Einstein's Universe Midterm 1

What does Wolfson call "a good definition of a wave?"

"A traveling disturbance that carries energy but not matter."

List the properties that the ether must have and why it must have them. Identify any apparent contradiction between these properties.

(a) It must be a solid, since light is a transverse wave. (b) It must be very dense, as the speed of light is so great. (c) It must exert no frictional forces on bodies moving through it, or we would notice things like the planets deviating from their orbits around the sun. (d) It must fill the spaces between atoms and molecules since light passes through clear substances like water and glass, yet it must also fill space since we can see the light from the sun and stars. Certainly properties (a) and (b) conflict with property (c), for how can something be solid and very dense and yet exert no frictional forces on bodies moving through it.

If someone is moving through the air at 20 miles per hour, what speed will they measure for the speed of sound if sound waves are moving (a) towards them, and (b) away from them?

(a) They will measure a faster speed of sound if the sound waves are moving towards them. (b) They will measure a slower speed of sound if the sound waves are moving away from them.

State Newton's three laws of motion.

1. An object at rest remains at rest and an object in uniform motion remains in uniform motion unless acted upon by a force. 2. Force = mass x acceleration 3. For every force there is an equal and opposite force.

What are the four fundamental laws of electricity and magnetism?

1. Electric charges exert forces on each other. There are two types of electric charge; these are the sources of electric fields. Opposite charges attract and similar charges repel. 2. Magnetic poles exert forces on each other. There are no isolated magnetic poles. 3. A changing magnetic field generates an electric field. 4. A current generates a magnetic field. A changing electric field generates a magnetic field.

What are Einstein's two postulates of special relativity?

1. The laws of physics are the same in all frames of reference in uniform motion. 2. The speed of light is independent of the motion of the source.

What four measurable quantities from electricity and magnetism are referred to in Maxwell's equations?

1. electric fields 2. magnetic fields 3. electric charge 4. electric current

In Newton's view what is needed to change motion?

A force is required to change motion. A non-zero net force, produces a non-zero acceleration.

According to the Ancient Greeks, what caused motion?

A push or a pull was required to create motion on earth. This would disturb the object from its natural state, which was to be at rest with respect to and on the surface of the earth.

How do we make electromagnetic waves?

Accelerating charges, such as vibrating charges, produce electromagnetic waves.

According to Einstein, with respect to what does the speed of light move at speed c?

According to Einstein, light moves at speed c with respect to anyone in uniform motion, who cares to measure it. The relative motion between two observers in different reference frames has no affect on the measurement of the speed of light; this last statement would not be true for sound waves and water waves.

What is an electromagnetic wave?

An electromagnetic wave is a self-perpetuating structure of electric and magnetic fields that propagates at the speed of light.

What is the definition of average velocity?

Average velocity is defined, operationally, as the distance moved divided by the time it took to move that distance.

What is the source of all magnetism?

Charged objects in motion. For example, electrons in motion create a magnetic field.

What entities respond to magnetism?

Charged objects in motion. For example, electrons in motion will respond to a magnetic field, but if the electrons are at rest then they will not respond to a magnetic field.

What contribution did Copernicus make to our view of the earth's place in the universe?

Copernicus removed the Earth from occupying a special location in the solar system. This was the first step in the idea that the Earth does not occupy a special location and was later extended by Newton into the idea that the Earth does not execute a special motion, nor are the laws of physics special to Earth, and different elsewhere in the cosmos.

Describe Faraday's experiment that demonstrated another connection between electric current and magnetism.

Faraday discovered that moving a magnet near a loop of wire generates a current in the wire. A battery can create electric current; but now electric current can be created by a moving magnet. In terms of the magnetic field, a changing magnetic field generates an electric current. To put it another way, a changing magnetic field generates an electric field.

Describe Galileo's experiments with rolling balls and what he concluded regarding the question about the natural state of motion of objects.

Galileo rolled balls down inclines and followed their motion as they then went up other inclines with successively smaller angles of inclination with the horizontal. From this he deduced the law of inertia.

If gravity acts between all objects, why don't everyday objects fall together in a great clump?

Gravity is a very weak force and the gravitational pull of the Earth on everyday objects is much larger than the gravitational force that acts between objects on Earth.

What was some of the observations made by Galileo Galilei with a telescope and what was their significance with respect to the ancient view of the heavens?

He observed four of Jupiter's moons and saw astronomical bodies orbiting something other than the earth. He observed the phases of Venus, and saw Venus change size with the changing of the phases: this is hard to explain with a circular orbit around the earth. He saw sunspots and craters on the moon, confirming the idea that the heavens were not the realm of perfection.

Describe the experiment that constituted the first demonstration of electromagnetic waves.

Hertz set up an electric circuit with a power source that made electrons wiggle back and forth, creating a changing electric field. A few feet away sat another circuit with no source of power. When the first circuit was energized, a spark jumped in the second circuit - indicating arrive of energy via Maxwell's electromagnetic waves.

How does the ether allow for the possibility of absolute motion?

If one is out in empty space how could you tell if you were moving or not, without reference to any star, planet, galaxy or fast food restaurant? You couldn't if you limited yourself to a mechanics experiment, like throwing a ball because then you are referring to the motion of something else, and you cannot specify the motion of this thing in any absolute sense either, just as you cannot specify your motion in any absolute sense. Suppose the ether exists. If it fills all of space and is unaffected by bodies moving through it (remember that one of the properties of the ether is that it does not affect bodies moving through it) then it could reasonably be regarded as being at rest in absolute space, constituting the embodiment of absolute space. This means that you could do an experiment involving light, in particular, measuring the speed of light rays moving in different directions and without referring to any object in the universe, conclude if you were moving through absolute space, i.e, through the ether. If the speed of light varies with direction of propagation of the light then you could conclude you are moving with respect to the ether. The degree of variation of the speed of light moving in different directions would tell you have fast you are moving with respect to the ether and the direction of the fasting moving light beam would indicate your direction of motion through the ether.

What is the Newtonian idea of "action-at-a-distance"?

In the context of gravitation, this is the idea that in the attraction between two masses, such as the Earth and the Moon, they reach across empty space to exert this attractive force, even though there is no contact between them. There is no explanation of how the Earth reaches across empty space to attract the Moon. This statement goes for the gravitational attraction between any two objects in Newton's Theory of Gravitation, not just the Moon and the Earth. A corollary of "action-at-a-distance" is that each body reacts instantaneously to the attractive force of the other; if one body was to suddenly disappear, or change its distance from the other body, the first body would know about this instantly via a change in the attractive force it feels. It is a non-local description of gravity, in the sense that the Moon does not react to something immediately around it, but rather the distant Earth.

What characteristic of "action-at-a-distance" do Physicists find troubling?

It is troubling that if the Earth were to suddenly disappear, or change its distance from the Moon, the Moon would, according to the mathematics of Newton's theory of gravitation, know instantaneously of the disappearance or shift in position of the Earth. The idea of information being transmitted instantaneously from one place to another is what physicists find troubling.

Describe ether drag and how it relates to the question of the Earth's motion with respect to the ether.

It violates the Copernican principle for the Earth to be at rest with respect to the ether while just about every other astronomical body moves with respect to the ether (since most astronomical bodies move with respect to the Earth, and the Earth moves with respect to them). The ether drag was the proposal that the earth might seem to be at rest with respect to the ether because it drags the ether immediately around it with it as it moves through space. In other words, the Earth would be at rest with respect to the ether that is dragged by the Earth. The same would be true for all bodies, such as the other planets and stars, moving with respect to the ether, not only the Earth. Thus, the idea of ether drag does not violate the Copernican principle. If the Earth did drag ether around with it, then when someone (on Earth) tried to measure the speeds of light beams traveling in different directions they would find that the speeds of these light beams are all the same, regardless of the direction the light beam was traveling. If this was the result of the experiment, then the interpretation would not be that only the Earth, in all the universe, was at rest with respect to the ether. Rather, this result would be interpreted as being due to the Earth dragging ether around with it, because being done on Earth, the experiment is being done in an environment at rest with respect to the ether (because this ether is being dragged around by the Earth.) If you accept the idea of the ether, then whether or not you observed the aberration of starlight could decide whether or not the Earth drags ether around with it.

What was Aristotle's argument for claiming that the earth is not moving? What argument might you construct to counter Aristotle's argument?

Jump up off of the ground and you will land not on the spot on the ground you jumped from, but you will land somewhere else. The ground will move out from under you. See the accompanying figure in which the person jumps from point A on the ground and lands at point B. Since this does not happen the Earth is not moving. As to a counter argument, try standing on a moving ship and dropping an object. Does the object land at your feet?

How did Kepler account for the careful observations of planetary motion by Tycho Brahe?

Kepler proposed that the planets move in elliptical orbits around the sun.

What is the 19th century answer to the question, with respect to what does light move at speed c? Why did physicists of the 19th century answer this question in the way they did?

Light moves at speed c with respect to the ether, according to 19th century physicists. They posited the existence of the ether since Young demonstrated the wave nature of light and waves require a medium. The vibrations of the medium constitute the wave: sound waves are the vibrations of the air, for example.

In what ways are light waves different from sound waves and water waves?

Light waves do not require a medium, whereas sound waves require air and water waves require water. The speed of light waves is a constant of nature, the same for all observers in uniform motion, whereas the speeds of sound waves and water waves will vary with the state of motion of the observer (measurer) relative to the water or air.

Why and how did Maxwell modify one of the four fundamental statements about electricity and magnetism?

Maxwell changed: • A current generates a magnetic field. Into: • A current generates a magnetic field. A changing electric field generates a magnetic field.

By the late 1800's what two branches of physics described much of physical reality?

Mechanics and electromagnetism.

What constitutes the branch of physics known as mechanics?

Mechanics is the branch of physics that deals with motion: so Newton's Laws of Motion constitutes Mechanics. This includes the 2nd law, F = m a; one of those forces, F, was the law of universal gravitation deduced by Newton. Other forces were contact forces, such as when you push or pull on something. Examples of motion include the motion of the planets around the sun, the motion of the moon around the earth, and the motion of air molecules, which is what sound is. Newton's Laws of Motion apply to all of these.

How does Newton treat celestial and terrestrial motion?

Newton's treats celestial and terrestrial motion on an equal footing in the sense that he assumes that the same laws of nature that operate on earth, also operate in the heavens. This is contrary to Aristotle and the ancient Greeks that believed that different laws of nature operated in the two realms. The answer to the question "what is the natural state of motion?" had different answers on earth and in the heavens.

Does light go at speed c relative to the source of the light waves? What type of astronomical observation answers the previous question? What laboratory experiment done in the 20th century answers this question?

No, the speed of light does not move at speed relative to the source of the light. Observations of binary star systems demonstrates this as light comes from one star moving towards us and at the same time light comes from the other star which might be moving away from us, yet this does not alter what we observe of the stars orbital motions. In the 20th century experiments with unstable particles called neutral pions, which decay into light. When these particles decay to light while moving at more than 99% of the speed of light, the light that is created from their decay is measured to go the same speed as light coming from a stationary light source.

According to Einstein is there still a dichotomy between the laws of mechanics that do obey a relativity principle and the laws of electromagnetism that do not obey a relativity principle?

No. Einstein's first postulate of special relativity applies to all of physics, not just to mechanics.

Can one do an experiment using light to determine whether a lab is moving at constant velocity or is at rest?

No. If one could, this would violate the principle of special relativity (Einstein's first postulate of special relativity.) 19th century physicists did believe you could so such an experiment. The Michelson-Morley experiment was such an experiment, and it measured no changes in the speeds of light beams moving in different directions. 19th century physicists believed that it failed to measure the Earth's motion through the ether.

What experiment, done by Oersted, demonstrated a connection between electric current and magnetism?

Oersted held a compass near a current-carrying wire and the needle was deflected. The current carrying wire thus had a similar effect on the compass needle as did the earth's magnetic field. The wire generated a magnetic field. Thus moving electric charge creates magnetism.

Describe the analogy between observing starlight through a telescope and holding an umbrella while it's raining.

On a windless rainy day one would hold the umbrella straight up if you were at rest with respect to air, but would have to tilt the umbrella in the direction you were walking if you were moving with respect to the air. This is like the aberration of starlight with the umbrella playing the role of the telescope and the rain playing the role of the starlight falling to earth from the stars. If you walk forward you tilt the umbrella forward and if you stop and walk backward (without turning your body around) you would tilt your umbrella backward, in the direction of your motion. Since the earth moves in an ellipse, the stars appear to move in elliptical paths and we have to tilt the telescope slightly in the direction of the Earth's motion.

What is the natural state of motion on Earth, according to the Ancient Greeks?

On earth the natural state of motion was to be at rest as close to the center of the earth as possible.

What is the 19th century answer to the question do the laws of electromagnetism obey a relativity principle? A related question is in what frame of reference are the laws of electromagnetism valid?

One of the predications of the laws of electromagnetism is that there is light at speed c. Since the 19th century physicists believed that light moves at speed c with respect to the ether, then if you were not at rest in the ether you would not measure light waves moving at speed c and so the laws of electromagnetism would be different. This means that identical experiments done in different frames of reference in uniform motion would give different results, and so you could differentiate different states of motion based on the outcomes of electromagnetic experiments, without referring to any other object. So the laws of electromagnetism do not obey a relativity principle. They are only valid in a frame of reference at rest with respect to the ether.

State the Principle of Newtonian/Galilean Relativity in two equivalent ways.

One way: "The laws of mechanics are the same in all reference frames in uniform motion." Second way: "There is no mechanics experiment you can do to distinguish between two uniformly moving frames in relative motion. Identical experiments done in two reference frames in uniform motion will give identical results."

What is the operational definition of electric field?

Place a charged particle at a point in space and measure the net force that acts on the particle (by measuring the particle's acceleration and dividing by its mass). The ratio of the force on the particle to the amount of charge of the particle is the electric field. It is independent of how much charge you placed at that point in space.

What was the response of ancient astronomers, like Ptolemy, to observations of retrograde motion and to the prevailing view of motion in the heavens?

Ptolemy and earlier astronomers proposed that the planets move in circles, with the centers of these circles moving in circular orbits around the earth: these smaller circles that the planets move in were called epicycles. Again there is a nice simulation of epicycles at:

What are some technologies that rely on electromagnetic waves?

Radio, television, cell phones, satellite dishes, microwave ovens, electronic car keys, wireless computer mice, police radar, garage door openers, radio telescopes.

Are sound waves explainable under the umbrella of Newton's Laws of Motion?

Since sound is a manifestation of the motion of air molecules, this phenomenon falls under the description of Newton's Laws of Motion.

What kind of experiments, according to 19th century physicists, could be done to answer the question "Am I moving?" Can Mechanics questions answer the question "Am I moving?"

Since the 19th century physicists thought that the laws of electromagnetism does not obey a relativity principle, they did believe you could do an experiment measuring motion without referring to any other object in the universe. Do an experiment in which the speed of light beams moving in different directions is measured. If these speeds are the same, regardless of the direction the light is moving, then you are not moving with respect to the ether. If speed of light depends on the direction the light is moving then you are moving with respect to the ether. By measuring the difference in these speeds it is possible to find your speed with respect to the ether, without referring to any other body in the universe. (This is what makes it absolute motion.) This is analogous to the situation in the following problem from the "Sound Waves, Water Waves and Relative Motion" homework: Problem 7: There are two loud speakers, facing each other, in a room. You are in between the two speakers and you measure the speed of sound coming from one speaker to be 342 meters per second and the speed of sound coming from the other speaker to be 338 meters per second. What is your speed through the air? Take the speed of sound in air to be 340 meters per second. On the other hand, Mechanics, which obeys a relativity principle ("The laws of mechanics are the same in all frames of reference in uniform motion") could not be used to answer the question "am I moving?" since absolute motion is meaningless for any branch of physics that obeys a relativity principle. Mechanics could be used only to answer questions like am I moving relative to something else.

In what frame of reference are the laws of electromagnetism valid, according to Einstein?

Since the laws of electromagnetism (and all laws of physics) obey a relativity principle, according to Einstein, the laws of electromagnetism are the same in all frames of reference in uniform motion.

What did Maxwell calculate for the speed of electromagnetic waves?

Speed of light.

In what frame of reference are the laws of electromagnetism valid, according to 19th century physicists?

The 19th century physicists believed the laws of electromagnetism are valid in the reference frame of the ether, the frame which is at rest with respect to the ether. When one is at rest with respect to the ether one would measure the speed of light to be c.

Relate the aberration of starlight to the question of the Earth's motion through the ether.

The 19th century physicists interpreted the aberration of starlight as proof that the earth was not at rest with respect to the ether and did not drag a blob of ether around in space with it as it moved through the ether.

How does the law of inertia differ from the Aristotelian view of motion on earth?

The Aristotelian view of motion on Earth was that the natural state of motion was to be at rest on Earth, as close to the center of the Earth as the object can get. The law of inertia (an object at rest remains at rest or an object in motion remains in motion unless acted upon by a force) states that the natural state of motion is that with constant speed and constant direction (uniform motion). So the law of inertia implies that only changes in motion require a causative agent, while the Aristotelian view says that if something is moving there must be a causative agent (a force) even if the motion is uniform.

Comment on the Copernican principle and the idea that the Earth is at rest with respect to the ether. Does the possibility that the Earth is at rest with respect to the ether violate the spirit of the Copernican principle?

The Copernican principle said that the Earth is not the center of the Solar System, nor any special location in the Universe. The relativity principle obeyed by mechanics was very much in this spirit since it asserted that the laws of mechanics are the same everywhere, and are not just valid on Earth. To put it another way, there is nothing special about Earth's motion, at least as far as the laws of mechanics are concerned. But there is a preferred frame of reference with respect to electromagnetism: the ether frame of reference. It is in this frame that light moves at speed c. It is in this frame that the laws of electromagnetism are valid. The cosmos contains approximately 1 trillion (10 raised to the 12th power) galaxies, each with a trillion stars. The bulk of these galaxies are in motion with respect to one another. Galaxies rotate around their center, just as the planets move around the sun. With all of this motion, why should only the Earth be at rest with respect to the ether. This would seem to give the Earth a special motion, in violation of the Copernican principle.

What is the significance of the Michelson-Morley experiment for the question does the Earth move with respect to the ether?

The Michelson-Morley experiment failed to detect the Earth's motion through the ether. Since the Aberration of Starlight experiment was interpreted by the 19th century physicists as meaning that the Earth moves through the ether, the Michelson-Morley experiment should have detected this motion by observing the shifting of the position of the interference fringes as the apparatus was rotated (corresponding to changes in the speed of the two light beams in the apparatus.) The experiment was sensitive enough to detect the difference in the speeds of light moving in different directions but no fringe shifts were observed: meaning there was no difference in the speeds of light moving in different directions. To those who believed in the ether as the medium for light, this meant that the Earth was not moving with respect to the ether (like the identical speeds of water waves moving in different directions that you measure when you are not moving with respect to the water.) Thus the 19th century physicists were left with the contradiction between the aberration of starlight (which says the Earth moves with respect to the ether) and the Michelson-Morley experiment (which says the Earth does not move with respect to the ether.)

How does Einstein remove the 19th century dilemma created by the contradictory conclusions drawn from the aberration of starlight and the Michelson-Morley experiment?

The Michelson-Morley experiment failed to measure the motion of the Earth through the ether because there is no ether. The aberration of starlight is observed because of the motion of the earth perpendicular to the line of sight of the star; this has nothing to do with the ether, so there is no contradiction between the aberration of starlight and the Michelson-Morley experiment.

What is the Michelson-Morley experiment? What was it designed to measure? Did it succeed in measuring what it was designed to measure? Include a description of a Michelson Inteferometer.

The Michelson-Morley experiment was designed to measure differences in the speed of light beams moving in two different directions. From this information the Earth's speed through the ether could be calculated. It failed to measure any such differences in the speed of light beams moving in different directions. The experiment used a Michelson interferometer, which took a beam of light and, using a half-silvered mirror called a beam-splitter, broke it into to two beams moving at approximately right angles with respect to each other. These beams would strike two mirrors, also at approximately right angles with respect to each other and would bounce back to the beam splitter, where parts of the two beams would be recombined. Constructive or destructive interference would be observed in this recombined beam.

How is it that both the apple and the Moon are falling, when the apple is on a collision course with the ground while the Moon remains in its orbit?

The Moon has a component of velocity perpendicular to the line joining the Moon and the Earth that the apple does not have. If the Moon did not have this component of velocity it would fall directly to the Earth and strike it. The Earth's gravitational force causes the Moon's motion to deviate from the straight line motion it would execute otherwise. The figure below shows the trajectories of different objects with different tangential velocity components. The Moon has a large enough tangential velocity component so that it does not strike the ground.

What is significance of the aberration of starlight for the question does the Earth move with respect to the ether?

The aberration of starlight demonstrated to 19th century physicists that the earth is moving with respect to the ether, and so an experiment should be designed to try to detect that motion by measuring variations in the speed of light beams traveling in different directions.

What dichotomy is revealed in the ancient world in response to the question, "what is the natural state of motion on Earth and in the heavens"?

The dichotomy is about the two answers the ancient Greeks had to the question about natural motion. The answer on Earth was different from the answer in the heavens. On Earth, the natural state of motion was to be at rest as close to the center of the Earth as is possible. If something moved then there had to be a cause - an ox has to pull a cart and when it stopped pulling the cart came to a stop. In the heavens the natural state of motion was not rest; it was circular motion. And there is the dichotomy. Earth and Heaven are two different realms with two different laws of motion.

Why was the field concept introduced? Contrast the field concept (and the idea of local conditions) with the action-at-a-distance concept.

The field concept was introduced to explain non-contact forces, such as the electrical force and the gravitational force, which acts between objects even though they do not touch. The idea of the field concept was to provide a local explanation to these forces. The charge does not magically respond to the other distant charge, but instead it responds to the space around it. Likewise for gravitation, for example, the Moon responds not to the distant Earth, but to the gravitational field around it.

What are characteristics of the force between electric charges?

The force can be attractive or repulsive. It is a non-contact force, in that charged objects do not have to be in direct physical contact for the force to be felt by the objects. (This is also true for gravity). Such observations leads to the hypothesis that there are two kinds of charge; they are called positive and negative. Like charged objects repel and opposites attract. The farther apart the charges are the weaker the force between them.

What are characteristics of the force between magnetic poles?

The force can be attractive or repulsive. It is a non-contact force, like gravity and the electrical force. Each magnet has two poles, called north and south. You cannot find isolated poles; cut a magnet in half and you have two magnets, each with north and south poles. The farther apart the magnets are the weaker the force between them.

What does the law of inertia imply about relative and absolute motion?

The law of inertia states that an object at rest remains at rest or an object in motion remains in motion unless acted upon by a force. In other words, the law does not distinguish between a state of rest and a state of uniform motion, so there is nothing absolute about uniform motion. Neither rest nor uniform motion will change unless something (a force) causes a change in the motion. In fact, you cannot distinguish between the two, meaning there is no experiment you can do that can tell you that you are moving, without referring to something else, such as the earth. If you were out in empty space, far from Earth or any other planet of star, how could you tell if something was at rest or in uniform motion? There are no markers in space to refer to. You could state if the object was moving with respect to you, but this is relative motion, not absolute motion. If something is moving then you have to state what it is moving with respect to, and this is what makes the motion relative, and not absolute. Two individuals in uniform motion with respect to one another, for example, someone in a car moving at 50 mph with respect to Earth and another person at rest with respect to Earth each can claim to be at rest and claim the other person is moving at 50 mph with respect to them. If there are no forces on either of them then the law of inertia states that the relative speed of 50 mph between them will not change. On the other hand, all the person at rest on Earth has to do is to get into another car, accelerate to 50 mph and then hold that speed, traveling in the same direction as the person in the other car, and then there will be no relative motion between the two people and each will claim the other is at rest with respect to them. If there are no forces on them then they will continue to be at rest with respect to each other, again because of the law of inertia.

What philosophically disturbing dichotomy existed in the laws of physics around the late 1800's?

The laws of mechanics obeyed a relativity principle. Absolute motion was meaningless and no experiment could answer the question "am I moving"? The laws of electromagnetism did not seem to obey a relativity principle and absolute motion had a meaning in a sense that you could determine your speed through empty space by doing a Michelson-Morley experiment.

Describe what is meant by retrograde motion of the planets.

The planets motion is not simply described by the statement that they rise in the east and set in the west, as is true for the stars. Usually planets move from west to east against the background stars, but other times they move from east to west against the background stars from one night to the next: this is called retrograde motion. Go to the following link for a simulation:

What is the difference between the Principle of Relativity according to Galileo and Newton and the Principle of Relativity stated by Einstein?

The principle of Galilean relativity applied to mechanics, whereas the principle of Special Relativity applies to all of physics, not just mechanics.

Based on the principle of relativity, why can't someone travel at the speed of light?

The principle of relativity: the laws of electromagnetism are the same for all observers in uniform motion. One of those predictions is that there are electromagnetic waves that move at speed c. If you moved at the speed of light, then you would not measure light waves moving at speed c, in violation of the principle of relativity. Thus you can never inhabit a frame of reference where light is stationary in a vacuum, i.e., you cannot move at the speed of light.

Where does the invariance of the speed of light come from?

The principle of relativity: the laws of electromagnetism are the same for all observers in uniform motion. One of those predictions is that there are electromagnetic waves that move at speed c. Since all observers in uniform motion measure the same speed for light, despite being in different frames of reference (meaning that they are in relative motion with respect to each other), the speed of light is absolute then the quantities from which speed is calculated, distance traveled divided by time it takes to travel that distance, must be relative. That means that the different observers in relative motion measure different distances between events and different time intervals between events.

What two astronomical observations did Copernicus's heliocentric model of the Universe explain?

The retrograde motion of the planets. If they are circular motion why would they change direction? The brightening and dimming of the planets. If they are equally distant from Earth, in circular motion, then why would they appear to brighten?

What determines the speed of a water wave, sound wave or seismic wave?

The speed of a water wave is determined by the strength of gravity pulling on the water and the density of the water. The speed of a sound wave is determined by the density of the air and the speed of a seismic wave depends on the density of the earth at which the wave occurs.

In what two ways can motion change?

The speed of an object can change and/or the direction of motion can change. If either or both of these are the case then this object is accelerating.

Describe the analogy between the two light beams in a Michelson interferometer and the two people swimming up and downstream and across and back in a river.

The two people swimming through moving water, upstream/downstream and across/and back, is analogous to the two beams of light moving through the ether wind. Because the people are swimming in different directions through flowing water, they take different amounts of time to make round trips of equal distance. The 19th century physicists thought this would be true for light as well, since they believed, based on their interpretation of the aberration of starlight, that the earth was moving through the ether. The ether wind is present because the Earth is moving through the ether. Just as it takes different times for a round trip up and down the river and across the river and back, even though the distance traveled is equal for the two swimmers, because of the flowing water affecting the two swimmers differently, it was thought that the round trip time in the each arm of the Michelson interferometer would be different due to the ether wind altering the speeds of the two light beams by different amounts. Since the Michelson Morley experiment involves light waves overlapping you get constructive/destructive interference. The positions of the interference fringes would shift if the round trip time for each beam of light changed, and they thought this would happen as the apparatus was rotated; they believed it was being rotated with respect to the ether.

What property of light waves does the Michelson-Morley interferometer directly demonstrate?

The wave nature of light, since the output of the experiment is a series of bright and dark bands corresponding to places where you have constructive and destructive interference occurring. These fringes are shown in Figure 6.2 and Figure 6.3 in Wolfson.

What is the same for light and the invisible electromagnetic waves that were demonstrated by Hertz and Marconi?

Their structure is the same: they are vibrating electric and magnetic fields. And the electric and magnetic fields strengths are changing at each point in space. The changing electric field generates a changing magnetic field, which in turn generates a changing electric field, producing the self-perpetuating structure. This is true for light and invisible forms of electromagnetic radiation like x-rays, microwaves, radio waves, etc.

A person standing on earth, a person in a car moving at 60 mph, a person in an airplane moving at 600 mph and someone in a spaceship moving at ½ c all measure the speed of sound emitted from the same source. Do they all get the same value for the speed of sound emitted from this source? If they got different answers would that violate the Principle of Relativity?

They all get different speeds for the speed of sound and that does not violate the principle of relativity. The speed of sound is relative to the air in which the sound is a disturbance. Move with respect to the air and you measure a different speed for sound. Different observers moving at different speeds with respect to the air will measure different speeds for sound.

In what way are the Moon and an apple that comes loose from a tree both falling? In other words, in what way is their motion the same?

They are both accelerating towards the Earth. This is how their motion is the same.

What is meant by a natural state of motion?

This is a state of motion that requires no explanation. When something is left alone it will assume this state of motion (which might be rest, i.e., lack of motion).

What radical philosophical shift was present in Newton's recognition of universal gravitation?

This is closely related to question 12. Newton assumes that all objects with mass attract all other objects with mass. So the earth attracts things on its surface and it attracts the Moon. And the Moon attracts the Earth and the Sun attracts all of the planets etc.. So the same thing that makes the apple fall to earth, keeps the Moon in orbit around Earth. This is an example of Newton's assumption that the same laws of nature apply on earth and in the heavens and this was a radical philosophical shift. Previously, the Earth and the Heavens were considered different realms with different physical laws describing reality, so Newton's was a radical philosophical shift.

What is the aberration of starlight?

This is the apparent elliptical motions of the stars, with a period of 1 year, induced by the motion of the Earth around the sun. As Wolfson puts it in the glossary on page 245, "The change in apparent position of a star, due to Earth's orbital motion. Used to show that Earth did not drag ether with it."

How did this alter the view of planetary motion by Ptolemy?

This was in direct opposition to the idea that the planets move in circles, and because the circle was considered the most perfect geometrical form (no edges), that the heavens were the realm of perfection, including perfection in motion: perfect circles.

What is wave interference?

Two or more waves can occupy the same point in space; when they do so they interfere with each other. When two peaks overlap you get a larger wave - this is constructive interference. When a peak and a trough overlap they can cancel out (if they have the same amplitude) - this is destructive interference.

Describe the Lorentz-Fitzgerald contraction and its relationship to the results of the Michelson-Morley experiment.

Two physicists tried the explain the Michelson-Morley experiments failure to measure the difference in the speeds of light moving in different directions by supposing that one arm of the interferometer was shortened due to motion through the ether. The arm along which light moves slower would be shortened so that the light beam that is moving slower would be making the round trip along a shorter path. This would allow it to make the round trip from the half-silvered mirror to the mirror and back in the same time as the other, faster moving, beam makes its round trip. Thus there would be no fringe shifts in the apparatus as it was rotated, and the time difference that it takes the light beams to make the round trips in the apparatus would be zero. They failed to explain how the ether could do this, though; especially since the ether was not supposed to exert any frictional type forces on bodies moving through it (remember why?). See Wolfson, page 77.

What is uniform motion? What is the acceleration of an object in uniform motion?

Uniform motion is that in a straight line at a constant speed. The acceleration of an object in uniform motion is zero.

Sixty years after Young's experiment demonstrated the wave nature of light, what is Maxwell's answer to what kind of wave is light?

Vibrating or oscillating electric and magnetic fields - waves made up of electric and magnetic fields.

What is the difference between light and the invisible electromagnetic waves that were demonstrated by Hertz and Marconi?

Wavelength and frequency are different.

Why isn't the wave nature of light (visible electromagnetic radiation) obvious to us?

Wavelength of visible light is too small - 2.5 millionths of an inch for red light and about 14 millions of an inch for deep violet light.

List four numbers that characterize a wave.

Wavelength, frequency, speed of the wave, period and amplitude. FWSP

If we seek to understand the nature of space and time, why would we study motion?

We move from one point in space to another; furthermore it takes time to get from one place to another. So we move through space and in time; this is one way to understand the nature of space and time since we move through both.

Why is motion important?

With no motion there is no beating heart, no blood flowing, no flow of air into lungs, no flow of gas out of the lungs, no synapses; in other words, no life.

The speed of sound is about 700 miles per hour; but relative to what do sound waves move at 700 miles per hour?

With respect to the air in which it is a disturbance.

A person standing still on Earth, a person in a car moving at 60 mph on Earth, a person in an airplane moving at 600 mph with respect to Earth and someone in a spaceship moving at ½ c all measure the speed of light of the same beam of light. What do they measure for the speed of light? If they got different answers would that violate the Principle of Relativity?

Yes. All of these observers, all being in a uniform state of motion, must measure the same speed for light. That is one of the predictions of the laws of electromagnetism and for those laws to be the same for all of these observers they must measure the same speed for light. In this example, the source of light is moving at different speeds according to the different observers, but that makes no difference regarding the speed of light, since that speed is independent of the motion of the source.

Describe the early 19th century experiment by Young that argued for a wave model of light.

Young sent light through a pair of closely spaced, very thin, slits and produced a series of spots of light. A wave model of light can explain the spots by stating that they are locations of constructive interference.