This is a page I am currently working on which provides an alternate viewpoint concerning potential paradoxes which might occur with the use of a FTL communications system. The page is still in a rather rough state, and will no doubt benefit mightily from further editing. Nevertheless, I decided to include it as an unfinished thought for whatever value it may have at this point in its development. At the least, you can get a glimpse into the webpage development process, and to see what happens when the coffee supply gets too low...
A closer look at superluminal motion and time reversibility
When asked for a good reason why information can not propagate at faster than light speed, many scientists will mention an argument stemming from the deepest levels of Einstein's relativity theory, namely that having velocities equal to or greater than C, the speed of light, will break the maths used to derive solutions to the various formulas used in relativity. The main problem is visible to anyone with a basic algebra background. The Lorentz transformation equation (H.A. Lorentz, 1853-1928) for t', for example, is:
t' = γ (t- ( vx )/cē)
here's what each term in this equation represents:
t' (t prime) = the time measured by the observer moving with velocity v
t = the time measured by the stationary observer
v= the relative velocity between the two observers
x= the position of the event as measured by the stationary observer
c= the speed of light
γ =gamma= the Lorentz factor, defined as 1/ √(1-(vē/cē)
This transform works as long as the v term doesn't equal the speed of light, c. When it does, the answer becomes undefined due to division by zero in the Lorentz factor. When v is greater than c the Lorentz term becomes an imaginary number. This leads to time t' becoming an imaginary number as well. A common interpretation of relativity maths taken literally shows that for speeds exceeding the speed of light C, time runs in reverse and it is possible to go into the past. Never mind there is no physical evidence to back up this mathematical assertion... even so what's the problem? Who wouldn't wish for another chance to try things again? Rekindle a lost love, warn a loved one of impending disaster, or to simply go back to last week with the winning mega-lottery numbers?
Yes, well, that is one of the reasons you can't be allowed to upset the order of things. The universe forces us to live with the consequences of our decisions. Scientists have even gone so far as to give this grand order a name: causality. There is a cause, and then there is an effect. Never the other way around. Allowing an effect to come before its cause can lead to a paradox - for example, if you went back in time and killed your grandfather before he brought your father into this world, means you were never born. But if you are not alive, who then killed your grandfather? That is a paradox: a problem that seems to be true, yet attacks our common sense notion of how things should be.
In general relativity, it is an accepted notion that time is not an absolute. If the clock in your spaceship is moving at a fast enough speed relative to the clock in your brothers spaceship, they will measure different amounts of time. When compared later, it will be found that the faster moving clock has measured the least amount of time. Is this just a mechanical effect of clocks ticking at different rates? No. If your brother traveled very close to light speed for a significant amount of time, when he finally got back, you would see that the relativity effect also applied to his biological clock. While you had become a stoop shouldered, gray haired old man, whose high point of the day happens when the prune juice finally kicks in, you would see (if you still had good eyes) that your brother was still exactly like how you remembered him when you were kids of thirty - young, virile, and constipation free.
This cute example shows how time slows down as you approach the speed of light. What happens when you actually move at C (light speed) - Einstein showed that time would completely stop for the mover. This effect has actually been measured many times over the years, and is accepted as fact. For example, the lifetimes of unstable particles created in particle accelerator experiments increases due to the speed of their motion. Years ago, scientists actually flew ultra accurate, synchronized atomic clocks in fast moving aircraft and then compared times after the flights. The clocks showed time dilation due to both gravity and velocity effects (Hafele-Keating experiment, 1971). At the time, there was some controversy hovering around this experiment, because the actual data was hard to extract due to other factors which might have made the synchronization inaccurate. The experiment has since then been repeated many times and the results have been well confirmed.
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This is the paradox
most trundle out to show how impossible it is to either move or communicate
superluminally. In the case of FTL communicating devices, a straight forward
interpretation of the Lorentz transformation equation used in relativity theory
will mean at speeds where velocity v is greater than the speed of light c, time
t becomes negative. If you are using a superluminal communication scheme, for
example, in some reference frame that is relativistically accelerated with
respect to the home frame, it will be possible to experience the reception of information before it is
generated. This needs closer looking into. A good question to ask is "How may we
decide if a transmission we are listening to is indeed being sent from the future
in this manner?
There is no easy way to determine
this without having prior knowledge of the home frame, something which is not assumed in conventional information transfer theory so should
also not be assumed in superluminal information transfer frameworks. If we have
learned one thing from researchers running EPR style experiments where
superluminal entanglements have been demonstrated, it is this: You need a point
of reference to compare with or it is impossible to see if such a connection has
been made. In the case of EPR experiments, the researchers need to compare their
data at a later time at which point they are able to tell whether such a
connection has taken place or not. But, this is non-immediate. The only way it
can be immediate requires a God-like (omnipotent) perspective. If some god-like
third party is able to view both the sender and the receiver from his own
reference frame he may -or may not- see temporal reversibility, but this is not
a valid solution for the persons conducting the experiment because the third
party is outside the light cones of the individuals conducting the experiment,
and can not communicate his observations to them until a later time. This is a valuable insight
into future FTL schema: it can only be party to party, and not third party
without also admitting potential global causality violations. In my experiments, P2
probability wave generation does indeed satisfy this 2-party requirement, as
there is currently no method to allow a third party to directly influence
information flow without the use
of a remote access point, which by its very nature introduces a proportionate
time delay which keeps time positive valued. This is but one fundamental
difference between FTL 'radio' communications and conventional radio
communications, and also points out why the term 'radio' is not an appropriate
adjective to use with superluminal communications.
There are only two major solutions to the so-called paradox of global causality violation owing to temporal effects:1) Negative values for transform results while valid mathematically, are a phenomenologically disallowed state in reality, or, 2) because of the limitations of physical processes, even if experimenters are communicating superluminally, they will never be in a position to observe causality violations caused by their own actions. Either way, if you can never see causality being violated by your own actions, it is a meaningless exercise to consider anything you do is not allowed by present theory.
If you've already read the FTL Working Group's paper on EPR Kindred Methodologies a couple sections above, you already know where I am going with this. You'll understand that the communication devices themselves aren't altered by relativistic effects. However, the superluminal pipeline linking them together is sensitive to changes in dynamic, non-inertial frames of reference. It may seem like you can communicate with the future or past, but you're actually connecting to a time-shifted alternate reality. The larger the temporal displacement, the more these realities will differ from yours. While this non-local effect could be a fascinating research topic, it poses a problem for superluminal communications. As data integrity is crucial, interference from alternate realities could eventually make meaningful communication unfeasible. When it comes to communications on Earth, the impact of non-local relativistic effects is likely to be negligible. However, the situation becomes more complex when faster-than-light (FTL) communicators are used over interplanetary distances.
In the "Kindred Methodologies" paper, I examined the 14 millisecond time-shift that occurs when an FTL communications device is placed inside an orbiting GPS satellite for a year. Imagine trying to establish a connection from a station on Earth to one on the Moon, Mars, or even further away - these relativistic non-inertial effects accumulate over time. Fortunately, there's a straightforward solution. After a certain period, the FTL communication pipeline needs to be reset. This can be achieved by periodically disconnecting and reconnecting the system. Just as rebooting a computer from time to time can help maintain its performance, FTL communicators will need to be managed in a similar way. This practice will ensure their continued optimal operation.
This phenomena might eventually introduce distance limits of a kind on FTL super-communication. Eventually, this brand of relativistic distortion might involve rebooting the FTL pipeline so often that it approaches the working limits of our electronics circuitry. The ultimate limitation will be when the time to do a re-set approaches the time needed to establish a FTL link... and, honestly, at this time I have no idea how fast that is. I feel comfortable in saying my device will cover the Milky Way Galaxy at least - as long as you stay away from high gravity objects such as neutron stars and black holes, or relativistic speeds. For FTL happiness, the mantra will be to keep relativity to a minimum...