RELATIVITY

Special Relativity # Who is Albert Einstein ? A. The concepts of relativity B. Postulates of relativity C. Relativity of time D. Relativity of mass E. Relativity of length F. simultaneity G. energy-mass equivalence

German–American Physicist Albert Einstein German–American Physicist 1955 – 1879 One of the greatest physicists of all time, Einstein was born in Ulm, Germany. In 1905 at the age of 26 he published four scientific papers that revolutionized physics. Two of these papers introduced the special theory of relativity, considered by many to be his most important work. In 1916, in an exciting race with mathematician David Hilbert, Einstein published his theory of gravity, called the general theory of relativity.

Halliday ch. 37 sections : 1-7 Serway ch. 26 sections : 1-7 The most dramatic prediction of this theory is the degree to which light is deflected by a gravitational field. Measurements made by astronomers on bright stars in the vicinity of the eclipsed Sun in 1919 confirmed Einstein’s prediction, and as a result Einstein became a world celebrity. Einstein was deeply disturbed by the development of quantum mechanics in the 1920s despite his own role as a scientific revolutionary. In particular, he could never accept the probabilistic view of events in nature that is a central feature of quantum theory. The last few decades of his life were devoted to an unsuccessful search for a unified theory that would combine gravitation and electromagnetism. resources Halliday ch. 37 sections : 1-7 Serway ch. 26 sections : 1-7

A. The concepts of relativity: Relative motion: Special relativity has the reputation of being difficult. It is not difficult mathematically. However, it is difficult in that we must be very careful about who measures what about an event and just how that measurement is made—and it can be difficult because it can contradict routine experience .

any engineer involved with the Global Positioning System GPS of the satellites must routinely use relativity (both special relativity and general relativity) to determine the rate at which time passes on the satellites because that rate differs from the rate on Earth’s surface. If the engineers failed to take relativity into account, GPS would become almost useless .

Frames of Reference A system, almost always a coordinate system, used to describe the position, and also the velocity and acceleration, of an object is called a frame of reference.

Types of Frames of Reference Inertial Frame of Reference An inertial frame of reference has a constant velocity. That is, it is moving at a constant speed in a straight line, or it is standing still. Understand that when something is standing still, it has a constant velocity. Its velocity is constantly zero m/s. Non-inertial Frame of Reference A non-inertial frame of reference does not have a constant velocity. It is accelerating. There are several ways to imagine this motion.

The speed of light is the same regardless of the source.

B. Postulates of relativity 1 B. Postulates of relativity 1. The Relativity Postulate: The laws of physics are the same for observers in all inertial reference frames. No one frame is preferred over any other. 2. The constancy of the speed of light: The speed of light in a vacuum has the same value, = 2997 924 58 .0 m/s, in all inertial reference frames, regardless of the velocity of the observer or the velocity of the source emitting the light.

C. Relativity of time

A clock moving past an observer at speed v runs more slowly than an identical clock at rest with respect to the observer by a factor of ɣ -1. The time interval Δtp is called the proper time. In general, proper time is the time interval between two events as measured by an observer who sees the events occur at the same position.

Recall β = v/c < 1 for all observers. Properties of γ Recall β = v/c < 1 for all observers. and equals 1 only when v = 0. Graph of β: (note v ≠ c)

9.61 s , 448 y

Time dilation is a very real phenomenon that has been verified by various experiments involving the ticking of natural clocks. An interesting example of time dilation involves the observation of muons, unstable elementary particles that are very similar to electrons, having the same charge, but 207 times the mass. Muons can be produced by the collision of cosmic radiation with atoms high in the atmosphere. These particles have a lifetime of 2.2 μs when measured in a reference frame at rest with respect to them. If we take 2.2 μ s as the average lifetime of a muon and assume that their speed is close to the speed of light, we find that these particles can travel only about 600 m before they decay

The Twin Paradox

D. Relativity of mass By the method of time

E. Relativity of length The measured distance between two points depends on the frame of reference of the observer. The proper length Lp of an object is the length of the object as measured by an observer at rest relative to the object.

According to this result, if an observer at rest with respect to an object measures its length to be Lp, an observer moving at a speed v relative to the object will find it to be shorter than its proper length by the factor Note that length contraction takes place only along the direction of motion.

PROBLEM a) An observer on Earth sees a spaceship at an altitude of 4 350 km moving downward toward Earth with a speed of 0.970c. What is the distance from the spaceship to Earth as measured by the spaceship’s captain? (b) After firing his engines, the captain measures her ship’s altitude as 267 km, whereas the observer on Earth measures it to be 625 km. What is the speed of the spaceship at this instant? ( 1.06 x 10 3 km ) (0.904 c m /s )

F. simultaneity Light in center of car flashes, hits front and back simultaneously. To an observer watching the car move, the car travels while the light is in motion. So the light hits the back of the car before the front.

THE LORENTZ TRANSFORMATION

THE LORENTZ TRANSFORMATION

G. energy-mass equivalence

Questions: 1. Which of the following statements are fundamental postulates of the special theory of relativity? (a) Light moves through a substance called the ether. (b) The speed of light depends on the inertial reference frame in which it is measured. (c) The laws of physics depend on the inertial reference frame in which they are used. (d) The laws of physics are the same in all inertial reference frames. (e) The speed of light is independent of the inertial reference frame in which it is measured.

Questions: 2- A spaceship moves at one-quarter the speed of light relative to Earth in a direction perpendicular to the line of sight of an observer at rest with respect to Earth. If the spaceship has a length L when at rest, which statement is true concerning the moving ship’s length L* as measured by the observer? L* > L (b) L* < L (c) L* = L (d) L* << L (e) L* >> L

Questions: 4. An astronaut is traveling in a rocket in outer space in a straight line at a constant speed of 0.5c. Which of the following effects would she experience? She would feel heavier. She would find it harder to breathe. (c) Her heart rate would change. (d) Some of her dimensions would be shorter. (e) None of these effects would occur.

Questions: 6. A cube measured at rest has volume V. An observer then passes the cube parallel to one of its sides at 0.98c, so ɣ = 5. What is the volume of the cube as measured by the moving observer? (a) V/125 (b) V/25 (c) V/5 (d) V (e) 5V

Questions: 7. Suppose a photon, proton, and electron all have the same total energy E. Rank their momenta from smallest to greatest. photon, electron, proton (b) proton, photon, electron (c) electron, photon, proton (d) electron, proton, photon (e) proton, electron, photon

Questions: 11. A distant astronomical object (a quasar) is moving away from us at half the speed of light. What is the speed of the light we receive from this quasar? (a) greater than c (b) c (c) between c/2 and c (d) c/2 (e) between 0 and c/2

Questions: 8. Two identical clocks are set side by side and synchronized. One remains on the Earth. The other is put into orbit around the Earth moving rapidly toward the east. As measured by an observer on the Earth, does the orbiting clock run faster than the Earth-based clock, (b) run at the same rate, or (c) run slower?

12-Special theory of relativity treats problems involving a) accelerated frame of reference b) inertial frame of reference c) non-inertial frame of reference d)non-accelerated frame of reference

13- According to special theory of relativity which one is not an absolute quantity a)time b)mass c) height d)both a and b

14- Length contraction happens only: a) perpendicular to direction of motion b) along direction of motion c) parallel to direction of motion d)both a and b