Relativity of Time and Length

Objective: The purpose of this experiment is to study the concept of Relativity of Time and Length. Different people in different frame of reference can feel the time, length of object, or velocity of events differently. For example, according to equation ∆t = γ∆t₀, observer who sees moving motion can feel a longer time than the person who is in a resting frame. For l=l₀ /γ
it states that the length measured by moving frame should be shorter than that measured by resting frame.

However, the relativity of time and length has to follow

Einstein’s Principle of Relativity

1.  The principle of relativity: The laws of physics must be the same in all inertial reference frames.

2.  The  constancy  of  the  speed  of  light:  The  speed  of  light  in  vacuum  has  the same value, c = 3.00 * 10⁸ m/s, in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light.

 v

γ = 1.20

 

 γ = 1.12             

          

 γ = 1.41

γ = 1.30

 

Conclusion

The time measured by the observer in moving frame is longer than that measured by the person in resting frame. This effect is called time dilation. Observers measure any clock to run slow if it moves relative to them. ∆t = γ∆t₀ With ∆t₀ represents the observer at rest in the same frame as the events. Besides the time difference, the distance between the two points is affected by different frame of reference. It is shown that the distance observed by moving frame is shorter than that observed by a resting frame, the proper length. This is called length contraction. This is consistent with the equation.When γ get larger, the speed increases. This is based on ratio u²/c2.  Also, the length, which is indicated by the blue line, measured by the resting frame is longer than that of moving frame, this is also consistent with the equation. However, only length parallel to the relative motion is affected by difference frame of reference. Lengths perpendicular to the relative motion is not affected.