Special relativity

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The special theory of relativity (or special relativity) was developed and pulished by Einstein in 1905 because he was unhappy with the explanations of electromagnetism in classical physics. Einstein thought these explanations contradicted the principle of relativity.

Contents 1 Basics of special relativity 2 The Lorentz transformations 3 Mass, energy and momentum 4 History 5 Experimental confirmations 6 Notes 7 References 8 See Also

[edit] Basics of special relativity

Before Einstein, many people tried to find something in the universe that was totally at rest, and had no motion. They wanted this to measure the speed of all other things including the speed of light. Einstein said this thing did not exist. He said it was not needed for physics.

Einstein proposed that Special relativity is based on two ideas:

1. The special principle of relativity: The laws of physics are the same for all observers in an inertial state of motion. ('Inertial' means without acceleration. All observers move in different directions without acceleration.)
2. The constancy of the speed of light in a vacuum (c): All inertial observers always measure the speed of light as being the same.

(c = 299,798,458 m/s (metres per second). The constancy of a thing means that the thing is always the same.)

The difficulty is in the constancy of c.

Let us think of two observers, A and B. Let us say each can move, and each has an instrument to measure the speed of light. Let us say that light moving towards B is passing A at the speed of c. Let us say that B is moving towards A at a speed of 1 m/s. Then classical physics (or Newtonian physics) predicts B would find the light to have the speed of (c + 1) m/s with respect to B. But this is wrong, B finds that the speed is still c m/s. Einstein says this is because A's view of space and time is different from B's view of space and time.

In this discussion, a view is called a frame of reference. The views of A and B are related by the Lorentz transformations.

Let us say that A has a clock and a measuring rod. Let us say that B, in a different frame of reference, has an identical clock and an identical measuring rod.

The mathematics of special relativity creates three primary effects relating to the behavior of clocks and measuring rods which are moving with respect to each other:

1. Time dilation: A observes that B's moving clock is ticking slower than A's own physically identical clock.
2. Lorentz contraction: A observes that B's moving rod is shorter than A's own physically identical rod. (It is shorter in the direction of the relative motion.)
3. Relativity of simultaneity: Take a linear series of clocks which read the same time in the frame of reference in which they are stationary K. In a frame of reference in which those clocks are moving K' , they will be found to read different times at what is considered to be the same time in K' based on how far apart they are in K' in the direction of motion.

[edit] The Lorentz transformations

The mathematical core of special relativity is the Lorentz Transformations, which relates the views of space and time for two comoving inertial observers. To understand them, let there be an observer K who describes when events occur with a temporal coordinate t, and who describes where events occur with spatial coordinates x, y, and z. To be more explicit, let us specify that the time of an event is given by the time that it is observed minus that distance to the event divided by c. Now with this understanding in place, let there be another observer K' who is

• moving along the x axis of K' at a rate of v,
• has a spatial coordinate system of x' , y' , and z' , where x' axis is coincident with the x axis, and with the y' and z' axes always being parallel to the y and z axes, and
• where K and K' are coincident at t = t' = 0 [meaning that the coordinate (0,0,0,0) is the same event for both observers].

The Lorentz Transformations then are

y' = y, and

z' = z.

[edit] Mass, energy and momentum

In special relativity, the momentum p and the energy E of an object as a function its rest mass m₀ are

and

.

These equations can be rewritten to use a "relativistic mass" (in the direction of motion) of . In this case, one finds that momentum is still described by p = mv, while energy is described by the famous equation E = mc².

In special relativity, energy and momentum are related by the equation

.

For a massless particle (such as a photon of light), m₀ = 0 and this equation becomes E = pc.

[edit] History

The need for special relativity arose from Maxwell's equations of electromagnetism, which were published in 1865. It was later found that they call for electromagnetic waves (such as light) to move at a constant speed (i.e., the speed of light).

To have Maxwell's Equations be consistent with both astronomical observations^[1] and Newtonian physics^[2], Maxwell proposed in 1877 that light travels through a luminferous ether which permeates the universe.

In 1887, the famous Michelson-Morley experiment tried to detect the "ether wind" generated by the movement of the Earth^[3]. The persistent null results of this experiment puzzled physicists, and called the ether theory into question.

In 1895, Lorentz and Fitzgerald noted that the null result of the Michelson-Morley experiment could be explained by the ether wind contracting the experiment in the direction of motion of the ether. This effect is called the Lorentz contraction, and (without ether) is a consequence of special relativity.

In 1899, Lorentz first published the Lorentz Equations. Although this was not the first time they had been published, this was the first time that they were used as an exaplantion of the Michelson-Morley experiment's null result, since the Lorentz contraction is a result of them.

In 1900, Poincare gave a famous speech in which he considered the posibility that some "new physics" was needed to explain the Michelson-Morley experiment.

In 1904, Lorentz showed that electrical and magnetic fields can be modified into each other through the Lorentz transformations.

In 1905, Einstein published his article introducing special relativity, "On the Eletrodynamics of Moving Bodies", in Annalen der Physik. In this article, he presented the postulates of relativity, derived the Lorentz transformations from them, and (unaware of Lorentz's 1904 article) also showed how the Lorentz Transformations affect electric and magnetic fields.

Later in 1905, Einstein published another article presenting E = mc².

In 1908, Max Plank endorsed Einstein's theory and named it "relativity". In that same year, Minkowski gave a famous speech on Space and Time in which he showed that relativity is self-consistent and further developed the theory. These events forced the physics community to take relativity seriously. Relativity came to be more and more accepted after that.

In 1912 Einstein and Lorentz were nominated for the Nobel prize in physics due to their pioneering work on relativity. Unfortunately, relativity remained so controversial then, and for a long time after that, that a Nobel prize was never awarded for it.

[edit] Experimental confirmations

• The Michelson-Morley experiment, which failed to detect any difference in the speed of light based on the direction of the light's movement.
• Fizeau's experiment, in which the index of refraction for light in moving water cannot be made to be less than 1. The observed results are expained by the relativistic rule for adding velocities.
• The energy and momentum of light obey the equation E = pc. (In Newtonian physics, this is expected to be .)
• The transverse doppler effect, which is where the light emitted by a quickly moving object is red-shifted due to time dilation.
• The presense of muons created in the upper atmosphere at the surface of the Earth. The issue is that it takes much longer than the half-life of the muons to get down to the surface of the Earth even at nearly the speed of light. Their presense can be seen as either being due to time dilation (in our view) or length contraction of the distance to the surface of the Earth (in the muon's view).
• particle accelerators cannot be made to perform properly unless relativistic physics is used.

[edit] Notes

• ^[1] Observations of binary stars show that light takes the same amount of time to reach the Earth over the same distance for both stars in such systems. If the speed of light was constant with respect to its source, the light from the approaching star would arrive sooner than the light from the receding star. This would cause binary starts to appear to move in ways that violate Keppler's Laws, but this is not seen.
• ^[2] The second potulate of special relativity (that the speed of light is a constant for the observer) contradicts Newtonian physics.
• ^[3] Since the Earth is constantly being accelerated as it orbits the Sun, the initial null result was not a concern. However, that did mean that a strong ether wind should have been present 6 months later, but none was observed.

[edit] References

• W. Rindler, Introduction to Special Relativity, 2^nd edition, Oxford Science Publications, 1991, ISBN 0-19-853952-5.

• Web article on the history of special relativity

[edit] See Also

• en:special relativity
• en:special relativity for beginners