Is it possible to send messages backwards in time? This may actually be a testable hypothesis today. Here is a possible way to test it. Let's assume this is possible and that at some point in time in the future, humans on earth develop this technology. We can test whether or not this actually will happen in the future by constructing a suitable receiving device now, and making its presence known in the global digital landscape such that it becomes part of the historical record. In the future, if and when suitable technology is developed, the inventors at that time may discover the existence of our device in their past and then may attempt to send a message back in time to our device. Of course, if they are smart they will send us instructions to make a better receiver, and possibly even a transmitter. That would get interesting! Similar ideas to this have been proposed by others, including Jack Sarfatti. My approach is as follows:
1. Construct the receiver device. This device needs to be designed such that it could be receptive to potential messages from the future. For example, it could be a highly ordered crystal lattice, or a sensitive measuring device that could detect any changes to a local region of space (such as the temperature of something or the local physical constants or topology of a small area). The challenge is to construct a system that can do this. It would take a lot of thought to come up with the right type of receiver.
2. We then publicize the location of the Receiver in digital online media and the press. This is to ensure that it becomes part of the historical record, so that in the future, anyone searching for "faster than light communication" or "communicating backwards in time" will find our information and learn enough about the receiver to send us a message.
3. Then we just wait and see what happens. If we are lucky, we might receive a message right away. Maybe it will take a while. If we never receive a message we can conclude that either (a) Humans destroyed themselves in our future and there is nobody left to send the message, (b) Humans (or some form of suitably intelligent lie) exist in the future but never develop the technology for sending messages backwards in time, (c) Intelligent beings exist and do develop such technology in the future, but our physics was wrong and they can't communicate without our Receiver, (d) Suitably intelligent beings do exist in our future and they do have the technology but for some reason they cannot or will not send us a message (perhaps safety, or the Prime Directive, or fear of changing their own past in uncontrolled ways).
Now the physics of this proposal could be changed -- for example, perhaps there is a better way to construct a receiver. For example, use a satellite and enable it to receive optical messages from some location nearbye for example, or from Earth. But in any case, the basic design of this project could work. But only if widely publicized -- otherwise what is the chance that a future civilization will find out about it and try to make contact?