We have conducted “mind experiments” in this chapter, many of which require us to suspend reality. In real life, scenarios such as these would kill anyone attempting to make the observations. So why is relativity theory
Source of incredibly strong gravitation!
Three-dimensional space
Figure 16-11. Spatial curvature in the vicinity of an object that produces an intense gravitational field.
important? If space is bent and time is slowed by incredibly powerful grav- itational fields, so what?
The theory of general relativity plays an important role in astronomers’
quests to unravel the mysteries of the structure and evolution of the Universe. On a cosmic scale, gravitation acquires a different aspect than on a local scale. A small black hole, such as that surrounding a collapsed star, is dense and produces gravitation strong enough to destroy any material thing crossing the event horizon. However, if a black hole contains enough mass, the density within the event horizon is not so large. Black holes with quadrillions of solar masses can exist, at least in theory, without life-threat- ening forces at any point near their event horizons. If such a black hole is ever found, and if we develop space ships capable of intergalactic flight, we will be able to cross its event horizon unscathed and enter another Universe. We can be sure someone will try it if they think they can do it, even if they are never able to communicate back to us what they find.
According to some theorists, we need not travel far to find the ultimate black hole. It has been suggested that our entire Universe is such an object and that we are inside it.
Quiz
Refer to the text if necessary. A good score is 8 correct. Answers are in the back of the book.
1. A common unit of acceleration is the (a) meter per second.
(b) kilometer per second.
(c) kilometer per hour.
(d) gravity.
2. Suppose that you have a spherical ball with mass of a hundred grams (100 g) at rest. If you throw the ball at three-quarters of the speed of light, what will its mass become, as measured from a stationary point of view?
(a) 100 g (b) 133 g (c) 151 g
(d) It cannot be calculated from this information.
3. Suppose that the ball in Problem 2 has an apparent diameter, as measured lat- erally (sideways to the direction of its motion), of a hundred millimeters (100 mm) when it is speeding along at three-quarters of the speed of light. What will its diameter be when it comes to rest?
(a) 100 mm (b) 133 mm (c) 151 mm
(d) It cannot be calculated from this information.
4. If a space ship is slowing down, that is, losing speed in the forward direction, the acceleration force inside the ship is directed
(a) toward the rear.
(b) toward the front.
(c) toward the side.
(d) nowhere; there is no acceleration force.
5. The Michelson-Morley experiment
(a) showed that the speed of light depends on the direction in which it is measured.
(b) showed that the speed of light depends on the velocity of the observer.
(c) showed that the speed of light does not depend on the direction in which it is measured.
(d) proved that the ether passes right through the Earth.
6. If you are in a spacecraft accelerating at 9.8 m/s2through interplanetary space, you will feel the same force as you feel if you are sitting still on the surface of the Earth. This is an expression of
(a) a complete falsehood! Traveling through space is nothing at all like being on Earth.
(b) the fact that the speed of light is absolute, finite, and constant and is the fastest known speed.
(c) Einstein’s equivalence principle.
(d) the results of the Michelson-Morley experiment.
7. Suppose that you see a space ship whiz by at the speed of light. What is the time dilation factor kthat you observe when you measure the speed of a clock inside that ship and compare it with the speed of a clock that is stationary relative to you?
(a) 1 (b) 0 (c) Infinity (d) It is not defined.
8. Some light beams will follow curved paths (a) under no circumstances.
(b) when measured inside a space ship that is coasting at high speed.
(c) when measured in the presence of an extreme gravitational field.
(d) when measured from a reference frame that is not accelerating.
9. Suppose that you get on a space ship and travel toward the star Sirius at 150,000 km/s, which is approximately half the speed of light. If you measure the speed of the light arriving from Sirius, what figure will you obtain?
(a) 150,000 km/s (b) 300,000 km/s (c) 450,000 km/s
(d) It cannot be calculated from this information.
10. Clocks in different locations are impossible to synchronize from every possi- ble reference frame because
(a) the speed of light is absolute, finite, and constant and is the fastest known speed.
(b) the speed of light depends on the location of the reference frame from which it is measured.
(c) the speed of light depends on velocity of the reference frame from which it is measured.
(d) there is no such thing as a perfect clock.
Test: Part Four
Do not refer to the text when taking this test. A good score is at least 30 correct. Answers are in the back of the book. It is best to have a friend check your score the first time so that you won’t memorize the answers if you want to take the test again.
1. The main sequence on the Hertzsprung-Russell diagram is (a) where the red giants are found.
(b) where the white dwarfs are found.
(c) where the Sun is found.
(d) where stars are before hydrogen fusion begins.
(e) where stars end up after they have burned out.
2. Stars seem to twinkle when observed from Earth’s surface because (a) dispersion of the starlight occurs in outer space.
(b) turbulence in Earth’s atmosphere refracts the starlight.
(c) the stars actually are changing in brilliance.
(d) the solar wind refracts the starlight.
(e) the geomagnetic field bends the starlight.
3. If a neutron star is massive enough so that gravitation overpowers all other forces during the final collapse, the object will in theory become
(a) a black dwarf.
(b) a supernova.
(c) a white dwarf.
(d) an event horizon.
(e) a space-time singularity.
4. When Michelson and Morley measured the speed of light in various directions, they discovered that
(a) the speed of light is slowest in the direction in which Earth travels through space.
(b) the speed of light is fastest in the direction in which Earth travels through space.
(c) Earth drags the luminiferous ether along with itself.
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(d) the speed of light is the same in all directions.
(e) the speed of light cannot be accurately determined.
5. A black dwarf is
(a) a small planet with low albedo.
(b) a star in the process of formation, still dark because nuclear fusion has not yet begun.
(c) any small, dark object in the Cosmos.
(d) an object whose gravitation is so intense that not even light can escape.
(e) a white dwarf that has burned out and cooled down.
6. Near the plane of our own Milky Way’s spiral disk, it is almost impossible to see distant galaxies and quasars because
(a) they are too far away.
(b) the gas and dust in the plane of the Milky Way obscure the view.
(c) there are few distant objects in the plane of the Milky Way.
(d) the gravitation of the Milky Way bends light from such objects away from us.
(e) No! It is easier to see distant objects near the plane of the Milky Way than in other regions of space.
7. Suppose that a space ship whizzes by so fast that clocks on board seem, as seen from our point of view, to be running at half speed. If the rest mass of the ship is 50 metric tons, what will be the mass of the ship from our point of view as it whizzes by?
(a) 25 metric tons (b) 50 metric tons (c) 100 metric tons (d) 400 metric tons
(e) It cannot be determined without more information.
8. Gravitational waves
(a) are like ripples in space and time.
(b) cannot penetrate solid objects.
(c) have been proven to be a theoretical fiction and not to exist in reality.
(d) cause black holes to form.
(e) travel faster than light.
9. Einstein’s principle of equivalence states that (a) gravitational force is just like acceleration force.
(b) force equals mass times acceleration.
(c) the speed of light is constant no matter what.
(d) the speed of light is the highest possible speed.
(e) the shortest distance between two points is a straight line.
10. The term near IRrefers to
(a) energy at wavelengths slightly longer than visible red light.
(b) energy at wavelengths slightly shorter than visible red light.
(c) energy at wavelengths slightly longer than visible violet light.
(d) energy at wavelengths slightly shorter than visible violet light.
(e) energy from objects comparatively near the Solar System.
11. Regardless of whether a reference frame is accelerating or not, light rays always
(a) travel in straight lines.
(b) follow the shortest possible path between two points in space.
(c) travel in curved paths.
(d) are repelled by gravitational fields.
(e) travel fastest in the direction of motion.
12. The distances to galaxies closer than about 10 million light years can be inferred by observing
(a) Cepheid variables in the galaxies.
(b) the extent to which the galaxies are tilted as we view them.
(c) the extent to which the spectra of the galaxies are blue-shifted.
(d) the waveforms of the pulses emitted by the galactic nuclei.
(e) the intensity of x-rays emitted by the spiral arms of the galaxies.
13. A teaspoonful of neutrons packed tightly together (a) would mass many thousands of kilograms.
(b) would fly apart because like charges repel.
(c) would instantly disintegrate.
(d) would mass about the same as a teaspoonful of electrons.
(e) would undergo nuclear fusion.
14. Fill in the blank in the following sentence: “According to astronomer Thomas Gold, the magnetic field in the immediate vicinity of a pulsar can be ______.”
(a) as intense as the field at Earth’s surface (b) perfectly uniform
(c) trillions of times as intense as the field at Earth’s surface (d) doughnut-shaped
(e) as weak as a trillionth of the intensity of the field at Earth’s surface 15. No quasar has ever been observed that has blue-shifted spectral lines. This
lends support to the theory that
(a) quasars are objects that have been ejected from our galaxy.
(b) quasars are objects in the Solar System.
(c) quasars have weak gravitational fields.
(d) quasars are distant and are receding from us.
(e) No! There are plenty of quasars with blue-shifted spectra.
16. One minute of arc is equal to
(a) the distance light travels in 1 minute.
(b) 1/60 of an angular degree.
(c) 1/60 of a full circle.
(d) the angular distance the Sun travels across the sky in 1 minute.
(e) 1/60 of 1 hour of right ascension.
17. When astronomers scrutinized the so-called spiral nebulae, it was eventually discovered that they are
(a) rotating clouds of gas and dust in the Milky Way.
(b) black holes sucking in interstellar gas.
(c) exploding stars.
(d) distant congregations of stars outside the Milky Way.
(e) a mystery to this day; no one yet knows what they are.
18. The “ticks” emitted by a pulsar
(a) occur at irregular and unpredictable intervals.
(b) occur fastest when the pulsar is high in the sky and slowest when the pul- sar is low in the sky.
(c) occur fastest when the pulsar is low in the sky and slowest when the pul- sar is high in the sky.
(d) generally have rough waveforms, unlike the signals from radio transmitters.
(e) have regular waveforms, just like the signals from radio transmitters.
19. A hypothetical point where matter enters our Universe from another space- time continuum is sometimes called
(a) a quasar.
(b) a white hole.
(c) a black hole.
(d) an event horizon.
(e) a pulsar.
20. Most astronomers believe the Sun will explode as a supernova (a) 1 million to 2 million years from now.
(b) 500 million to 1 billion years from now.
(c) 1 billion to 2 billion years from now.
(d) 5 billion to 15 billion years from now.
(e) never.
21. If a space ship from Earth landed on a planet made of antimatter, (a) the space ship would sink to the center of the planet.
(b) the space ship would land normally, but no passengers could get off with- out being annihilated.
(c) there would be a terrific explosion.
(d) it would be just the same as if the planet were made of matter.
(e) No! The ship could never land because it would be repelled by the anti- matter planet.
22. Relativistic spatial distortion occurs
(a) only at speeds faster than the speed of light.
(b) only when objects accelerate.
(c) only along the axis of relative motion.
(d) only for extremely dense or massive objects.
(e) only within black holes.
23. A spectroscope is used for
(a) enhancing the quality of images seen through a telescope.
(b) evaluating electromagnetic signals received at radio wavelengths.
(c) transmitting signals in the hope of contacting extraterrestrial beings.
(d) scrutinizing visible light by breaking it down by wavelength.
(e) measuring the parallax of stars.
24. Imagine that a space ship whizzes by so fast that clocks on board seem, as seen from our point of view on Earth, to be running at one-third their normal speed.
Suppose that you mass 60 kg on Earth and have a friend riding on the ship who also masses 60 kg on Earth. If your friend measures his mass while traveling on the ship, what will he observe it to be?
(a) 20 kg (b) 60 kg (c) 180 kg (d) 540 kg
(e) It cannot be determined without more information.
25. Planetary nebulae
(a) form around massive planets.
(b) are clouds of gas and dust from which planets form.
(c) are gas and dust attracted by the gravitational fields of planets.
(d) have stars at their centers.
(e) are irregular in shape.
26. Spatial distortion can be caused by all the following except (a) acceleration.
(b) gravitation.
(c) high relative speed.
(d) black holes.
(e) the solar wind.
27. The gravitational radius of an object (a) is directly proportional to its mass.
(b) is inversely proportional to its mass.
(c) is directly proportional to the square of its mass.
(d) is inversely proportional to the square of its mass.
(e) does not depend on its mass.
28. When we look at a quasar that is 8 billion light-years away, we see (a) the quasar as it appears right now.
(b) the quasar as it will appear 8 billion years in the future.
(c) the quasar as it appeared before the Solar System existed.
(d) an image that has traveled all the way around the known Universe.
(e) an illusion because astronomers doubt that anything exists that is 8 billion light-years distant.
29. The heliopause is
(a) the region in space where the solar wind gives way to the general circula- tion of interstellar gas and dust.
(b) the region in the Sun’s corona beyond which the temperature begins to drop.
(c) the region inside the Sun where radiation gives way to the convection.
(d) the time in the future at which the Sun’s hydrogen fuel will be all used up.
(e) the time in the future at which the Sun’s nuclear fusion reactions will all cease.
30. Time travel into the future might be possible by taking advantage of (a) relativistic time dilation.
(b) relativistic mass distortion.
(c) relativistic spatial distortion.
(d) the gravitational pull of the Earth.
(e) nothing! Time travel into the future is theoretically impossible.
31. Suppose that two superaccurate atomic clocks, called clock A and clock B, are synchronized on Earth so that they agree exactly. Now imagine that clock B is placed aboard a space vessel and sent to Mars and back. The clock readings are compared after the ship returns. What do we find?
(a) Clocks A and B still agree precisely.
(b) Clock A is behind clock B.
(c) Clock A is ahead of clock B.
(d) Any of the above, depending on the extent to which the ship accelerated during its journey.
(e) None of the above
32. Which of the following terms does notrefer to a type of variable star?
(a) RR Lyrae (b) Mira (c) White dwarf (d) Eclipsing binary (e) Cepheid
33. In the Milky Way galaxy, the Solar System is believed to be located
(a) in one of the spiral arms halfway from the center of the disk to the edge.
(b) high above the plane of the galaxy’s disk.
(c) in a black hole at the center.
(d) between spiral arms at the outer edge of the galaxy’s disk.
(e) in the central bulge but not within the central black hole itself.
34. In today’s conventional model of the atom,
(a) electrons orbit in circles and all in the same plane.
(b) electrons orbit in ellipses with the nucleus at one focus.
(c) electrons and protons comprise the nucleus.
(d) there are more electrons than protons.
(e) electrons exist in spherical shells surrounding the nucleus.
35. When astronomers talk about “dark matter,” they are referring to (a) clouds of dust in interstellar space.
(b) planets and moons in the Solar System.
(c) black-dwarf stars.
(d) asteroids, meteoroids, and comets that are too far from the Sun to glow.
(e) hypothetical cosmic “stuff” that has mass but cannot be seen.
36. Fill in the blank in the following sentence: “When a space ship moves at a speed approaching the speed of light relative to an observer, that observer will see a clock on the ship appear to ______.”
(a) run too fast (b) stop
(c) run too slowly (d) run infinitely fast (e) run at normal speed 37. A distance of 1 Mpc is
(a) 0.001 parsec.
(b) 1,000 parsecs.
(c) 1 million parsecs.
(d) 1 billion parsecs.
(e) dependent on the angle at which it is measured.
38. If a neutron star collapses to within its event horizon,
(a) electromagnetic rays leaving the surface at low angles are trapped.
(b) electromagnetic rays cannot escape from the surface into outer space.
(c) it rebounds and explodes, causing a supernova.
(d) it disappears without a trace.
(e) No! A neutron star cannot collapse to within its event horizon.
39. Suppose that an astronomer finds an object that looks like a glowing ball of stars, and its spectrum is significantly red-shifted. The astronomer concludes that the object is
(a) an elliptical galaxy.
(b) a quasar.
(c) a black hole.
(d) a globular cluster.
(e) an emission nebula.
40. Globular star clusters are believed to be (a) galaxies far from the Milky Way.
(b) comprised of young stars.
(c) comprised of old stars.
(d) approaching us at high speed.
(e) receding from us at high speed.
Space Observation
and Travel
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Optics and Telescopes
Until a few hundred years ago, the only instrument available for astronom- ical observation was the human eye. This changed in the 1600s when sev- eral experimenters, including such notables as Galileo Galilei and Isaac Newton, combined lenses and mirrors to make distant objects look closer.
Since then,optical telescopeshave become larger and more sophisticated.
So have the ways in which the light they gather is scrutinized.
Basic Optics
You have learned that visible light always take the shortest path between two points and that it always travels at the same speed. These are the cor- nerstones of relativity theory and can be taken as axiomatic as long as the light stays in a vacuum. However, if the medium through which light pass- es is significantly different from a vacuum, and especially if the medium changes as the light ray travels through it, these principles of relativity do not apply.
Let’s focus our attention on what happens when light passes through a medium such as glass or is reflected by mirrors. If a ray of light passes from air into glass or from glass into air, the path of the ray is bent. Light rays change direction when they are reflected from mirrors. This has noth- ing to do with relativity. It happens all the time, everywhere you look. It even takes place within your own eyes.
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