Special Relativity

Relativity:

Albert Einstein's theory of Relativity introduced the notion that there is no absolute motion in the universe, and that there is only relative motion. This proved the 200-year old concept theory of mechanics of Isaac Newton to be wrong, and implied that we do not in fact reside in the flat, Euclidean space and uniform time of everyday experience, but in an environment containing curved space-time. The theory of relativity broadened our view of cosmology, with its allowances for predictions of apparently bizarre astronomical phenomena like the big bang theory, neutron stars, and black holes.

There are two very separate branches of the theory of relativity. The first one presented was the theory of SPECIAL RELATIVITY by Albert Einstein in 1905, while GENERAL RELATIVITY was not presented in its final form until 1916. The theory of special relativity was understood and accepted by science to be correct almost right away, while its more encompassing from different angles evil cousin, general relativity, was less accepted at first as it did not appear to have as much connection with experiment as the special theory. And as well, in the theory of special relativity most of its applications were on astronomical scales.

The distinction made between the two theories special relativity and of the curved space-time of general relativity is mostly based on precision. Special relativity is actually an approximation of the curved space-time and is valid in sufficiently small regions of space-time. This can be compared to the assumption that our earth is (relatively, huh huh) flat in places. Even though the earth’s surface is curved, this assumption can be considered to be accurate to a certain degree. Special relativity may thus be used wherever the scale of the phenomena being studied is comparatively small to that of which the space -time curvature (gravitation ) begins to be noticed. With most applications in nuclear or atomic physics, this approximation is so accurate or on such a small scale, that relativity can be assumed to be exact ; in other words, special relativity implies that "gravity can be assumed to be completely absent" from the calculations. General relativity is applied to depict the extent that space-time is curved by matter.

Special Relativity: There are two basic concepts of special relativity:

Inertial frame: An Inertial frame of reference is any region, such as a freely falling laboratory, in which all objects move in straight lines with uniform velocity. This region is free from gravity and is called a Galilean system. The principle of relativity states that the results from any physical experiment done inside a laboratory inertial frame is independant of the uniform velocity of the frame.

In other words, the laws of physics must have the same constant-like form in every inertial frame. A result of this is that the speed of light must be the same in every inertial frame regardless of the speed of its source or that of the observer. Essentially all of the laws and consequences of special relativity can be derived from these concepts

The first important consequence is the relativity of simultaneity. Because definitions of simultaneous events at different locations involves the sending of light signals between them to verify, then two events that are simultaneous when compared in one inertial frame may not be considered simultaneous when viewed from different inertial frames, or when viewing from a frame moving relative to the first. This is proof that there is curved space-time instead of absolute, universal time as Sir Isaac Newton's laws proposed.

Perhaps the most important consequences and confirmations of special relativity take place when with quantum mechanics; elementary particle spin, antimatter and other topics are helped by special relativity.

A German mathematician by the name of Hermann Minkowski explored the mathematical foundations of special relativity in 1908 and developed that concept of a "four dimensional space-time continuum." In this, time is the fourth dimension and is treated the same as the three spatial dimensions.

The exact Minkowski space-time of special relativity is incompatible with the existence of gravity. A frame chosen to be inertial for a particle far from the Earth where the gravitational field is negligible will not be inertial for a particle near the Earth. An approximate compatibility between the two, however, can be achieved through a property of gravitation called the weak equivalence principle (WEP): all modest sized bodies fall in a given external gravitational field with the same acceleration regardless of their mass, composition, or structure. An example would be: if an observer were to ride in an elevator falling freely in a gravitational field, then all bodies inside the elevator, because they are falling at the same rate, would consequently move uniformally in straight lines as if gravity had vanished. Gravity outside does not affect the bodies inside the inertial frame.

Einstein's insight was to theorize that the vanishing of gravity in free-fall as described above applied not only to motion, but to all the laws of physics. In any freely falling frame, the laws of physics should take on their special relativistic forms. This postulate is called the Einstein equivalence principle (EEP)

E=m(°)c² m=E/c ² c ²=E/m

The equation E=mc² is perhaps the most famous of all equations in the world and is one of the fundamental equations in special relativity. It demonstrates that the energy (E) of a body is equivalent to the mass of the body at rest (m(°))multiplied by the speed of light squared (c).

This equation demonstrates that mass and energy are quite the same. This equation means that the body in question cannot travel at speeds equal to, or greater than the speed of light because this would require an immense body to be propelled. With the need for the body to be propelled at the speed of light, there is a need for an immense amount of energy. This energy is proportional to the mass of the body in the way that such as this amount of energy is proportional to an object the size of a quark. An immense body would be the only design humans can as of yet make physically, and the magnitude of energy required to put it into ‘hyperspace’ is larger than can be represented by most ordinary scientific calculators. This relationship between energy and mass implies that the energy needed would have to be made by a super-ultra-small body that is super-quasi-ultra-efficient. This device would have to be so efficient that it would have to make energy equal to 9.00 * 10e16 times its mass.

This efficiency can not yet be achieved. Perhaps, it is a good reason that it cannot because another stipulation of the special theory of relativity states that bodies can not move at the speed of light.

L(r)=L(°)(1-v²/c²)e½

Dutch physicist Hendrik Lorentz had derived a mathematical equation in 1903 based on the assumption that George Fitzgerald had made about how objects shrink in motion. Lorentz then changed this so that it would coincide with the theory of special relativity that had been published later, by Einstein in 1905. It was named the Lorentz Transformation and can be used for calulating many relative things. His equation [ L(r)= L(º)*(1-v²/c²)to the power of ½ ], when applied with the special theory of relativity would include many factors. One would be the (L(r)) which is relativistic length of an object in motion, relative to (L(°)) the length of the object at rest. The v is the velocity of the object relative to the observer, and c is the speed of light, which is a constant (3.00 x 10e8 m/s) in most cases.

This formula is used to calculate the differences between two objects; one an inertial frame and another at rest (usually an observer). This equation implies that objects lose length (or what ever their unit of measurement may be) when moving in an inertial frame. It also implies that objects may not travel faster than the speed of light constant. If an object were to travel faster than light, this would mean that the (L(r)) in this formula would be zero and this is not easily conceivable to us. If the object’s speed were greater than the speed of light, and (L(r)) became zero, than the object would have appeared to have disappeared, and this is impossible as defined by the laws of special relativity. However, the object can keep getting infinitely closer to the speed of light , as Einstien suggested that no distance may be covered entirely, it can just be halved, and halved, an infinite number of times. This can only be considered correct if sig.figs. are not accounted for!

The Lorentz Transformation is very versatile in that it can be used to find the value of anything in an inertial frame relative to its value at rest. For example it can be used with time (t(r)=t(°)*(1-v²/c²)e ½). Time is a particularly interesting concept when applied to the Lorentz Transformation.

With time, the concept that an object loses its length in a moving inertial frame is replaced with the concept of time passing slower in a moving inertial frame, relative to the time at rest. This is hard to imagine as physically happening.

The two aforementioned formulas have been responsible for helping to explain the concept of special relativity over the years to many physicists. Special relativity as first presented by Albert Einstein in 1905 has revolutionized physics, and soon after his theory of general relativity confused the hell out of the physics world, nonetheless, these two theories create one large fundamental part of space-time calculations. The theory of relativity has allowed the further definition of time in our universe, and as well has defined the limitations of space and time, relative to what we know about the speed of light.

The search for extra-terrestrial life may not be limited to the "X-Files" . With the development of the special theory of relativity, physicists were capable of predicting the possibility of space travel(which requires immense amounts of energy, using E=mc²) and the possibility of the existence of synthetic fusion energy and of the reality of fission energy and of the atom bomb.

There are a lot of assumptions made in the theory of special relativity, and it is accepted to be so, because of the validity of the formulas and of the discoveries that the theory has led to and their importance in today's technologically advanced space-time