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SI2371 Special Relativity
Conceptual problems 2013

This page contains a listing of the conceptual problems discussed in class during the 2013 course.

Lecture 1:
The principle of special relativity ...
  1. ... is unique for special relativity
  2. ... appears in special and general relativity
  3. ... is broken by Maxwell’s equations
  4. ... is not part of quantum mechanics

Lecture 2:
Which two of the following observers might consider themselves to be in an inertial frame?
  1. An observer in a rocket travelling at velocity v=0.99c with the engines turned off
  2. An observer in a rocket travelling at velocity v=0.99c with the engines turned on in a direction perpendicular to the motion
  3. An astronaut performing a space walk
  4. An astronaut on a rotating space station

Lecture 3:
Which of the following is not true?
  1. The sum of two (forward) time-like vectors is time-like
  2. The sum of two space-like vectors is time-like
  3. A light-like vector is orthogonal to itself
  4. Two time-like vectors cannot be orthogonal

Lecture 4:
Which statement is not universally true about the pole-in-garage paradox?
  1. The pole never touches the garage doors
  2. The pole is entirely inside the garage (at some time)
  3. The pole is short enough as seen in the garage system
  4. The doors do not close simultaneously in the runner’s system
What is true about the 4-acceleration?
  1. With a given proper acceleration, an object moving with velocity v will have the same acceleration regardless of the direction of acceleration
  2. We do need to transform the 4-acceleration to the (instantaneous) rest-frame of a moving object to know its proper acceleration
  3. The 4-acceleration must always be a space-like 4-vector
  4. Just as velocities of physical objects have to be lower than c, the proper acceleration also has a maximal value

Lecture 5:
Which of the following processes correspond to a pure force?
  1. An exothermic chemical reaction’s influence on its surroundings
  2. The influence of the ground on an accelerating car
  3. The acceleration of an electron in a particle accelerator
  4. The collapse of a star into a black hole or neutron star
What is true about electromagnetism?
  1. Maxwell’s equations are not invariant under Lorentz transformations
  2. The electromagnetic force has a large heat-like component
  3. The electromagnetic force is always orthogonal to the 4-velocity of a particle
  4. The electromagnetic field tensor has 12 non-zero independent components

Lecture 6:
A current I is passing through an overall neutral conductor at rest in S. What is true in S’, which is moving with velocity v with respect to S (parallel to the conductor)?
  1. The electric field is zero
  2. The electric field is larger than the magnetic
  3. The electric and magnetic fields are orthogonal
  4. The conductor is neutral
What two statements are true for a space-like surface?
  1. The normal vector is time-like
  2. All tangent vectors have time-component zero
  3. There is no system where two events on the surface are simultaneous
  4. No event on the surface is within the light-cone drawn from another event on the surface

Lecture 7:
What is not true about the de Broglie wave describing a massive particle?
  1. It is time-like
  2. The de Broglie frequency is indpendent of the inertial frame
  3. The phase velocity is larger than the speed of light
  4. The 4-frequency is proportional to the 4-momentum
What is true about the relativistic Doppler effect?
  1. A Lorentz transformation must be performed to compute it
  2. An observer moving orthogonal to the source will not see a Doppler shift
  3. The frequency will always be higher for an observer moving straight towards the source
  4. A time-like wave will not experience a Doppler shift

Lecture 8:
When a rocket accelerates, the stars will seem to ...
  1. Gather in front of the rocket
  2. Become red-shifted due to Doppler shift
  3. Gather behind the rocket
  4. Gather in a plane perpendicular to the rocket’s acceleration
  5. Become blue-shifted due to Doppler shift
Which of the following reactions is possible for free particles?
  1. γ → e+ + e-
  2. p → n + e+ + νe
  3. e+ + e- → μ+ + μ-
  4. μ+ → μ+ + γ

Lecture 9:
In order for a reaction to be kinematically allowed, it is not sufficient that ...
  1. The total energy is greater than the summed mass of any created particles
  2. The total 4-momentum squared is at least as large as the square of the summed masses of the outgoing particles
  3. The summed mass of the incoming particles is larger than the summed masses of the products
  4. Energy and momentum is conserved in the reaction
What is not true in special relativity?
  1. An object will be in constant rectilinear motion unless acted upon by a force.
  2. The 4-acceleration of an object is directly proportional to the pure component of the 4-force and inversely proportional to the mass of the object.
  3. For every force Fμ acting on an object, there is a counter force –Fμ acting on something else.
  4. A change in the charge of an object will lead to an instantaneous change in the electromagnetic force on other charged objects.

Lecture 10:
Which of the following statements regarding an electromagnetic wave is a consequence of using the Lorentz gauge condition?
  1. The electric and magnetic fields are perpendicular
  2. The zero component of the polarization 4-vector εμ is vanishing
  3. The polarization 4-vector εμ is orthogonal to the wave vector kμ
  4. A polarization 4-vector parallel to the wave vector is unphysical
For two fluids described by the energy tensors M1μν and M2μν, the relation ∂ν(M1μν + M2μν) = 0 is corresponding to the classical concept of:
  1. Newton’s first law (inertial movement)
  2. Newton’s second law (F = ma)
  3. Newton’s third law (action-reaction)
  4. Newton’s law of gravitation (F = Gm1m2/r2)

Lecture 11:
What is not true about the energy tensor of a perfect fluid?
  1. The rest-frame is the frame with the lowest energy density
  2. It always has zero pressure
  3. It is always isotropic in the rest frame
  4. It can be used to describe the cosmic microwave background (CMB)
The classical interpretation of the integral
Pν(t1)-Pν(t2) = ∫t1t2 dt ∫ dV ∂μTνμ
is
  1. Newton’s first law (inertial movement)
  2. Newton’s second law (F = ma)
  3. Newton’s third law (action-reaction)
  4. Newton’s law of gravitation (F = Gm1m2/r2)

Last updated: Dec 18, 2013