A Falling Rock

2000-07-01 00:00:00

Any observant person recognizes that there is a magnificent, astonishing, and unbelievable order in the universe and what happens within it. Moreover, scientists cannot help but notice that things are so incredibly well-adjusted that chance is not an option. Science is just a result of that order.

During the Renaissance, science began to develop rapidly. New discoveries about how the universe functions were termed scientific laws, even though they were actually descriptions of what had been observed. Moreover, they were believed to be the main causes. Science gradually became the ultimate explanation of existence, and caused many people to reject religion as obsolete.

All of this changed with the beginning of the twentieth century. Modern physics showed that the universe functions completely differently from what we see in daily life. The basic laws of mechanical physics, once thought to be the creator of the action, turned out to be valid only under certain approximations. The concept of absolute space-time was replaced with a relative and dynamic one. We discovered our limitations in measuring certain physical quantities, and that some particles cannot be observed directly. We recognized that physical laws are not deterministic, and thus cannot predict how a system’s state will change over time. All they can do is present possible alternatives.

Such drastic changes in our understanding forced many to reconsider science’s claim to provide the final explanation of the universe. Today, new discoveries are termed scientific theories. We know that much remains to be discovered, and are expecting more surprises. It also is becoming increasingly harder to claim that one day we will produce a complete description and resolve all mysteries.

In this article, we will illustrate some of the changes in our understanding of the universe and scientific philosophy by analyzing a simple physical event: a falling rock. Since it is an ordinary event, one may think there is nothing mysterious about it. It seems to be a completely deterministic event with no exceptions. One also may think that there is a simple reason for the rock to fall down: the attractive force between objects with mass. As we will see, however, the story turns out to be completely different.

From experience, we know that a rock left in the air falls to the ground. We also know from astrophysical observations that the Earth circles around the sun. In these examples, the main interaction between the rock and the Earth, or between the Earth and the sun, is called gravity. Through observation, we know that gravity has an attractive nature. Let’s consider the following question, which science should be able to answer if it is the ultimate explanation: Why does a rock fall down?

A nineteenth-century physicist would reply: “A very simple question! Newton’s law of attraction. Objects with mass apply an attractive force to each other, the magnitude of which is proportional to the objects’ mass and inversely proportional to the square of the distance between the objects. Since the Earth and the rock both have mass, they are subject to this law. This is why a rock falls down.”

But this only describes a falling rock. Many who believed this claimed that there could be no change in this scenario, and especially no room for a Creator Who actually let the rock fall down. But, we ask, how do masses apply their forces to each other? Why is this force proportional to mass and inversely proportional to distance?

We do not have to pursue this argument, for we know that the so-called final explanation is incorrect. If the nineteenth-century physicist could have observed more carefully, he or she would have realized that Newton’s law of attraction could not answer all questions involving gravity. For instance, why is light, a particle without mass, deflected by gravity? Such a physicist also could not calculate correctly Mercury’s perihelion around the sun.

We now know that objects with mass do not apply attractive forces to each other. In describing gravity, Newton’s law of attraction can be used as an approximation when gravity is weak. What we see or feel as gravitational attraction is explained more accurately, but completely differently, by the theory of general relativity.

What does the theory of general relativity say about a falling rock? According to it, objects with mass curve space-time, a dynamic object, in a definite manner. In this curved space-time, a free particle that is affected only by gravity moves in a geodesic path. In the space-time curved by the Earth, the geodesic path for an object with mass can be calculated through the Earth’s center. As it has mass, a rock should follow this geodesic path. Thus it moves through the Earth’s center, and we see it as falling down.

This description is radically different from the one derived from Newton’s law of attraction. Space-time is considered dynamic, rather than absolute, and is affected by matter. Also, a falling rock is in free motion and is not acted upon by any of force belonging to the Earth.

The general theory of relativity can describe many physical phenomena related to black holes, gravitational collapse, gravitational radiation, and the large-scale structure of the universe that Newton’s theory cannot. It also covers Newton’s law of attraction in a weak gravity approximation, and fits with observations made so far.

However, it has some problems. Starting from its basic principles, it can be proven that the theory cannot describe some physical phenomena properly. Equations governing the dynamics of space-time and matter allow an initial, ordinary configuration of matter to end up in a state that can no longer be analyzed by general relativity. This final state is called a singularity. A black hole’s formation by gravitational collapse is an example of this.

Thus general relativity is also an approximate description that is sensible under certain conditions. Our understanding of gravity and a falling rock is much improved when compared to the past. But this is not the end of the story.

There is another important reason why general relativity is not the final theory of gravity. Other than gravity, three known interactions occur between matter: electromagnetic, strong, and weak. These interactions can be observed in the atomic world, and are described successfully by quantum theory. The basic principles of quantum theory are very different from those of general relativity.

While general relativity is deterministic, quantum theory is indeterministic. In general relativity, a system’s state can be specified in the usual physical terms, for instance, by giving positions and velocities. In quantum theory, a system’s state is described in abstract mathematical terms by a vector in a Hilbert space, which has no a priori relation with the physical world. Furthermore, positions and velocities can no longer be known together. The formalisms of two theories are very different and contradictory.

At first, this seems to be a philosophical problem. On a large scale involving planetary distances, quantum effects are negligible and gravity dominates other interactions. But on an atomic scale, gravitational interactions are generically very weak and can be neglected when compared to other interactions. Therefore, quantum theory and general relativity seem to be complementary for a large-scale general relativity. However, quantum theory provides appropriate descriptions on an atomic scale.

Based on these ideas, one may claim that the rather deep philosophical conflict between two successful theories is, for all practical purposes, harmless and unimportant. But this is incorrect, for in some cases both gravitational and quantum effects are not negligible. For instance, a black hole may have an atomic size, which can be described properly by quantum theory. On the other hand, since black holes naturally involve strong gravitational interactions, general relativity plays a crucial role in their description. This is an important feature of black holes, one that makes them interesting objects to study.

The quantum theory of gravity describes both gravitational and quantum effects properly. Apart from the fact that there are few candidates (like string theory), we still do not know this theory’s basic principles, which should cover the principles of quantum theory and general relativity. The two main obstacles to this are that sophisticated (and as yet undeveloped) mathematics are needed to attack theoretical problems, and that direct experimentation is impossible, since such experiments involve energies that cannot be produced on Earth.

This simply means that we do not have a complete description of a rock falling, one of the simplest physical events one can imagine. On the other hand, why is a rather deeper question then describing the event. It seems that such classical deterministic theories as general relativity can answer this question if some basic principles are assumed. But these basic assumptions can be questioned, and it is hard to claim that they are immutable. As discussed earlier, the basic principles of Newton’s theory turn out to be sensible in an approximation involving weak gravity. The existence of such nonphysical states as singularities imply that a similar conclusion holds for general relativity. Therefore, even in classical deterministic theories, the question of why cannot be answered honestly.

The situation in quantum theory is completely different. In classical theories, a system’s state changes over time and in a definite manner. In quantum theory, however, only probabilities of possible changes can be calculated, and the system may change according to one of these alternatives. Furthermore, among the possible alternatives, classically forbidden ones may be present. More important, according to basic quantum theory principles, the question of why a specific alternative is chosen cannot be answered in scientific terms.

It is interesting to see the implications of quantum theory’s uncommon features for our simple example, since the unknown quantum theory of gravity should have all of these indeterministic features. According to general relativity, all rocks left free in the air fall in exactly the same manner. But this description is not completely correct, for general relativity is not the final theory of gravity.

By roughly analyzing the same event from a quantum theory point of view, one can see that, due to seemingly strange quantum effects, a rock left in the air may go up as well as down, although going up is forbidden by general relativity. This seems to conflict with daily experience, and one may wonder why we always see objects left free in the air as falling down but not up. The reason is that for macroscopic objects like rocks, quantum effects are generically very small and a system’s state changes, most probably, as classically expected. Stated differently, the ratio of rocks going up to the ones going down is incredibly small. This is why we believe that every time we let go of a rock it will fall down. However, this does not rule out exceptions.

In this article, we analyzed a simple event to illustrate some of the changes in our understanding of how the universe functions. Many physicists used to believe that the order around us could be explained by assuming simple physical laws. However, the more we learn about the universe, the more we encounter new principles and new surprises-and the more we recognize our ignorance. Furthermore, modern physics states that the universe does not function according to strict causality and determinism.

In light of these developments, it is clear that we should renew our understanding of physical laws and the idea that they have a role in creating the action and the order around us. Being the most fundamental natural science, this conclusion of modern physics also influences other sciences. Therefore, science should be accepted as an important tool for seeking and seeing the beauty of the created order around us, and nothing more.

- Hawking, S. W. and G. F. R. Ellis. The Large-Scale Structure of Space-Time. USA: Cambridge University Press, 1991.
- Wald, R. M. General Relativity. Chicago; University of Chicago Press, 1984.

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