# Heisenberg Uncertainty Principle

The Heisenberg uncertainty principle first formulated by German physicist Werner Heisenberg (1901–1976), has broad implications for quantum theory. The principle asserts that it is physically impossible to measure both the exact position and the exact **momentum** of a particle (like 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 (Δ*p*) and an uncertainty in position (Δ*x*), and these two uncertainties cannot be reduced to **zero** together. Their product is given by Δ*p* Δ*x* > *h*/4PI, where *h* is **Planck's constant** (6.63 × 10^{-34} joules &NA; second). Thus, if Δ*p* → 0, then Δ*x* → ∞, 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 Hein seberg'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 Δ*E* and an uncertainty in duration Δ*t*, and these two complementary uncertainties, like Δ*p* and Δ*x*, cannot be reduced to zero simultaneously. Their product is given by Δ *E* × Δ*t* > *h*/4PI.

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.

## Resources

### Books

Barnett, R. Michael, Henry Mühry, and Helen R. Quinn. *The Charm of Strange Quarks.* New York: Springer-Verlag, 2000.

Gribbin, John. *Q is for Quantum: An Encyclopedia of Particle Physics.* New York: The Free Press, 1998.

Ne'eman, Yuval, and Yoram Kirsh. *The Particle Hunters.* Cambridge, UK: Cambridge University Press, 1996.

Silverman, Mark. *Probing the Atom* Princeton, NJ: Princeton University Press, 2000.

### Other

Kalmus, P.I.P. "Particle Physics at the Turn of the Century." *Contemporary Physics* 41 (2000):129–142.

Lambrecht, Astrid. "The Casimir Effect: A Force From Nothing." PhysicsWeb. Sep. 2002 [cited Feb. 14, 2003]. <http://physicsweb.org/article/world/15/9/6>.

K. Lee Lerner

Larry Gilman

Terry Watkins

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