Question 1

How did physicists try to detect the luminiferous aether in the late 19th century?

Accepted Answer

The most famous attempt to detect the luminiferous aether was the Michelson-Morley experiment, which aimed to measure the Earth's motion through the aether by observing changes in the speed of light in different directions. This experiment, and others like it, sought to detect the aether by measuring its relative velocity to Earth, not by measuring its production of light, its refractive properties, or its density.

Question 2

Two observers in different frames of reference will measure different:

Accepted Answer

According to the theory of special relativity, the speed of material objects is relative and depends on the observer's frame of reference. Therefore, two observers in different frames of reference will measure different values for the speed of material objects. The laws of physics, the speed of light, and Newton's gravitational constant are all considered to be constants that are the same for all observers regardless of their frame of reference.

Question 3

An airline pilot spends a considerable fraction of his life traveling at a speed of several hundred kilometers per hour relative to his identical twin brother.How does the pilot's lifetime compare to that of his brother,all other things being equal?

Accepted Answer

A

Question 4

The general theory of relativity includes an explanation of:

Accepted Answer

The general theory of relativity explains the relationship between gravity and space-time.

Question 5

Light waves emitted from a laser at rest will travel at a speed c relative to:

Accepted Answer

According to the theory of relativity, the speed of light is constant and the same for all observers, regardless of their relative motion or position. Therefore, light waves emitted from a laser at rest will travel at a speed c relative to any observer, including the Sun, a laboratory in Paris, and the cosmic microwave background.

Question 6

A spaceship moves at 3/5 the speed of light relative to an observer.How long will each tick of a clock on the spaceship take,relative to an identical clock held by the observer?

Accepted Answer

According to the theory of relativity, when an object is moving at a high velocity relative to an observer, time appears to pass more slowly for the moving object. This phenomenon is known as time dilation.

The formula for time dilation is:

t = t_0 / sqrt(1 - v^2/c^2)

where t is the time measured by the observer, t_0 is the time measured by the moving object, v is the velocity of the moving object, and c is the speed of light.

Plugging in the values given in the problem, we get:

t = t_0 / sqrt(1 - (3/5)^2)

t = t_0 / sqrt(1 - 9/25)

t = t_0 / sqrt(16/25)

t = t_0 / (4/5)

t = 5/4 * t_0

This means that each tick of the clock on the spaceship will take 5/4 as long as an identical clock held by the observer. Therefore, the best choice is C) 5/4 as long.

Question 7

If the speed of light were infinite,how would black holes change?

Accepted Answer

Black holes are defined as regions in space where the escape velocity is greater than the speed of light. If the speed of light were infinite, then the escape velocity requirement for a black hole would be impossible to achieve, and therefore black holes could not exist.

Question 8

Two observers travel perpendicular to each other,as shown in the figure below.If observer B shone a light toward observer A,what velocity would observer A measure the beam to have?

Accepted Answer

The answer of Two observers travel perpendicular to each other,as...

Question 9

How do the laws of physics change for moving observers?

Accepted Answer

The laws of physics, as we have discovered them, do not change for moving observers. The fundamental principles of physics, such as conservation of energy, momentum, and angular momentum, are observed to be the same for all observers, regardless of their motion or orientation. Some specific phenomena, such as the Doppler effect, may appear different for moving observers, but this is due to the relative motion between the observer and the observed object, not a change in the underlying physics. Similarly, gravity is also observed to be the same for all observers, regardless of their motion.

Question 10

Einstein showed that Newton's physics is:

Accepted Answer

Einstein's theory of relativity demonstrated that Newtonian physics is a good approximation at low velocities compared to the speed of light, but it does not hold at high velocities or in strong gravitational fields.

Question 11

Gravitational waves are:

Accepted Answer

Gravitational waves are ripples in the fabric of space-time, which propagate at the speed of light and are produced by the acceleration of massive objects, such as the collision of two black holes, neutron stars, or other astrophysical phenomena. They were predicted by Einstein's theory of general relativity and have been detected by gravitational wave observatories since 2015. Gravitational waves are not observed during planetary conjunctions, responsible for periodic orbits, or solely produced by supermassive black holes.

Question 12

Imagine that a spaceship is traveling at half the speed of light relative to an observer.The spaceship shoots a laser in the direction of its motion.How fast is the laser traveling relative to the observer?

Accepted Answer

According to the theory of relativity, the speed of light in a vacuum is constant and independent of the motion of the observer or the source. Therefore, the laser will also be traveling at the speed of light from the perspective of the observer, regardless of the spaceship's velocity. Thus, the correct answer is B, the speed of light.

Question 13

Imagine that a child is inside a car traveling at 8 m/s.The child throws a ball with a velocity of 1 m/s in the direction of the car's motion.How fast is the ball traveling relative to an observer at rest on the side of the road?

Accepted Answer

The ball's velocity relative to the car is 1 m/s, and the car's velocity relative to the observer on the side of the road is 8 m/s. Therefore, to find the ball's velocity relative to the observer, we need to add the two velocities using the formula for relative velocity:

Vrelative = Vobject  + Vobserver

Vrelative = 1 m/s + 8 m/s 
Vrelative = 9 m/s

So the ball is traveling at 9 m/s relative to an observer at rest on the side of the road. Therefore, the best choice is C) 9 m/s.

Question 14

Experiments to measure the properties of the luminiferous aether were problematic for scientists in the early 20th century because there was no evidence for:

Accepted Answer

The luminiferous aether was hypothesized as the medium for light waves, similar to how sound waves travel through air. However, experiments like the Michelson-Morley experiment failed to detect any difference in the speed of light due to the motion of the Earth through the supposed aether, leading to the conclusion that there was no evidence for the motion of observers relative to the aether. This was a key factor in the development of Einstein's theory of relativity, which eliminated the need for the aether concept by showing that the speed of light is constant in all inertial frames of reference.

Question 15

What is invariant between different frames of reference?

Accepted Answer

The law of gravity is invariant between different frames of reference. This means that the force of attraction between two masses is the same regardless of the reference frame from which it is observed. The speed of an object and the kinetic energy of an object can vary between different frames of reference, and are therefore not invariant.

Question 16

What remnant will a star with an initial total mass of 100 M_sun leave at the end of its life?

Accepted Answer

A star with an initial total mass of 100 solar masses is much larger than the upper mass limit of stars that can become neutron stars or white dwarfs after supernova explosions. As a result, it will likely undergo complete gravitational collapse and become a black hole at the end of its life.

Question 17

The first experimental verification of the general theory of relativity was:

Accepted Answer

The first experimental verification of the general theory of relativity was the observation of a total solar eclipse in 1919, during which the position of starlight passing near the sun was observed to be shifted due to the bending of space-time by the sun's gravity. This phenomenon, known as gravitational lensing, provided the first empirical evidence in support of Einstein's theory. The other options listed (gravitational waves, time dilation, and the detection of black holes) are all also predictions of general relativity that have since been observed or confirmed through various experiments, but they did not represent the first experimental verification of the theory.

Question 18

Which of the following did Einstein determine to be a constant of nature?

Accepted Answer

Einstein determined that the speed of light in a vacuum (often referred to as "the speed of a photon") is a constant of nature, fundamental to his theory of relativity.

Question 19

A muon is a type of subatomic particle.If a muon is at rest in the laboratory,it will decay into an electron after about 2 microseconds.Suppose an observer watches a muon travel through the atmosphere at 90 percent of the speed of light.How does the lifetime of the moving muon compare to the laboratory muon,for an observer at rest with respect to the lab?

Accepted Answer

According to special relativity, the lifetime of a moving particle appears longer to an observer at rest with respect to the laboratory than the lifetime of a particle at rest in the laboratory. This is due to time dilation, where time appears to slow down for moving objects relative to a stationary observer. Therefore, the lifetime of the moving muon will be longer than 2 microseconds, and so the best choice is B.

Question 20

What are black holes?

Accepted Answer

Black holes are regions in space where the gravitational pull is so strong that nothing, not even light, can escape from them. This definition does not necessarily imply they are the densest or most massive objects in the universe, just that their gravity is strong enough to prevent anything from escaping.

Quiz 14: Down the Rabbit Hole: Relativity and Black Holes