# Heisenberg Uncertainty Principle

# Heisenberg Uncertainty Principle

The Heisenberg uncertainty, principle first formulated by German physicist Werner Heisenberg (1901–1976), is basic to quantum theory. The principle asserts that it is physically impossible to measure both the exact position and the exact momentum of a particle (such as an electron) at the same time. The more precisely one quantity is measured, the less precisely the other is known.

Heisenberg’s uncertainty principle, which also helps to explain the existence of virtual particles, is most commonly stated as follows: It is impossible to exactly and simultaneously measure both the momentum p (mass times velocity) and position *x* of a particle. In fact, it is not only impossible to *measure* simultaneously the exact values of *p* and *x;* they do not *have* exact, simultaneous values. There is always an uncertainty in momentum *(Δp)* and an uncertainty in position (Δx), and these two uncertainties cannot be reduced to zero together. Their product is given by *Δp* **x** *Δx* > *h* /4π*,* where *h* is Planck’s constant (6.63 **x** 10^{-34} joulesc second). Thus, if *Δp → * 0, then

*Δx*

**→ ∞**, and vice versa.

Heisenberg’s uncertainty principle is *not* equivalent to the statement that it is impossible to observe a system without perturbing it at least slightly; this is a true, but is not uniquely true in quantum mechanics (it is also true in Newtonian mechanics) and is not the source of Heisenberg’s uncertainty principle.

Heisenberg’s uncertainty principle applies even to particles that are not interacting with other systems, that is are not being “observed.”

One consequence of Heisenberg’s uncertainty principle is that the energy and duration of a particle are also characterized by complementary uncertainties. There is always, at every point in space and time, even in a perfect vacuum, an uncertainty in energy *DE* and an uncertainty in duration *Δt,* and these two complementary uncertainties, like *Δp* and *Δx,* cannot be reduced to zero simultaneously. Their product is given by *ΔE* **x** *Δt* > *h* /4π.

Electrons and other subatomic particles exist in a dual particle and wave state and so one can only speak of their positions in terms of probability as to location when their velocity (energy state) is known. In fact, these properties apply not only to subatomic particles but to all objects; however, their effects on objects larger than atomic size are too small to measure.

## Resources

### BOOKS

Buschhorn, Gerd W., et al. *Fundamental Physics-Heisenberg*

*and Beyond.* New York: Springer, 2004.

Griffiths, David J. *Introduction to Quantum Mechanics.* Upper Saddle River, NJ: Prentice Hall, 2004.

Lindley, David. *Uncertainty: Einstein, Heisenberg, Bohr, and the Struggle for the Soul of Science.* New York:Doubleday, 2007.

### OTHER

Geremia, J.M., et al. “Real-Time Quantum Feedback Control of Atomic Spin-Squeezing.” *Science*. 304 (2004): 270-273.

Seife, Charles. “Do Deeper Principles Underlie Quantum Uncertainty and Nonlocality?.” *Science*. 309 (2005): 98.

K. Lee Lerner

Larry Gilman

Terry Watkins

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