Transcript Document

Relativity and Quanta
ENPH / PHYS 242
Fall 2014
Lecture: concepts, ideas, some derivations of fundamental formulae
Lecture notes available ahead of time
- look at them and answer Pre-Lecture Quiz (Moodle)
Tell me your questions via Moodle (or in class) – that’s what we’ll discuss
Tutorial: application of the concepts, examples (help for assignments)
Will discuss example problems, answer questions for lecture/assignments
Regular Quizzes (every 2-3 weeks, 15-20 min each) during tutorial
Marking scheme:
Lecture Quizzes:
Tutorial Quizzes:
Assignments:
Exam (final):
10 %
15 %
25 %
50 %
Assignments: examples: experience in applying concepts to actual
problems, feedback on learning success, practice for exam (assessment)
Will be posted between Wed. and Fri., are due Friday, the week after, at
the end of the Friday lecture.
Exam: motivator for learning, assessment
Final exam in December (3 h), covers the whole course
Relativity and Quanta
ENPH / PHYS 242
Fall 2014
Assignments:
– You are EXPECTED to work in groups (typically 4-5 people)
– Everybody needs to hand in a solution; write down all members of
your group! If possible at all hand in together
– You may hand in identical solutions
– Photocopies or duplicate printouts are ABSOLUTELY NOT
ACCEPTABLE
Everybody must write / type out the solution individually
---------------------------------------------------------------------------------------– Make sure you write down units where appropriate; we will subtract
marks if you don’t
– Write down a reasonable number of significant figures; we will
subtract marks if you don’t
– Diagrams need axis labels and scales and all objects must be
identifiable – use a ruler
– Late Penalties apply – see web page
Relativity and Quanta
ENPH / PHYS 242
Fall 2013
Course Web page:
http://www.physics.queensu.ca/~phys242/ :
Lecture Notes, Assignments, Tutorial Questions, Solutions
Moodle: Pre-Lecture Quizzes, Grades, Discussion Forum
Books
Relativity and Quanta
Custom 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
Coordinate Transformation
→
→
→
x =x'+R
t = t' + Dt
S'
y1
S
x'
⃑
t1
α
x1'
⃑ = (∆x,∆y)
R
S''
y1'
x⃑
x1
cos a -sin a
cos a
x→ ' = ( sin a
t1'
x1''
y1''
cos a -sin a
cos a
→
x = ( sin a
t1''
→
→
→
) x→ ''
→
→
) x '' + R
→
→
→
d(x '+ R ) = ––
dx '+ –––
dR = →
v = dx
–– = –––––––
v' + V
dt
d(t' + Dt) dt' dt
→
Galilean law for the addition of velocities:
→
→
v =→
v'+V
→
(V: velocity of S ' w.r.t. S )
Coordinate Transformation
→
→
→
x =x'+R
t = t' + Dt
S'
y1
S
S''
y1'
x'
⃑
t1
cos a -sin a
cos a
x→ ' = ( sin a
t1'
x1''
α
x⃑
x1'
⃑ = (∆x,∆y)
R
x1
y1''
cos a -sin a
cos a
→
→
→
→
→
→
x = ( sin a
t1''
) x→ ''
) x '' + R
→
→
→
d(x '+ R ) = ––
dx '+ –––
dR = →
v = dx
–– = –––––––
v' + V
dt
d(t' + Dt) dt' dt
→
Galilean law for the addition of velocities:
→
→
v =→
v'+V
→
(V: velocity of S ' w.r.t. S )
Choose: x = x' = 0 for t = t' = 0, V ║ x
V
S
S'
Coordinate transformation:
x = x' + Vt'
y = y'
z=z'
Velocity transformation:
vx = vx' + V
vy = vy'
vz = vz'
t = t'
Classical mechanics
Newton’s laws:
1. Inertia:
Any object moves with constant velocity as long as no net force acts upon it
2. Action:
Any object experiences acceleration in presence of a net force: F = ma
3. Reaction: If force F acts upon an object, –F acts upon the object where the force originates.
From previous Slide:
Galilean law for the addition of velocities:
v=v'+V
(V: velocity of S ' w.r.t. S )
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
Reference frame of the boat
Fog
Fog
Boat
 W. Rau
Reference frame of the wood
Fog
Fog
 W. Rau
Reference frame of the wood
(but observer on the boat)
Fog
 W. Rau
Reference frame of the boat
vx,ball = 0
vy,ball = v0 - gt
v0
S
vx = 0
vy = 0
S'
 W. Rau
Reference frame of the wood
vx,bqll = v
vy,ball = v0 - gt
v0
S
vx = v
vy = 0
S''
v
S'
 W. Rau
Reference frame of the elevator
vx,ball = v
vy,ball = - gt
v
S''
S
vx = v
vy = – v0
v
v0
S'
 W. Rau
How to Produce Spacetime diagrams
 W. Rau
How to produce spacetime diagrams (II)
 W. Rau
Spacetime diagram
Boat
(at rest)
Time
Wood
(moving)
Space
 W. Rau
Boat
 W. Rau
 W. Rau
Spacetime diagrams
Ball 1
Ball 2
Ball 1
Ball 2
Passenger
(back)
Passenger
(front)
Wood
Passenger
(back)
Passenger
(front)
Boat
(center)
Wood
Boat
(center)
vB1 = v ; vB2 = – v
vB1 = vB1' + V  vB1' = vB1 – V = v – V
vB2 = vB2' + V  vB2' = vB2 – V = – v – V
 W. Rau
Reference frame of boat and water
Boat
 W. Rau
Source at rest with respect to medium
 W. Rau
Source moving with respect to medium, frame of medium
 W. Rau
Source moving with respect to medium, frame of source
 W. Rau
Reference frame of the boat; water moving
Boat
 W. Rau
Reference frame of the wood;
boat moving with water
 W. Rau
Source at rest with respect to medium;
both are moving relative to reference frame
 W. Rau
Case A:
Source and Receiver
at rest
Case B:
Source moving with
velocity v
s
X
X
vc
v
Case C:
Receiver moving
with velocity – v
 W. Rau
Rest frame of source
(and water)
Case A
Rest frame of receiver
(and water)
Case C
Case B
x = v Dt x = 0
t1
DtR,C
t = Dt
t=0
Receiver
Source
Receiver
Source
 W. Rau
Rest
Rest frame
frame of
of receiver
source
(and water)
water)
(and
Rest frame of source
Case
Case
BC
Case B
DtR,B

Receiver
Source
Receiver
Source
 W. Rau
Summary
Newton’s Laws
1. Inertia: v constant for F = 0
2. Action: F = ma
3. Reaction: each force is balanced
by counter force
Inertial frame
Reference frame where Newton’s 1. law applies
Spacetime Diagrams
A way to keep track of the position of objects in time
Ball 1
Reference Frames, Coordinate Systems
Reference frame:
“point of view”
Coordinate system / transformation:
Specify position / time in different frames
V
S
t
Passenger
(front)
x
Wood
Passenger
(back)
Boat
(center)
S'
x = x' = 0 for t = t' = 0, V = Vx = const.:
x = x' + Vt ;
vx = vx' + V ;
a = a‘
Galilean velocity transformation
v= v'+V
Ball 2
Propagation of Waves, Doppler Effect
- Waves propagate with constant vc relative to medium
- Observed frequency f depends on velocity v of source
(S) and receiver (R) relative to medium:
S moving with v towards R: fR = fS / (1 – v/vc)
R moving with v towards S: fR = fS (1 + v/vc)
- Wavelength depends on f measured in the frame of
the medium
 W. Rau