Hard SF : SF Tech Issues : Instantaneous Interstellar Communication
By the end of the book Ender's Game, instantaneous interstellar communications becomes essential to the story. This is stretching things very far. We are not only talking about faster than light communication (which current science suggests is impossible), but communication at infinite speed (much less likely). Even if one could manage to create this for comparatively short distances, it is questionable whether power requirements and other issues would allow it to be practical at interstellar distances.
There is one thing in physics that is believed to be able to take place instantaneously – even over vast distances. Quantum physicists believe that two particles that have been associated in the past can be "entangled". In this case, a change in the properties of one of the particles can instantly have an effect on the other particle regardless of their distance. However, other quantum effects make it necessary to use more than just the two entangled particles for us to make sense out of any messages sent between those particles. Understanding the message requires we send additional information by some means other than quantum entanglement – and that other means will not be instantaneous. Therefore, if you want to know what the message says, the entire process will take at least the time required by other means. See: Quantum Entanglement
The alternatives would depend on us having some form of energy that can be controlled and manipulated that travels over vast distances instantaneously. We don't know of any such thing at present. Current scientific theories suggest it is not possible. For instance, current theory may permit the existence of faster-than-light tachyons, but the same theories indicate we could not manipulate tachyons into meaningful messages. This suggests message-capable faster than light energy is not a realistic speculative extrapolation of any well-founded science. It's basically wishful thinking.
A nearly instantaneous communications could be implemented if / when wormholes can be used to connect distant locations. That would allow slower than light signals to travel an effectively short distance through a short-cut to a destination that would otherwise be far away. Although many physicists believe wormholes could exist, it is not an established fact. Again, making practical use out of wormholes would involve additional issues that make their actual use very uncertain. See: Wormholes
Even this I might have turned a blind eye towards. But in Ender's Game this kind of communication is managed by the bodies of the aliens, whose biology we are told is not that different than our own. So one can ask how a more-or-less human-sized body of a being not so different from humans could control the power requirements and forces to send instantaneous interstellar messages. An organism is essentially a complex network of chemical reactions. Chemical activity has a limited potential power output and will only implement forces of nature that operate at scales going from whole atoms to large molecules. It is highly doubtful there are any such forces that we are not aware of, can operate at those limited power levels and can produce such extraordinary results - and not harm the organism in the process.
The book never says how this form of communication functions or give any clues for deducing how much energy / power would be needed to send a message. However, it may be helpful to try to give some perspective. A human athlete running a mile in 4 minutes burns calories at a rate that can be expressed as about 2500 watts. (A human body can maintain a higher wattage for a shorter period of time, but this seems to give a general idea for the greatest possible body wattage.) Compare this to the wattage of commercial radio stations trying to broadcast to people on the same planet. The body's wattage does not sound as if it would be capable of more demanding communications tasks.
Perhaps there is an important part of Ender's Game that would not have worked without this contrivance, and perhaps that might justify it in this book. I would strongly recommend it is a contrivance to be avoided whenever possible and whenever one does not have a very good benefit flowing from its use.
Let's assume you have an instantaneous interstellar communications system. It doesn't send signals down telephone wires, so how does the message get from one place to the other?
If you had some way to know the exact location of the person you were sending the message to and assuming your system involved a type of energy that could be focused into an extremely tight beam, you could encode the message in a beam. The beam could go to that person and nobody else. However, knowing the other person's position that precisely is not realistic unless perhaps if the other person is on a spaceship flying on a straight line directly towards or away from your position. If the other person is on a planet or space station orbiting in another star system, he will be constantly moving relative to you. At interstellar distances, it wouldn't be realistic to pinpoint a single individual in motion. Perhaps you could judge his position closely enough to send a beam that would be received in an area of a few kilometers, but we're not really talking about a signal that will only be picked up by one person.
If you had separate wormholes connecting you to every person you might want to send a message to, you could send the message through the appropriate wormhole for the desired recipient. This could be rather cumbersome and depends on practical use of wormholes. There are many potential issues with trying to use wormholes – see Wormhole article. Sending something through a wormhole will not by itself necessary make it literally instantaneous – it may be necessary to have some new kind of instantaneous signal to send through the wormhole. We can't entirely exclude the possibility, but this is a doubtful solution.
But the most plausible means of long-distance communications is by sending out some sort of energy waves (for instance, radio waves). The problem with this is that this sort of communication means everyone receives the signal. Assuming this is not some secret government device only used by a handful of people, over interstellar distances this means everyone will probably be surrounded by messages from millions of other people. Even assuming each message includes some indicator of who the intended recipient is, it could be overwhelming to sort through the millions of messages to determine which are yours. It's not likely to be practical for every person to have their own private receiving wavelength, so it seems there would be interference between all the messages. Imagine being in range of just 2 radio stations of more-or-less the same wavelength. The result could be so garbled that even if one periodically said "This is a message for Joe" and the other periodically said "This is a message for Sally", neither Joe nor Sally could understand enough of their message for it to work. Even if each person only received signals on one wavelength and there were a million different wavelengths, in an interstellar community with billions of people, many people would be sharing the same wavelength. Even in large cities today with 5 million people, that would mean 5 people just in that local area would be receiving each other's messages.
A radio-type system is a good method for a central location to send the same message to numerous listeners who know the appropriate wavelength to tune to. And it can work OK for short-range 2-way communications when there are few enough people within range so there's aren't multiple separate conversations at the same time interfering with each other. And assuming you don't mind anybody else in range hearing your conversation. But widely-used, long-range, 2-way radio-type communication does not seem to fit our needs.