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The Photonics Spotlight

Heisenberg's Uncertainty Principle and the Transform Limit

Posted on 2008-06-13 as a part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2008_06_13.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Abstract: It is sometimes claimed that the transform limit for pulses is strongly related to Heisenbergs uncertainty limit. The article shows that this is nonsense; there is nothing more than a vague similarity. One should not confuse physics (statements on nature) with mathematics.

Dr. Rüdiger Paschotta

Ref.: encyclopedia articles on transform limit, bandwidth-limited pulses, time–bandwidth product, Spotlight article of 2007-10-11: "Understanding Fourier Spectra"

Optical pulses are subject to the well-known transform limit: for a given pulse duration, there is a minimum spectral bandwidth (width of the Fourier spectrum). This limit is sometimes connected with Heisenberg's uncertainty principle, saying (in one form) that the more well-defined the time of some process is, the bigger the uncertainty on the involved energy transfer.

This does sound somewhat similar, taking into account that energy is related to frequency in quantum mechanics, and Fourier transform pairs are involved in both cases. Nevertheless, it is nonsense to claim that the transform limit for pulses is strongly related to Heisenberg's uncertainty limit. After all, we are dealing with two very different issues:

In conclusion, there is a vague similarity, nothing more. The transform limit has essentially nothing to do with quantum mechanics (or quantum optics).

Another question would be whether it was a good idea to call Heisenberg's uncertainty principle a principle. But before making too many enemies, including famous (dead) physicists, I stop the discussion at this point!

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the Encyclopedia of Laser Physics and Technology.

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