Special Relativity

Special Relativity 

 *RELATIVITY BEFORE EINSTEIN:

• Absolute space and time
• Newton’s Laws of Motion
• These laws allow us to describe the motion of objects, regardless of size or position.
• This leads to a ‘Clockwork-type’ of the World.
• Clocks tick at the same rate regardless of their movement and position.
• The laws of physics remain the same whether one is moving steadily or at rest.
• ‘Frame of reference’

 *JAMES CLERK MAXWELL: 

• His theory of Electromagnetism showed that light is an electromagnetic wave.
• Maxwell’s equations allowed the speed of light to be predicted theoretically.
• Experiments undertaken by Michelson was in agreement with the predicted value.
• Einstein concluded that the speed of light is constant for all observers.
• Maxwell’s equation didn’t take speed or direction into account.


* CONSEQUENCES: 

• Newtonian idea of absolute space and time was rejected.
• Observers moving relative to each other with a constant velocity, in different reference frames,            would disagree about the measured separation in space and time of events they observed.
• So, two events may be simultaneous for one observer but not for the other observer.

* SUMMARY: 

Special relativity (which applies to observer/reference frames in relative motion with constant velocity) has two postulates:

1. The laws of physics are the same for all observers inside their frame of reference in all parts of the universe.

2. Light always travels at the same speed in vacuum 299,792,458 m/s. It is also the same for all observers irrespective of their relative velocities.

From these two postulates Einstein produced a new theory of motion.
We know that speed = Distance/time, and speed = fλ, hence if the speed is to remain constant ‘something’ must happen to the distance and time! This is the essence of special relativity.

 *SPECIAL RELATIVITY: 

• Special because it considers only the case where different observers are in relative motion with a   constant velocity.

• Einstein supported the Newtonian view that the laws of physics should apply everywhere.

• Work of James Clerk Maxwell led to an apparent contradiction with this principle.

* EXAMPLE: 

A spaceship traveling at 100 million m/s approaches a planet considered to be at rest. An observer on the planet sends a light signal to the spaceship. The spaceship will measure the speed as 299,792,458 m/s and not (299,792,458 + 100,000,000 ) m/s. We can not apply our usual ‘Newtonian rules’ for relative velocity.

* PROOF OF GENERAL RELATIVITY: 

 *MUONS:

• Muons are unstable particles.
• They decay into electrons with an average lifetime of 2.2 microseconds as measured in their inertial frame of reference.
• When high energy particles called cosmic rays enter the atmosphere from outer space, they interact with air molecules in the upper atmosphere creating a cosmic ray shower of particles including muons that reach the Earth’s surface.
• Muons travel at a speed of 0.98c (2.94x10^8 m/s).
• Average distance traveled by Muons before decaying, S=vt.
• S= 294x10^8 x 2.2x10^-6=650 m.
• Hence, from a Newtonian point of view, muons would not be able to reach the Earth’s surface from the upper atmosphere.
• They still reach Earth because of ‘Time Dilation’.

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