Special Theory of Relativity

Introduction

--The special theory of relativity shows that time and space are affected by motion

Hello?...Does this sound something strange to you? Ok, i agree! This did have a scaring effect on me when i started to do my research on it, but later i found it rather interesting even though there was only text for me to carry on reading.

To appreciate fully the nature of a massive stellar corpse, we must use the best theory of gravity at our disposal. The gravitational field around one of these massive dead stars is so strong that Newton's theory of gravity is not valid. Instead, we must turn to Albert Einstein's general theory of relativity. Before we can understand this theory, however, we must first look at his special theory of relativity. (This theory is "special" in the sense of being specialized. In particular, it does not include effects of gravity.)

According to the classical physics of Newton, space is perfectly uniform and fills the universe like a frigid framework. Similarly, time passes monotonous, unchanging rate, It is always possible to know exactly how fast you are moving through this frigid fabric of space and time.

Fundamental laws

Einstein began a revolution in physics with his special theory of relativity in 1905. He was guided in his theory of relativity in 1905. He was guided in his thinking by the following postulate:

--The fundamental laws of the universe do not depend on a person's location or motion.

In other words, the laws of physics should be the same whether we happen to be sitting on the earth or moving through space at a high speed.

Soon after 1900, Einstein began developing a new approach to the phenomena of electricity and magnetism. The basic properties of electricity and magnetism had been summarized in four equations formulated in 1865 by the great Scottish physicist James Clerk Maxwell. Maxwell's equations are the basis of electromagnetic theory, which today has a wide range of practical applications, from television sets to microwave ovens. Maxwell's electromagnetic theory predicts various effects, depending upon the motion of electric charges and magnets. For example, a moving electric charge creates a magnetic field, whereas a stationary electric charge does not. Such predictions imply some absolute or fixed spatial framework within which an object is either stationary or moving.

Einstein's goal was to eliminate this assumption of absolute space from electromagnetic theory. He wanted to recast the theory so that it would depend only on the relative motions of the observer and the electric charges or magnets. In 1905 he succeeded and published his results in a famous entitled "On the Electrodynamics of Moving Bodies." In that paper, he came to the following remarkable conclusion: Everyone who measures the speed of electromagnetic waves - that is, light - gets the same answer (3 x 10 8 m/s), regardless of the person's state of motion. This seemingly innocuous statement is in direct conflict with Newtonian view that a stationary person and a moving person should measure different speeds (Figure below). Einstein's efforts to incorporate light's constant speed into physics gave us a new understanding of the nature of space and time, called the special theory of relativity.

As seen by the outfielder, ball is approaching her at (30 m/s) + (10 m/s) = 40 m/s

Speed of light

The special theory of relativity begins with two principals. We have already stated the first of these, that the laws of physics are the same to all observers. The second principal follows from Einstein's work on electromagnetism:

The speed of light is the same to all observers.

From these principals, the basic equations of the special theory of relativity follow logically (refer to time dilation section). These equations relate measurements by observers moving at different speeds. They ensure, for example, that both you on the Earth and a friend in a spacecraft traveling near the speed of light agree on the same laws of physics, unaffected by any pitfalls or paradoxes caused by how you and your friend are moving relative to each other.

In developing the special theory of relativity, Einstein found that he had to abandon old-fashioned, rigid notions of space and time. For example, imagine a friend whizzing across or solar system in a spacecraft while you remain here on the Earth. Einstein proved that your friend's clock would seem to tick more slowly than your own. In addition, your friend's rulers when held parallel to the direction of motion will seem shorter than yours. In brief, moving clocks are slowed and moving rulers are shortened in the direction of the motion. These strange results are direct consequences of the speed of light being an absolute constant.

(a)As seen by the outfielder, ball is approaching her at (30 m/s) + (10 m/s) = 40 m/s

(b)Incorrect Newtonian description:
As seen by astronaut in spaceship, light is approaching her at (3x108 m/s) = 4x108 m/s

Correct Einsteinian description:
As seen by astronaut in spaceship, light is approaching her at 3x108 m/s

The Speed of Light is the Same to All Observers.

(a) in Newtonian physics, the speed of light of any object depends on how the observer is moving.

(b) Einstein showed that this commonsense principle does not apply to light. No matter how an observer is moving, he will always measure light to have the same speed. This remarkable fact about light, which goes completely against intuition, is at the heart of Einstein's special theory of relativity. This theory has other bizarre consequences. For example, the astronaut with the flashlight will see the flying astronaut's spaceship as being shortened along the direction of motion and will see the flying astronaut's clocks (including his wristwatch and his heartbeat) as ticking slowly. Furthermore, the special theory of relativity says that the laws of physics are the same no matter how fast you are moving, so both astronauts see the same effects of relativity. Here the flying astronaut will see the astronaut with the flashlight (who is moving relative to him) as shortened along the direction of motion and as having slowly ticking clocks.

Time Dilation

The special theory of relativity describes how motion affects measurements of time and distance. Einstein concluded that these measurements must depend on how the person making the measurements is moving. The basis of this theory is that all people, whether moving or stationary, must agree on certain basic physical phenomena, especially those involving the behavior of light.
Imagine that you are standing on the Earth while our friend is traveling across our solar system at a high speed, as shown in the accompanying sketch. You set off a flashbulb that emits sudden bright flash of light. The radiation moves away from you at the same speed at all directions, and thus you see an expanding spherical shell of light. What does your high-speed friend see?
Einstein argued that this person must also see light moving away from her at the same speed in all directions, and thus she also sees an expanding spherical shell of light.By requiring that both people observe a spherical shell, Einstein derived a series of equations to relate specific measurements of time and distance between two people. These equations are named the Lorentz transformations, after the famous Dutch physicist Hendrik Antoon Lorentz (a contemporary of Einstein who developed these equations independently but did not grasp their true meaning.) These equations tell us exactly how a moving person's clock slow down and how rulers shrink.
To appreciate the Lorentz transformations, again imagine that you are on Earth while a friend is moving at a speed v with respect to you. Suppose that you both observe the same phenomenon on Earth - say, the beating of your heart or the ticking of your watch, which appears to occur over an interval of time. According to your clock (which is not moving relative to the phenomenon), the phenomenon lasts for T0 seconds. This is called the proper time of the phenomenon. But according to your friend's clock (which is moving relative to the phenomenon), the same phenomenon lasts for a different length of time, T seconds. The Lorentz transformation for time tells us that these two time intervals are related by:

Lorentz transformation for time

T = time interval measured by an observer moving relative to the phenomenon
T0 = time interval measured by an observer not moving relative to the phonomenon
v = speed of the moving observer
c = speed of light

EXAMPLE: Suppose that your friend is moving at 98% of the speed of light. Then, v/c = 0.98 so that

=> T = 5T0

The Lorentz transformation for time is plotted in the accompanying graph, which shows how 1 second measured on a stationary clock is stretched out when measured using a clock carried by a moving observer. Note that significant differencesEXAMPLE: Fast-moving protons from interstellar space frequently collide with atoms in the Earth's upper atmosphere. When they do, they can create unstable particles called muons (pronounced "mewons") that decay in an average time of 2.2 x 10 to power -6 seconds. Such muons typically move at 99.9% of the speed of light and are formed at an altitude of 10kn. As measured by an observer on the Earth, the time that a muon would take to reach the Earth's surface is

This is 15 times longer than the life expectancy of a muon, so it would seem that muon would never reach the Earth's surface before decaying. In fact, these muons are detected by experiments on the surface! The reason is that as seen by an Earth observer, the muon is a "moving clock", and hence its decay is slowed down by time dilation. To an Earth observer, the actual lifetime of a muon is

Thus, as measured by an Earth observer, muons live more than long enough for them to reach the surface. The detection at the Earth's surface of muons from the upper atmosphere is compelling evidence for the reality of the time dilation.

Length Contraction

In the same terminology as proper time, we say that a ruler at rest measures proper length or proper distance (L0). According to the Lorentz transformations, distances perpendicular to the direction of motion are unaffected. However, a ruler of proper length Lo held parallel to the direction of the motion shrinks to a length L, given by

Lorentz transformation for length

L = length of a moving object along the direction of motion
L0 = length of the same object at rest(proper length)
v = speed of the moving object
c = speed of light

EXAMPLE: If your friend is traveling at 98% of the speed of light relative to you, you have concluded that her clocks are ticking only one-fifth as fast as yours. You will also conclude that her 1-metre ruler is only one-fifth as long (20cm) when held parallel to the direction of the motion:

This shrinkage of length is often called length contraction.

EXAMPLE: Length contraction gives us another way to explain why unstable muons created high in the atmosphere are able to reach the Earth's surface. The proper distance from where the muon is created to the Earths surface is 10km. But as measured by a muon moving at 99.9% of the speed of light, the distance is much shorter:

As measured by the muon, the time required to travel this contracted distance is

This is less time than the 2.2 x 10 to the power of -6 seconds that an average muon takes to decay, and muons can thus successfully reach the Earth's surface.