Special Theory of Relativity
Edited by TheGuyLoveNY, Jen Moreau
Theory of Relativity:
Theory of relativity deals with effects of relative motions on physical phenomena. These effects become more appreciable only at speeds equal to or greater than one tenth of speed of light called Relativistic Speed.
Relativistic Speed: It was proposed by Albert Einstein. There are two types of theories of relativity:
- 1General theory of relativity.Advertisement
- 2Special theory of relativity.
General theory of relativity:
Einstein put forward general theory of Relativity In 1916.
Statement: It is the branch of theory of relativity which deals with non inertial or accelerated frames of reference. This theory treats problems relating to frames of reference accelerating with respect to one another. In this branch gravitational field does play some part.
Special theory of relativity:
Introduction:
This theory was put forward by Albert Einstein in 1905.
Statement: This theory deals with inertial or non-accelerating frames of references. In this theory gravitational field does not play any part. This theory treats problems involving inertial frames.
Postulates of Special theory of Relativity:
Special theory of relativity is based upon two postulates which can be stated as follows:
- The laws of physics are the same in all inertial frames. This postulate is the generalization of the fact that all physical laws are the same in frames of reference moving with uniform velocity with respect to one another. In laws of physics were differences for different observers in relative motions, the observer could determine from this difference that which of them were stationary in space and which were moving. But such a distinction does not exists, so this postulate implies that there is no way to detect absolute uniform motion.
- The speed of light in free space has the same value for all observers, regardless of their state of motion. This postulate states an experimental fact that speed of light in free space is the universal constant.
C = 3 X 108m/sec
Results of Special theory of Relativity:
Some Interesting results of special theory of relativity can be summarized as follows without going into their mathematical derivations.
Time Dilation: According to classical physics time is an absolute quantity (i.e time interval between two events occurred in same position would be same, whoever measures it). But according to special theory of relativity, Time is not absolute quantity. It depends upon the motion of the frame of reference.
Expression: Suppose an observer is stationary in an inertial frame. He measures time interval between two events in this frame. Let it be "t_{0}", This is known as proper time.
If the observer is moving with respect to frame of events with very high velocity "v" or if the frame of events is moving with respect to observer with very high uniform velocity "V", the time measured by the observer would not be "t_{0}", but it would be given by expression:
As "V < C" so √1 - V^{2}/C^{2} is always less than one (1). Therefore, "t" is greater than "t_{0}".
Conclusion: if t >t_{0}, this shows that time has dilated or stretched due to the relative motion of the observer and the frame of reference of events.
Application: This astonishing result applies to all timing process physical, chemical and biological. Even aging process of the human body is showed by motion at very high speeds.
Length Contraction:
Introduction: The distance from earth to a star measured by an observer in a moving spaceship would seem smaller than the distance measured by an observer on earth. i.e: (i-e S^{l} < S).
Definition: If an observer is in motion relative to two points that are a fixed distance apart, the distance between the two points appears shorter if the observer was at rest relative to them. This effect is known as length contraction. The Length contraction happens only along the direction of motion.
Expression:
- Proper length: The length of an object or distance between two points measured by an observer who is relativity at rest is called proper length "L_{0}".
- Contracted Length: If an object and an observer are in relative motion with speed 'V' then the contracted length "L" in given by
L = L_{0} √1 - V^{2}/C^{2}
Conclusion:
As V < C So,
V^{2}/C^{2} < 1 → 1 - V^{2}C^{2} < 1.
So, L < L_{0}.
The Length along the direction of motion has decreased.
Mass Uranium:
According to classical mechanics, Mass of an object is considered as constant quantity. But according to special theory of relativity, mass of an object is a varying quantity and depends upon the speed of the object.
Expression: Proper mass is the mass of an object measured by the observer who is relatively at rest is called proper mass which is denoted by "m_{0}". Increase in Mass: An object whose mass when measured at rest is "m_{0}" will have an increased mass "m" when observed to be moving at speed 'V.' The increased mass 'm' is given by the relation:
Conclusion: Since the term √1 - V^{2}/C^{2} < 1
So, m > m_{0}
It means that mass of an object in motion increases. The Increase in mass indicates an Increase in inertia of the object at high speeds as mass is direct measures of inertia. No material object can be accelerated at the speed of light "c" in free space.
Proof:
Importance of Einstein Equation:
In our everyday life, we deal with extremely small speeds, compared to the speed of light. Even the earth's orbital speed is only 30 km/sec. On the other hand, the speed of light in free space is 300000 km/ sec. This is the reason why newton's laws are valid in an everyday situation. However, when experimenting with atomic particles moving at velocities approaching speed of light, the relativistic effects, are very prominent and experimental results cannot be explained without taking Einstein's equations into account.
Energy Mass Relation:
According to the special theory of relativity, mass and energy are different entities but are interconvertible, or we can only say that energy can be converted into mass and mass can be converted into energy. The total energy 'E" and mass "m" of an object are related by the expression:
E = mc^{2}
Where m depends on the speed of the object.
Rest Mass Energy:
At rest, the energy equivalent of an object mass, m_{0} is called rest mass energy E_{0}
E_{0} = m_{0} C^{2}
As m > m_{0} So, E > E_{0} The difference of energy (mC^{2} - m_{0} C^{2}) is due to motion, as such it represents the Kinetic Energy of the mass. Hence, We can say,
KE = (mC^{2} - m_{0} C^{2})
= (m - m_{0} )C^{2}
The change in mass (m - m_{0} ) is due to change in energy ΔE or, In other words, the Kinetic energy of the object appears as the increase in mass.
ΔM = ΔE/C^{2}
Because, C^{2} is a very large quantity, this implies that small change in mass require very large change in energy.
Note: In our everyday world, Energy changes are too small to provide measurable mass changes. However, energy and mass changes in nuclear reactions are found to be exactly in accordance with the above-mentioned equations.
Application of Special Theory of Relativity:
NAVSTAR Navigation System:
The results of special theory of relativity are put to practical use even in everyday life by a modern system of navigation satellites called NAVSTAR.
- Speed:
Earth can now be determined to an accuracy of about 2 cm/sec. However, If relativity effects are not taken into account, speed could not be determined any closer than about 20 cm/sec.
- Location:
By using these results the location of an aircraft after an hour's flight can be predicted to about 50 m as compared to about 760 m determined, without using relativistic effects.
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