Chapter Questions
The idea that force causes acceleration doesn't seem strange. This and other ideas of Newtonian mechanics are consistent with our everyday experience. But. the ideas of relativity do seem odd and more difficult to grasp. Why is this?
If you were in a smooth riding train with no windows, could you sense the difference between uniform motion and rest? Between accelerated morion and rest? Explain how you could make such a distinction with a bowl filed with water.
A person riding on the roof of a freight train fires a gun pointed forward. (a) Relative to the ground, is the bullet moving faster or slower when the train is moving than when it is standing still? (b) Rebtive to the freight car, is the bullet moving faster or slower when the train is moving than when the train is standing still?
Suppose instead that the person niding on top of the freight car shines a searchlight beam in the direction in which the train is traveling. Compare the speed of the light beam relative to the ground when the train is at rest and when it is in motion. How does the be havior of the light beam differ from the behavior of the bullet in Exercise 3 ?
Why did Michelson and Morley at first consider their experiment a failure? (Have you ever encountered other examples where failure has to do not with the lack of ability but with the impossibility of the task?)
When you drive down the highway, you are moving through space. What else are you moving through?
In Chapter 26, we leamed that light travels more slowly in glass than in air, Does this contradict Finstein's second postulate?
Astronomers view light coming from distant galaxies moving away from the Earth at speeds greater than $10 \%$ the speed of light. How fast does this light meet the telescopes of the astronomers?
Does special relativity allow anything to travel faster than light? Explain.
When a light beam approaches you, its frequency is greater and its wavelength less. Does this contradict the postulate that the speed of light cannot change? Defend your answer.
The beam of light from a laser on a rotating turntable casts into space. At some distance, the beam moves across space faster than c. Why does this not contradict relativity?
Can an electron beam sweep across the face of a cathode-ray tube at a speed greater than the speed of light? Explain.
Consider the speed of the point where scissors blades meet when the scissors are closed. The closer the blades are to being closed, the faster the point moves. The point could, in principle, move faster than light. Likewise for the speed of the point where an ax mects wood when the ax blade meets the wood not quite horizontally. The contact point travels faster than the ax. Similarly, a pair of laser beams that are crossed and moved toward being paraliel produce a point of intersection that can move faster than light. Why do. these examples not contradict special relativity?
If two lightning bolts hit exactly the same place at exactly the same time in one frame of reference, is it possible that observers in other frames will see the bolts hitting at different times or at different places?
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?
Suppose that the lightbulb in the rocket ship in Figures $35.4$ and Figure $35.5$ is closer to the front than to the rear of the compartment, so that the observer in the ship sees the light reaching the front before it reaches the back. Is it still possitle that the outside observer will see the light reaching the back first?
The speed of light is a speed limit in the universe -at least for the four-dimensional universe we comprehend. No material particle can attain or surpass this limit even when a continuous, unremitting force is exerted on it. What evidence supports this?
Since there is an upper limit on the speed of a partcle, does it follow that there is also an upper limit on its momentum? On its hinetic energy? Explain
Light travels a certain distance in, $\mathrm{aa} y, 20,000$ years. How is it possible that an astronaut, traveling slower than light, could go as far in 20 years of her life as light travels in 20,000 years?
Is it possible for a hurrian being who has a life expectancy of 70 years to make a round-trip joumey to a part of the universe thousands of light-years distant? Explain.
A win who makes a long trip at relativistic speeds returns younger than his stay-at-home twin sister. Could he retum before his twin sister was born? Defend your answer.
Is it possible for a son or daughter to be biologically older than his or her parents? Explain.
If you were in a rochet ship traveling away from Earth at a speed close to the speed of light, what changes would you note in your pulse? In your volume? Explain.
If you were on Earth monitoring a person in a rocket ship traveling away from Earth at a speed close to the speed of light, what changes would you note in his pulse? In his volume? Explain.
Due to length contraction, you see people in a spaceship passing by you as being slightly narrower than they nomally appear. How do these people view you?
Because of time dilation, you observe the hands of your friend's watch to be moving slowly. How does your friend view your watch - as running slowly, nunning rapidly, or neither?
Does the equation for time dilation show dilation occurring for all speeds, whether slow or fast? Explain.
If you lived in a world where people regularly traveled at speeds near the speed of light, why would it be risky to make a dental appointment for $10: 00$ a.m. next Thursday?
How do the measured densities of a body compare at rest and in motion?
If stationary observers measure the shape of a passing object to be exactly circular, what is the shape of the object according to observers on board the ob. ject, traveling with it?
The formula relating speed, frequency, and wavelength of electromagnetic waves, $v=f \lambda$, was known before relativity was developed. Relativity has not changed this equation, but it has added a new fea. ture to it. What is that feature?
Light is reflected from a moving mirror. How is the reficcted light different from the incident light, and how is it the same?
As a meterstick moves past you, your measurements show its momentum to be twice its classical momen. tum and its length to be $1 \mathrm{~m}$. In what direction is the stick pointing?
In the preceding exercise, if the stick is moving in a direction along its length (Tike a properly thrown spear), how long will you measure its length to be?
If a high-speed spaceship appears shrunken to half its normal length, how does its momentum compare with the classical formula $p=m v ?$
How can the momentum of a particle increase by $5 \%$, with only a 19 increase in speed?
The two-mile linear accelerator at Stanford University in California "appears" to be less than a meter long to the electrons that travel in it. Explain.
Electrons end their trip in the Stanford accelerator with an energy thousands of times greater than their initial rest energy. In theory, if you could travel with them, would you notice an increase in their energy? In their momentum? In your moving frame of reference, what would be the approximate speed of the target they are about to hit?
Two safety pins, identical except that one is larched and one is unlatched, are placed in identical acid baths. After the pins are dissolved, what, if anything. is different about the two acid baths?
A chunk of radioactive material encased in an ideal. ized, perfectly insulating blanket gets warmer as its nuclei decay and release energy. Does the mass of the radioactive marerial and the blanket change? If so, does it increase or decrease?
The electrons that illuminate the screen in a typical television picture tube travel at nearly one-fourth the speed of light and possess nearly 39 more energy than hypothetical nonrelativistic electrons traveling at the same speed. Does this relativistic effect tend to increase or decrease your electric bill?
Muons are elementary particles that are formed high in the atmosphere by the interactions of cosmic rays with atomic nuclei in the upper atmosphere. Muons are radioactive and have average lifetimes of about two-millionths of a second. Even though they travel at almost the speed of light, very few should be detected at sea level after traveling through the atmosphere -at least according to classical physics. Laboratory measurements, however, show that muons in great number do reach the Earth's surface. What is the explanation?
How might the idea of the correspondence principle be applied outside the field of physics?
What does the equation $E=m c^{2}$ mean?
According to $E=m c^{2}$, how does the amount of energy in a kilogram of feathers compare with the arnount of energy in a kilogram of iron?
Does a fully charged flashlight battery weigh more than the same battery when dead? Defend your answer.
When we look out into the universe, we see into the past. John Dobson, founder of the San Francisco Sidewalk Astronomers, says that we cannot even see the backs of our own hands now - in fact, we can't see anything now. Do you agree? Explain.
One of the fads of the future might be "century hopping," where occupants of high-speed spaceships would depart from the Earth for several years and retum centuries later. What are the present-day obstares to such a practice?
Is the statement by the philosopher Kerkegaard that "Life can only be understood backwards; but it must be lived forwards" consistent with the theory of special relativity?
Make up four multiple-choice questions, one each. that would check a classmate's understanding of(a) time dilation.(b) length contraction,(c) relativistic momentum, and(d) $E=m c^{2}$,