Furthermore, I imagine it would be very easy for such a party to accidently blunder into a situation where they lose control of the time-messaging device, erasing all evidence of its own existence and leaving the timeline perturbation-free until such "time" as reverse time travel is rediscovered.
Anyway, it has only one hard "commandment": Nobody can violate causality anywhere inside its own historic light-cone, since doing so could be a potential attack (or competition) to its own existence.
Anyways.
This is touched upon by a favorite sci-fi story of mine, where humans come in possession of such technology and make huge leaps in capabilities in short timeframes. Those leaps are unexplainable to most alien species they are in contact with.
Especially later on in the books a huge part of the story is told from alien POVs. The author has some interesting ideas about how other species may find us impressive, and in what respects they may consider us primitive.
The books are mostly about on-planet fighting and some ship-to-ship battles though. In fact there's little politics and communication at all until the cold-war arc. So don't expect the books to dive deeply into it at all.
But I really recommend the books just for how many interesting ideas Evan Currie managed to compress into a fast-paced action story. They left me with a lot of stuff to mull over long after putting the books down.
1. the type of time travel in effect. I'll assume Marvel-flavor time travel, where going back is really jumping to a different universe that shares the same history till the arrival time. But if it's something more complicated then relaying info back might Marty McFade the prognosticator out of existence.
2. the level of information available to the prognosticator (future communicator). Is it near-total, so they could tell the recipient to "duck… now!" or is it just public info like stock prices, weather, and what's on the news?
Best case for the recipient is that for each change they make, they still have an ally relaying valuable info from the future that includes those changes. And also that said ally has near-total information to help protect the recipient.
Worst case for the recipient is that after they make one change, they are now in a timeline where their future ally no longer communicates with them. This is also the most detectable for others in the recipient's time because the recipient will likely make some big bets based on the one-shot info they receive, and won't have additional info to help avoid detection.
To continue the thought experiment: if you developed that technology in the year 2120, how would you use it, and would that be detectable in the year 2020?
Even ones without a TARDIS?
Any timemachine that produces self-consistent timelines (arrives at a fixed point after a finite amount of iterations) can be used to solve problems in PSPACE.[1]
[0] https://en.wikipedia.org/wiki/PSPACE [1] https://www.scottaaronson.com/papers/ctc.pdf
@Theophite: the existence of nonzero interest rates implies the nonexistence of time travel.
Essentially, if there were a system that could send information from the future to the past, the future agent would want to be "as discreet as" possible, while still achieving "nearly perfect" outcome. Note that the future agent has the advantage of reiterating over and over his/her choices, because, well, the "future-future" he/she can still send a signal to his/her past about want went wrong the previous time.
This happens to be a common plot for a lot of various time-travel movies and TV shows like Dark, Umbrella Academy, etc.
Bootstrapping the singularity is unlikely to be achieved with a single application of a time machine since you are only sending information to the past, not the technology itself.
And repeated application allows other actors to intervene during each iteration, which may result in the CTC settling into a different fixed point than the desired one.
You can't expect to own and use a time machine and be left alone while doing so.
Suppose you had a means of transmitting information back in time - a one-node network that effectively could email to itself with a timestamp (in the past) being the message's "recipient."
Suppose such a thing existed in the world today. Assume the individuals in possession of such a thing were very intelligent, very careful and very guarded about its use.
Could you still detect that such a thing existed by observing real-world events - stock market changes, tech innovations, amazing coincidences and the like? What evidence would you look for?