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wk heisenberg

Heisenberg's microscope

Heisenberg's microscope exists only as a thought experiment, one that was proposed by Werner Heisenberg, criticized by his mentor Niels Bohr, and subsequently served as the nucleus of some commonly held ideas, and misunderstandings, about Quantum Mechanics.

Basic ideas behind the experiment

The above two drawings show a view of the apparatus imagined by Werner Heisenberg, and a picture of a gun that shoots gamma photons in the general direction of an atom, hoping to hit an otherwise undetectable electron and detect its rebound.

The above photograph would be impossible to take of the real thing because it is impossible to see a photon, and it is impossible to see an electron. But this experiment is a thought experiment. The image shows the nucleus of an atom, in black, and an electron in its orbit in grey. At this very instant, a gamma particle (the red object) is going to impact the electron. When the gamma particle strikes the electron, its original trajectory will be disturbed. Heisenberg's purpose was to demonstrate to those who held a classical view of physics that by their own understanding of how the universe works the idea that one can know the exact position and momentum of a small particle such as an electron must be false.

Starting with traditional ideas of physics and working through thought experiments step by step, physicists learned that the ideas people had started out with were inappropriate to help understand events on the atomic scale. It is possible to start with a classical physics way of portraying microscopic events and arrive at one of the basic problems that troubled Heisenberg. Before the development of quantum mechanics and related developments in modern physics, electrons were imagined to be particles. Photons can also be imagined to be particles. Atoms of some elements can be held fairly rigidly in place in crystals. A crude model of this situation (as pictured above) would consist of a ball fixed in a hole in a board and surrounded by circular groves holding one or a few large ball bearings. The whole apparatus rotates to represent the motion of electrons in their orbits. An air pistol shooting .22 caliber ammunition is used to try to find an electron. The gun is fired at regular intervals, and most of the time it does not hit a ball bearing. When it does hit a ball bearing, it rebounds and is detected by noticing that it penetrates a paper dome surrounding the whole apparatus. The direction in which the gun was fired is known, and the time it was fired is known, so it is possible to use this method to detect the presence of a ball bearing at a certain place and time. The direction of the ricochet, and the question whether the marksman will be hit by his own ammunition, will depend on whether the pellet shot from the gun hits the ball bearing head on or with a glancing blow. A lesser consequence (at least in terms of safety) will be that the ball bearing will be blasted out of its original track. Since its original velocity was unknown, the degree to which the blow dealt by the pellet was glancing is also unknown, etc., it becomes impossible to say anything definite about its trajectory. This thought experiment is a good bit coarser than the thought experiment of Heisenberg on which it is based.

Heisenberg asked what would happen if one would attempt to locate the position and momentum of an electron by viewing it with a microscope. Several problems appeared: (1) The field of view may be larger than the diameter of an electron and the depth of field of a microscope includes a range of distances, so the fact that something is visible through a microscope does not give an exact indication of its location. (2) The frequency of electromagnetic radiation used determines how sharply a small object can be imaged. The higher the frequency, the sharper the image. Since precision in locating the electron was the main goal, Heisenberg used the highest frequency electromagnetic radiation, gamma rays, in his thought experiment. (3) The frequency of electromagnetic radiation is directly correlated to the energy that it carries. The result is that the higher the frequency the greater the force that is applied to the object being measured, in this case, to the electron. The radiation that would give the clearest indication of position would also give the greatest impetus to the electron, and the ratio between the frequency of the radiation and the energy it delivers turns out to be an ineradicable factor in the uncertainty of measurements of position and momentum. In discussing this experiment, Heisenberg says, "From this photon the electron receives a Compton recoil of order of magnitude h/λ," where h is Planck's_constant and λ is the wave length of the photon."

This thought experiment, which began by describing both electrons and photons as though they were discrete entities with exact positions and momenta that could be known and measured, concluded that when all of the operational definitions pertinent to the experiment were completely drawn out it became clear that one could never expect to determine both an exact position and an exact momentum for any electron.

This thought experiment was written out to help in introducing Heisenberg's Uncertainty Principle, which stands as one of the pillars of modern physics, a theory that has been tested and confirmed countless times. That being said, the thought experiment has the somewhat unusual characteristic of attacking the premises under which it was constructed (Reductio ad absurdum), or at least of being involved in the development of an area of physics, quantum mechanics, that redefined the terms under which the original thought experiment was conceived. Quantum mechanics questions whether electrons actually have a determinate position before they are disturbed by the measurement that one might try to use to establish that they have such determinate positions. Under a more thorough quantum mechanical analysis, an electron has the probability of showing up at any point in the universe, but the probability that it will be far from where one might expect it to be becomes very low for places at great distances from the neighborhood in which it was originally found. In other words, the "position" of an electron can only be stated in terms of a probability distribution, and predictions of where it will move to can also only be given in terms of a probability distribution.

Footnotes

¹ Heisenberg, excerpt giving his own description of this thought experiment in The World of Mathematics, II, p. 1052.

Sources

  • Amir D. Aezel, Entanglement, pp. 77-79.
  • Neils Bohr, Nature, 121, p. 580, 1928.
  • Werner Heisenberg, Physics and Philosophy, pp. 46ff.
  • Werner Heisenberg, The Physical Principles of the Quantum Theory, 1930.
  • Albert Messiah, Quantum Mechanics, I, p. 143f
  • James R. Newman, ed., The World of Mathematics, II, pp. 1051-1055

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