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:

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

The second postulate of Special Relativity is:

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:

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?

The symbol given to the quantity would be:

For the equation Δt _A = γΔt _B to apply, the two events under consideration must occur:

For the equation Δl _A = Δt _B/γ to apply, the two events under consideration must occur:

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?

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?

Allen speeds past Belinda in his car; in Belinda's frame the car moves with speed 1.5×10⁷ 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?

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?

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

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:

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):

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.

The worldline of a photon is:

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()

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

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

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

What is the energy of an electron moving with speed 2.45×10⁸ m/s? (The mass of an electron is 9.11×10^-31 kilograms).

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

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

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:

(C)

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

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 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?

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 particle has instantaneous velocity v _x = 2.3×10⁸ 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?

Which of the following is not valid in Special Relativity?

(A) F =

(B) F =

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 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 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:

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.

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 ?

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

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?

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

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

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)

(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:

(D) P =

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

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?

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

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 v c i n every frame)?