# 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 (Δp) and an uncertainty in position (Δx), and these two uncertainties cannot be reduced to zero together. Their product is given by Δp Δx > h/4PI, where h is Planck's constant (6.63 × 10-34 joules &NA; 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 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 ΔE 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 Δ E × Δt > 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