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The factor which relates the length of an object in one frame to the length
in another frame moving with
speed
v
is:

(A)

(B)

(C)

(D)

"If two events occur simultaneously in one frame, they occur simultaneously
in some other frame." This statement is:

(A)
True of all frames.

(B)
True of an frames, so long as they are inertial.

(C)
True of no inertial frames.

(D)
True of no inertial frames, except two that are stationary with respect to
one another.

Which of the following is not a consequence of the relativity
principle?

(A)
All inertial frames are equivalent.

(B)
Physical laws have the same form in every inertial frame.

(C)
The speed of light is the same in all frames.

(D)
Every point in space looks the same as every other point, ignoring matter.

The second postulate of Special Relativity is:

(A)
The speed of light is the same in all frames.

(B)
All inertial frames are equivalent.

(C)
All observers in inertial reference frames measure light as having a
different speed.

(D)
The inner product of any two 4-vectors is invariant between inertial
reference frames.

An observer on the ground measures two events
l
meters apart as occurring
simultaneously. An observer moving with speed
v
with respect to this
system measures the time between events as:

(A)

(B)

(C)

(D)

The experiments of Michelson and Morley showed that:

(A)
The earth moves through an ether.

(B)
Light traveled at different speeds, depending on the direction of one's
motion through the ether.

(C)
Special Relativity correctly predicted a length contraction.

(D)
Light traveled at the same speed regardless of the direction of motion
through the ether, hence proving that there was no ether.

The ether was supposed to be: I) incorporeal and undetectable; II) An
absolute reference frame in which the speed of light was equal to
c
; III)
the medium in which light waves traveled. Which of these statements is
true?

(A)
II only

(B)
I and II only.

(C)
II and III only.

(D)
I, II, and III.

The symbol given to the quantity
would be:

(A)
γ

(B)
γ^{2}

(C)
β

(D)
β^{2}

For the equation
Δt_{A} = γΔt_{B}
to apply, the two events
under consideration must occur:

(A)
At the same time in A's frame.

(B)
At the same time in B's frame.

(C)
At the same place in A's frame.

(D)
At the same place in B's frame.

For the equation
Δl_{A} = Δt_{B}/γ
to apply, the two events
under consideration must occur:

(A)
At the same time in A's frame.

(B)
At the same time in B's frame.

(C)
At the same place in A's frame.

(D)
At the same place in B's frame.

Bill is standing on earth. A spaceship of proper length 50 meters flies
past. Bill measures the spaceship as having length 40 meters. What is the
speed of the spaceship?

(A)
0.8c

(B)
0.6c

(C)
0.4c

(D)
None of the above.

Astronauts on a long space journey are playing golf inside their spaceship,
which is traveling away from the earth with speed
0.6c
. One of the
astronauts hits a drive exactly along the length of the spaceship (in its
direction of travel) at speed
0.1c
in the frame of the spaceship. What
is the speed of the golf ball as observed from earth?

(A)
0.66c

(B)
0.7c

(C)
0.5c

(D)
0.74c

Allen speeds past Belinda in his car; in Belinda's frame the car moves with
speed
1.5×10^{7}
meters/second. Allen's radio is blaring out music
with a beat that occurs every 0.5 seconds. How often does Belinda hear the
beats?

(A)
Every 0.5006 seconds.

(B)
Every 0.4994 seconds.

(C)
Every 0.5 seconds.

(D)
Every 2 seconds.

Which of the following is true of the Lorentz transformations: I) they
relate spacetime coordinates in one frame to spacetime coordinates in
another frame; II) they were derived some time after Special Relativity was
introduced; III) they do not predict the loss of simultaneity?

(A)
I only.

(B)
I and II only.

(C)
I and III only.

(D)
II only.

Lorentz and Fitzgerald initially wrote down the Lorentz transformations in
order to:

(A)
Simplify calculations in Special Relativity.

(B)
Show that an ether could not exist.

(C)
'Save' the concept of the ether after Michelson and Morley's findings.

(D)
Show how electricy and magnetism are related to light.

In a frame with speed
3c/5
with respect to the ground, two explosions
occur 10 meters apart with 2 seconds between them. The observed time
between the explosions in the frame of the ground is:

(A)
About 2.5 seconds

(B)
About 1.6 seconds.

(C)
2.5×10^{-8}
seconds.

(D)
Not enough information given.

The correct expression for finding the distance between two events in a
frame moving with speed
v
with respect to a stationary frame when the
spacetime coordinates of the events in the stationary frame are known is
(where primed coordinate, as usual, correspond to the moving frame):

(A)
γ(Δx' + vΔt')

(B)
γ(Δx - vΔt)

(C)
γ(Δx + vΔt)

(D)
γ(Δt - vΔx/c^{2})

Which of the following is true of a Minkowski diagram: I) One unit on the
primed axes is less than on unit on the unprimed axes; II) The worldline of
a particle remains the same irrespective of the axes; III) The area under a
worldline can be used to calculate the time dilation between the frames.

(A)
I only.

(B)
II only.

(C)
I and III only.

(D)
II and III only.

The worldline of a photon is:

(A)
Along the
x
-axis.

(B)
Along the
ct
-axis.

(C)
Along the
ct'
-axis.

(D)
Along the 45 degree line
x = ct
.

A Minkowski diagram exploits the fact that the Lorentz Transformations are
a rotation of the spacetime coordinates. By what angle in the
x - ct
plane
do the Lorentz transformations rotate the coodinates when the speed of the
frame in question is
v
.

(A)
θ = tan^{-1}()

(B)
θ = tan^{-1}()

(C)
θ = tan^{-1}(v/c)

(D)
θ = cos^{-1}(v/c)

The point
(x, ct) = (γ(1 + v/c), γ(1 + v/c))
is which point in terms of the rotated coordinates?

(A)
(0, 0)

(B)
(0, 1)

(C)
(1, 0)

(D)
(1, 1)

The correct expressions for energy, first in non-relativistic, and then in relativistic units are:

(A)
γmc^{2}
and
γm
.

(B)
γ^{2}mc^{2}
and
γm
.

(C)
γm^{2}c^{4}
and
γm^{2}
.

(D)
mc^{2}
and
γm
.

The correct expressions for momentum, first in non-relativistic, and then in relativistic units are:

(A)
γmvc^{2}
and
γmv
.

(B)
γmv
and
γmv
.

(C)
γmv
and
γm
.

(D)
γmc
and
γm
.

What is the energy of an electron moving with speed
2.45×10^{8}
m/s? (The mass of an electron is
9.11×10^{-31}
kilograms).

(A)
1.58×10^{-30}
Joules

(B)
4.74×10^{-22}
Joules

(C)
0.88 MeV

(D)
9.75×10^{29}
MeV

Which of the following is a 4-vector: I)
m(cdt, 2dx, dy, dz)
; II)
(E, c
; III)
(mγc, γ
?

(A)
All of these.

(B)
I and III, but not II.

(C)
I and II, but not III.

(D)
II, but not I or III.

Which of the following are conserved in all collisions: I)
m
; II)
γm
III)
1/2mv^{2}
; IV)
mc^{2}
?

(A)
I and III only.

(B)
II only.

(C)
IV only.

(D)
II and IV only.

A particle of mass
m
is moving to the right with speed
v
. What is its momentum in a frame moving to the left with speed
v
?

(A)

(B)

(C)

(D)

Which of the following is an expression in relativistic units for the momentum of a particle with mass
m
and energy
E
?

(A)
p =

(B)
p =

(C)
p =

(D)
p =

The second term in a Taylor expansion of
γmc^{2}
in
v
is:

(A)
mc^{2}

(B)
1/2mv^{2}

(C)

(D)
None of the above.

The inner product of the two 4-vectors
(1, - 2, 1, 2)
and
(- 1, - 1, 2, 2)
is:

(A)
+9

(B)
+7

(C)
-9

(D)
-7

The inner product of the energy-momentum 4-vector of a particle (mass
m
, energy
E
) is found to be
m^{2}c^{4}
in its rest frame. What is the inner product in a frame moving to the right with speed
v
?

(A)
γ_{v}m^{2}c^{4}

(B)
vm^{2}c^{4}

(C)
γ_{v}m^{2}v

(D)
m^{2}c^{4}

A particle is constrained to move in the
x - y
plane and is initially moving in the
x
-direction. If you wish to accelerate as much as possible in any direction, in which direction should a force be applied?

(A)
x
-direction.

(B)
y
-direction.

(C)
z
-direction.

(D)
Doesn't matter, any direction will be equally effective.

The force on a particle in a particular frame is given by
(F_{x}, F_{y}) = (3, 5)
. What is the force as measured in a frame moving with speed
3c/5
with respect to this one?

(A)
(F_{x}', F_{y}') = (4, 4)

(B)
(F_{x}', F_{y}') = (0, 3)

(C)
(F_{x}', F_{y}') = (3, 4)

(D)
(F_{x}', F_{y}') = (3, 5)

A particle has instantaneous velocity
v_{x} = 2.3×10^{8}
m/s, mass
m = 1.65×10^{-27}
kilograms and acceleration
a_{x} = 9.8
m/s
^{2}
. What is the force being applied to it?

(A)
2.52×10^{-26}
Newtons.

(B)
6.11×10^{-26}
Newtons.

(C)
3.92×10^{-26}
Newtons.

(D)
1.62×10^{-26}
Newtons.

Which of the following is not valid in Special Relativity?

(A)
F =

(B)
F =

(C)
F = γ^{3}ma

(D)
F = ma

A train is moving directly towards you at speeed
2c/5
along a straight track. It has a monochromatic light on it which emits 450 nm light. What wavelength do you observe?

(A)
295 nm

(B)
687 nm

(C)
450 nm

(D)
532 nm

A train moves past you at high speed some distance away. If the train moves from left to right across your field of view, the frequency (from the light on the engine) you observe when the train appears just to the left of its position of closest approach
to you is:

(A)
Greater than the frequency emitted by the train light.

(B)
Less than the frequency emitted by the train light.

(C)
The same as the frequency emitted by the train light.

(D)
It is impossible to conclude anything about the observed frequency.

A train moves past you at high speed some distance away. If the train moves from left to right across your field of view, the frequency (from the light on the engine) you observe when the train is at its distance of closest approach to you is:

(A)
Greater than the frequency emitted by the train light.

(B)
Less than the frequency emitted by the train light.

(C)
The same as the frequency emitted by the train light.

(D)
It is impossible to conclude anything about the observed frequency.

The relativistic Doppler effect is caused by: I) time dilation effects between source and observer; II) interference effects as the light takes different paths to the observer; III) 'compression' and 'expansion' of light waves due to motion of the source
or observer.

(A)
All of these.

(B)
I and II, but not III.

(C)
I only.

(D)
I and III, but not II.

An extra-solar planet is 20 light years away. How many years of earth time does it takes to make a roundtrip at
0.8c
?

(A)
40 years.

(B)
67 years.

(C)
24 years.

(D)
12 years.

How long would a roundtrip to a star 20 light years distant appear to take to the passengers on board the spaceship?

(A)
40 years.

(B)
67 years.

(C)
24 years.

(D)
12 years.

If one of a set of twins remains on earth and the other travels to a distant star at high speed and then returns to earth, who will age less?

(A)
The twin on earth.

(B)
The traveling twin.

(C)
They are both the same age.

(D)
Unknown -- this is an unresolved paradox of Special Relativity.

The reason why the traveling twin cannot simply apply time dilation to calculate the age of his twin is:

(A)
The relevant events do not occur at the same place in his frame.

(B)
A moving observer cannot apply time dilation in the same way a stationary one can.

(C)
Time dilation only applies in gravitational fields, and not in free space.

(D)
During the trip he is in a non-inertial reference frame.

If
P
is the energy-momentum 4-vector, conservation of energy and momentum is expressed by:

(A)
P.P = m^{2}c^{4}

(B)
P_{i} = P_{f}

(C)
P = (E/c, p_{x}, p_{y}, p_{z})

(D)
P = 0

A particle of mass M and energy E moves in the
y - zplane
at angle
θ
with respect to the
y
-axis. What is the energy-momentum 4-vector of this particle?

(A)
(E/c, 0,cosθ,sinθ)

(B)
(E/c,cosθ,sinθ, 0)

(C)
(E/c, 0, E cosθ, E sinθ)

(D)
(E, 0,sinθ,cosθ)
.

If
P
is the energy momentum 4-vector, which equation best expresses the invariance of the inner product between frames:

The energy momentum 4-vector of a particle with mass
m
at rest is:

(A)
(0, 0, 0, 0)

(B)
(0, γmc, 0, 0)

(C)
(γmc^{2}, 0, 0, 0)

(D)
(γmc^{2}, γmc, 0, 0)

Two spaceships are joined by a cable, floating in space at rest relative to each other. The cable between them is very strong but it cannot be stretched indefinitely before breaking. At some time the spaceships simultaneously begin to accelerate at exac
tly the same rate in the direction along the cable between them. Will the cable break?

(A)
No, the cable will not break.

(B)
Yes, the cable will break.

(C)
Cannot tell -- it depends on the magnitude of the acceleration.

(D)
Cannot tell -- it depends on the length of the cable.

If the speed of light was infinite, the equivalent of the Lorentz transformations between frames would be:

(A)
Exactly the same.

(B)
irrelevant -- it would be impossible to transform between frames.

(C)
like the Galilean transformations.

(D)
irrelevant -- there would only be one 'absolute' frame.

Would it be possible to construct a universe in which the speed of light and the, say, the speed of sound were both the same in every inertial frame (that is, light travels at
c
in every frame and sound travels at some other speed
vc
i
n every frame)?

(A)
Yes.

(B)
No.

(C)
The answer depends on whether
v > c
or
v < c
.

(D)
The answer depends on the nature of sound (that is, what sort of particle it is carried by or what medium it travels through).