The applicable limitation here is utility. Broadly speaking, utility means that the invention must have some practical use. As described, the invention does have a practical use, which is “to transmit and receive electromagnetic waves”. That the waves allow faster-than-light transmission of information is not intrinsic in the workings of the invention. The invention may be worthless from a business perspective if it only allows traditional light-speed transmission, but that is solely the applicant's problem — if he wishes to squander his resources on an invention that is inferior (in a business sense) to other known methods, he may. So to my non-legal eye the patent doesn't seem to be dismissable on these grounds.
A further requirement is that the wording of the patent must enable a reader skilled in the art to reproduce the invention. Since the claimed conclusion that the communication signal travels faster than light is not inherent in building an apparatus that embodies the method, the patent is not invalid on these grounds alone.
I am not qualified to judge whether the technical terms used in the claims (such as “accelerator”, “injection point”, etc.) are defined sufficiently precisely in the description.
Some patent offices (I'm not sure about the US) do systematically refuse inventions that clearly require perpetual motion. However, in general, it is not the job of patent examiners to judge whether a claimed invention contradicts the known laws of physics. This is especially true as, while a newly discovered law of physics is not patentable, an invention that makes practical use of a hitherto unknown law of physics would be patentable.
In any case, there is a loophole in the claim wording:
thereby sending and receiving the communication signal at a speed faster than a known speed of light.
A known speed of light — which could be the speed of light in a medium with a high refractive index. Admittedly, this medium would be the “new dimension” that is mentioned in the background but not in the description of the preferred embodiment — the interpretation would take some work to defend.