chapt1 relativity dr. maha torjman

Modern Physics ( PHY 250)

Chapt1 Relativity

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

1.2 Einstein’s Principle of Relativity

- impossibility of measuring the speed of the ether with respect to the Earth and the faliure of the Galilean velocity transformation equation in the case of light.

- Einstein proposed a theory that boldly removed these difficulties and at the same time completely altered our notion of space and time.

He based his special theory of relativity on two postulates:

Dr. Maha Torjman

He based his special theory of relativity on two postulates

Dr. Maha Torjman

Dr. Maha Torjman

1-3 C0nsequences of the Special Therory 0f Relativity

We restrict the discussion to the concepts of simultaneity, time intervals, and lengths

This three of which are quite different in relativistic mehanics from Newtonian mechanics .

1-3-1- Simultaneity and the Relativity of Time:

Einstein devised the following thught experiment to illustrate this Point :

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

1-3-2 Time Dilation

Dr. Maha Torjman

Dr. Maha Torjman

1-3-2 Time Dilation

O concludes that, because of the motion of the vehicle, if the light is to hit the mirror, it must leave the Laser at an angle with respect to the vertical direction.

Comparing Figure (a) with Figure(b) , we see that the Light must travel faster in (b) than in (a).

Second postulate of the special theory of relativity : O and O/ must both measure C for the speed of Light .

The light travels farter in the frame of O so ( The time interval ∆t measured by O is longer than the time interval ∆tp measured by O/ .

This effect is known as time dilation .

Using the right triangle shown in Figure ( 1.5.c) , the Pythagorean theorem gives :

Dr. Maha Torjman

Dr. Maha Torjman

∆tp is called the proper time

Dr. Maha Torjman

Dr. Maha Torjman

The time interval between two events is always longer than the Proper time

Dr. Maha Torjman

1-3-3 Length Contraction

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

The Proper Length

Dr. Maha Torjman

Dr. Maha Torjman

1-4 The Lorentz Velocity Transformation Equation

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

1-5 The Lorentz velocity Transformation Equation

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

1-6 Relativistic Linear Momentum

Dr. Maha Torjman

Dr. Maha Torjman

1-7 Relativistic Energy

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Dr. Maha Torjman

Mass as A Measure of Energy

- Energy unit in subatomic physics

Dr. Maha Torjman

Dr. Maha Torjman

1-8 Mass and energy

Dr. Maha Torjman