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THE ELEGANT UNIVERSE, Brian Greene, 1999, 2003
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 2 - Space, Time, and the Eye of the Beholder
The Principle of Relativity
There are two simple yet deeply rooted structures that form the foundation of special relativity. As mentioned, one concerns properties of light; we shall discuss this more fully in the next section. The other is more abstract. It is concerned not with any specific physical law but rather with all physical laws, and is known as the principle of relativity. The principle of relativity rests on a simple fact: Whenever we discuss speed or velocity (an object's speed and its direction of motion), we must specify precisely who or what is doing the measuring. Understanding the meaning and importance of this statement is easily accomplished by contemplating the following situation.
Imagine that George, who is wearing a spacesuit with a small, red flashing light, is floating in the absolute darkness of completely empty space, far away from any planets, stars, or galaxies. From George's perspective, he is completely stationary, engulfed in the uniform, still blackness of the cosmos. Off in the distance, George catches sight of a tiny, green flashing light that appears to be coming closer and closer. Finally, it gets close enough for George to see that the light is attached to the spacesuit of another space-dweller, Gracie, who is slowly floating by. She waves as she passes, as does George, and she recedes into the distance. This story can be told with equal validity from Gracie's perspective. It begins in the same manner with Gracie completely alone in the immense still darkness of outer space. Off in the distance, Gracie sees a red flashing light, which appears to be coming closer and closer. Finally, it gets close enough for Gracie to see that it is attached to the spacesuit of another being, George, who is slowly floating by. He waves as he passes, as does Gracie, and he recedes into the distance.
The two stories describe one and the same situation from two distinct but equally valid points of view. Each observer feels stationary and perceives the other as moving. Each perspective is understandable and justifiable. As there is symmetry between the two space-dwellers, there is, on quite fundamental grounds, no way of saying one perspective is "right" and the other "wrong." Each perspective has an equal claim on truth.
This example captures the meaning of the principle of relativity: The concept of motion is relative. We can speak about the motion of an object, but only relative to or by comparison with another. There is thus no meaning to the statement "George is traveling at 10 miles per hour," as we have not specified any other object for comparison. There is meaning to the statement "George is traveling at 10 miles per hour past Gracie," as we have now specified Gracie as the benchmark. As our example shows, this last statement is completely equivalent to "Gracie is traveling at 10 miles per hour past George (in the opposite direction)." In other words, there is no "absolute" notion of motion. Motion is relative.
A key element of this story is that neither George nor Gracie is being pushed, pulled, or in any other way acted upon by a force or influence that could disturb their serene state of force-free, constant-velocity motion. Thus, a more precise statement is that force-free motion has meaning only by comparison with other objects. This is an important clarification, because if forces are involved, they cause changes in the velocity of the observers—changes to their speed and/or their direction of motion—and these changes can be felt. For instance, if George were wearing a jet-pack firing away from his back, he would definitely feel that he was moving. This feeling is intrinsic. If the jet-pack is firing away, George knows he is moving, even if his eyes are closed and therefore can make no comparisons with other objects. Even without such comparisons, he would no longer claim that he was stationary while "the rest of the world was moving by him." Constant-velocity motion is relative; not so for non-constant-velocity motion, or, equivalently, accelerated motion. (We will re-examine this statement in the next chapter when we take up accelerated motion and discuss Einstein's general theory of relativity.)
Setting these stories in the darkness of empty space aids understanding by removing such familiar things as streets and buildings, which we typically, although unjustifiably, accord the special status of "stationary." Nonetheless, the same principle applies to terrestrial settings, and in fact is commonly experienced. 1 For example, imagine that after you have fallen asleep on a train, you awake just as your train is passing another on adjacent parallel tracks. With your view through the window completely blocked by the other train, thereby preventing you from seeing any other objects, you may temporarily be uncertain as to whether your train is moving, the other train is moving, or both. Of course, if your train shakes or jostles, or if the train changes direction by rounding a bend, you can feel that you are moving. But if the ride is perfectly smooth—if the train's velocity remains constant—you will observe relative motion between the trains without being able to tell for certain which is moving.
Let's take this one step further. Imagine you are on such a train and that you pull down the shades so that the windows are fully covered. Without the ability to see anything outside your own compartment, and assuming that the train moves at absolutely constant velocity, there will be no way for you to determine your state of motion. The compartment around you will look [I]precisely the same regardless of whether the train is sitting still on the tracks or moving at high speed. Einstein formalized this idea, one that actually goes back to insights of Galileo, by proclairriing that it is impossible for you or any fellow traveler to perform an experiment within the closed compartment that will determine whether or not the train is moving. This again captures the principle of relativity: since all force-free motion is relative, it has meaning only by comparison with other objects or individuals also undergoing force-free motion. There is no way for you to determine anything about your state of motion without making some direct or indirect comparison with "outside" objects. There simply is no notion of "absolute" constant-velocity motion; only comparisons have any physical meaning.
In fact, Einstein realized that the principle of relativity makes an even grander claim: the laws of physics—whatever they may be must be absolutely identical for all observers undergoing constant-velocity motion. If George and Gracie are not just floating solo in space, but, rather, are each conducting the same set of experiments in their respective floating space-stations, the results they find will be identical. Once again, each is perfectly justified in believing that his or her station is at rest, even though the two stations are in relative motion. If all of their equipment is identical, there is nothing distinguishing the two experimental setups—they are completely symmetric. The laws of physics that each deduces from the experiments will likewise be identical. Neither they nor their experiments can feel—that is, depend upon in any way—constant-velocity travel. It is this simple concept that establishes complete symmetry between such observers; it is this concept that is embodied in the principle of relativity. We shall shortly make use of this principle to profound effect.
Imagine that George, who is wearing a spacesuit with a small, red flashing light, is floating in the absolute darkness of completely empty space, far away from any planets, stars, or galaxies. From George's perspective, he is completely stationary, engulfed in the uniform, still blackness of the cosmos. Off in the distance, George catches sight of a tiny, green flashing light that appears to be coming closer and closer. Finally, it gets close enough for George to see that the light is attached to the spacesuit of another space-dweller, Gracie, who is slowly floating by. She waves as she passes, as does George, and she recedes into the distance. This story can be told with equal validity from Gracie's perspective. It begins in the same manner with Gracie completely alone in the immense still darkness of outer space. Off in the distance, Gracie sees a red flashing light, which appears to be coming closer and closer. Finally, it gets close enough for Gracie to see that it is attached to the spacesuit of another being, George, who is slowly floating by. He waves as he passes, as does Gracie, and he recedes into the distance.
The two stories describe one and the same situation from two distinct but equally valid points of view. Each observer feels stationary and perceives the other as moving. Each perspective is understandable and justifiable. As there is symmetry between the two space-dwellers, there is, on quite fundamental grounds, no way of saying one perspective is "right" and the other "wrong." Each perspective has an equal claim on truth.
This example captures the meaning of the principle of relativity: The concept of motion is relative. We can speak about the motion of an object, but only relative to or by comparison with another. There is thus no meaning to the statement "George is traveling at 10 miles per hour," as we have not specified any other object for comparison. There is meaning to the statement "George is traveling at 10 miles per hour past Gracie," as we have now specified Gracie as the benchmark. As our example shows, this last statement is completely equivalent to "Gracie is traveling at 10 miles per hour past George (in the opposite direction)." In other words, there is no "absolute" notion of motion. Motion is relative.
A key element of this story is that neither George nor Gracie is being pushed, pulled, or in any other way acted upon by a force or influence that could disturb their serene state of force-free, constant-velocity motion. Thus, a more precise statement is that force-free motion has meaning only by comparison with other objects. This is an important clarification, because if forces are involved, they cause changes in the velocity of the observers—changes to their speed and/or their direction of motion—and these changes can be felt. For instance, if George were wearing a jet-pack firing away from his back, he would definitely feel that he was moving. This feeling is intrinsic. If the jet-pack is firing away, George knows he is moving, even if his eyes are closed and therefore can make no comparisons with other objects. Even without such comparisons, he would no longer claim that he was stationary while "the rest of the world was moving by him." Constant-velocity motion is relative; not so for non-constant-velocity motion, or, equivalently, accelerated motion. (We will re-examine this statement in the next chapter when we take up accelerated motion and discuss Einstein's general theory of relativity.)
Setting these stories in the darkness of empty space aids understanding by removing such familiar things as streets and buildings, which we typically, although unjustifiably, accord the special status of "stationary." Nonetheless, the same principle applies to terrestrial settings, and in fact is commonly experienced. 1 For example, imagine that after you have fallen asleep on a train, you awake just as your train is passing another on adjacent parallel tracks. With your view through the window completely blocked by the other train, thereby preventing you from seeing any other objects, you may temporarily be uncertain as to whether your train is moving, the other train is moving, or both. Of course, if your train shakes or jostles, or if the train changes direction by rounding a bend, you can feel that you are moving. But if the ride is perfectly smooth—if the train's velocity remains constant—you will observe relative motion between the trains without being able to tell for certain which is moving.
Let's take this one step further. Imagine you are on such a train and that you pull down the shades so that the windows are fully covered. Without the ability to see anything outside your own compartment, and assuming that the train moves at absolutely constant velocity, there will be no way for you to determine your state of motion. The compartment around you will look [I]precisely the same regardless of whether the train is sitting still on the tracks or moving at high speed. Einstein formalized this idea, one that actually goes back to insights of Galileo, by proclairriing that it is impossible for you or any fellow traveler to perform an experiment within the closed compartment that will determine whether or not the train is moving. This again captures the principle of relativity: since all force-free motion is relative, it has meaning only by comparison with other objects or individuals also undergoing force-free motion. There is no way for you to determine anything about your state of motion without making some direct or indirect comparison with "outside" objects. There simply is no notion of "absolute" constant-velocity motion; only comparisons have any physical meaning.
In fact, Einstein realized that the principle of relativity makes an even grander claim: the laws of physics—whatever they may be must be absolutely identical for all observers undergoing constant-velocity motion. If George and Gracie are not just floating solo in space, but, rather, are each conducting the same set of experiments in their respective floating space-stations, the results they find will be identical. Once again, each is perfectly justified in believing that his or her station is at rest, even though the two stations are in relative motion. If all of their equipment is identical, there is nothing distinguishing the two experimental setups—they are completely symmetric. The laws of physics that each deduces from the experiments will likewise be identical. Neither they nor their experiments can feel—that is, depend upon in any way—constant-velocity travel. It is this simple concept that establishes complete symmetry between such observers; it is this concept that is embodied in the principle of relativity. We shall shortly make use of this principle to profound effect.