- The laws of physics are the same in all inertial frames of reference.
- The speed of light in free space has the same value in all inertial frames of reference in all directions.
Theory of Relativity
The theory of relativity is concerned with the way in which the observers who are in a state of relative motion describe the physical phenomenon.
The theory of relativity is given by Albert Einstein in 1905 which states that there is no absolute state that exists in the universe, all states are relative.
The theory of relativity is concerned with the way in which the observers who are in a state of relative motion describe the physical phenomenon. The special theory of relativity has an undeserved reputation as a difficult subject. It is not mathematically complicated; most of its details can be understood using techniques well known to readers of this text. Perhaps the most challenging aspect of special relativity is its insistence that we replace some of our ideas about space and time, which we have acquired years of common sense experiences with new ideas.
The kinematics developed by Galileo and mechanics developed by Newton, which forms the basis of what we call classical physics, had many triumphs. Particularly noteworthy are the understanding of the motion of the planets and the use of kinetic theory to explain certain observed properties of gasses.
However, a number of experimental phenomena cannot be understood, with the otherwise successful classical theories. Let us discuss a few of these difficulties.
- Troubles with our ideas about time
- Troubles with our Ideas about the length
- Troubles with our Ideas about velocity
- Troubles with our Ideas about light
There are two parts of the theory of relativity:
- The general theory of relativity (1916)
- The special theory of relativity (1905)
The general theory of relativity
The general theory of relativity deals with the problems involving frames of reference accelerated with respect to each other.
The special theory of relativity
The special theory of relativity deals with the problems involving non-accelerated frames of reference..
Postulates of the theory of relativity
A scientific theory usually begins with general statements called postulates, which attempt to provide a basis for the theory. From these postulates, we can obtain a set of mathematical laws in the form of equations that relate to physical variables.
For about two centuries, the mechanics of Galileo and Newton withstood all experimental tests. In this case, the postulates concern the absolute nature of space and time.
Based on his thought experiment about catching a light beam, Einstein realized the need to replace the Galilean laws of relative motion. In his paper, entitled On the Electrodynamics of moving bodies, Einstein offered two postulates that form the basis of his Special theory of relativity.
The laws of physics are the same in all initial frames of reference.
The speed of light in free space has the same value in all initial frames of reference in all directions.
The 1st postulate is the generalization of the fact that all physical laws are the same in the frame of reference moving with the uniform velocity with respect to one another.
If the laws of physics are different for different observers in the relative motion, the observer could determine from this difference that which of them were stationary in space and which of them were moving. But such distinction does not exist, so this postulate implies that there is no way to detect absolute uniform motion.
The 2nd postulate states an experimental fact the speed of light in free space is the universal constant whose value is 3 x 108 m/sec.
Results of the special theory of relativity
The following results are concluded from the special theory of relativity and we discuss them here with outgoing their mathematical derivation.
- Time Dilation
According to the special theory of relativity, time is not an absolute quantity. It depends upon the motion of the frame of reference.
Suppose an observer is stationary in an inertial frame. He measures the time interval between two events in this frame. This is known as the proper time.
If the observer is moving with respect to the frame of events with velocity v or the frame of events is moving with respect to the observer would not time interval, but it would be such that
As the quantity is less than one, so t is greater than. i.e., the time has dilated or stretched due to the relative motion of the observer and the frame of reference of events.
The amazing result applies to all timing processes e.g., physical, chemical, and biological processes. Even the aging process of the human body is slowed by motion at a very high speed.
- Length Contraction
If you are in motion relative to two points that are a fixed distance apart, the distance between two points appears to be shorter than when you were at rest relative to them. This effect is known as length contraction. Length contraction happens only along the direction of motion. No such contraction would be observed perpendicular to the direction of motion.
The length of an object or the distance between two points measured by an observer who is relatively at rest is called proper length.
If an observer and an object are in relative motion with the speed v, then the contracted length is given by
As the quantity is less than one, so the proper length is always greater than the relativistic length.
Let us see the video about length contraction.
The distance from the earth to a star measured by an observer in a moving spaceship would seem smaller than that the distance measured by an observer on earth frame.
Importance of Special theory of relativity
- Relativity affects every aspect of physics; we have concentrated on mechanics, and later in this text, we consider the effect of relativity on electromagnetism.
- Indeed, we must carefully reexamine every subfield of physics from the perspective of the special theory, verifying that each is consistent with the two postulates. We must also note that relativity has passed every experimental test without the slightest discrepancy.
- It is a theory that is of great aesthetic value, providing us with a view more satisfying than that of classical physics about the validity of different perspectives and symmetries.
- It is also a theory of great practical value, providing engineers with the proper guidance to construct large particle accelerators and providing those concerned about maintaining standards with the proper producers for correcting the reading of the atomic clocks when they are transported from one location to another.
- The first postulate of relativity is really an outgrowth of Newton’s first law, the law of inertia, which defined the concept of an inertial frame and gave us the first notion that inertia observes would draw identical conclusions from observing an experiment in which no net force acts. It is not too great a leap to extend that view to assert that inertial observers should also draw identical conclusions from observing an experiment in which there is a net force. Finally, why should we single out the laws of mechanics for this equivalence? By expending it to equivalence for inertial observers for all the laws of physics, we arrive at the first postulate.
- The second postulate is also a reasonable one. It seems unrealistic to be able to transmit a signal at an infinite speed, thereby providing instantaneous communication throughout the universe. Moreover, experiments on the relativity of the time show that such instant communication between distant points is not consistent with observation. If there is limiting speed, then surely (by the first postulate) it must be the same for all observers, regardless of their state of motion.
- For some, the first exposure to the relativity of simultaneity, the apparent shrinking of moving rods, and the slowing down of time may be disturbing. However, a bit of thought will persuade you that classical alternatives are even more disturbing. For example, a classical rigid rod of definite length is not a concept that is consistent with relativity; a signal at one end cannot be transmitted instantly to the other end. We must give up the idea of all observers being able to use the same measuring rod. We replace this idea with one that gives each observer a measuring rod and permits that observer to use that rod to make measurements within a particular frame of reference. No observers measuring instruments or results are preferred over any others. finally, relativity gives us a wonderful symmetry between these observers; it doesn’t assert the reality of slowing clocks, but that, from their two differing perspectives, two observers in relative motion each observe that the other’s clock are slow. There is no necessity to grant preferred status to either of them or to any other inertial observer.
- According to classical physics, space and time are absolute. This leads to the result the laws of physics must be different or different observers. Relativity, on the other hand, tells us that the laws of physics must be the same for all observers, and as a consequence space and time become relative concepts. Clearly, relativity is “more absolute” than classical physics. The arbitrary and complex physical world of classical physics, in which each observer must use a different set of physical laws, becomes the more uniform and simple physical world of relativity.
- Relativity broadens our view of the universe by placing them among the many inertial observers of that universe. It brings together concepts that, according to classical physics, were treated separately; for instance, space and time into space-time, or mass and energy into rest energy. It points the way toward a single, unifying theory that includes all possible interactions between particles; electricity and magnetism into electromagnetism; electromagnetism and the so-called weak forces into the electroweak interactions, the electroweak and the strong nuclear interactions into one of the proposed Grand Unified Theories (GUTs); and finally GUTs and gravity into the hypothetical theory of Everything. Einstein, who knew about only the first of this unification, would surely be very pleased with these developments.
For related Topics visit: Mechanics