# Special Relativity

## Newtonian Mechanics ( Low Speed ) - ## Newtonian Mechanics ( High Speed ) - ## Time Dilation

### In order to explain how Time can be variable, Einstein created a series of Thought Experiments to aid understanding :- ## Time Dilation Calculations

### The formula below is used to calculate the effects of Time Dilation :- ## The Lorentz Factor

### The scaling factor in the above equation is called the Lorentz Factor. The Lorentz Factor is used both in Time Dilation and Length Contraction to take into account the effects of relative speed. The Lorentz Factor is given the symbol Ɣ and is given by :- ### Note - Due to the ratio of v2/c2 within the Lorentz Factor, for low speeds the value of is approximately 1 and no time dilation is seen and classical mechanics can apply. However, at speeds greater than 0.1C, the value rises rapidly and time dilation can be observed. ## Example 1 -

### c = 3x108 ms-1 ## Example 2 -

### Mean lifetime by Earth observer :- ## Length Contraction

### Length Contraction is the second alternative effect of Special Relativity. Length Contraction again occurs in order to keep the speed of light a constant in all Inertial frames of reference. ## Length Contraction Visually

### The diagram below shows the effect of Length Contraction on an object for varying values of velocity :- ## Length Contraction Calculations

### The formula below is used to calculate the effects of Time Dilation :- ## The Lorentz Factor

### The scaling factor in the above equation is called the Lorentz Factor. The Lorentz Factor is used both in Time Dilation and Length Contraction to take into account the effects of relative speed. The Lorentz Factor is given the symbol Ɣ and is given by :- ## Example 2 -

### c = 3x108 ms-1 