That's only true in special relativity. In general relativity where you are dealing with the expansion or warping of space this constraint is not there globally. For example, objects that recede past our cosmic event horizon are moving away from us faster than the speed of light, but only because the space between us is expanding such that it appears that way. Locally nobody is traveling faster than light, but on a global scale this is essentially what is happening. That is why we have a cosmic event horizon. However the necessity of exotic matter, as alluded to in a previous comment puts a dampener on the whole thing sadly.

If I recall cell phones operate somewhere between 0.8 - 3 GHz. This is a wavelength range of 10cm - 37cm. Not entirely small. Additionally the only likely effect would be some localized heating which is more than easily compensated for by our body's natural ability to dissipate and regulate heat.

If I recall correctly CPT presumes the correctness of Lorentz invariance. And Lorentz invariance is one of the bedrocks of relativity. In other words CPT comes about from assuming your theory is Lorentz invariant and if CPT were violated it would mean Lorentz invariance is violated as well (check out Physical Review Letters 89: 231602 by Greenberg, O.W, which shows CPT violation implies Lorentz violation).

Some replies: 1)This is basic quantum physics. The energy of a photon depends upon its frequency. Simple as that. Microwave photons in any quantity just don't have enough energy to ionize anything. The highest frequency I can think of for a cell would be around 2700MHz. That means the energy of 1 photon is only about 1e-5 eV. 2)Regarding the heat effects: The minuscule heating that would result from a cell phone (these aren't exactly things that carry lots of power, often less than 3 W) will fall off as you go into the body following a skin-depth relation. Any heating from these is going to be small compared to that of a heat press. Yes one is outside but given the much larger amount of thermal radiation it throws off you'll get more heating deeper than a cell phone. Indeed the primary heating is going to be on the surface of the skin right by the phone and that is shown to be far less than heating that occurs from just being out in the sun. 3)A molecular resonance would be the last likely thing to remain, however if it were likely to happen then it should happen to everybody and mess things up. Overall if this effect was present and causing problems (indeed any problems) then given the rapid rise and prevalence of cell-phones now if they caused cancers we'd expect to see a large uptick in brain cancer rates. The rates have remained more or less flat as far as I've ever seen. There just doesn't seem to be any physics based reason to expect cell phones to cause problems based on what what is known. I suspect the study will confirm that, but I guess it is good to check because as said our knowledge is not ever 100% correct. If they were to show an effect then I'd be curious to know what the mechanism was because the most likely ways (above) are easily ruled out.

Cannot break apart molecules. How exactly would an electromagnetic wave that can't ionize anything cause cancer? Usually to cause a cancer from radiation you need to cause some sort of ionization damage as far as I'm aware. Physics quite strongly says that these microwaves do not have the proper energy to do this, even if you have a lot of them. People can go on about 'heating effects' which is a common response I see to the non-ionizing radiation bit, but if that were the case, prolonged exposure to heat packs should also cause cancer. Luckily the body is quite good at dissipating heat. Based on physics there is no plausible mechanism for a cell phone to cause a cancer. The radiation just isn't energetic enough to break any bonds, and that is what counts.