I'm reading this article (the link is to the PDF file), and I got stuck on a detail right away.(adsbygoogle = window.adsbygoogle || []).push({});

There's a clock at A and a mirror at B. We want to measure the distance L between A and B by measuring the time it takes a light signal to travel from A to B and back. The mass of the clock is m. Its position is represented by a wave function spread out over an interval of length dL. (Pretend that space is one-dimensional). The article claims that in the time that it takes a photon to travel from A to B and back, the clock's wave function will have spread out further, so that the width is now dL+(hbar*L)/(mc*dL).

Appareantly this is something that Wigner proved in 1957. I don't see how to obtain this result. Am I missing something simple?

I assume that we can take the wave function to have a gaussian shape (exp(-ax^2)), but how do we find how much the width has increased in a certain time? I suppose we should have a time evolution operator exp(-iHt) act on this wave function, but I don't see a way to simplify the result. I'm hoping it's just because I haven't been doing this sort of thing in a while.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How much does the uncertainty in position increase with time?

Loading...

Similar Threads for much does uncertainty |
---|

A Does the Frauchiger-Renner Theorem prove only MWI is correct |

A In what sense does MWI fail to predict the Born Rule? |

I What does this equation for a free particle mean? |

I Does quantum physics predict all isotope decays |

**Physics Forums | Science Articles, Homework Help, Discussion**