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This question already has an answer here:

It is easy to send a message to myself in the future: I can put a letter in the post and will receive it tomorrow.

Can you think about a way to send a message to myself in the past; it does not need to be a complex message, only a bit of information would be enough.

Moreover, consider that money, physical resources, and manpower are infinite.

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marked as duplicate by Peter Diehr, user10851, CuriousOne, John Rennie, Qmechanic Jun 26 '16 at 10:25

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ If it was possible to send information even a very short time into the past then it would be possible to reliably predict the behaviour of financial markets for that window. Anyone who can do that can extract all the money in those markets. There is no real upper bound on the amount a market participant would pay to be able to do this. This has not happened, therefore no way of doing it is known to exist and it is strongly believed that no way of doing it is possible. $\endgroup$ – tfb Jun 26 '16 at 10:58
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    $\begingroup$ If there is a way of sending a message to the past that can be implemented any time in the future, we should be submerged by messages from the future. Or forced to imagine that either nobody in the future cares about our time (nobody at all, in the whole future!), or that our future is not very bright and ends before time-travel is discovered... $\endgroup$ – Stéphane Rollandin Jun 26 '16 at 19:29
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We don't believe this is possible. The justification for this belief is nothing less and nothing more than experimental observation. We have never observed a process where an effect comes before its cause, so we simply reason inductively to establish a postulate that the preferred order of events in physical processes is always the same, for any observer.

Indeed, it is this postulate that leads us to the conclusion that there is no physical inertial frame that travels at greater than $c$ relative to any other; as long as this is true, then relative motion cannot make event order observer dependent. On the other hand, if there were such a frame, one can always find a physical process whose events are reversed in time by the supraluminal boost.

See my answer here for more details.

See also the Einstein Tolman Paradox, also called the Tachyonic Antitelephone. This is almost exactly analogous to your scenario.

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