I have two questions on this. Say scientists managed to create a stable wormhole through space using McGuffinium to provide a power source. (1) How large/small would this wormhole have to be for the transmission of (a) audio communication? (b) audio/visual communication? (c) inanimate matter as is or dematerialized into a compressed data stream? (c) human beings as is or dematerialized into a compressed data stream? (2) How much energy would each of the above need?
At a wild guess (assuming you use a laser to transmit the data digitally) I'd say about the width of a photon. So not very big. As for the power...assuming the Space Mcguffin is powering whatever mechanism is keeping the wormhole open (and assuming the transmitter/receivers are right next to their respective ends of the wormhole and assuming the wormhole itself doesn't somehow generate it's own interference) you'd probably be able to run it on a couple of AA batteries.
In order to determine how large the wormhole would need to be for each type of communication, you would have to know what bandwidth you are considering. The wider the event horizon, the larger the available bandwidth. The narrower, the longer it will take to send the same quantity of information. For audio communication, what type are you sending? Is it standard EM modulated frequencies? If so, that is limited to the speed of light and dependent on line of sight. Same goes for video. (I'm an electrical engineer, so this is REAAAALLL SCIENCE!!!!) Is it Subspace macguffin? In which case, I imagine enough for a photon should suffice, but I don't really know how subspace is supposed to work. Same would go for matter transport.
1) a) and b) - larger than 1 wavelength of the EM radiation being used (assuming EM). c) and d) as is - larger than the dimension of the object; compressed data stream - same as a) and b) 2) above and beyond the energy needed to maintain the wormhole which would be enormous a) and b) a few Watts. c) and d) as is - nearly none; compressed data stream - a few Watts. Bullshit factor = exponential.
In Trek universe, I would surmise that a micro wormhole is enough to send virtually any sort of signal through (provided it's stable enough to carry the signal), whether it's of audio, visual or transportation nature. If 'Eye of the needle' was any indication, then a size of the anomaly might play a sporadic role for signals, but also not necessarily so. Starships were able to send transporter signals through miniscule cracks in forcefields and other types of barriers for instance - it was implied, that if there's an opening, regardless of how small, a signal could go through. In case of the wormhole, size might not be important, but whether if it's stable enough to carry the transmission. SF was able to create a micro wormhole to communicate with Voyager for a few minutes, so it would stand to reason it was probably of the same size if not much smaller than the one in Eye of the needle (minus the temporal displacement).
You would also be careful not to destablized the wormhole by sending too much positive energy into it.
This isn't Trek. I'm trying to rework my original universe with some real science and long distance communication is an issue.
I read a book a decade ago with the premise of micro wormholes being used for this very thing. At first it revolutionized communication, and then when light was able to be transmitted, it completely eliminated privacy. Then things get weird and they find a way to transmit light from the past and view historical events.
Does a wormhole have to be three-dimensional? For communication, any sort of wave, two dimensions should do the job.
I'm submitting this through my 17 dimensional wormhole. Wormholes of 5 or less dimensions are only for backward crackpots who insist on using outdated technologies.