## Introduction

Newton's three laws of motion for several decades remained a matter of course. Until 1905, the physicist Einstein published a paper questioning the accuracy of these laws, which are now known as the Special Theory of Relativity, followed by the General Theory of Relativity, Its lack of understanding, where this understanding was based primarily on Newton's law of gravity. The theory of relativity states that the laws of physics do not change and are the same everywhere. The theory has explained the behavior of objects and elements in time and space; it can be used to predict anything from the presence of black holes to the curvature of light due to gravity and the behavior of Mercury in its orbit. In this assignment it will be discussed firstly, the operational definition and a brief discussion of the Special Theory of Relativity, then a solved sample problem illustrating the theory. Finally a general conclusion on the solved problem.

## Literature Review

The theory of special relativity contains two basic hypotheses. The first states that the laws of physics are variable and relative depending on the position or context. Einstein has reached this belief by observing static and moving objects at constant velocities. For example, when observing a suspended object on a moving train, the train sees that the body moves from one position to another at a certain speed, but if a person looks at the train itself it will not distinguish the movement of the body, and its rest is static. This hypothesis applies to all particles by nature, except for light. Special relativity theory: and stressed that the speed of light constant, even with reference different context. In other words, the speed of light in vacuum is always constant and its value is 3x108 m/s regardless of the speed of the light source itself or the speed of the monitor.

As a result of the first hypothesis, absolute velocities cannot be measured but only velocities are determined for another body. If we find out about the speed of a car, it is for the Earth. If you find another car moving at the same speed as the first car in the same direction, the speed seen by a person in the second car is zero and so for someone in the first car, he will see the second car moving at a speed equal to zero. As a result of Einstein's hypotheses we can, by logic, prove that the speed of light is the upper limit of all velocities and that no particle with energy can accelerate the speed of light.

### Sample Problem:

An observer standing on the platform of a train station passing by a train of speed v= 0.8 c This observer measures the length of the platform and finds it 60 m long. This observer also notes that the front of the train and its back ends are line up with the end of platform at same time.

- How long does it take the train to pass a fixed point on the platform for the observer standing on the platform?
- What is the real length of the train, as measured by a train passenger?
- What is the length of the platform as measured by a passenger on the train?
- What is the time it takes for the train to pass to a fixed point on the platform as measured by a passenger on the train?

### The answer:

Suppose that the O observer is standing on the platform of the train station and the observer 'O' is a passenger train.

(a) Train speed v = 0.8 c. Platform length L= 60 m

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The time taken by the train to pass a fixed point on the platform for the observer standing on the platform is:

Δt =L/v = 60/0.8c = 2.5x10-7sec.

(b) The real length of the train, as measured by a train passenger is: 100m

(c) The length of the platform as measured by a passenger on the train is: 36m

(d) The time taken by the train to pass a fixed point on the platform as measured by a passenger on the train is: L1/v = 100 m / 0.8 c = 0.417 µЅ

## Conclusion

As it was discussed that Einstein's theory of special relativity is based on two basic assumptions: The laws of physical phenomena are the same in all systems and take the same mathematical picture, for example Newton's laws of motion can be expressed in the same form in all systems, regardless of the different values. The speed of light in vacuum is always constant regardless of the speed of the light source itself or the speed of the monitor.

It can be concluded from the solved problem that the observation of same event for a person on the train is different from a person standing on the platform of a train station. That means simultaneity between two events is relative (i.e., different from one person to another), and that what a person sees as two specific events may not be seen by another person as well. This led to an intuitive idea: that time flows differently according to the state of motion, and to the conclusion that the distance is also proportional. Therefore, the theory of Special relativity can be seen as an introduction to operational definitions of event and distance synchronization, which provides the processes needed to define these terms.

### References

- E.Howell. (2017). Einstein's Theory of Special Relativity .Retrieved from: https://www.space.com.
- J.Emspak. (2017). 8 Ways You Can See Einstein's Theory of Relativity in Real Life. Retrieved from: https://www.livescience.com/58245-theory-of-relativity-in-real-life.html
- H.Klus. (n.d).Einstein’s theory of Special Relativity. Retrieved from: http://www.thestargarden.co.uk/Special-relativity.html
- Special relativity. (n.d). Retrieved from: https://en.wikipedia.org/wiki/Special_relativity
- Special relativity. (n.d). Retrieved from: https://www.physicsoftheuniverse.com/topics_relativity_special.html
- What is the Special Theory of Relativity? (n.d). Retrieved from: https://www.scienceabc.com/pure-sciences/what-is-special-theory-of-relativity.html