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Quantum Mechanics
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Bohm's 'ambiguity principle'
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from Infinite Potential: The Life and Times of David Bohm, by Dr. David Peat
In formulating quantum mechanics, Heisenberg had arrived at his famous uncertainty principle, which dictates that, at the subatomic level, it is impossible to measure simultaneously both the position and the momentum of a particle with absolute accuracy. (Momentum is the velocity of a particle multiplied by its mass, and one may think of the problem of determining momentum as essentially the same as that of measuring its velocity.)
Heisenberg’s uncertainty principle follows directly from the mathematics of his theory. Its meaning, however, calls for an explanation. Position and momentum are the two cornerstones of classical physics. In the large-scale world of planets, billiard balls, and Newtonian apples, the path of an object is defined by its position and momentum. If one knows both the position and the momentum of a comet at a single instant, then one can compute its entire future trajectory.
Admittedly, there are always experimental errors involved in measuring position and momentum, but in principle at least, these errors can be progressively reduced or compensated for by refining the measurements. More important, classical physics takes for granted that a falling apple, a comet, or an orbiting satellite actually possesses a well-defined position and momentum at every instant of its existence.
Heisenberg’s uncertainty principle indicated that, at the sub-atomic level, nature limits the accuracy with which position and momentum can be measured. But if an electron’s momentum and position cannot be defined exactly at one instant, then physicists will be unable to compute its path. At one stroke, Heisenberg’s principle denied much of the intuitive imagery common to classical physics— the very sort of imagery that the young Bohm liked to employ.
To demonstrate his principle, Heisenberg imagined an actual experiment to measure the exact path of an electron. An ordinary microscope, one that makes use of visible light, would be too gross to determine the position of an electron, but suppose this microscope used gamma rays of exceptionally short wavelength. With this hypothetical microscope, it would be possible to determine the electron’s position with a good degree of accuracy. But when a gamma ray photon hits the electron and is reflected back into the microscope, it gives the electron such a jolt that it alters its momentum in an uncontrollable and unpredictable way. The shorter the wavelength of the gamma ray and the more accurately it determines the electron’s position, the greater is its unpredictable disturbance of the electron’s momentum.
Heisenberg was able to show, by this commonsense argument, that any attempt to measure momentum or position of an elementary particle produces an uncontrollable and unpredictable disturbance.
So, he concluded, does nature prevent us from ever knowing the precise value of these variables simultaneously and, consequently, the trajectory of the electron’s path.
Niels Bohr rejected the whole tenor of this example. Indeed, so forceful were his objections that they actually reduced Heisenberg to tears. He pointed out that in setting up his argument, Heisenberg had tacitly assumed that the electron actually has a path and actually does possess a precise position and momentum at each instant. When a measurement is made, it produces an uncontrollable disturbance in one of the two variables.
But Heisenberg was totally wrong, Bohr argued, to begin with this concept of a well-defined, even if in principle unmeasurable, path. He was guilty of confusing new quantum ideas with older classical concepts, such as a path. It is not so much that we disturb the intrinsic properties of an electron by observing it, Bohr argued, but rather that such properties are already ambiguous within the subatomic domain.
When Bohm read Bohr’s comments, he suggested that Heisenberg’s uncertainty principle would be far better called the “ambiguity principle.”
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