The Principle of Relativity

What is the principle of relativity? The principle of relativity is, as you can see by its name, the concept representing the central mechanism behind which the well-known theory of relativity operates. What single concept, you may reason, could be dynamic enough to live up to the teachings of a theory as diverse and varied as the themes presented by the theory of relativity? How, you may further reason, could the entire theory be expressable in a single concept? Our means of approaching the principle of relativity will be by means of a vivid thought experiment set up for the purposes of our own understanding. As the first step in visualizing this thought experiment we are to picture a small planet. This planet is covered completely by water. Next, we are to visualize someone afloat on the planet, seated in a small inflatable raft. Having documented this, let us continue. What the person on the raft knows: he is afloat on a planet covered completely by water. What the person on the raft does not know: exactly where on the surface of the planet he is located. What we are to put into consideration: that the surface of a sphere appears the same from all points on its surface, from every angle on each point.

To better understand the nature of the rafter's situation we will perform 2 experiments. These experiments will introduce us to the nature of what we call the principle of relativity. As the means of performing the first experiment we are to focus our attention on the raft on the planet described above: a planet covered completely by water, inhabited only by someone seated on a small raft. We are then to put into consideration the following question: where on the planet is the raft? Could a simpler question be presented? Yet this question requires of us to think as we may have never thought before. This involves specifying the particular point of view we are to consider the planet to be viewed from. Our experiments will involve 2 points of view: our view of the planet and the rafter's view of his placement on the planet. Both views are of equal importance. Our view of the planet is an external view of the planet in which we are viewing the planet from above, able to perceive the entire spherical contour of the planet. The rafter, in contrast, is surrounded on all sides by water, as described. From our point of view, we have no difficulty in answering the question of where on the planet the raft is located: we need only associate the raft's location with our overhead, external view of the planet. From the rafter's point of view, however, the question of where the raft is becomes of a totally different nature. To understand the rafter's point of view, let us recall the proposal presented above: the surface of a sphere appears the same from all point on its surface, from every angle on each point. What does this mean? It means that no matter the rafter's location on the planet, his perception of his surroundings will always be the same! How, then, does one designate location within a spatial system of arrangement in which all occupiable locations within that system appear identical? The answer is that one can't! From the rafter's point of view, the raft is to be considered to lie both anywhere and everywhere on the surface of the planet! No further conclusion can be made!

As the means of performing the second experiment we are to once again focus our attention on the planet described above: a planet covered completely by water, inhabited only by someone seated on a small raft. We are then to tell the rafter to start paddling so that the raft begins to advance forward. We are then to put into consideration the following question: is the raft described here stationary or in motion? At first, this may seem like an odd question to ask. To properly understand the question, however, we must be fully aware of the significance of the point of view from which we choose to experience the situation: the rafter's view or our view. From our external, overhead view of the planet, we have no difficulty documenting the apparent forward motion of the raft. From the rafter's point of view, however, the question of whether or not the raft is in motion becomes much trickier. To understand the nature of the rafter's point of view, let us once again recall the proposal presented earlier: the surface of a sphere appears the same from all points on its surface, from every angle on each point. What does this mean? It means that no matter where on the planet the rafter paddles himself to, and no matter what the speed at which the raft advances forward, the rafter's perception of his surroundings will never change! How, then, does one designate a state of motion within a spatial system of arrangement in which all occupiable locations within that system appear identical? The answer is that one can't! From the rafter's point of view, the raft is neither stationary nor in motion! No further conclusion can be made!

What, then, is the principle of relativity? The principle of relativity can be summarized in 3 given postulates. The first postulate can be reasoned from the 2 experiments we've just performed and can be expressed in the statement that location and motion have no means of interacting with empty space. We are to make note, next, that the surface of the water in the experiments represents what in reality would be empty space. As we witnessed, furthermore, the raft was the only floating object on the planet. The planet in these experiments, therefore, represents a cosmos devoid of matter. What did the experiments conclude, then, concerning such a universe? The conclusion was that in a universe devoid of matter, location and motion have no meaning! This is because, as stated, location and motion have no means of interacting with empty space. For the purpose of study, we are to perform a second thought experiment. We are to visualize a universe devoid of matter, consisting only of empty space. Amongst the void is a rocket ship. As the first part of the thought experiment we are to ask ourselves a question. The question: where is the rocket ship? According to the reasoning presented concerning location and empty space, the best answer as to the location of the rocket ship is that it is nowhere! Let our previous experience with location verify this. We are next to imagine the rocket ship to start its forward thrust mechanism. The thrusters ignite. At what speed, and in what direction, is the rocket ship now travelling? We are once again required to think as we may have never thought before. According to the reasoning just presented concerning motion and empty space, the best answer as to the rocket ship's speed and direction is that it is covering no distance whatsoever! This demonstrates the first postulate of the principle of relativity as presented above: location and motion have no means of interacting with empty space. What is the solution to this dilemma - this inability to designate location and state of motion? To understand the solution we must become familiar with the second postulate summarizing the concept behind the principle of relativity.

The second postulate summarizing the principle of relativity can be expressed in the statement that location and motion are products of the presence of external objects. The solution, quite clearly, to the rocket ship's situation is to place the rocket ship in a universe in which matter is present. Doing so puts before the rocket ship external objects in positions relative to which the rocket ship can compare its own position and determine its location and state of motion. It's that simple. This is a key concept in the principle of relativity. To better familiarize ourselves with the concept behind the second postulate we will perform an experiment. This experiment, as before, involves a planet covered completely by water, inhabited only by someone seated on a small raft. As the means of performing the present (third) experiment we are to imagine placing a float somewhere on the surface of the water that is near the raft. We are then to consider once again the following question: where on the planet is the raft? From our point of view, determining the raft's location means only associating the raft's location with our overhead, external view of the planet. We can locate the float in a similar manner. What of the rafter's point of view? In earlier experiments, as you may recall, our means of reasoning this question was to emphasize the fact that the surface of a sphere appears the same from all points on its surface, from every angle on each point. This meant, as stated, that no matter the rafter's location on the planet, his perception of his surroundings would always be the same. It was therefore impossible for the rafter to designate his own location. This conclusion, however, was made based upon the understanding that the raft was the only object afloat on the planet - which, however, is no longer the case. How, then, does the float contribute to the rafter's situation? The float is an external object in a position relative to which the rafter can compare his own position and in doing so determine his location. The presence of external objects, then, would appear to solve the issue of the rafter's uncertainty of his location on the planet. In many ways it does. To grasp the full meaning of the principle of relativity, however, we must cover it in greater detail: we must address the third and final postulate summarizing the principle of relativity.

The third postulate summarizing the principle of relativity can be expressed in the statement that the first postulate applies to all external objects. The first postulate, in turn, as you may recall, states that location and motion have no means of interacting with empty space. How do we give the third postulate meaning? Upon having encountered the first postulate, it is possible that one could have come to the conclusion that location and motion are nonexistent within the universe. The second postulate, however, gave us a reason to change our minds concerning that view by showing us how to rely upon external objects to designate location and motion. The third postulate, finally, tells us that though external objects successfully bring about the effects we call location and motion, location and motion are, as the first postulate indicates, illusions. That is, if the external objects you are relying upon to designate location and motion are themselves able to be affected by the effects of the first postulate, then the location and state of motion of any external object is no more spatially reliable than your own location and state of motion (which you are attempting to designate by referring to external objects)! As stated: the first postulate applies to all external objects. Does a simpler means exist, you may ask, through which this concept can be understood? Yes - there exists a thought experiment assembled for that very purpose. Imagine yourself in a small hovering flying saucer in a large array of flying saucers. Given the reasoning of the first postulate, you are basically 'nowhere' and must rely upon a flying saucer external to yourself to designate your own location and motion. In response, you choose another flying saucer to act as your reference. The catch: the flying saucer you have just chosen to act as your reference is not a self-contained entity. To act as your reference, the flying saucer to which you are referring must first have a location. To possess this location, the flying saucer to which you are referring must itself have another flying saucer external to itself to act as its own reference! This forms an endless loop of external reference. Every flying saucer's location will always be a reference to another flying saucer!

To better familiarize ourselves with the concept behind the third postulate, we will perform yet another experiment. As before, the experiment involves a planet covered completely by water, inhabited only by someone seated on a small raft. As the means of performing the present (fourth) experiment we are to imagine a float somewhere near the raft, in a state of motion toward the raft. Quite clearly, the distance in between the float and the raft decreases as time goes by. Given this fact, we are to put into consideration the following question: what is responsible for the evident decrease in distance between the float and the raft? From our external, overhead view of the planet, it is quite clear that the decrease in distance between the float and the raft is a result of the float's forward motion. From the rafter's point of view, however, the question of what is responsible for the evident decrease in distance between the float and the raft becomes more of an enigma than one might think. Let us start from the beginning. We will first, for the sake of the experiment, temporarily assume that the float moving toward the raft is not there. Next, we will, as done in previous experiments, present the statement that explains the general nature of the raft's orientation: the surface of a sphere appears the same from all points on its surface, from every angle on each point. This means, as in previous experiments, that no matter what location or state of motion the raft assumes on the surface of the planet, his perception of his surroundings will always be the same.

How does the rafter respond to being 'nowhere'? He must find an external object relative to which the rafter can compare his own position and in doing so determine his location and state of motion. We now introduce the float moving toward the raft back into the situation. Next, the rafter, attempting to determine his location and state of motion, focuses upon the float as the external reference relative to which he compares himself. In the third experiment, as you may recall, the presence of the float appeared to be the answer to the raft being 'nowhere'. We were then introduced to the third postulate: the first postulate applies to all external objects. Because the float the rafter is referring to must itself have an external reference to which to compare its own location and state of motion, the location and state of motion of the float is no more spatially reliable than the raft's own location and state of motion (which the rafter is attempting to designate by referring to the float)! Therefore, the raft and the float are both nowhere. What this means, take note, is that the rafter can be certain neither of his own location and state of motion, nor of the float's location and state of motion!

Let us return to the question presented earlier: what is responsible for the evident decrease in distance between the float and the raft? Can the rafter answer this question? What do the results of the experiment tell us? The results of the experiment tell us what the rafter can and cannot know. What will always be certain to the rafter, first of all, is the distance in between the raft and the float at any given time. The rafter will always be aware of any increase or decrease placed upon this distance, as the increase or decrease takes place. The rafter, in turn, can document the decrease in distance occurring between the float and the raft as easily as we can. What the rafter can never be certain of, however, is of what is responsible for this observed decrease in distance in between the float and the raft: the rafter has no means of knowing whether the decrease in distance is being caused by the raft's motion toward the float, the float's motion toward the raft, or a combination of these two elements! Given the evidence the rafter has to work with, none of these situations has any more validity than any of the others! Upon having performed this experiment we will have completed a study of the proposed third postulate of the principle of relativity, and in doing so can claim to have been sufficiently informed concerning the underlying concept behind what we call the principle of relativity.