence - The now legendary equation E = mc2, describes the relationship between mass and energy as being equivalent and transmutable. This means that mass (matter) can be transmuted into “pure” energy. This is the principle upon which the development of nuclear weapons was based.
Time Dilation - Moving clocks measure time slower than “stationary” clocks.
Length Contraction - With respect to the observer, objects are measured to be shorter in the direction in which they are traveling.
Relative Simultaneity - Events appearing to be simultaneous to an observer A do not appear to be simultaneous to an observer B if observer B is moving relative to observer A.
The Theory of Special Relativity in Essence
The essential defining feature of Einstein's theory of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. This is the crux of Einstein's theory ofspecial relativity.
As a matter of interest, it was Max Planck, who in 1908 named Einstein's theory of special relativity after the principle of special relativity and not Einstein. Einstein did however, follow suit when he named his theory of general relativity after the principle of general relativity.
The Principle of General Relativity
The principle of general relativity states that physical laws are the same in all reference frames be they inertial or non-inertial.
Einstein's Theory of General Relativity (1907 - 1915)
Einstein's theory of general relativity postulates that matter by its very presence changes (deforms) the spacetime continuum in its vicinity. This is because the global Lorentz covariance of special relativity becomes a local Lorentz covariance in the presence of matter.
The deformation of the spacetime continuum caused by the presence of matter is consistent with the idea of “curved” spacetime (see Fig.1). This curvature affects the path of free particles and even the path of light.
Figure 1 Curved Spacetime
In order to explain this, Einstein devised the Einstien field equations which use the mathematics of differential geometry and tensors to describe gravitation as an effect of the geometry of spacetime. In this way he was able to relate the curvature of spacetime with the mass, energy and momentum within it.
That is to say that the effect of matter (mass) on spacetime is to “tilt” the direction of spacetime towards the matter itself. The result is that objects tend to move towards masses and that it is this “tilting” of spacetime that we call gravity.
As you get closer to the mass, the “tilt” effect becomes stronger. In other words the curvature in the spacetime continuum becomes steeper the closer you are to a mass.
The amount of “tilt” effect (or degree of curvature) that a mass exerts on the spacetime continuum is directly proportional to its mass, its density and the distance from the center of the mass.
If an object is massive enough and dense enough you will reach a point (a specific distance form the center of the mass) where all possible paths forward in the spacetime continuum will be in the direction of the center of that mass. We call these massively dense objects black holes.
The point at which, all possible paths forward in the spacetime continuum lead to the center of the black hole is the event horizon. Once past the event horizon not even light can escape hence the name “black hole”.
So one way of looking at the reason as to why you cannot escape a black hole is simply that you cannot go backwards in time or travel faster than the speed of light.
Other consequences of Einstein's theory of general relativity include:
Gravitational Time Dilation - Time progresses slower at lower gravitational potentials.
Curvatures In the Spacetime Continuum Bend Light - Deviations in the path taken by light as it passes close by regions of highly curved spacetime. Even light rays (which are almost weightless) “bend” in the presence of a strong curvature in the spacetime continuum caused by the presence of a massive object such as a star or a black hole.
Orbital Precession - Astronomical orbital precession anomalies unexplainable using Newton's theory of gravity are accurately predictable with Einstein's theory of general relativity and have been observed in the orbits of the planet Mercury and in binary pulsars. Precession refers to a change in the direction of the axis of a rotating object.
It was through observing the orbit of a star named star S2 in a region of our Milky Way galaxy known as Sagittarius A* that the first evidence pointing to the existence of a super massive black hole at this location was obtained. The orbital precession effect predicted by Einstein's theory of general relativity helped to determine the mass of that black hole as being equivalent to approximately 3.7 million times that of our sun.
The Rate of Expansion of the Universe - The universe is expanding and to observers here on earth some distant parts of the universe are moving away faster than the speed of light. The theory of special relativity still holds true since it is the spacetime continuum that is expanding and not just objects within it.
Frame Dragging - Rotating masses produce a “drag effect” upon the spacetime around them. The more massive and dense an object is, the greater the “drag” effect exerted upon the surrounding spacetime.
The Theory of General Relativity in Essence
Essentially, Einstein's theory of general relativity is a metric theory of gravitation whose defining feature is its use of the Einstein field equations. The solutions of the Einstein field equations are therefore metric tensors defining the topology of the spacetime continuum and how objects move inertially.
Until next time enjoy!
