# Heisenberg Uncertainty Principle

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The Heisenberg Uncertainty Principle, named for Werner Heisenberg, [1] states that certain pairs of properties (called conjugate quantities) cannot simultaneously be measured with absolute precision, for a given physical object. This is important in many fields such as spectroscopy, medical imaging, astrophysics, satelite communications and laser design.

For particle physics, this was the problem of determining the state of a fundamental particle (electron, etc.) at any given moment. The problem arises experimentally as, in order to determine the state of any particle, we (the observers) must look at it. In order to see it, we must bombard it with photons. The interaction of photons with the sub-atomic particles changes the state of the particle leading us to the ironic conclusion that it is impossible for an observer to determine experimentally the state of any particle, because there is always an error margin equal to the wavelength of the photon. Though the wavelength can be made shorter in order to reduce the error margin, this also disturbs the motion of the measured particle.[2] Thus, for Heisenberg, physicists can only predict the probabilities of where or what the given state of a particle would be.

Fundamental particles thus exist in a fog of probabilities. It was this theorem that led to Einstein's famous quip that "God does not play dice."

## The Principle

The principle deals with certain pairs of quantities called conjugate quantities. Position and momentum are conjugate quantities, as are energy and time. The principle then states:

For a system, conjugate quantities cannot simultaneously be precisely measured.

The principle also provides an estimate of the maximum precision possible for a given system. In the case of position x and linear momentum in x-direction px, this is given by

${\displaystyle \Delta x\cdot \Delta p_{x}\geq {\frac {h}{4\pi }}}$.

For energy and time:

${\displaystyle \Delta E\cdot \Delta t\geq {\frac {h}{4\pi }}}$.

h denotes Planck's constant, which is very small. The uncertainties are here understood to be variances.

### Example

Let's say that we want to locate a light wave precisely. One way to do this is to add several waves together in such a way that we get a pulse. If we add many such pulses together, we will eventually get a very sharp pulse, which we can locate to good precision. But there is an uncertainty involved in measuring the wavelengths of each of those pulses. When the pulses are added together, so are their uncertanties. This means that while we know where the pulse is (position), we have little knowledge of its wavelength (momentum).

Conversely, in order to measure wavelength precisely, we must study many oscillations of a wave. But the more oscillations we allow, the more we lose concept of where the wave is. For instance, a laser ray is essentially "everywhere" along the laser beam. Thus, we see that the principle is valid for electromagnetic radiation (light).

## Applications

In string theory, another constant (C) related to the Planck scale is introduced into the equation. This constant poses a minimal value on the uncertainty with which particles can be located.[3]

In other fields, such as the behavioral sciences, this principle also applies. For anthropologists studying the interactions of social groups, interactions may change as a result of the researcher's presence. For psychologists studying individual behavior, reasons and actions may change because the individual knows he is being observed.

## References

1. W. Heisenberg (1927). "Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik (On the Physical Content of Quantum Kinematics and Mechanics)". Zeitschrift für Physik 43: 172-198.
2. Brian Greene, The Elegant Universe, 2003: 113
3. Lee Smolin, Three Roads to Quantum Gravity, 2001: 165