Read Online Quantum Man: Richard Feynman's Life in Science by Lawrence M. Krauss - Free Book Online
Authors: Lawrence M. Krauss
Tags: Science / Physics
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such an action principle, but not by more conventional methods.
Physics, or at least the physics that Feynman and Wheeler were imagining, had driven Feynman to a place he never would have expected to be a half-dozen years earlier. The transformation in his thinking following his intensive efforts to explore their new theory had been dramatic. He was now convinced that focusing on events at a fixed time was not the way to think, and that the action principle, based on exploring complete trajectories through space and time, was. As he later wrote, “We have in [the action principle] a thing that describes the character of the path throughout all of space and time. The behavior of nature is determined by saying her whole-space-time path has a certain character.”But how could this principle be translated into quantum mechanics, which thus far depended so crucially on defining a system at one time in order to calculate what would happen at later times? For Feynman, the key to the answer came from a fortuitous beer party in Princeton. But to appreciate this key, we first have to make a short detour to revisit our picture of the mysterious quantum world that Feynman was about to change.
CHAPTER 4
Alice in Quantumland
The Universe is not only queerer than we suppose, but queerer than we can suppose.
J. B. S. H ALDANE , 1924
W hile the distinguished British scientist J. B. S. Haldane was a biologist and not a physicist, his statement about the universe could not be more apt, at least to the realm of quantum mechanics that Richard Feynman was about to conquer. For, as we have seen, at the small scales where quantum mechanical effects become significant, particles can appear to be in many different places at once, while also doing many different things at the same time in each place.
The mathematical quantity that can account for all of this apparent lunacy is the function discovered by the famous Austrian physicist Erwin Schrödinger, who derived what became the conventional understanding of quantum mechanics during a busy two-week period in which he too was doing many different things at the same time—in the midst of trysts with perhaps two different women while holed up in a mountain chalet. It probably was the perfect atmosphere to imagine a world where all of the classical rules of behavior would ultimately be broken.
This function of Schrödinger’s is called the wave function of an object, and it accounts for the mysterious fact, at the heart of quantum mechanics, that all particles behave in some sense like waves, and all waves behave in some sense like particles—the difference between a particle and a wave being that a particle is located at a specific point, whereas a wave is spread out over some region.
So, if a particle, which isn’t spread out, is to be described by something that behaves like a wave and is spread out, the wave function must accommodate this fact. As Max Born later demonstrated, this was possible if the wave function, which itself might behave like a wave, did not describe the particle itself but rather the probability of finding the particle at any given place in space at a specific time. If the wave function, and hence the probability of finding a particle, is nonzero at many different places, then the particle acts like it is in many different places at any one time.
So far so good, even if the notion itself seems crazy. But there is one more crucial bit of craziness at the heart of quantum mechanics, and I should stress that physicists do not have a fundamental understanding of why nature behaves this way, except to say that it does. If the laws of quantum physics determine the behavior of the wave function, then physics tells us that given the wave function of a particle at one time, quantum mechanics in principle allows us to calculate, in a completely deterministic way, the wave function of the particle at a later time. Up to this point it is just like Newton’s laws, which tell us
Physics, or at least the physics that Feynman and Wheeler were imagining, had driven Feynman to a place he never would have expected to be a half-dozen years earlier. The transformation in his thinking following his intensive efforts to explore their new theory had been dramatic. He was now convinced that focusing on events at a fixed time was not the way to think, and that the action principle, based on exploring complete trajectories through space and time, was. As he later wrote, “We have in [the action principle] a thing that describes the character of the path throughout all of space and time. The behavior of nature is determined by saying her whole-space-time path has a certain character.”But how could this principle be translated into quantum mechanics, which thus far depended so crucially on defining a system at one time in order to calculate what would happen at later times? For Feynman, the key to the answer came from a fortuitous beer party in Princeton. But to appreciate this key, we first have to make a short detour to revisit our picture of the mysterious quantum world that Feynman was about to change.
CHAPTER 4
Alice in Quantumland
The Universe is not only queerer than we suppose, but queerer than we can suppose.
J. B. S. H ALDANE , 1924
W hile the distinguished British scientist J. B. S. Haldane was a biologist and not a physicist, his statement about the universe could not be more apt, at least to the realm of quantum mechanics that Richard Feynman was about to conquer. For, as we have seen, at the small scales where quantum mechanical effects become significant, particles can appear to be in many different places at once, while also doing many different things at the same time in each place.
The mathematical quantity that can account for all of this apparent lunacy is the function discovered by the famous Austrian physicist Erwin Schrödinger, who derived what became the conventional understanding of quantum mechanics during a busy two-week period in which he too was doing many different things at the same time—in the midst of trysts with perhaps two different women while holed up in a mountain chalet. It probably was the perfect atmosphere to imagine a world where all of the classical rules of behavior would ultimately be broken.
This function of Schrödinger’s is called the wave function of an object, and it accounts for the mysterious fact, at the heart of quantum mechanics, that all particles behave in some sense like waves, and all waves behave in some sense like particles—the difference between a particle and a wave being that a particle is located at a specific point, whereas a wave is spread out over some region.
So, if a particle, which isn’t spread out, is to be described by something that behaves like a wave and is spread out, the wave function must accommodate this fact. As Max Born later demonstrated, this was possible if the wave function, which itself might behave like a wave, did not describe the particle itself but rather the probability of finding the particle at any given place in space at a specific time. If the wave function, and hence the probability of finding a particle, is nonzero at many different places, then the particle acts like it is in many different places at any one time.
So far so good, even if the notion itself seems crazy. But there is one more crucial bit of craziness at the heart of quantum mechanics, and I should stress that physicists do not have a fundamental understanding of why nature behaves this way, except to say that it does. If the laws of quantum physics determine the behavior of the wave function, then physics tells us that given the wave function of a particle at one time, quantum mechanics in principle allows us to calculate, in a completely deterministic way, the wave function of the particle at a later time. Up to this point it is just like Newton’s laws, which tell us
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