If you walk at 1 km/h down the aisle toward the front of a train that moves at 60 km/h, what is your speed relative to the ground?

61 km/h

In the preceding question, is your approximate speed relative to the Sun as you walk down the aisle of the train changed slightly or by a lot?

A lot! Relative to the Sun, it is nearly 110,000 km/hr. And the Sun is not at rest; it orbits the center of the galaxy, which moves with respect to other galaxies.

What hypothesis did G. F. FitzGerald make to explain the findings of Michelson and Morley?

The length of the material in the experiment contracted in the direction of motion. (by just the amount required to counteract the presumed variation in the speed of light.) The needed “shrinkage factor” was worked out by Hendrik Lorentz.

What classical idea about space and time did Einstein reject?

Einstein rejected the idea that space and time are independent.

What is the same in Einstein’s first postulate?

All laws of nature in all uniformly moving frames of reference

What is constant in Einstein’s second postulate?

The speed of light in a vacuum

Inside the moving compartment of Figure 35.4, light travels a certain distance to the front end and a certain distance to the back end of the compartment. How do these distances compare as seen in the frame of reference of the moving rocket?

The distances traveled by light are the same.

How do the distances in Reading Check Question 7 compare as seen in the frame of reference of an observer on a stationary planet?

The distance travelled by light to the back is shorter.

How many coordinate axes are usually used to describe three-dimensional space? What does the fourth dimension measure?

Usually three axes used to describe three-dimensional space. Coordinate axes x, y, z of the reference frame specify the position of any location in space. The fourth dimension measures time.

Under what condition will you and a friend share the same realm of spacetime?

We experience the same spacetime when we are in the same frame of reference with zero velocity relative to each other.

What is special about the ratio of the distance traveled by a flash of light to the time the light takes to travel this distance in a vacuum?

The ratio is always the same, the speed of light.

Time is required for light to travel along a path from one point to another. If this path is seen to be longer because of motion, what happens to the time it takes for light to travel this longer path?

It takes longer.

What do we call the “stretching out” of time?

Time dilation

What is an algebraic expression for the Lorentz factor γ (gamma)? Why is γ never less than 1?

1/(1 – v 2/c 2)1/2; v 2/c 2 is always a positive number, so the denominator is less than 1, making the ratio greater than 1.

How do measurements of time differ for events in a frame of reference that moves at 50% of the speed of light relative to us? At 99.5% of the speed of light relative to us?

For 0.50c, time dilates to 1.15 times the proper time. For 0.995c, time dilates to 10 times the proper time.

What is the evidence for time dilation?

Atomic clocks in orbit in the GPS system run slower because they are in orbit.

Short-lived particles travelling at high speeds in particle accelerators live longer.

Atomic clocks flown in jets run slower because they are in motion.

When a flashing light approaches you, each flash that reaches you has a shorter distance to travel. What effect does this have on how frequently you receive the flashes?

The frequency increases.

When a flashing light source approaches you, does the speed of light or the frequency of light – or both – increase?

Only frequency increases.

If a flashing light source moves toward you fast enough so that the time interval between flashes is half as long, how long will the time interval between flashes be if the source is moving away from you at the same speed?

Twice as long

How many frames of reference does the stay-at-home twin experience in the twin trip? How many frames of reference does the traveling twin experience?

Stay-at-home, 1; traveler, 2 (separated by the acceleration of the spaceship in turning around)

What is the maximum value of v1v2/c2 in an extreme situation? What is the smallest value?

Maximum 1, minimum 0

Is the relativistic rule V = (v1 + v2) /(1 + v1v2/c2) consistent with the fact that light can have only one speed in all uniformly moving reference frames? How?

Yes. If either v1 or v2 is equal to c, then V = c.

What two main obstacles prevent us from traveling today throughout the galaxy at relativistic speeds?

The large quantity of energy needed and radiation shielding

What is the universal standard of time?

There is none.

How long would a meterstick appear to be if it were traveling like a properly thrown spear at 99.5% of the speed of light?

1/10 m

How long would the meterstick in the preceding question appear to be if it were traveling with its length perpendicular to its direction of motion?

1 m. No contraction takes place vertically when an object is moving horizontally. Contraction takes place only in the direction of motion!

If you were traveling in a high-speed rocket ship, would metersticks on board appear to you to be contracted? Defend your answer

No. The stick is in your frame of reference.

What would be the momentum of an object if it were moving at the speed of light?

The momentum would be infinite. pg 677

When a beam of charged particles moves through a magnetic field, what is the evidence that particles in the beam have momentum greater than the value mv?

The radius of curvature when subjected to a sideways force is greater.

Compare the amounts of mass converted to energy in nuclear reactions and in chemical reactions.

In a single reaction, nuclear reactions release more than a million times the energy of chemical reactions. But, in releasing the same total amount of energy, the same amount of mass is lost in both types of reactions.

How does the energy from the fissioning of a single uranium nucleus compare with the energy from the combustion of a single carbon atom?

Fissioning one uranium nucleus produces 10 million times more energy than the combustion of one carbon atom.

Does the equation E=mc2 apply to chemical reactions? To potential energy stored in a spring? To electrical potential energy?

All three!

How does E = mc2 describe the identities of energy and mass?

Energy is mass and c2 is the conversion factor for the units.

How does the correspondence principle relate to special relativity?

At everyday low velocities, relativistic equations approach the Newtonian equations.

Do the relativity equations for time, length, and momentum hold true for everyday speeds? Explain.

They hold true but the differences they predict are hard to measure. In Quantum Mechanics, the correspondence principle is that for large quantum numbers (large energies) the classical limit is reached.

Likewise, in relativity, the correspondence principle is that for slow speeds relative to the velocity of light, classical mechanics is recovered (as it should!).

If you were in a smooth-riding train with no windows, could you sense the difference between uniform motion and rest? Between accelerated motion and rest? Explain how you could make such a distinction with a bowl filled with water.

Assuming that there are no vibrations etc to indicate motion and assuming that the observer becomes conscious of being in the train only after uniform motion is underway – as would happen if the observer were to awake from deep slumber after the train had achieved uniform motion. The sense of motion can only be conveyed if there are vibrations or acceleration/deceleration in any direction.

Can an electron beam sweep across the face of a cathode-ray tube at a speed greater than the speed of light? Explain.

If the sweep rate were made to be faster than 30 cm per nanosecond, ( 0.033 nanoSec per cm ).

The actual electrons in the beam, will be traveling at less than the speed of light. Another example is if you take a laser and shine it on a little cube shaped mirror, and spin the mirror at thousands of RPM, and the light from the mirror is directed toward the moon. The line of light that impacts the moon will appear to travel across the surface at a speed that may exceed the speed of light. But its kind of an illusion. No ‘thing’ is actually traveling faster than light. You cannot interrupt the light at one point on the surface and have any information travel to another point on the surface at super luminal speed. No actual matter, energy, or information is travelling faster than the speed of light.

Event A occurs before event B in a certain frame of reference. How could event B occur before event A in some other frame of reference?

the speed of light is not infinite. As a result, there will be a time difference between when an event happens, and when the light containing the information about the event reaches different points in space at different distances from the event.