Announcements

Announcements
NONCLASSICAL PHYSICS
Beyond Newton’s View
* 9/1 (Thursday) at 3:40 pm (Sci 234) – Physics
Colloquium by Prof.Grave-de-Peralta on nano-optics
(Refreshment at 3:00 pm in Sci 103)
•! SPS meeting tomorrow (5:00pm; sps room)
•! 9/2 (Friday) at 5 pm: meeting between faculty &
phyiscs majors/minors.
*** Course Web Page **
http://highenergy.phys.ttu.edu/~slee/2402/
Lecture Notes, HW Assignments,
Schedule for the Physics Colloquium, etc..
No
ncl
ass
ica
l Ph
y si
cs
Small => e.g. atomic size
How Small
Fast => v~c
is “Small”?
c= the velocity of light
How Fast
is “Fast”?
Lecture 2 – Chapter. 2
Special Relativity
!"#$%&'()
Our First Topic
!!"Basic Ideas
•! Consequences of Einstein’s Postulates
•! The Lorenz Transformation Equations
•! The Twin Paradox
•! The Doppler Effect
•! Velocity Transformation
•! Momentum & Energy
•! General Relativity & a 1st Look at Cosmology
Einstein’s Postulates of Relativity:
(Albert Einstein, 1905)
Postulated in an attempt to explain the laws of Classical
Electromagnetism
(Maxwell’s Equations, constancy of the speed of light)
1st Postulate:
The form of each physical law is the same in all
inertial frames of reference
INERTIAL FRAME = ?
Einstein’s Postulates of Relativity:
•
•
•
Light Souce, Medium and Michelson- Morley
Experiment (Discussion sessions, see Appendix A)
Definition of an “Event”
Consequences of Einstein’s Postulates:
1. Relative Simultaneity
2. Time Dilation
3. Length Contraction
2nd Postulate:
Light moves with the same speed (c)
relative to all observers
Anna measures:
Speed of light = c
The reference frame in which an
object experiencing zero net force – a “free” object –
moves at constant velocity
v = constant
?
Bob measures:
Speed of light = c
and not
v+c
Michelson-Morley Experiment
Proves that There is no Medium that light
travels in
(Hypothetical Aether)
Will be discussed at Discussion Sessions
Einstein’s Postulates of Relativity:
Consequence 1:
Relative Simultaneity, or
The absence of absolute simultaneity
Simultaneous Flash
•
•
Light Souce, Medium and Michelson- Morley
Experiment (Discussion sessions, see Appendix A)
Definition of an “Event”
• Consequences of Einstein’s Postulates:
1. Relative Simultaneity
2. Time Dilation
3. Length Contraction
Simultaneous Arrival
=> AN EVENT
2nd Postulate
THEN:
Simultaneous Arrival
Simultaneous Arrival
!The same EVENT
For Bob as well!
!AN EVENT
For Bob as well!
Simultaneous
Emission is
impossible
for Bob
2nd Postulate
Both emission
and arrival are
simultaneous
BUT THEN:
Simultaneous Arrival
!AN EVENT
For Bob as well!
Simultaneous
Emission is
impossible
for Bob
Consequence 2:
Time Dilation, or
The absence of absolute time
Arrival is simultaneous
But Emission is not
simultaneous
The time for the light to return:
!= 2"/c
The time for the light to return:
! = 2"/c
2"/
The time for the light to return:
# > 2"/c
2"/
Galilean-Newtonian Relativity
PRECISELY =>
T = 2 L/c
L2 = H2 + (v T/2)2
Longer Path (L) +
2nd Postulate
The time for the
light to return:
! > 2"/c
2"/
Longer
Path + 2nd
Postulate
# = 2"/c
2"/
•! Galilean-Newtonian relativity is known as
a “classical” theory.
•! Einstein’s special theory of relativity is
known as a “modern” theory.
L
T = # (1 – (v/c)2 )-1/2
28
Galileany Transformation
´
K´
y
K
O
Galilean Transformation
v
O
´
x
vt
x
´
O
x´ = x – vt
z
y K´
´
v
y K
z
´
Time is absolute
x
x O
´
x
´
x
´
x´ = x – vt
y´ = y
y´ = y
z´ = z
z´ = z
t´ = t
Time is absolute
29
EVENT
t´ = t
30
The Michelson-Morley Experiment
Historical Perspective
•! Light is a wave.
•! Waves require a medium through which
to propagate.
•! Medium as called the “ether.” (from the
Greek , meaning upper air)
•! Maxwell’s equations assume that light
obeys the Newtonian-Galilean
transformation.
31
•! Experiment designed to measure small changes in
the speed of light was performed by Albert A.
Michelson (1852 – 1931, Nobel ) and Edward W.
Morley (1838 – 1923).
•! Used an optical instrument called an
interferometer that Michelson invented.
•! Device was to detect the presence of the ether.
•! Outcome of the experiment was negative, thus
contradicting the ether hypothesis.
•! A.A. Michelson and E.W. Morley, American
Journal of Science, 134 – 333, 1887)
32
Einstein’s Postulates
Inertial Reference Frame
Big problem at the turn of the century:
1.! Michelson-Morley showed that the
Galilean transformation did not hold
for Maxwell’s equation.
2.! Maxwell’s equations could not be wrong.
3.! Galilean transformation did hold for
the laws of mechanics.
4.! Einstein proposed a solution.
An inertial reference frame is one
–!in which no accelerations are observed
in the absence of external forces.
–!that is not accelerating.
–!Newton’s laws hold in all inertial
reference frames.
33
34
Principle of Simultaneity
Einstein’s Postulates
Two events that are simultaneous in one
reference frame (K) are not necessarily
simultaneous in another reference
frame (K´) moving with respect to the
first frame.
Recall that in the Galilean transformation time is
considered absolute regardless of the relative
motion of the reference inertial reference
frames.
35
1.! The Principle of Relativity
2.! The constancy of the speed of light.
36
The Constancy
of the Speed of Light
The Principle of Relativity
All the laws of physics are the same in
all inertial systems.* There is no way to
detect absolute motion, and no
preferred inertial system exists.
*Particular quantities (velocity, momentum,
kinetic energy, …) have different values in
different inertial reference frames, but the
laws of physics (conservation of energy and
momentum, …) are the same.
Observers in all inertial systems measure
the same value for the speed of light in
a vacuum.
(c = 2.9979 x 108 m/s)
37
The Ultimate Speed
•! The speed of light has been defined to be exactly:
c = 299 792 458 m/s
38
2.4 The Lorentz Transformation
•! Einstein needed to find a new
transformation (the old one being the
Galilean transformation).
•! Light travels at this ultimate speed, as do any
massless particles.
•! No entity that carries energy or information can
exceed this speed limit.
•! It must fit both the laws of mechanics
and Maxwell’s electrodynamic equations.
•! No particle that does have a mass, can actually
reach c.
•! Electrons have been accelerated to at least 0.999
999 999 95 times the speed of light—still less
than c.
39
•! It must allow time to be relative.
40
Galilean Transformation
y K´
´
v
y K
vt
O
x
x O
´
x
´
x’ = x –vt is wrong?
Let’s start with the following
linear (Lorenz) transformation
and see if this works or not.
EVENT
x
´
x´ = x – vt
x’ = !(x-vt)
y´ = y
z´ = z
Time is absolute
t´ = t
41