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G
Relativity
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Section Number
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Topic
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Descriptor
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Option G:
Relativity (15h)
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G.1
Introduction (1h)
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Frames of
reference
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Note: This links to core
section 2.2. While it does not imply any further
knowledge, it helps develop an
understanding of the relative motion of two
observers.
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G.1.1
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Explain what is meant by a
frame of reference.
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G.1.2
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Describe what is meant by a
Galilean transformation.
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G.1.3
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Calculate relative velocities
using the Galilean transformation equations.
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Electromagnetic
theory and the speed of light
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G.1.4
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State that Maxwell's theory of
electromagnetic radiation predicted a speed
of electromagnetic waves in a
vacuum that is independent of the velocity of
the source.
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Students should be
familiar with the concept of oscillating electric and
magnetic fields and
that the speed of these fields is dependent only on the
electric and magnetic constants of the medium through which
they travel. The
speed is therefore independent of the source. Students do
not need any other
details of Maxwell's four equations.
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G.1.5
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State that the Galilean
transformation equations fail if applied to a moving
source of light.
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Students should know
that Maxwell's prediction implies that the speed of
light in a vacuum has
the same value for all observers.
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G.2 Concepts
and Postulates of Special Relativity (2h)
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G.2.1
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Explain what is meant by an
inertial frame of reference.
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G.2.2
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State the two postulates of
the special theory of relativity.
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G.2.3
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Discuss the concept of
simultaneity.
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Students should be
able to describe a situation where two events that
are simultaneous
in one frame of reference are not simultaneous in
another.
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G.3
Relativistic Kinematics (5h)
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Time
dilation
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G.3.1
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Explain the concept of a
light clock.
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Only a very simple
explanation is required here. For example, the time
taken for a beam of
light to bounce between two perfect, parallel mirrors
can be used to measure
time.
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G.3.2
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Derive the time dilation
formula.
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Students should be
able to construct a simple proof of the time dilation
formula based on the
concept of the Òlight clockÓ and the
postulates of relativity.
Students should also understand that for two observers in
two different
inertial reference frames, all measurements are
symmetrical.
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G.3.3
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Draw and annotate a graph of
how the Lorentz factor varies with relative
velocity.
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Students do not need
to remember values, but they should be aware that at
low velocities (less
than 0.5c) the Lorentz factor is very close to 1 and
that it
approaches infinity at very high velocities.
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G.3.4
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Define the term proper
time.
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G.3.5
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Solve problems using the time
dilation formula.
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Length
contraction
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G.3.6
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Describe the phenomenon of
length contraction.
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Students will not be
examined on a proof of the length contraction
formula.
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G.3.7
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Define the term proper
length.
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G.3.8
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Solve problems involving
length contraction.
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G.4 Some
Consequences of Special Relativity (4h)
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The twin
paradox
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G.4.1
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Describe how the concept of
time dilation leads to the Òtwin
paradoxÓ.
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Different observers'
versions of the time taken for a journey at speeds
close to light speed
could be compared. Students should be aware that,
since one of the twins
makes an outward and return journey, this is no
longer a symmetric
situation for the twins. (See G.3.2.)
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Velocity
addition
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G.4.2
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Solve one-dimensional problems
involving the relativistic addition of velocities.
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The derivation of
the velocity addition formula is not required.
Students should
realize that Galilean and relativistic velocity addition
give the same answer
at low relative velocities and that relativistic velocity
addition does not
give a relative velocity greater than the speed of
light.
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Relativistic
mass increase
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G.4.3
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Define the term rest
mass.
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G.4.4
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Solve problems involving
relativistic mass increase.
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The derivation of
the mass increase formula will not be examined.
Students should be able
to calculate the total mass of a moving object and
to apply this value in
a subsequent calculation of, for example, an electron
accelerated through a
potential difference.
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G.4.5
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Explain in terms of the
relativistic mass equation why no mass can ever
attain or exceed the speed of
light in a vacuum.
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Mass-energy
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G.4.6
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State that the equivalence of
mass and energy is predicted by special
relativity.
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G.4.7
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Distinguish between rest mass
energy and total energy.
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G.5 Evidence to
Support Special Relativity (3h)
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Muon
experiments
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G.5.1
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Discuss muon decay as
experimental evidence for time dilation and length
contraction.
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The
Michelson-Morley experiment
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G.5.2
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Outline the set-up of the
Michelson-Morley experiment.
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Students should be
able to outline the principles behind the Michelson
interferometer using a
simple sketch of the apparatus.
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G.5.3
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Outline the result of the
Michelson-Morley experiment and its implication.
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The constancy of the
speed of light and the fact that there is no absolute
reference frame is the
accepted explanation.
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Option G:
Extension Material (HL only) (7h)
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G.6
Relativistic Momentum and Energy (2h)
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Note: Derivation of the
relativistic momentum and energy formulas will not be
examined.
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G.6.1
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Solve problems involving
objects moving at relativistic speeds using
Einstein's mass-energy
equation.
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G.6.2
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Solve problems involving
relativistic momentum and energy.
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Students should be
able to calculate, for example, the kinetic energy,
total energy,
speed and momentum of an electron accelerated through a
given potential
difference. Students should be familiar with the units of
MeVc-2
for mass and
MeVc-1
for momentum.
Other multiples could also be considered
(eg GeVc-2
for
mass).
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G.7 General
Relativity (4h)
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Note: This section is
intended as an introduction to the ideas of general
relativity and is
non-mathematical in its approach .
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The equivalence
principle
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G.7.1
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Explain the difference between
the terms gravitational mass and inertial
mass.
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G.7.2
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Describe and discuss
Einstein's principle of equivalence.
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Students should be
familiar with Einstein's closed elevator
Òthought experimentÓ.
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G.7.3
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Deduce that the principle of
equivalence predicts bending of light rays in a
gravitational field.
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Spacetime
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G.7.4
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Describe the concept of
spacetime.
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G.7.5
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State that moving objects take
the shortest path between two points in spacetime.
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G.7.6
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Explain gravitational
attraction in terms of the warping of spacetime by
matter.
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The model
representing the curving of spacetime in terms of the
bending of a
ÒsheetÓ of spacetime is sufficient.
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Gravitational
red shift
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G.7.7
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Describe the concept of
gravitational red shift.
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Students should be
aware that this gravitational red shift is a prediction
of the general
theory of relativity.
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G.7.8
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Solve problems involving
frequency shifts between different points in a
uniform gravitational
field.
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Only the simplified
formula is required.
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Black
holes
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G.7.9
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Describe black
holes.
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Students should know
that black holes are a region of spacetime with
extreme curvatures due
to the presence of a mass.
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G.7.10
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Define the term
Schwarzchild radius.
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G.7.11
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Apply the equation for
calculating the Schwarzchild radius.
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G.8 Evidence to
Support General Relativity (1h)
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G.8.1
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Outline the experimental
evidence for the bending of star light rays by the
Sun.
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An outline of the
principles used in, for example, Arthur Eddington's
measurements of the
1919 eclipse is sufficient.
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G.8.2
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Explain the effect of
Ògravitational lensingÓ.
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Evidence for
gravitational red shift
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G.8.3
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Outline an experiment that
provides evidence for gravitational red shift.
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The Pound-Rebka
experiment (or a suitable alternative such as the shift
in frequency of
an atomic clock) is sufficient
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