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Considering photons only travel at the speed of light (and cannot travel faster), our main technique of digital communication (at least I believe, but I could be wrong) is off the table.
What techniques are being investigated for digital superluminal communication? Would these techniques be applicable to space missions where communication lag is significant?
Currently, no techniques exist to send information faster than the speed of light. However, there are some theories:
From the Wikipedia article on the subject:
According to the currently accepted theory, three of those four phenomena do not produce superluminal communication, even though they may give that appearance under some conditions. The third, tachyons, arguably do not exist as their existence is hypothetical; even if their existence were to be proven, attempts to quantize them appear to indicate that they may not be used for superluminal communication, because experiments to produce or absorb tachyons cannot be fully controlled.
If wormholes are possible, they could be used to transmit information:
If wormholes are possible, then ordinary subluminal methods of communication could be sent through them to achieve superluminal transmission speeds. Considering the immense energy that current theories suggest would be required to open a wormhole large enough to pass spacecraft through it may be that only atomic-scale wormholes would be practical to build, limiting their use solely to information transmission.
There is some small possibility that quantum entanglement would achieve the desired effect:
some argue that superluminal communication could be achieved via quantum entanglement using other methods that don't rely on cloning a quantum system. One suggested method would use an ensemble of entangled particles to transmit information, similar to a type of quantum eraser experiments. As the quantum eraser experiments rely on a classical, subluminal channel for coincidence detection, it is unclear whether superluminal communication would be possible by this method. Physicist John G. Cramer at the University of Washington is attempting to replicate one of these experiments and demonstrate whether or not it can produce superluminal communication.
Therefore, we currently don't have any means of superluminal communications, but there are theories. If we can create a wormhole (very unlikely anytime soon), then it would be possible...
