Tutorial:

Tutorial examples will be posted at least a day before the tutorial so you can think about them to benefit most from the tutorial

Regular Quizzes (every 2-3 weeks, 15-20 min each) during tutorial

Relativity and QuantaPHYS 242Fall 2013

Lecture:

Lecture notes available ahead of time - READ and answer Pre-Lecture Quiz (Moodle)Tell me your questions via Moodle (or in class) – that’s what we’ll discuss

Assignments:

Will be posted Fridays, are due Monday, 10 days later, during the tutorial.

Exam:

Final exam in December (3 h)

Marking scheme:

Lecture Quizzes: 10 %Tutorial Quizzes: 15 %Assignments: 25 %Exam (final): 50 %

concepts, ideas, some derivations of fundamental formulae

application of the concepts, examples (help for assignments)

examples: experience in applying concepts to actual problems, feedback on learning success, practice for exam (assessment)

Motivator for learning, assessment

W. Rau

Books

Relativity and QuantaCustom version of: Serway, Moses, Moyer: Modern Physics ; Brooks/Cole -- Thomson Learning (available at Campus Book Store)

A.P. French: Special Relativity  W.W.Norton & Company Inc. New York

R. Eisberg, R. Resnick: QUANTUM PHYSICS of Atoms, Molecules, Solids, Nuclei and Particles John Wiley & Sons, New York, London, Sydney, Toronto

Course Web page:

http://www.physics.queensu.ca/~phys242/ :Lecture Notes, Assignments, Tutorial Questions, Solutions

Moodle: Pre-Lecture Quizzes, YOUR Questions, Grades

Relativity and QuantaPHYS 242Fall 2013

W. Rau

Newton’s laws:1. Inertia: Any object moves with constant velocity as long as no net force acts upon it2. Action: Any object experiences acceleration in presence of a net force: F = ma3. Reaction: If force F acts upon an object, –F acts upon the object where the force originates.

Classical mechanics

Inertial system: Reference frame where Newton’s 1. law applies.

any reference frame that moves with a constant velocity relative to a given inertial system, is also an inertial system and vice versa (any inertial system moves with constant velocity relative to any other inertial system)

Relativity Principle: The evaluation of an observation leads to the same conclusions about the laws of physics in any inertial system

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S S '

V

Coordinate transformation:x = x' + Vt' y = y' z = z ' t = t'

Velocity transformation:vx = vx' + V vy = vy' vz = vz'

x = x ' + R

x ' = ( ) x ''

x = ( ) x '' + R

t = t' + Dt

→ → →

cos a sin a-sin a cos a

→ →

cos a sin a-sin a cos a

→ → →

Coordinate Transformation

v = –– = ––––––– = –– + ––– = v ' + V dx d(x '+ R ) dx ' dRdt d(t' + Dt) dt' dt

→→ →

→→→→ →

Choose: x = x‘ = 0 for t = t‘ = 0, V ║ x

Galilean law for the addition of velocities:

v = v ' + V

(V: velocity of S ' w.r.t. S )

→ → →

→

St1

x1

y1

x1''

y1''

S'' t1''

αx1'

y1'

S'

t1'

R = (∆x,∆y)⃑x⃑

x'⃑

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Boat

Fog

Fog Reference frame of the boat

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Fog

Fog

Wood

Reference frame of the wood

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Wood

Fog

Boat

Fog

Reference frame of the wood(but observer on the boat)

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vx = 0vy = 0

v0

vx,ball = 0vy,ball = v0 - gt

S

S'

Reference frame of the boat

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S''v0

vx,bqll = vvy,ball = v0 - gt

vvx = vvy = 0

S

S'

Reference frame of the wood

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vx,ball = vvy,ball = - gt

v

v0

v

S''

vx = vvy = – v0

S

S'

Reference frame of the elevator

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How to Produce Spacetime diagrams

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How to produce spacetime diagrams (II)

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Spacetime diagram Boat(at rest)

Wood(moving)

Space

Tim

e

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Boat

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Spacetime diagrams

Boat (center)

Passenger (front)

Passenger (back)

Ball 1

Wood

Ball 2

Boat(center)

Passenger (front)

Passenger (back)

Ball 2

Wood

Ball 1

vB1 = v ; vB2 = – v

vB1 = vB1' + V vB1' = vB1 – V = v – V

vB2 = vB2' + V vB2' = vB2 – V = – v – V

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Boat

Reference frame of boat and water

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Source at rest with respect to medium

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Source moving with respect to medium, frame of medium

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Source moving with respect to medium, frame of source

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Boat

Reference frame of the boat; water moving

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Wood

Reference frame of the wood; boat moving with water

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Source at rest with respect to medium;both are moving relative to reference frame

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vc

Xs

v

X

Case A:Source and Receiver

at rest

Case B:Source moving with

velocity v

Case C:Receiver moving with velocity – v

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SourceReceiver SourceReceiver

Case B

Rest frame of source(and water)

Rest frame of receiver(and water)

Case A Case C

DtR,C

x = v Dt x = 0

t = Dt

t = 0

t1

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SourceReceiver

Case B

Rest frame of receiver(and water)

SourceReceiver

Case B

Rest frame of source

Case C

DtR,B

Rest frame of source(and water)

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Summary

Newton’s Laws1. Inertia: v constant for F = 02. Action: F = ma3. Reaction: each force is balanced

by counter force

Reference Frames, Coordinate SystemsReference frame: “point of view”Coordinate system / transformation: Specify position / time in different frames

S S '

V

x = x' = 0 for t = t' = 0, V = Vx = const.:x = x' + Vt ; vx = vx' + V ; a = a‘

Inertial frame Reference frame where N.’s 1. law applies

Spacetime DiagramsA way to keep track of the position of objects in time

Propagation of Waves, Doppler Effect- Waves propagate with constant vc relative to medium- Observed frequency n depends on velocity of source

vs and receiver vr relative to medium:Moving source: nr = ns / (1 – v/vc)Moving receiver: nr = ns (1 + v/vc)

- Wavelength depends only on vs

Boat (center)

Passenger (front)

Passenger (back)

Ball 1

Wood

Ball 2

t

x

Galilean velocity transformationv= v'+V

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