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Short Module In Understanding The Theory Of Relativity

Sir Isaac Newton considered space and time constant, but in a new understanding given by the general theory of relativity and special relativity theory, space and time are not constant, but can change and fluctuate like a fluid . Albert Einstein is the scientist behind this theory where he published the first part of this theory, namely the special theory of relativity in 1905. A decade later, Einstein published the second part, namely the general theory of relativity. Judi Slot Online MPO

Einstein’s Theory of Relativity

The special theory of relativity refers to two concepts:

  • The laws of physics apply to any object in all frames of reference that is moving at a constant velocity with respect to another; This means that the shape of the physical equation will always be the same even if it is observed in a moving state.
  • The speed of light in a vacuum is always the same for all observers and does not depend on the motion of the light source or observer (light travels as fast as c = 300,000,000 m/s).Einstein showed that no object with mass can travel at the speed of light.

In addition, Einstein’s theory of relativity above results in changes that slightly deviate from the experience we feel everyday, such as:

1. Velocity Relativity

We can know the speed of object I with respect to object II if we know the speed of another object (object III) with respect to object II and the speed of object I with respect to object III expressed by the formula:

v = \ frac {v_1 + v_2} {1 + \ frac {v_1v_2} {c ^ 2}}

where:

v is the speed of object I to object II
v 1 is the speed of object III to object II
v 2 is the speed of object II to object I
c is the speed of light

2. Time Expansion

Since space and time are not constant, the time interval observed by an observer at rest and the time interval observed by an observer moving with velocity v is not the same.

\Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}}

where:

\Delta t is the time interval observed by an observer moving with velocity v
\Delta t_0is the time interval observed by an observer at rest
v is the observer’s velocity

3. Lorentz contractions

Since space and time are not constant, an object of length L 0 will be observed as large as L by an observer moving parallel to the object with velocity v; The greater the speed of the observer, the object will appear shorter than its original length.

L = L_0 \sqrt{1 - \frac{v^2}{c^2}}

where:

L is the length of the object observed by the observer moving with a speed v
L 0 is the length of the object observed by the observer at rest
v is the speed of the observer

4. Relativity of Mass and Energy

Like space and time, the mass of an object observed by an observer at rest will be different from the mass of an object observed by an observer moving with velocity v.

m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}

where:

m is the mass of the object observed by the observer moving at a speed
m 0 is the mass of the object observed by the observer at rest
v is the speed of the observer

In addition, in relativistic mechanics, the energy of an object of mass m 0 (at rest) with a velocity v is defined by:

Ek = \frac{m_0c^2}{\sqrt{1 - \frac{v^2}{c^2}}} - m_0c^2

The total energy of an object with mass is found by:

E = E_0 + E_k

where E 0 is rest energy ( E = m_0 c^2).

From the interpretation above, an object with mass m has an energy of:

E = mc 2

So, another consequence of special relativity is that mass and energy have a relationship or can be said to be equivalent.

General Theory of Relativity

The general theory of relativity The general theory of relativity is a theory of gravity. In Newton’s statement, gravity is an invisible force that attracts objects to each other; but in general relativity, gravity is the curvature of space-time caused by the mass of an object. The heavier an object, the greater the curvature of space-time it creates. This curvature has an effect on time, the greater the gravity, the slower time will run in the curvature of space-time.

Examples of Relativity Theory Questions and Discussion

An astronaut who has a twin brother goes to space at the age of 32 in a spacecraft traveling at speeds up to 80% the speed of light. The astronaut returned to earth and at that time his twin brother was 44 years old. How old is the twin brother according to the astronaut who just returned to earth?
Discussion:

It is known that v = 0.8c

Because the question is according to the astronaut, the astronaut is a stationary frame, while his twin brother (who lives on earth) is a moving frame against the spacecraft.

then t = 44 – 32 = 12 years

So that:

\Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}}
12 = \frac{\Delta t_0}{\sqrt{1 - \frac{(0,8c)^2}{c^2}}}
12 = \frac{\Delta t_0}{\sqrt{1 - 0,64}}
12 = \frac{\Delta t_0}{0,6}

\Delta t_0 = 7,2 year

So according to the astronaut, the age of his twin sister should only increase by 7.2 years ( \Delta t_0), not by 12 years ( \Delta t).

So according to astronauts, his twin brother is only 32 – 7.2 = 39.2 years.

Read Also : SWPS Scientist : What are the Main Concepts of Physics