Can anyone explain this preprint physics paper for FTL travel?

Question

I'm writing a Science Fiction tale, and I am trying to get something together on the FTL physics involved in the story.

By chance I came across this paper, "A General Local Causality Principle of Space-Time", a preprint, by Colombian astrophysicist B. Calvo-Mozo.

From what I understand ;), he refers to various velocity regimes c1, c2, c3, …, where c1 is subluminal and c2, etc., are superluminal/FTL. The first FTL, c2, is 5.2E26 c; which is -- I'm sure you will agree -- truckin'.

I'd like to use this in my story, but don't understand the transition from one regime to another, i.e., c1 to c2, etc. He mentions a discrete something, whatever that means. Could anyone explain in plain English, please?

Answer 1

As objects with mass are acted upon by force they increase their velocity, as their velocity becomes relativistic, ie begins to approach the speed of light, for every incremental gain in velocity an increasingly large force must be imparted - more and more energy.

This process goes on indefinitely, the object's mass increasing slower and slower according to the Lorentz factor:

$$\gamma = \frac {1}{\sqrt{1 - v^2 / c^2}}$$

This means that no matter what increments of energy are added, the speed of light is never achieved, just an increased fraction of the speed. Somewhat like Zeno's paradox of Achilles and the Tortoise :

Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Supposing that each racer starts running at some constant speed, one faster than the other. After some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say 2 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere the tortoise has been, he still has some distance to go before he can even reach the tortoise.

The paper seems to go about saying that to bypass the need for an infinite amount of energy to be added, resulting in a continuum of change but never reaching $c$, a discrete (ie. finite) change would need to occur pushing the object from sub-luminal speeds to super-luminal ones. The author then goes on to fudge lots of different mathematical concepts and techniques to endeavour to demonstrate a self consistent logic to model what happens. (At no point is it suggested that a way has been found to make it happen, but he does reference Alcubierre at one point to add to the credibility of the argument).

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Edit to add:

I neglected to mention that one upshot of the theory is that in the process of becoming super-luminal the object takes a vector (unspecified) in a second time-like dimension. (The practical upshot of this is not discussed, but could lead to some very strange effects both in Super-L travel and when returning to sub-lightspeed).

The three spatial dimensions seem to have been preserved, in fact the inversion of the Lorentz factor at super-luminal speed would indicate that the faster you go, the more the spatial compression (maybe temporal compression too) and increase in mass that occurred as light-speed was approached from the other side would be negated.

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Another possible inference is that during acceleration after passing the super-luminal barrier, the object would shed photons - starting at the highest frequency gamma end and decreasing with increased velocity. A civilization like ours would perceive a streaking flash from high to low energy photons (ie. from gamma through x-ray then blue through the visible spectrum, infra-red, then radio to background noise).

Slowing down in super-luminal velocity mode could produce the opposite effect. Exiting from super-l to ordinary space-time constraints would require the same input of infinite energy or a "discrete" shift. It's a sort of mirror effect to special relativity. Weirdness again.

Addendum.

Personally, I thought the paper was absolute nonsense - it introduced irrelevant variables purely for the purpose of justifying the equations (and one which is completely fantastical quite early on). The math is not consistent with math as we know it, it frankly seems like a "mock-up" by physics graduates to use as a joke on undergrads. It didn't offer anything substantial regarding a new understanding.

Answer 2

One of the first rules of writing science-fiction is to never explain more than you know. Remarks in your question indicate you're are not a scientist, or if you are you're not a physicist.

The simplest explanation, the one I can derive from a cursory examination of the paper, is that a material object might pass from the subluminal velocity regime to the next superluminal velocity regime not by changing its velocity continuously, but could do so in a jump.

In science-fiction terms, assume a spaceship accelerates to a velocity very, very close to lightspeed it will reach a point where its velocity is high enough and its velocity will change from a subluminal velocity into a superluminal one. Crudely put, the spaceship "jumps" over the lightspeed barrier. One moment it is moving at a subluminal velocity just below lightspeed and the next it is traveling at a superluminal velocity just above lightspeed. The top speed is this superluminal velocity regime is 5 x 10^26 c.

The energy requirements to do so are unthinkably colossal. But you're writing science-fiction, so you can to ignore them or not.

PS: The more scientifically minded WBers will undoubtedly want to excoriate my simplified explanation. But this is it in simple language.