Uncertainty principle
From Wikipedia, the free encyclopedia
 |
The English used in this article or section may not be easy for everybody to understand. You can help Wikipedia by making this page or section simpler. |
The Heisenberg uncertainty principle states that the more we know about where a particle is, the less we know about the speed and direction the particle is traveling.
This uncertainty principle was an important step in the development of quantum mechanics when it was discovered by Werner Heisenberg in 1927. In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution. The larger the associated standard deviation is, the more "uncertain" we might say that that characteristic is for the system.
The uncertainty principle is often confused with the observer effect.
Contents |
[change] Wave-particle duality
An important part of quantum mechanics, which shows itself in the Heisenberg Uncertainty Principle, is that no physical event can be (to arbitrary accuracy) described as a "classic point particle" or as a wave but rather the tiny event is best described in terms of wave-particle duality. Essentially, small bits of matter and small waves of energy are sometimes very hard to tell apart, because they can act like both at the same time.
The Heisenberg uncertainty principle is a consequence of this picture.
A helpful analogy can be drawn between the wave associated with a quantum-mechanical particle and a more familiar wave, the time-varying signal associated with, say, a sound wave. It is meaningless to ask about the frequency spectrum at a single moment in time, because the measure of frequency is the measure of a repetition recurring over a period of time. Indeed, in order for a signal to have a relatively well-defined frequency, it must persist for a long period of time, and conversely, a signal that occurs at a relatively well-defined moment in time (i.e., of short duration) will necessary encompass a broad frequency band. This is, indeed, a close mathematical analogue of the Heisenberg uncertainty principle.
[change] Uncertainty principle versus observer effect
The uncertainty principle in quantum mechanics is sometimes explained in a wrong way by claiming that the measurement of position necessarily disturbs a particle's momentum, and vice versa—i.e., that the uncertainty principle is a manifestation of the observer effect. Indeed, Heisenberg himself may have initially offered explanations which suggested this view. Prior to the more modern understanding, a measurement was often visualized as a physical disturbance inflicted directly on the measured system, being sometimes illustrated as a thought experiment called Heisenberg's microscope. For instance, when measuring the position of an electron, one imagines shining a light on it, thus disturbing the electron and producing the quantum mechanical uncertainties in its position.
The EPR paradox is one indication that it is wrong to view the uncertanty principle as simply a measurement directly disturbing a particle. This "paradox" shows that a measurement can be performed on a particle without disturbing it directly, by performing a measurement on a distant entangled particle.
Another problem with this view is that it misperceives the way measurement in quantum mechanics is understood. To test the uncertainty principle, a hypothetical physicist would use some specific procedure over and over to prepare an ensemble of particles in the same quantum state. For half of this ensemble, the position would be measured and recorded, giving a probability distribution for position. For the other half of the ensemble, momentum would be measured, giving a probability distribution for momentum. Finally, the product of the standard deviations would be computed, giving a value of at least 
.
In this setup, the position and momentum would and could never be measured subsequently for the same particle. (If they were, the results of the second measurement would not reflect the original state, due to a correct application of the observer effect.) Therefore, one measurement cannot affect the other. Moreover, although each measurement collapses the quantum state of the particle, the probability distribution resulting from these measurements will correctly reflect the quantum state as it existed before the measurement.
In any case, it is now understood that the uncertainties in the system exist prior to and independent of the measurement, and the uncertainty principle is therefore independent of the observer effect.
[change] History and interpretations
The Uncertainty Principle was developed as an answer to the question: How does one measure the location of an electron around a nucleus?
In the summer of 1922 Heisenberg met Niels Bohr, the founding father of quantum mechanics, and in September 1924 Heisenberg went to Copenhagen, where Bohr had invited him as a research associate and later as his assistant. In 1925 Werner Heisenberg laid down the basic principles of a complete quantum mechanics. In his new matrix theory he replaced classical commuting variables with non-commuting ones. Heisenberg's paper marked a radical departure from previous attempts to solve atomic problems by making use of observable quantities only. He wrote in a 1925 letter, "My entire meagre efforts go toward killing off and suitably replacing the concept of the orbital paths that one cannot observe." Rather than struggle with the complexities of three-dimensional orbits, Heisenberg dealt with the mechanics of a one-dimensional vibrating system, an anharmonic oscillator. The result was formulae in which quantum numbers were related to observable radiation frequencies and intensities. In March 1926, working in Bohr's institute, Heisenberg formulated the principle of uncertainty thereby laying the foundation of what became known as the Copenhagen interpretation of quantum mechanics.
Albert Einstein was not happy with the uncertainty principle, and he challenged Niels Bohr and Werner Heisenberg with a famous thought experiment (See the Bohr-Einstein debates for more details): we fill a box with a radioactive material which randomly emits radiation. The box has a shutter, which is opened and soon thereafter shut by a clock at a precise time, thereby allowing some radiation to escape. So the time is already known with precision. We still want to measure the conjugate variable energy precisely. Einstein proposed doing this by weighing the box before and after. The equivalence between mass and energy from special relativity will allow you to determine precisely how much energy was left in the box. Bohr countered as follows: should energy leave, then the now lighter box will rise slightly on the scale. That changes the position of the clock. Thus the clock deviates from our stationary reference frame, and by general relativity, its measurement of time will be different from ours, leading to some unavoidable margin of error. In fact, a detailed analysis shows that the imprecision is correctly given by Heisenberg's relation.
The term Copenhagen interpretation of quantum mechanics was often used interchangeably with and as a synonym for Heisenberg's Uncertainty Principle by detractors who believed in fate and determinism and saw the common features of the Bohr-Heisenberg theories as a threat. Within the widely but not universally accepted Copenhagen interpretation of quantum mechanics (i.e., it was not accepted by Einstein or other physicists such as Alfred Lande), the uncertainty principle is taken to mean that on an elementary level, the physical universe does not exist in a deterministic form — but rather as a collection of probabilities, or potentials. For example, the pattern (probability distribution) produced by millions of photons passing through a diffraction slit can be calculated using quantum mechanics, but the exact path of each photon cannot be predicted by any known method. The Copenhagen interpretation holds that it cannot be predicted by any method, not even with theoretically infinitely precise measurements.
It is this interpretation that Einstein was questioning when he said "I cannot believe that God would choose to play dice with the universe." Bohr, who was one of the authors of the Copenhagen interpretation responded, "Einstein, don't tell God what to do." Niels Bohr himself acknowledged that quantum mechanics and the uncertainty principle were counter-intuitive when he stated, "Anyone who is not shocked by quantum theory has not understood a single word."
The basic debate between Einstein and Bohr (including Heisenberg's Uncertainty Principle) was that Einstein was in essence saying: "Of course, we can know where something is; we can know the position of a moving particle if we know every possible detail, and therefore by extension, we can predict where it will go." Bohr and Heisenberg were saying: "We can only know the probable position of a moving particle, therefore by extension, we can only know its probable destination; we can never know with absolute certainty where it will go."
Einstein was convinced that this interpretation was in error. His reasoning was that all previously known probability distributions arose from deterministic events. The distribution of a flipped coin or a rolled die can be described with a probability distribution (50% heads, 50% tails), but this does not mean that their physical motions are unpredictable. Ordinary mechanics can be used to calculate exactly how each coin will land, if the forces acting on it are known. And the heads/tails distribution will still line up with the probability distribution (given random initial forces).
Einstein assumed that there are similar hidden variables in quantum mechanics which underlie the observed probabilities and that these variables, if known, would show that there was what Einstein termed "local realism," a description opposite to the uncertainty principle, being that all objects must already have their properties before they are observed or measured. For the greater part of the twentieth century, there were many such hidden variable theories proposed, but in 1964 John Bell theorized the Bell inequality to counter them, which postulated that although the behavior of an individual particle is random, it is also correlated with the behavior of other particles. Therefore, if the uncertainty principle is the result of some deterministic process in which a particle has local realism, it must be the case that particles at great distances instantly transmit information to each other to ensure that the correlations in behavior between particles occur. The interpretation of Bell's theorem explicitly prevents any local hidden variable theory from holding true because it shows the necessity of a system to describe correlations between objects. The implication is, if a hidden local variable is the cause of particle 1 being at a position, then a second hidden local variable would be responsible for particle 2 being in its own position — and there is no system to correlate the behavior between them. Experiments have demonstrated that there is correlation. In the years following, Bell's theorem was tested and has held up experimentally time and time again, and these experiments are in a sense the clearest experimental confirmation of quantum mechanics. It is worth noting that Bell's theorem only applies to local hidden variable theories; non-local hidden variable theories can still exist (which some, including Bell, think is what can bridge the conceptual gap between quantum mechanics and the observable world).
Whether Einstein's view or Heisenberg's view is true or false is not a directly empirical matter. One criterion by which we may judge the success of a scientific theory is the explanatory power it gives us, and to date it seems that Heisenberg's view has been the better at explaining physical subatomic phenomena.
[change] Popular culture
The uncertainty principle is stated in popular culture in many ways, for example, by some stating that it is impossible to know both where an electron is and where it is going at the same time. This is roughly correct, although it fails to mention an important part of the Heisenberg principle, which is the quantitative bounds on the uncertainties. Heisenberg stated that it is impossible to determine simultaneously and with unlimited accuracy the position and momentum of a particle, but due to Planck's Constant being so small, the Uncertainty Principle was intended to apply only to the motion of atomic particles. However, culture often misinterprets this to mean that it is impossible to make a completely accurate measurement.
In the 1997 film The Lost World: Jurassic Park, chaostician Ian Malcolm claims that the effort "to observe and document, not interact" with the dinosaurs is a scientific impossibility because of "the Heisenberg Uncertainty Principle, whatever you study, you also change." This is an inaccurate confusion with the observer effect, as explained above.
In the science fiction television series Star Trek: The Next Generation, the fictional transporters used to "beam" characters to different locations overcome the limitations of sampling the subject due to the uncertainty principle with the use of "Heisenberg compensators." When asked, "How does the Heisenberg compensator work?" by Time magazine on 28 November 1994, Michael Okuda, technical advisor on Star Trek, famously responded, "It works very well, thank you."[1]
In an episode of the television show Aqua Teen Hunger Force, Meatwad (who was temporarily made into a genius) tries to incorrectly explain Heisenberg's Uncertainty Principle to Frylock to explain his new found intelligence. "Heisenberg's Uncertainty Principle tells us that at a specific curvature of space, knowledge can be converted to energy, or -- and this is key now -- matter."
In an episode of Stargate SG-1, Samantha Carter explains, using the uncertainty principle, that the future is not pre-determined, one can only calculate possibilities.
[change] Notes
- ↑ "Reconfigure the Modulators!", Time Magazine, November 28, 1994.
[change] References
- W. Heisenberg, "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik", Zeitschrift für Physik, 43 1927, pp. 172-198. English translation: J. A. Wheeler and H. Zurek, Quantum Theory and Measurement Princeton Univ. Press, 1983, pp. 62-84.
- L. I. Mandelshtam, I. E. Tamm, "The uncertainty relation between energy and time in nonrelativistic quantum mechanics", Izv. Akad. Nauk SSSR (ser. fiz.) 9, 122-128 (1945). English translation: J. Phys. (USSR) 9, 249-254 (1945).
- G. Folland, A. Sitaram, "The Uncertainty Principle: A Mathematical Survey", Journal of Fourier Analysis and Applications, 1997 pp 207-238.
- G. Gabrielse, H. Dehmelt, "Observation of Inhibited Spontaneous Emission", Physical Review Letters, 55 (1985), 67-70.
[change] Other websites
- Matter as a Wave - a chapter from an online textbook
- The Uncertainty Relations: Description, Applications on Project PHYSNET
- Quantum mechanics: Myths and facts
- Stanford Encyclopedia of Philosophy entry
- aip.org: Quantum mechanics 1925-1927 - The uncertainty principle
- Eric Weisstein's World of Physics - Uncertainty principle
- Schrödinger equation from an exact uncertainty principle
- John Baez on the time-energy uncertainty relation
- The time-energy certainty relation
- The certainty principle
