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Astronomy

24.1 Introducing General Relativity

Astronomy24.1 Introducing General Relativity
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  1. Preface
  2. 1 Science and the Universe: A Brief Tour
    1. Introduction
    2. 1.1 The Nature of Astronomy
    3. 1.2 The Nature of Science
    4. 1.3 The Laws of Nature
    5. 1.4 Numbers in Astronomy
    6. 1.5 Consequences of Light Travel Time
    7. 1.6 A Tour of the Universe
    8. 1.7 The Universe on the Large Scale
    9. 1.8 The Universe of the Very Small
    10. 1.9 A Conclusion and a Beginning
    11. For Further Exploration
  3. 2 Observing the Sky: The Birth of Astronomy
    1. Thinking Ahead
    2. 2.1 The Sky Above
    3. 2.2 Ancient Astronomy
    4. 2.3 Astrology and Astronomy
    5. 2.4 The Birth of Modern Astronomy
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  4. 3 Orbits and Gravity
    1. Thinking Ahead
    2. 3.1 The Laws of Planetary Motion
    3. 3.2 Newton’s Great Synthesis
    4. 3.3 Newton’s Universal Law of Gravitation
    5. 3.4 Orbits in the Solar System
    6. 3.5 Motions of Satellites and Spacecraft
    7. 3.6 Gravity with More Than Two Bodies
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  5. 4 Earth, Moon, and Sky
    1. Thinking Ahead
    2. 4.1 Earth and Sky
    3. 4.2 The Seasons
    4. 4.3 Keeping Time
    5. 4.4 The Calendar
    6. 4.5 Phases and Motions of the Moon
    7. 4.6 Ocean Tides and the Moon
    8. 4.7 Eclipses of the Sun and Moon
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  6. 5 Radiation and Spectra
    1. Thinking Ahead
    2. 5.1 The Behavior of Light
    3. 5.2 The Electromagnetic Spectrum
    4. 5.3 Spectroscopy in Astronomy
    5. 5.4 The Structure of the Atom
    6. 5.5 Formation of Spectral Lines
    7. 5.6 The Doppler Effect
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  7. 6 Astronomical Instruments
    1. Thinking Ahead
    2. 6.1 Telescopes
    3. 6.2 Telescopes Today
    4. 6.3 Visible-Light Detectors and Instruments
    5. 6.4 Radio Telescopes
    6. 6.5 Observations outside Earth’s Atmosphere
    7. 6.6 The Future of Large Telescopes
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  8. 7 Other Worlds: An Introduction to the Solar System
    1. Thinking Ahead
    2. 7.1 Overview of Our Planetary System
    3. 7.2 Composition and Structure of Planets
    4. 7.3 Dating Planetary Surfaces
    5. 7.4 Origin of the Solar System
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  9. 8 Earth as a Planet
    1. Thinking Ahead
    2. 8.1 The Global Perspective
    3. 8.2 Earth’s Crust
    4. 8.3 Earth’s Atmosphere
    5. 8.4 Life, Chemical Evolution, and Climate Change
    6. 8.5 Cosmic Influences on the Evolution of Earth
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  10. 9 Cratered Worlds
    1. Thinking Ahead
    2. 9.1 General Properties of the Moon
    3. 9.2 The Lunar Surface
    4. 9.3 Impact Craters
    5. 9.4 The Origin of the Moon
    6. 9.5 Mercury
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  11. 10 Earthlike Planets: Venus and Mars
    1. Thinking Ahead
    2. 10.1 The Nearest Planets: An Overview
    3. 10.2 The Geology of Venus
    4. 10.3 The Massive Atmosphere of Venus
    5. 10.4 The Geology of Mars
    6. 10.5 Water and Life on Mars
    7. 10.6 Divergent Planetary Evolution
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  12. 11 The Giant Planets
    1. Thinking Ahead
    2. 11.1 Exploring the Outer Planets
    3. 11.2 The Giant Planets
    4. 11.3 Atmospheres of the Giant Planets
    5. Key Terms
    6. Summary
    7. For Further Exploration
    8. Collaborative Group Activities
    9. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  13. 12 Rings, Moons, and Pluto
    1. Thinking Ahead
    2. 12.1 Ring and Moon Systems Introduced
    3. 12.2 The Galilean Moons of Jupiter
    4. 12.3 Titan and Triton
    5. 12.4 Pluto and Charon
    6. 12.5 Planetary Rings
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  14. 13 Comets and Asteroids: Debris of the Solar System
    1. Thinking Ahead
    2. 13.1 Asteroids
    3. 13.2 Asteroids and Planetary Defense
    4. 13.3 The “Long-Haired” Comets
    5. 13.4 The Origin and Fate of Comets and Related Objects
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  15. 14 Cosmic Samples and the Origin of the Solar System
    1. Thinking Ahead
    2. 14.1 Meteors
    3. 14.2 Meteorites: Stones from Heaven
    4. 14.3 Formation of the Solar System
    5. 14.4 Comparison with Other Planetary Systems
    6. 14.5 Planetary Evolution
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  16. 15 The Sun: A Garden-Variety Star
    1. Thinking Ahead
    2. 15.1 The Structure and Composition of the Sun
    3. 15.2 The Solar Cycle
    4. 15.3 Solar Activity above the Photosphere
    5. 15.4 Space Weather
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  17. 16 The Sun: A Nuclear Powerhouse
    1. Thinking Ahead
    2. 16.1 Sources of Sunshine: Thermal and Gravitational Energy
    3. 16.2 Mass, Energy, and the Theory of Relativity
    4. 16.3 The Solar Interior: Theory
    5. 16.4 The Solar Interior: Observations
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  18. 17 Analyzing Starlight
    1. Thinking Ahead
    2. 17.1 The Brightness of Stars
    3. 17.2 Colors of Stars
    4. 17.3 The Spectra of Stars (and Brown Dwarfs)
    5. 17.4 Using Spectra to Measure Stellar Radius, Composition, and Motion
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  19. 18 The Stars: A Celestial Census
    1. Thinking Ahead
    2. 18.1 A Stellar Census
    3. 18.2 Measuring Stellar Masses
    4. 18.3 Diameters of Stars
    5. 18.4 The H–R Diagram
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  20. 19 Celestial Distances
    1. Thinking Ahead
    2. 19.1 Fundamental Units of Distance
    3. 19.2 Surveying the Stars
    4. 19.3 Variable Stars: One Key to Cosmic Distances
    5. 19.4 The H–R Diagram and Cosmic Distances
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  21. 20 Between the Stars: Gas and Dust in Space
    1. Thinking Ahead
    2. 20.1 The Interstellar Medium
    3. 20.2 Interstellar Gas
    4. 20.3 Cosmic Dust
    5. 20.4 Cosmic Rays
    6. 20.5 The Life Cycle of Cosmic Material
    7. 20.6 Interstellar Matter around the Sun
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  22. 21 The Birth of Stars and the Discovery of Planets outside the Solar System
    1. Thinking Ahead
    2. 21.1 Star Formation
    3. 21.2 The H–R Diagram and the Study of Stellar Evolution
    4. 21.3 Evidence That Planets Form around Other Stars
    5. 21.4 Planets beyond the Solar System: Search and Discovery
    6. 21.5 Exoplanets Everywhere: What We Are Learning
    7. 21.6 New Perspectives on Planet Formation
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  23. 22 Stars from Adolescence to Old Age
    1. Thinking Ahead
    2. 22.1 Evolution from the Main Sequence to Red Giants
    3. 22.2 Star Clusters
    4. 22.3 Checking Out the Theory
    5. 22.4 Further Evolution of Stars
    6. 22.5 The Evolution of More Massive Stars
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  24. 23 The Death of Stars
    1. Thinking Ahead
    2. 23.1 The Death of Low-Mass Stars
    3. 23.2 Evolution of Massive Stars: An Explosive Finish
    4. 23.3 Supernova Observations
    5. 23.4 Pulsars and the Discovery of Neutron Stars
    6. 23.5 The Evolution of Binary Star Systems
    7. 23.6 The Mystery of the Gamma-Ray Bursts
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  25. 24 Black Holes and Curved Spacetime
    1. Thinking Ahead
    2. 24.1 Introducing General Relativity
    3. 24.2 Spacetime and Gravity
    4. 24.3 Tests of General Relativity
    5. 24.4 Time in General Relativity
    6. 24.5 Black Holes
    7. 24.6 Evidence for Black Holes
    8. 24.7 Gravitational Wave Astronomy
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  26. 25 The Milky Way Galaxy
    1. Thinking Ahead
    2. 25.1 The Architecture of the Galaxy
    3. 25.2 Spiral Structure
    4. 25.3 The Mass of the Galaxy
    5. 25.4 The Center of the Galaxy
    6. 25.5 Stellar Populations in the Galaxy
    7. 25.6 The Formation of the Galaxy
    8. Key Terms
    9. Summary
    10. For Further Exploration
    11. Collaborative Group Activities
    12. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  27. 26 Galaxies
    1. Thinking Ahead
    2. 26.1 The Discovery of Galaxies
    3. 26.2 Types of Galaxies
    4. 26.3 Properties of Galaxies
    5. 26.4 The Extragalactic Distance Scale
    6. 26.5 The Expanding Universe
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  28. 27 Active Galaxies, Quasars, and Supermassive Black Holes
    1. Thinking Ahead
    2. 27.1 Quasars
    3. 27.2 Supermassive Black Holes: What Quasars Really Are
    4. 27.3 Quasars as Probes of Evolution in the Universe
    5. Key Terms
    6. Summary
    7. For Further Exploration
    8. Collaborative Group Activities
    9. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  29. 28 The Evolution and Distribution of Galaxies
    1. Thinking Ahead
    2. 28.1 Observations of Distant Galaxies
    3. 28.2 Galaxy Mergers and Active Galactic Nuclei
    4. 28.3 The Distribution of Galaxies in Space
    5. 28.4 The Challenge of Dark Matter
    6. 28.5 The Formation and Evolution of Galaxies and Structure in the Universe
    7. Key Terms
    8. Summary
    9. For Further Exploration
    10. Collaborative Group Activities
    11. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  30. 29 The Big Bang
    1. Thinking Ahead
    2. 29.1 The Age of the Universe
    3. 29.2 A Model of the Universe
    4. 29.3 The Beginning of the Universe
    5. 29.4 The Cosmic Microwave Background
    6. 29.5 What Is the Universe Really Made Of?
    7. 29.6 The Inflationary Universe
    8. 29.7 The Anthropic Principle
    9. Key Terms
    10. Summary
    11. For Further Exploration
    12. Collaborative Group Activities
    13. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  31. 30 Life in the Universe
    1. Thinking Ahead
    2. 30.1 The Cosmic Context for Life
    3. 30.2 Astrobiology
    4. 30.3 Searching for Life beyond Earth
    5. 30.4 The Search for Extraterrestrial Intelligence
    6. Key Terms
    7. Summary
    8. For Further Exploration
    9. Collaborative Group Activities
    10. Exercises
      1. Review Questions
      2. Thought Questions
      3. Figuring for Yourself
  32. A | How to Study for an Introductory Astronomy Class
  33. B | Astronomy Websites, Images, and Apps
  34. C | Scientific Notation
  35. D | Units Used in Science
  36. E | Some Useful Constants for Astronomy
  37. F | Physical and Orbital Data for the Planets
  38. G | Selected Moons of the Planets
  39. H | Future Total Eclipses
  40. I | The Nearest Stars, Brown Dwarfs, and White Dwarfs
  41. J | The Brightest Twenty Stars
  42. K | The Chemical Elements
  43. L | The Constellations
  44. M | Star Chart and Sky Event Resources
  45. Index

Learning Objectives

By the end of this section, you will be able to:

  • Discuss some of the key ideas of the theory of general relativity
  • Recognize that one’s experiences of gravity and acceleration are interchangeable and indistinguishable
  • Distinguish between Newtonian ideas of gravity and Einsteinian ideas of gravity
  • Recognize why the theory of general relativity is necessary for understanding the nature of black holes

Most stars end their lives as white dwarfs or neutron stars. When a very massive star collapses at the end of its life, however, not even the mutual repulsion between densely packed neutrons can support the core against its own weight. If the remaining mass of the star’s core is more than about three times that of the Sun (MSun), our theories predict that no known force can stop it from collapsing forever! Gravity simply overwhelms all other forces and crushes the core until it occupies an infinitely small volume. A star in which this occurs may become one of the strangest objects ever predicted by theory—a black hole.

To understand what a black hole is like and how it influences its surroundings, we need a theory that can describe the action of gravity under such extreme circumstances. To date, our best theory of gravity is the general theory of relativity, which was put forward in 1916 by Albert Einstein.

General relativity was one of the major intellectual achievements of the twentieth century; if it were music, we would compare it to the great symphonies of Beethoven or Mahler. Until recently, however, scientists had little need for a better theory of gravity; Isaac Newton’s ideas that led to his law of universal gravitation (see Orbits and Gravity) are perfectly sufficient for most of the objects we deal with in everyday life. In the past half century, however, general relativity has become more than just a beautiful idea; it is now essential in understanding pulsars, quasars (which will be discussed in Active Galaxies, Quasars, and Supermassive Black Holes), and many other astronomical objects and events, including the black holes we will discuss here.

We should perhaps mention that this is the point in an astronomy course when many students start to feel a little nervous (and perhaps wish they had taken botany or some other earthbound course to satisfy the science requirement). This is because in popular culture, Einstein has become a symbol for mathematical brilliance that is simply beyond the reach of most people (Figure 24.2).

Photograph of Albert Einstein.
Figure 24.2 Albert Einstein (1879–1955). This famous scientist, seen here younger than in the usual photos, has become a symbol for high intellect in popular culture. (credit: NASA)

So, when we wrote that the theory of general relativity was Einstein’s work, you may have worried just a bit, convinced that anything Einstein did must be beyond your understanding. This popular view is unfortunate and mistaken. Although the detailed calculations of general relativity do involve a good deal of higher mathematics, the basic ideas are not difficult to understand (and are, in fact, almost poetic in the way they give us a new perspective on the world). Moreover, general relativity goes beyond Newton’s famous “inverse-square” law of gravity; it helps explain how matter interacts with other matter in space and time. This explanatory power is one of the requirements that any successful scientific theory must meet.

The Principle of Equivalence

The fundamental insight that led to the formulation of the general theory of relativity starts with a very simple thought: if you were able to jump off a high building and fall freely, you would not feel your own weight. In this chapter, we will describe how Einstein built on this idea to reach sweeping conclusions about the very fabric of space and time itself. He called it the “happiest thought of my life.”

Einstein himself pointed out an everyday example that illustrates this effect (see Figure 24.3). Notice how your weight seems to be reduced in a high-speed elevator when it accelerates from a stop to a rapid descent. Similarly, your weight seems to increase in an elevator that starts to move quickly upward. This effect is not just a feeling you have: if you stood on a scale in such an elevator, you could measure your weight changing (you can actually perform this experiment in some science museums).

Acceleration and Weight. This cartoon has four sections. Beginning at left, the first section is labeled “Normal weight”. In it a person stands on a scale in an elevator at rest. The scale reads the person’s weight in arbitrary units. The next section, labeled “Lighter than normal”, shows the elevator moving downward, and the scale now reads a smaller value for the person’s weight. The next section, labeled “Heavier than normal”, shows the elevator moving upward, and the scale now reads a larger value for the person’s weight. The final section at right, labeled “No apparent weight”, shows the elevator in free-fall. In it the person and the scale are now “floating” within the elevator and the scale is blank.
Figure 24.3 Your Weight in an Elevator. In an elevator at rest, you feel your normal weight. In an elevator that accelerates as it descends, you would feel lighter than normal. In an elevator that accelerates as it ascends, you would feel heavier than normal. If an evil villain cut the elevator cable, you would feel weightless as you fell to your doom.

In a freely falling elevator, with no air friction, you would lose your weight altogether. We generally don’t like to cut the cables holding elevators to try this experiment, but near-weightlessness can be achieved by taking an airplane to high altitude and then dropping rapidly for a while. This is how NASA trains its astronauts for the experience of free fall in space; the scenes of weightlessness in the 1995 movie Apollo 13 were filmed in the same way. (Moviemakers have since devised other methods using underwater filming, wire stunts, and computer graphics to create the appearance of weightlessness seen in such movies as Gravity and The Martian.)

Another way to state Einstein’s idea is this: suppose we have a spaceship that contains a windowless laboratory equipped with all the tools needed to perform scientific experiments. Now, imagine that an astronomer wakes up after a long night celebrating some scientific breakthrough and finds herself sealed into this laboratory. She has no idea how it happened but notices that she is weightless. This could be because she and the laboratory are far away from any source of gravity, and both are either at rest or moving at some steady speed through space (in which case she has plenty of time to wake up). But it could also be because she and the laboratory are falling freely toward a planet like Earth (in which case she might first want to check her distance from the surface before making coffee).

What Einstein postulated is that there is no experiment she can perform inside the sealed laboratory to determine whether she is floating in space or falling freely in a gravitational field.1 As far as she is concerned, the two situations are completely equivalent. This idea that free fall is indistinguishable from, and hence equivalent to, zero gravity is called the equivalence principle.

Gravity or Acceleration?

Einstein’s simple idea has big consequences. Let’s begin by considering what happens if two foolhardy people jump from opposite banks into a bottomless chasm (Figure 24.4). If we ignore air friction, then we can say that while they freely fall, they both accelerate downward at the same rate and feel no external force acting on them. They can throw a ball back and forth, always aiming it straight at each other, as if there were no gravity. The ball falls at the same rate that they do, so it always remains in a line between them.

Free Fall. Two figures are drawn on opposite sides of a deep abyss. The figure at left holds a ball and both figures jump into the chasm at the same time. As the figures fall they pass the ball back and forth between them. From their perspective, the ball passes between them horizontally, indicated with a horizontal arrow connecting the figures when the ball is released. But from the perspective of an outside observer, the ball travels in a downward arc, indicated with a curved arrow drawn from where one figure releases the ball and where the other actually catches it.
Figure 24.4 Free Fall. Two people play catch as they descend into a bottomless abyss. Since the people and ball all fall at the same speed, it appears to them that they can play catch by throwing the ball in a straight line between them. Within their frame of reference, there appears to be no gravity.

Such a game of catch is very different on the surface of Earth. Everyone who grows up feeling gravity knows that a ball, once thrown, falls to the ground. Thus, in order to play catch with someone, you must aim the ball upward so that it follows an arc—rising and then falling as it moves forward—until it is caught at the other end.

Now suppose we isolate our falling people and ball inside a large box that is falling with them. No one inside the box is aware of any gravitational force. If they let go of the ball, it doesn’t fall to the bottom of the box or anywhere else but merely stays there or moves in a straight line, depending on whether it is given any motion.

Astronauts in the International Space Station (ISS) that is orbiting Earth live in an environment just like that of the people sealed in a freely falling box (Figure 24.5). The orbiting ISS is actually “falling” freely around Earth. While in free fall, the astronauts live in a strange world where there seems to be no gravitational force. One can give a wrench a shove, and it moves at constant speed across the orbiting laboratory. A pencil set in midair remains there as if no force were acting on it.

Photograph of Astronauts Aboard the Space Shuttle Endeavour. Two astronauts are seen, along with apples, oranges and pears, “floating” inside the shuttle.
Figure 24.5 Astronauts aboard the Space Shuttle. Shane Kimbrough and Sandra Magnus are shown aboard the Endeavour in 2008 with various fruit floating freely. Because the shuttle is in free fall as it orbits Earth, everything—including astronauts—stays put or moves uniformly relative to the walls of the spacecraft. This free-falling state produces a lack of apparent gravity inside the spacecraft. (credit: NASA)

Appearances are misleading, however. There is a force in this situation. Both the ISS and the astronauts continually fall around Earth, pulled by its gravity. But since all fall together—shuttle, astronauts, wrench, and pencil—inside the ISS all gravitational forces appear to be absent.

Thus, the orbiting ISS provides an excellent example of the principle of equivalence—how local effects of gravity can be completely compensated by the right acceleration. To the astronauts, falling around Earth creates the same effects as being far off in space, remote from all gravitational influences.

The Paths of Light and Matter

Einstein postulated that the equivalence principle is a fundamental fact of nature, and that there is no experiment inside any spacecraft by which an astronaut can ever distinguish between being weightless in remote space and being in free fall near a planet like Earth. This would apply to experiments done with beams of light as well. But the minute we use light in our experiments, we are led to some very disturbing conclusions—and it is these conclusions that lead us to general relativity and a new view of gravity.

It seems apparent to us, from everyday observations, that beams of light travel in straight lines. Imagine that a spaceship is moving through empty space far from any gravity. Send a laser beam from the back of the ship to the front, and it will travel in a nice straight line and land on the front wall exactly opposite the point from which it left the rear wall. If the equivalence principle really applies universally, then this same experiment performed in free fall around Earth should give us the same result.

Now imagine that the astronauts again shine a beam of light along the length of their ship. But, as shown in Figure 24.6, this time the orbiting space station falls a bit between the time the light leaves the back wall and the time it hits the front wall. (The amount of the fall is grossly exaggerated in Figure 24.6 to illustrate the effect.) Therefore, if the beam of light follows a straight line but the ship’s path curves downward, then the light should strike the front wall at a point higher than the point from which it left.

Curved Light Path. The Space Shuttle is drawn at right moving to the left (indicated with an arrow) with a ray of light drawn in yellow from point A at the rear toward point B near the front and continuing on toward the left to a point labeled B′. The point B′ is where the shuttle would be if it were moving in a straight line. Instead, the shuttle has moved downward to the left. The ray of light has moved with the shuttle, and strikes the front at point C, which is below B′.
Figure 24.6 Curved Light Path. In a spaceship moving to the left (in this figure) in its orbit about a planet, light is beamed from the rear, A, toward the front, B. Meanwhile, the ship is falling out of its straight path (exaggerated here). We might therefore expect the light to strike at B′, above the target in the ship. Instead, the light follows a curved path and strikes at C. In order for the principle of equivalence to be correct, gravity must be able to curve the path of a light beam just as it curves the path of the spaceship.

However, this would violate the principle of equivalence—the two experiments would give different results. We are thus faced with giving up one of our two assumptions. Either the principle of equivalence is not correct, or light does not always travel in straight lines. Instead of dropping what probably seemed at the time like a ridiculous idea, Einstein worked out what happens if light sometimes does not follow a straight path.

Let’s suppose the principle of equivalence is right. Then the light beam must arrive directly opposite the point from which it started in the ship. The light, like the ball thrown back and forth, must fall with the ship that is in orbit around Earth (see Figure 24.6). This would make its path curve downward, like the path of the ball, and thus the light would hit the front wall exactly opposite the spot from which it came.

Thinking this over, you might well conclude that it doesn’t seem like such a big problem: why can’t light fall the way balls do? But, as discussed in Radiation and Spectra, light is profoundly different from balls. Balls have mass, while light does not.

Here is where Einstein’s intuition and genius allowed him to make a profound leap. He gave physical meaning to the strange result of our thought experiment. Einstein suggested that the light curves down to meet the front of the shuttle because Earth’s gravity actually bends the fabric of space and time. This radical idea—which we will explain next—keeps the behavior of light the same in both empty space and free fall, but it changes some of our most basic and cherished ideas about space and time. The reason we take Einstein’s suggestion seriously is that, as we will see, experiments now clearly show his intuitive leap was correct.

Footnotes

  • 1 Strictly speaking, this is true only if the laboratory is infinitesimally small. Different locations in a real laboratory that is falling freely due to gravity cannot all be at identical distances from the object(s) responsible for producing the gravitational force. In this case, objects in different locations will experience slightly different accelerations. But this point does not invalidate the principle of equivalence that Einstein derived from this line of thinking.
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