Either because the laws of nature are couched in mathematical symbolism, or because science cannot progress safely in the presence of ambiguity and imprecision, scientists tend to express natural laws as mathematical statements. It would be wrong, however, to read too much into this. Consider a stone tumbling down a hillside, bouncing off rocks and molehills, until it reaches its final resting place at the bottom of the slope. If the stone really is implementing mathematical laws, then in a few seconds it will have performed a series of calculations beyond the capabilities of the fastest supercomputer. But is that really what the rock is doing? Measuring its own positing to the hundreds of decimal places that we know are needed to guarantee the “correct answer”? Computing its way from collision to collision in an orgy of dynamical equations? Some physicists and philosophers think so; in their view, information, rather than matter, is the basic material of the universe. The universe itself then becomes a supercomputer of unprecedented speed and power, busily pursuing the consequences of its “program,” its program being the laws of nature.
Alternatively, the simple laws that we consider fundamental may not be fundamental at all, but just approximations of how nature behaves, or consequences of that behavior. We now know that Newton’s laws are not rigid rules that nature just obeys; they are excellent but sometimes inaccurate descriptions of what nature does. They are not nature’s laws but human laws, and like all human laws they can be broken. Indeed, according to another human law, Murphy’s, they always will be – an interesting case of self-reference. If nature breaks our laws, then our calculations will bear no relation to the way in which nature actually works. We may use the laws of dynamics to calculate where the stone will fall; but that’s not how the stone does it. It certainly can’t if we’ve got the wrong laws. The Newtonian stone has no choice; it is forced to fall wherever it does. In this view the universe is a machine rather than a computer; it is composed of matter, and it is in the nature of matter to behave in ways that happen, coincidentally, to mimic certain computations that appeal to humans.
That was a classical picture of a moving stone. The quantum picture is more subtle, and far stranger to human intuition. In a quantum view, the subatomic particles that make up the stone actually follow all possible paths, consistent with the laws of quantum mechanics. According to the quantum paradigm, what we see is the superposition of all of those potentialities. It just happens that the result of this strange process looks like a lump of rock moving under Newtonian laws. In this picture the Newtonian laws are viewed as mathematical consequences of the real quantum laws, valid for modest but bulky quantities of matter moving at moderate speeds.
In other areas of science, especially those where really accurate measurements or repeatable experiments aren’t possible, people nowadays tend to speak of “models” rather than “laws”. They look for underlying rules and regularities that explain a limited range of phenomena in simple, graspable terms. From that point of view, “laws” may be just spectacularly successful, very simple, models. The important thing is that, even though we can’t be certain that what we think of as laws of nature are actually true, we do see a lot of patterns and regularities in the world, and we can use these patterns and regularities in the world, and we can use these patterns very effectively to bring certain aspects of the world under our control. For instance, the laws of aerodynamics work sufficiently well that airplanes designed using those laws stay up. The vast bulk of evidence, while not quite so conclusive points to the flight of birds as a consequence of those same laws. However, we can’t yet start with aerodynamics and end with a proof that a bird, too, will stay up; but despite such admitted uncertainties, there still seem to be simple laws at work. It’s just that some operate further behind the scenes than others. Indeed, the further behind the scenes the laws are, the more we tend to think of them as being “fundamental”.
Alternatively, the simple laws that we consider fundamental may not be fundamental at all, but just approximations of how nature behaves, or consequences of that behavior. We now know that Newton’s laws are not rigid rules that nature just obeys; they are excellent but sometimes inaccurate descriptions of what nature does. They are not nature’s laws but human laws, and like all human laws they can be broken. Indeed, according to another human law, Murphy’s, they always will be – an interesting case of self-reference. If nature breaks our laws, then our calculations will bear no relation to the way in which nature actually works. We may use the laws of dynamics to calculate where the stone will fall; but that’s not how the stone does it. It certainly can’t if we’ve got the wrong laws. The Newtonian stone has no choice; it is forced to fall wherever it does. In this view the universe is a machine rather than a computer; it is composed of matter, and it is in the nature of matter to behave in ways that happen, coincidentally, to mimic certain computations that appeal to humans.
That was a classical picture of a moving stone. The quantum picture is more subtle, and far stranger to human intuition. In a quantum view, the subatomic particles that make up the stone actually follow all possible paths, consistent with the laws of quantum mechanics. According to the quantum paradigm, what we see is the superposition of all of those potentialities. It just happens that the result of this strange process looks like a lump of rock moving under Newtonian laws. In this picture the Newtonian laws are viewed as mathematical consequences of the real quantum laws, valid for modest but bulky quantities of matter moving at moderate speeds.
In other areas of science, especially those where really accurate measurements or repeatable experiments aren’t possible, people nowadays tend to speak of “models” rather than “laws”. They look for underlying rules and regularities that explain a limited range of phenomena in simple, graspable terms. From that point of view, “laws” may be just spectacularly successful, very simple, models. The important thing is that, even though we can’t be certain that what we think of as laws of nature are actually true, we do see a lot of patterns and regularities in the world, and we can use these patterns and regularities in the world, and we can use these patterns very effectively to bring certain aspects of the world under our control. For instance, the laws of aerodynamics work sufficiently well that airplanes designed using those laws stay up. The vast bulk of evidence, while not quite so conclusive points to the flight of birds as a consequence of those same laws. However, we can’t yet start with aerodynamics and end with a proof that a bird, too, will stay up; but despite such admitted uncertainties, there still seem to be simple laws at work. It’s just that some operate further behind the scenes than others. Indeed, the further behind the scenes the laws are, the more we tend to think of them as being “fundamental”.
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