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?