# All calculations are off?? **URL:** \ **Category:** Factual Questions\ **Created:** [July 6, 2013, 4:32am UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773 "2013-07-06T04:32:25Z")\ **Posts on this page:** 1\ **Showing post:** 66
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [July 9, 2013, 1:38am UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/66 "2013-07-09T01:38:12Z")
> [@Asympotically\_fat](#): > > Assuming the principle of relativity is the same as assuming that the invariant speed ‘c’ is the same the ‘c’ that appears in Maxwell’s equations. Those are both classical theories. It shouldn’t be surprising that there could be small quantum effects. I believe the most accurate measurements of C come from actually measuring the speed of light. To say C(invariant) = C(speed of light), you’d need highly accurate independent measurements of both. This reminded me that this question came up before, in the [Can neutrinos travel Faster Than Light](http://boards.straightdope.com/sdmb/showthread.php?t=625273&highlight=neutrino) thread. [I asked there](http://boards.straightdope.com/sdmb/showpost.php?p=14291355&postcount=119) how accurately Cinvariant had been measured, without assuming it was equal to Clight, but I never felt like I got a good answer. **Pasta** pointed me at [this Wikipedia page](http://en.wikipedia.org/wiki/Precision_tests_of_QED), but it wasn’t clear which measurements were really independent. (I suspect that page has been modified in the mean time, and it’s even less clear now.) > [@Half\_Man\_Half\_Wit](#): > > I was using c in the sense of the parameter appearing in the Lorentz transformations, and ‘speed of light’ otherwise. Then when you say > [@](#): > > The vacuum in SR is Minkowsky space, and in that space, light propagates at c […] > > The speed of light in (Minkowski) vacuum in QED must equal c, because you put it into the theory by construction you’re just assuming C = speed of light. Certainly they are very close to equal. But you can’t rule out a very small effect. [The arxiv paper](http://arxiv.org/abs/gr-qc/0107091) that **Asympotically fat** linked to agrees (C = the invarient speed, c = speed of light): > [@](#): > > To determine the actual value of C when a choice for clocks and rulers has been made is an experimental problem. We know that C coincides, to a very good accuracy, with the value c of the speed of light in a vacuum with no boundaries, so we shall set C ≡ c in the rest of this paper. However, one should always keep in mind that tiny deviations from this empirically established equality are logically possible. > [@Half Man Half Wit](#): > > But the speed light travels at in the Minkowsky vacuum is necessarily c. The only way it couldn’t, would be for it to have a nonvanishing mass, which would mean a frequency-dependent speed distribution, etc. It’s just a fact of geometry, and that fact is built into relativistic QFT from the outset (via the assumption that spacelike separated fields commute), which hence can’t produce a different prediction. > > > [@ZenBeam](#): > > > > You can’t just assume c = ls here, because that is what we are questioning. > > I don’t think it’s really consistent to interpret the Scharnhorst effect as questioning c = ls (in the Minkowsky vacuum). Rather, it says ls \> c in the Casimir vacuum, due to the energy density between the plates being effectively negative. I [found](http://boards.straightdope.com/sdmb/showpost.php?p=14290968&postcount=114) [someone](http://boards.straightdope.com/sdmb/showpost.php?p=14288831&postcount=98) in that Can neutrinos travel Faster Than Light thread who disagrees with you: > [@Half Man Half Wit](#): > > Using photons alone, the Scharnhorst effect is generally thought to be undetectable, and at least in the approximation used by Scharnhorst, **the vacuum refractive index doesn’t depend on photon frequency, so one would expect a uniformly lowered speed of light**. > [@Can neutrinos travel Faster Than Light](https://boards.straightdope.com/t/can-neutrinos-travel-faster-than-light/597266/97): > > How about the [Scharnhorst effect](http://en.wikipedia.org/wiki/Scharnhorst_effect) as a possible explanation? **It would essentially amount to photons travelling slower than c in vacuum because of a small vacuum refractive index due to vacuum polarization** , which the neutrinos wouldn’t see, so even with a small rest mass, they could conceivably travel faster than photons in vacuum; this would also be in line with the 1987A neutrinos being slower, i.e. closer to the photon speed, due to their lower energy… --- _[View the full topic](https://boards.straightdope.com/t/all-calculations-are-off/662773)._