# Least and most uncertain Physical constants

**URL:** <https://boards.straightdope.com/t/least-and-most-uncertain-physical-constants/693696>\
**Category:** Factual Questions\
**Created:** [July 21, 2014, 10:14pm UTC](https://boards.straightdope.com/t/least-and-most-uncertain-physical-constants/693696 "2014-07-21T22:14:01Z")\
**Posts on this page:** 3\
**Page:** 2

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**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\
**Post date:** [July 24, 2014, 1:22am UTC](https://boards.straightdope.com/t/least-and-most-uncertain-physical-constants/693696/21 "2014-07-24T01:22:49Z")

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> [@Chronos](#):
>
> If it were massless, how could it take part in oscillations? Neutrino oscillation has a characteristic frequency to it, but massless objects are timeless.

If I’m not mistaken neutrino oscillation is a function of the difference between the squares of the neutrino masses, so a massless neutrino can oscillate with a massive one.

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**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\
**Post date:** [July 24, 2014, 2:03am UTC](https://boards.straightdope.com/t/least-and-most-uncertain-physical-constants/693696/22 "2014-07-24T02:03:25Z")

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> [@Chronos](#):
>
> If it were massless, how could it take part in oscillations? Neutrino oscillation has a characteristic frequency to it, but massless objects are timeless.

A neutrino with a definite mass (be it zero or finite) does not oscillate. Only superpositions of mass eigenstates oscillate.

> [@](#):
>
> But assuming there’s an answer to that, this isn’t a nit, and it does affect my point

I meant it doesn’t affect your larger point that one is free to pick a different metric for a quantity of interest and thereby change the apparent fractional uncertainty.

I offered the more run-of-the-mill mapping in the hopes that it was more intuitive pedagogically to the OP than one constructed specifically to yield infinite errors. (Also, a proper statistical treatment of a quantity that may or may not be infinite is non-trivial.)

> [@Andy L](#):
>
> If I’m not mistaken neutrino oscillation is a function of the difference between the squares of the neutrino masses, so a massless neutrino can oscillate with a massive one.

You are not mistaken.

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [July 24, 2014, 10:00pm UTC](https://boards.straightdope.com/t/least-and-most-uncertain-physical-constants/693696/23 "2014-07-24T22:00:51Z")

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Ah, right, even if nu\_1 is massless, nu\_e (which appears to be a mixture of roughly equal parts nu\_1 and nu\_2) will have a nonzero expectation value for its mass. It still doesn’t sit right with me, but I’ll have to give it some more thought.

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