Chapter 26 relativity

26.1 Introduction -> 26.5 Einstein’s Principle of Relativity

� The Postulates of Special Relativity �

1. The Relativity Postulate. The laws of physics are the same in every inertial reference systems.

2. The Speed of Light Postulate. The speed of light in a vacuum is always measured to be 3x 10⁸ m/s, no matter how fast the source of light and the observer are moving relative to each other.

26.2 The Principle of Relativity

• An inertial reference frame is one which Newton’s law of inertial (Newton’s first law) is valid. If the net force acting on a body is zero, the body either remains at rest or moves at a constant velocity.

• Figure 26.1 (There is no preferred frame of reference for describing the laws of mechanics.)

26.6 Consequences of Special Relativity

<Simultaneity and the Relativity of Time >

• Time interval measurements depend on the reference frame in which they are made.

• Two events that are simultaneous in one reference frame are in general not simultaneous in a second frame moving with respect to the first. That is, simultaneity is not an absolute concept.

• There is no preferred inertial frame of reference.

< Time Dilation >

• Time is measured by a light clock where a pulse of light bounces back and forth between mirror and detector (tick-tock).

• Figure 26.8 (The time interval between successive ticks for two observers.)

• To the ground observer, the pulse in the vehicle travels a longer path.

=

= time interval measured by the observer who is at rest with respect to the events and who views them as occurring at the same place (in the vehicle)

= time interval measured by an observer who is in motion with respect to the events and who views them as occurring at difference places (on earth)

v = relative speed between the two observers

c = speed of light in vacuum

• According to a stationary observer, a moving clock runs more slowly than an identical stationary clock by a factor of . This effect is known as time dilation.

• Examples

<Verification of Time Dilation>

• The lifetime measurements of muons

• In 1971 Hafele and Keating transported precise cesium-beam atomic clocks around the world on commercial jet for 45 hours and compared it with the ground-based reference atomic clocks. They found the clocks on the planes were different from those on earth.

• Examples

< The Twin Paradox >

< Length Contraction >

• The proper length is defined as the length of the object measured in the reference frame in which the object is at rest.

• The length of an object measured in a reference frame in which the object is moving is always less than the proper length. This effect is known as relativistic length contraction.

L = L_p

where L_p is the proper length, v is the relative speed between the two observers.

• Example

26.7 Relativistic Momentum (Skip)

26.8 Relativistic Addition of Velocities (Skip)

26.9 Relativistic Energy

<The Total Energy of an Object>

• The total energy E of the moving object with a velocity v and mass m is

E =

• When v = 0, the total energy is called the rest energy E_o.

E_R = mc²

• One of the most astonishing results of special relativity is that mass and energy are equivalent, in the sense that a gain or loss of mass can be regarded equally well as a gain or loss of energy.

• Examples

26.10 General Relativity (Skip)