Relativity. Chapter 26. Introduction. Major Physics accomplishments by the end of the 19 th century Newton’s laws Universal gravitation Kinetic-molecular theory Laws of thermodynamics Maxwell’s theories which unified electricity and magnetism.
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Introduction • Major Physics accomplishments by the end of the 19th century • Newton’s laws • Universal gravitation • Kinetic-molecular theory • Laws of thermodynamics • Maxwell’s theories which unified electricity and magnetism
The Speed of Light • Everyday speeds are much slower than the speed of light. • Newton’s laws describe the motion of objects at such speeds. • They don’t work with things traveling near the speed of light. • Newton’s laws don’t place a speed limit on particles.
Special Relativity • Einstein published his special theory of relativity in 1905, at age 26. • It was one of the greatest intellectual achievements of the 20th century. • He felt that it was simple and consistent in explaining deep contradictions in the old theories.
Relativity Postulates • Two postulates form the basis of the special theory of relativity. • The laws of physics are the same in all inertial reference systems. • The speed of light is constant and does not vary with the motion of the source or the observer. (c = 2.99 792 458 x 108 m/s)
The Principle Of Galilean Relativity • What is a frame of reference? • It is a set of objects that are assumed to be at rest with respect to the observedevent. • The laws of mechanics are the same in allinertial(non-accelerated) reference frames. • Newton’s law of inertia is valid.
Common observations • There is no preferred frame of reference for describing the laws of mechanics. • Examples: • A ball thrown straight up in a plane • A ball rolled across the aisle in a train • Galileo showed this in a boat.
The Speed Of Light Paradox • If relativity applies to Newtonian mechanics, does it also apply to electricity, magnetism, optics, and other areas? • The speed of light paradox • A pulse of light sent forward by an observer in a moving boxcar. 26.2
Resolving the paradox • Either: • The addition law for velocities is incorrect. • Or: • The laws of electricity and magnetism are not the same in all inertial frames.
The Speed Of Light • Does light require a medium to travel through? • The luminiferous ether theory of the 19th century said “Yes!”. • The ether was supposed to be a massless fluid in space. • Scientists tried to prove or disprove its existence.
The Michelson-Morley Experiment • It was designed to determine the existence of the ether. • It proved that there was no ether. • The Michelson interferometer did not detect any change in the speed of light when it was rotated 90o.
Consequences Of Special Relativity • Our basic notions of space and time must change. (Newton was wrong!!!) • There is no absolute length. • There is no absolute time. • Events at different locations that occur simultaneously in one frame are not necessarily simultaneous in another frame.
Frames of Reference • There is no preferred frame of reference. • Both observers are correct in their own reference frames.
Time Dilation • Example: A vehicle moving to the right at a speed v • The time measured by an observer in a stationary frame is longer than that measured by the moving observer in his own reference frame. • A moving clock runs more slowly than an identical stationary clock. 271, 26.8 272
Proper Time • Proper time (Dtp) • The time interval between two events as measured by an observer who sees the events occur at the same place. • Measured with a single clock at rest in the frame in which the events take place at the same position • All physical processes slow down .
Time dilation has been verified. • Unstable muons entering our atmosphere • They travel farther than they should. • Muons accelerated in the laboratory • They “live” 30 times longer. • Clocks in jets • Clocks with the lunar astronauts 269
Length Contraction • Proper length (Lp) • The length of the object measured in the reference frame in which the object is at rest • Relativistic length contraction (L) • The length contraction only takes place in the direction of motion. • Applications for space travel to the stars 26.11, 273
Conservation of Momentum • We must now generalize Newton’s laws of motion, and the definitions of momentum and energy. • Momentum is not always conserved if we always use p = mv. 267
Relativistic Momentum • Relativistic momentum must be conserved in all collisions. • As v approaches zero, relativistic momentum must approach classical momentum.
Relativistic Addition Of Velocities • Velocities can no longer be added together as we did in Newtonian mechanics. • Objects cannot travel faster than the speed of light. 268
Electron-Positron Pairs • The rest energy of an electron has already been found to be 0.511 MeV. • Therefore, the electron-positron pair would require a photon whose energy was at least1.02 MeV. • Gamma rays • Short wavelength x-rays
