This is a fascinating speculation. A few ideas to throw into
It doesn't make sense to transport raw information. Information is
carried by particles. The way the experiment was described, it sounds
like matter could and would traverse the time loop.
As I understand the physics, spacetime must be consistent. There can be
no paradoxes. The future which sends the message is a future whose past
received the message. As others have pointed out, this can in principle
provide virtually infinite computing power, although I believe to make
it work you have to set up near-paradoxes and eventually you are limited
by the reliability of the system. Hans Moravec wrote an article on this
in Extropy many years ago.
The original article noted that the conventional wisdom is that if you
set up closed timelike paths (i.e. time loops), virtual particles can
follow them and become amplified each time around. A beam of radiation
spontaneously appears and destroys the apparatus. We had some discussion
here in the past on Wormhole Wars, where the idea is to collapse the
enemy's wormhole network by adding wormholes to induce time loops.
However I think the predictions along these lines are restricted to
specific geometries and there is no proof that it would happen to all
possible time machines.
Even if it worked it doesn't necessarily mean that once you set it up,
the entire future has access to you. If you run it for a day then only
messages from that one day can reach you. However if and when these
things become common enough then messages from the distant future can
reach pretty far into the past, close to the time of the first machine,
via indirect relay and cultural effects.
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