heisenberg uncertainty principle fourier transform

Uncertainty is defined as lack of certainty, not being able to make a decision on a safe basis.

Introduction When considering uncertainty, the following concept must be applied: Schroeder said that one of the fundamental consequences of uncertainty is the very size of atoms, which, without it, would collapse to an infinitesimal point. Note that you can also receive the articles in the form of a newsletter or with an RSS feed.1. You may link to this page and cite it, because its location is permanent. This article is a posting of the Photonics Spotlight, authored by Dr.

But before making too many enemies, including famous (dead) physicists, I stop the discussion at this point! The transform limit has essentially nothing to do with quantum mechanics (or quantum optics).Īnother question would be whether it was a good idea to call Heisenberg's uncertainty principle a principle. In conclusion, there is a vague similarity, nothing more. This cannot disguise, however, that essentially it is physics, making statements on nature, rather than mathematics. Heisenberg's reasoning does of course use quite a bit of mathematics, including properties of Fourier transform pairs. On the other hand, Heisenberg's uncertainty principle is a piece of physics, which was revolutionary at its time, and is still not accepted by everybody.The involved property of Fourier transform pairs (that stronger localization of one partner implies weaker localization of the other one) is a purely mathematical issue, which has been known for a long time and is in no way controversial.After all, we are dealing with two very different issues: Nevertheless, it is nonsense to claim that the transform limit for pulses is strongly related to Heisenberg's uncertainty limit. 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. 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. 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). Ref.: encyclopedia articles on transform limit, bandwidth-limited pulses, time-bandwidth product, Spotlight article of : 'Understanding Fourier Spectra' One should not confuse physics (statements on nature) with mathematics. The article shows that this is nonsense there is nothing more than a vague similarity. Rüdiger Paschotta, RP Photonics AG, RP Photonics AGĪbstract: It is sometimes claimed that the transform limit for pulses is strongly related to Heisenbergs uncertainty limit. Posted on as part of the Photonics Spotlight (available as e-mail newsletter!)Īuthor: Dr.

The Photonics Spotlight > Heisenberg's Uncertainty Principle and the Transform Limit

Heisenberg uncertainty principle fourier transform