# 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:** 9\ **Page:** 4
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [July 8, 2013, 4:13am UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/61 "2013-07-08T04:13:02Z")
> [@Half\_Man\_Half\_Wit](#): > > The vacuum in SR is Minkowsky space, and in that space, light propagates at c; if you introduce the Casimir plates, you really just create a different vacuum, in which light may propagate faster. The Casimir vacuum isn’t really ‘vanilla SR’ anymore, and that you can obtain a different speed for light might not be any more shocking than the same thing happening in a non-inertial frame of reference. (But I’m not really sure about this point.) I think it becomes a question of causal structure, [this paper](http://arxiv.org/pdf/gr-qc/0107091) suggest that, assuming the Scharnhorst effect leads to signal velocities greater than c, then the ‘Scharnhorst photons’ have spacelike worldlines in Minkowski spacetime, i.e. they are like classical tachyons. As the paper points out, relativity can handle tachyons, however if you allow tachyons the relationship between causality and causal structure is weakened. In order to show that, under their presumptions, the Scharnhorst effect doesn’t lead to causality violations they define an effective metric on the region of Minkowski spacetime described by the Casimir vacuum that preserves the link between causality and causal structure and show that it obeys a fairly strong causality condition. So it seems that you can still describe the Casimir vacuum using a Minkowski spacetime background as the underlying theory is Lorentz-invariant, but as the Casimir vacuum itself isn’t Lorentz invariant, in some ways Minkowski spacetime isn’t necessarily the best background to describe it. > [@](#): > > The speed of light in (Minkowski) vacuum in QED must equal c, because you put it into the theory by construction; likewise, the speed of gravity, if gravity is described by a relativistic QFT (or some generalization true to the same principles, like string theory) must be c. That’s because all effects at spacelike separation commute, which is an assumption you include into the theory from the start. Some of the issues for these kind of quantum gravity theories are similar due to non-background independence. In this approach you have spacetime A + quantum field ≈ spacetime B where spacetime A is the background spacetime and spacetime B is a spacetime obeying the Einstein field equations. But the causal structure will be that of spacetime A rather than spacetime B. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [July 8, 2013, 4:24am UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/62 "2013-07-08T04:24:21Z")
> [@ZenBeam](#): > > You’re not correctly distinguishing between c and the speed of light here. The Lorentz equations use **c**. Light propagates at **ls** , to use **Francis Vaughn** ’s notation. > > You can’t just assume c = **ls** here, because that is what we are questioning. Perhaps the correct answer is **ls** = c \* (1 - 1e-30), but you’re currently unable to measure that difference. Your precision isn’t good enough to distinguish between c and **ls**. 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. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [July 8, 2013, 5:27am UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/63 "2013-07-08T05:27:54Z")
> [@ZenBeam](#): > > You’re not correctly distinguishing between c and the speed of light here. The Lorentz equations use **c**. Light propagates at **ls** , to use **Francis Vaughn** ’s notation. I was using c in the sense of the parameter appearing in the Lorentz transformations, and ‘speed of light’ otherwise. The constant c is simply a consequence of the spacetime geometry, which we change due to introducing the Casimir plates (though I haven’t read the paper **Asymptotically Fat** provides, which perhaps offers a different perspective; but even there, it appears it’s not that light in the Casimir vacuum travels at a speed closer to its ‘true’ speed, but that it becomes tachyonic when described in Minkowsky space). 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. > [@](#): > > 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. > [@Asympotically\_fat](#): > > I think it becomes a question of causal structure, [this paper](http://arxiv.org/pdf/gr-qc/0107091) suggest that, assuming the Scharnhorst effect leads to signal velocities greater than c, then the ‘Scharnhorst photons’ have spacelike worldlines in Minkowski spacetime, i.e. they are like classical tachyons. As the paper points out, relativity can handle tachyons, however if you allow tachyons the relationship between causality and causal structure is weakened. Interesting, thanks for pointing out the paper, I’ll have a look later. However, I would have thought that tachyons are far more problematic in QFT than they might be in SR, because you can then always lower the total energy by tachyon emission, thus leading to an unstable vacuum. And in SR, any tachyon should have a non-zero, though imaginary, mass, no? So a tachyon of zero mass should always propagate along lightlike worldlines. So, does there emerge some effective imaginary mass in such a case? ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [July 8, 2013, 5:49am UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/64 "2013-07-08T05:49:15Z")
> [@Half\_Man\_Half\_Wit](#): > > Interesting, thanks for pointing out the paper, I’ll have a look later. However, I would have thought that tachyons are far more problematic in QFT than they might be in SR, because you can then always lower the total energy by tachyon emission, thus leading to an unstable vacuum. And in SR, any tachyon should have a non-zero, though imaginary, mass, no? So a tachyon of zero mass should always propagate along lightlike worldlines. So, does there emerge some effective imaginary mass in such a case? This footnote covers this: > [@Stefano Liberati](#): > > This result [for tachyonic fields] also holds quantum mechanically where canonical quantization requires equal-time commutators to vanish, which then extends via Lorentz invariance to vanishing of the field commutators everywhere outside the light cone; thus quantum mechanically the signal speed is also limited to c. For field-theoretic “tachyons” with canonical kinetic energies it is not causality that is the problem, rather it is the issue of the instability of the field-theory ground state that leads to difficulties. Note that for the Scharnhorst photons we are chiefly concerned with in this article, one-loop quantum effects modify the kinetic energy terms so that they are not canonical; this shifts the characteristic surfaces, and so shifts the signal speed so that it is no longer equal to c. > **[Faster-than-c signals, special relativity, and causality](https://arxiv.org/abs/gr-qc/0107091)** > > Motivated by the recent attention on superluminal phenomena, we investigate the compatibility between faster-than-c propagation and the fundamental principles of relativity and causality. We first argue that special relativity can easily accommodate... ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [July 8, 2013, 4:09pm UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/65 "2013-07-08T16:09:33Z")
> [@Bremidon](#): > > Thanks guys. I was aware that the question is subtle, and I agree that the tests are worthwhile; I just was surprised at how often I run across tests of this nature. For this test in particular (photon mass), you can see the [current limits here (PDF)](http://pdg.lbl.gov/2012/listings/rpp2012-list-photon.pdf). The upper limit is around 27 orders of magnitude below the proton mass and comes from spacecraft-based studies of how the solar wind responds to the ambient magnetic fields. (A massive photon would modify the magnetic effects.) ---
**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… ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [July 9, 2013, 4:36am UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/67 "2013-07-09T04:36:21Z")
> [@ZenBeam](#): > > 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. I think in this context I would describe special relativity as providing the symmetry of the background to both classical and quantum theories. I mentioned Maxwell’s equations specifically because of the lack of an explicit assumption that c is the invariant speed, however ‘c’ (as the speed of a photon in a Minkowski vacuum) can be back-derived from the quantum equivalent QED. The precise meaning of “a speed of a particle” is altered due to the differences between classical physics where particles always have well-defined trajectories and quantum physics where it is not necessary to assume that they do. It’s clear though that in QED “the speed of a photon in a Minkowski vacuum” = “the invariant speed” and this comes from the assumption of Lorentz invariance. This is hardly surprising as the assumption of Lorentz invariance of classical electromagnetism is the same as the assumption that there must exist an invariant speed which is equal to the speed of light in a vacuum. Of course you’re not wrong that the existence of an invariant speed is independent of light travelling at that speed, though if light did not travel at that speed then it’s speed would be variable so there would be no constant light speed to measure. Therefore a direct measurement of the speed of light compared to a direct measurement of the invariant speed can only falsify that light travels at the invariant speed or in other words in the absence of 100% precise measurements you cannot prove 100% that the speed of light is invariant. That said the sum total of the evidence puts an incredibly small upper bound on the mass of a photon and the deviation from an invariant light speed. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [July 9, 2013, 5:15am UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/68 "2013-07-09T05:15:51Z")
> [@ZenBeam](#): > > 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. But if that’s the case (which is of course logically possible), then the only way to be consistent with QED is for the photon not to be a mass zero particle in Minkowski space. > [@](#): > > 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: Yes, my interpretation of the effect back then was somewhat muddled. I was speculating that the changed ‘vacuum’ the neutrinos see while travelling through matter could enable them to propagate faster than c (in this, I [wasn’t alone](http://arxiv.org/abs/1109.5411)), and used that faster speed as a baseline; I no longer think that made good sense. ---
**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 9, 2013, 11:36pm UTC](https://boards.straightdope.com/t/all-calculations-are-off/662773/69 "2013-07-09T23:36:32Z")
Any particle’s speed, even a massive one’s, will be a good approximation of c provided that the particle’s energy is much greater than its mass. For the current experimental bounds on the photon mass, and for photon energies typically used in experiments, the speed of light is at least an excellent approximation to c. [Previous page](https://boards.straightdope.com/t/all-calculations-are-off/662773.md?page=3)