This excerpt from Heisenberg's original paper shows his derivation of the uncertainty relation for momentum and position.

Here Heisenberg transforms the "bell curve" in quantum theory for the imprecision in the measurement of the position q of a moving electron to the corresponding bell curve of the measured momentum p. The uncertainty, or standard deviation, of each curve is Dp=p1 and Dq=q1. Heisenberg obtains an equal sign for the minimum uncertainty. He later included the possibility of even greater uncertainty by using the sign for "greater than or equal to."


Zeitschrift für Physik, 43 (1927), 172-198, received 23 March 1927. The image is from the facsimile reprint in Heisenberg, Gesammelte Werke / Collected Works, vol. A1, p. 486.

Heisenberg's uncertainty paper has been translated into English by John Archibald Wheeler and Hubert Zurek, in Quantum Theory and Measurement, Wheeler and Zurek, eds. (Princeton: Princeton Univ. Press, 1983), pp. 62-84.


Triumph of the Copenhagen Interpretation


The Uncertainty Relations

More Info:

The Uncertainty Principle

The Gamma-Ray Microscope

Implications of Uncertainty

What Good Is It?

Heisenberg Speaking on the Origins of Uncertainty

Further Reading



About this Exhibit

1998 - American Institute of Physics and David Cassidy ()