Atlearner-
April 19, 2023

December 31, 2020

The Special Theory of Relativity, also known as Special Relativity, is a scientific theory developed by **Albert Einstein** in 1905 regarding the relationship between space and time. Basically, this theory explained how to interpret the motion between different inertial (i.e constant speed or no acceleration) frames of reference, and also talked about the speed of light in a vacuum. This theory is based on two postulates the principle of relativity and the principle of the speed of light.

The laws of physics are invariant (i.e not changeable), in all inertial frames of reference (i.e the frame of reference with constant speed or no acceleration).

The speed of light in a vacuum is the same for all observers, regardless of their motion relative to the source of light or observer. ( The speed of light in the vacuum are represent with the symbol c and the value of it is 299,792,458 meters per second or about 186,000 miles per second).

This Special Relativity is applicable only in the special cases (that is why this name) where the motion is uniform. It only explains such motion where the object moves in a straight line at a constant speed. If the object starts to accelerate or do anything that changes the nature of the motion then this theory stops there.

But objects are not always in the inertial (or non-accelerating) frame of reference they are also in non-inertial (or accelerating) frames of reference. Hence, Einstein was trying to include acceleration in his theory. Then In 1915, he published his General Theory of Relativity that can explain the general cases of any sort of motion.

Space-time continuum

In Einstein’s special relativity he created a fundamental relation between space and time. Where the physical universe consists of four dimensions - the three dimensions of space (length, width, and height…or up/down, left/right, and forward/backward) and the fourth one is the dimension of time. This 4-dimensional space in the universe is referred to as the s**pace-time continuum**.

The reason why time is considered as the 4th dimension in relativity because the 3-dimensional coordinate system can't describe every event completely. That is why we have to include the time coordinate in describing events fully in space along with the time.

Mass variation

According to special relativity, the mass of an object in a frame of reference at rest is called its rest mass m0. Now if the object travels at a constant speed v then the mass will not remain constant. This mass variation can be measured by this formula -

Where,

m = mass of the object in motion

m0 = rest mass

v = speed of the object

c = speed of light in vacuum

When the velocity of the object v is very small compared to the velocity of light c (i.e v2/c2 is negligible compared to one), then m = m0.

When the velocity of object v is comparable to the velocity of light c (i.e √(1-v2/c2) is less than one), then the mass of the moving object appears greater than its rest mass, (i.e m>m0).

When the velocity of the object v is equal to the velocity of light c, then the mass of the moving object is possessed infinite mass.

Length contraction

In special relativity, it has been found that the measurement of the length of a rod in a fixed frame of reference is not the same as when measured by an observer in a moving frame of reference with a velocity corresponding to the rod. This means there is a length variation that happens in the observation. This length variation can be measured by this formula -

Where,

l = length of the object at motion

l0 = length of the object at rest

v = speed of the object

c = speed of light in vacuum

When the velocity of the rod v is very small compared to the velocity of light c (i.e v2/c2 is negligible compared to one), then l = l0.

When the velocity of rod v is comparable to the velocity of light c (i.e √(1-v2/c2) is less than one), then the rod appears shorter than its length when seen at rest (i.e l<l0).

When the velocity of the rod v is equal to the velocity of light c, then the length of the rod becomes zero (i.e l = 0).

In the hole process, the rod remains unchanged along the perpendicular direction but the contraction takes place in the direction of motion. Since the contraction of the rod takes place, the phenomenon are known as the length contraction.

Time dilation

In classical mechanics, time is regarded as an absolute quantity. But in special relativity, it is considered to be a relative entity based on the measurement of time in the frame of references in relative motion. The variation of the time in relative motion can be measured by this formula -

Where,

t = time in motion

t0 = time at rest

v = speed of the object

c = speed of light in vacuum

When the velocity of the object v of the moving frame of reference is very small compared to the velocity of light c (i.e v2/c2 is negligible compared to one), then t = t0.

When the velocity of object v of the moving frame of reference is comparable to the velocity of light c (i.e √(1-v2/c2) is less than one), then the time observation of the moving frame of reference appears greater than its in rest, (i.e t>t0).

When the velocity of the object v of the moving frame of reference is equal to the velocity of light c, then T = infinite. But Infinite time is meaningless, so we have come to the conclusion that no material body can move at the speed of light.

Mass energy relation

According to classical physics, there are two entities of nature - matter and energy. They are both immortal. That is, matter or energy is not destroyed, only one form of energy can be converted into another form of energy, similarly, it is applicable to matter. From all these things came the law of conservation of mass and conservation of energy.

Until Einstein, the concepts of mass and energy were seen as completely separate. He proved that the principles of conservation of mass and conservation of energy are part of the same large, unified principle, the conservation of mass energy.

In modern physics, according to Einstein's theory of relativity matters can be converted into energy and energy can be converted into matters because a fundamental relationship exists between these two kinds of entities. This relationship between mass and energy was first correctly deduced by Einstein, which is known as the mass-energy relation.

According to the mass-energy relation,

Where E = energy, m = mass of the objects, c = speed of light (299,792,458 m/s) in vaccum

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