Chapter R1 The Principle of Relativity Chapter R1 problems due Wednesday. R1B1, B2, and S.1.

Chapter R1

The Principle of Relativity

Chapter R1 problems due Wednesday. R1B1, B2, and S.1

Introduction

• If you wish to see your final exams from first semester, you may come to my office. The exams stay with me.

• Second semester (approximately)– 2 weeks of relativity (Unit R)– 9 weeks of unit E (electricity)– 4 weeks of unit Q (modern physics)

Lab• Because there are no relativity labs we will

begin with electricity labs. Some labs will be used relativity to work relativity problems.

• The first labs on electricity will require at least two lab periods to complete.

• The two labs next week will be the multimeter. Measuring voltage, current and resistance.

• Textbook issues– I will indicate sections of the book that merit special

interest and sections that can be skipped.– I welcome suggestions on how to improve the class.

• None of R1 can be skipped.

• I will collect the problems on the day they are due and will try to have them back by the next lecture. Late problems will receive 50%.– Look at the problems on the day they are assigned

and ask any questions in the following class. Hand them in the next class.

• I reiterate my opinion that an effort on the problems is the most efficient way to learn physics.

• Chapter R1 problems due Wednesday. R1B1, B2, and S.1.

Why study relativity?• Relativity is a description of the world as it

really is.• The study of relativity is an excellent mental

exercise – it will stretch your brain – change the way you think.

• Relativity is a very simple idea with very strange conclusions.

• Students tell me they enjoy it and believe it should stay in the course– At the end of the semester you will be asked your

opinion on this.

You are in a large box (the size of this room). What experiment can you do to tell you if you are moving or sitting still. You can ask for any piece of scientific

apparatus, regardless of cost to help you answer the question.

• There is no experiment that will tell you.

Chapter R1 – Reference Frames

• The Principle of Relativity

• The laws of physics are the same in a laboratory moving at constant velocity as they are in one at rest.– This principle was first stated by?– Galileo Galilei

Definitions

• What is a laboratory?– A place to measure the laws of physics.

• Which physics law is the easiest to test?– Newtons laws of motion.– Especially the first law

• What is the easiest way to test for this law?

Reference frames

• A reference frame is a tool we use that enables us to assign space-time coordinates

• An observer is one who interprets the results obtained in a reference frame to reconstruct the motions of particles

A reference frame is defined to be a rigid cubical lattice of appropriately synchronized clocks or its functional equivalent.

The spacetime coordinates of an event are an ordered set of four numbers

the time, t, and x, y and z.

• What name do we give to a coordinate system in which the first law of Newton is obeyed?– An inertial reference system

• How do we measure the space time coordinates of an event.– Give the x, y, and z coordinates and get the time from

the nearest clock.

• Our coordinate system has a clock at each (x,y,z) point.– When an event occurs, we record the position and the

time.

• How do we set all our clocks to the same time.– Take a “standard” clock to each point and set all the

clocks to the time on that standard clock

What is the principle of relativity?

• The laws of physics are the same in all inertial reference systems.

• Again, what is an inertial reference system?– One in which Newton’s first law is always obeyed.– One in which all the laws of physics are the same as

they are in a laboratory at rest.

• As the velocities of objects in two coordinate systems are different the momenta of the objects is different, but momentum is conserved in both systems.– This is what is meant by the laws of physics being the

same in both systems.

Standard Reference System

• The “home” system is usually chosen to be at rest with respect to the laboratory.

• The “other” or prime system is usually chosen so that it moves in the + x direction of the home reference system.

x

y

z

O

x’

y’

z’

O’

The “home” system (usually at rest with respect to us.)

The “other” system (moving with a constant velocity β in the x direction).

β

Pr(x,y,z)r’(x’,y’,z’)

βt

zz

yy

txx

tt

ttrtr

'

'

'

'

)'(')(

zz

vy

xx

vv

vv

vv

'

'

'

Newtonian Relativity• A bug is traveling 3 m/s East on a train that is

traveling north at 10 m/s. What is the velocity of the bug in the standard home system?– Standard reference system x = East, y = North, z

= up.

• vx=3 m/s, vy= 10 m/s, vz= 0• If the bug were crawling 3 m/s south on the

train?• vx=0 m/s, vy= 7 m/s, vz= 0

More transformation equations

• When the prime system is moving β m/s in the x direction with respect to the lab (x,y,z) system.

• t’=t

• x’=x-βt, y’=y, z’=z

• vx’=vx-β, vy’=vy, vz’=vz

• ax’=ax, ay’= ay, az’=az