In my story, people communicate through "orbs", which are spheres of a material similar to glass, but much more resistant. Basically people write a message on them with their fingers and the receiver, forgive the redundancy, receives it. The idea seems too far-fetched to me and I can't think how that could be possible without adding a factor like magic or something like that. Does anyone have any idea how to make it work "fairly logically"? And, if not, what could be a rapid communication method in an alternate world less developed than ours?
It might be possible even without magic, but I suggest to use glass sheets, almost like pocket mirrors, instead of spheres - it is much easier to produce, easier to carry around and easy to hold in one hand while you write with your other one - or perhaps you can write with a (inkless) pen for better accuracy, or even pick individual letters with your thumbs.
They can even come in three different factors - small ones that you can carry with you, middle sized ones primarily carried around your house, and big, stationary bulky items where you can even use special accessories where you touch the letters by your fingers (most proficient people can do it even without looking at your hands) while the sphere (or a glass sheet) is kept at your eye level, to lessen the strain on your back...
The idea seems too far-fetched to me and I can't think how that could be possible without adding a factor like magic or something like that.
The idea is not far fetched. You are just giving a fancy description of a fancily designed smartphone with a messaging app: the user taps their fingers on the smartphone surface and the other side receives the message, reading it through the equivalent surface.
It just requires the right amount of Shannon theory, electronic and the like, no magic at all.
If you're willing to except a "fairly logical" but exotic explanation, your orbs could be 3-dimensional projections of a 4-dimensional spherical object. This would explain the seemingly invisible interconnection between orbs since they would essentially be the same object. One way to think of the orbs would be as individual slices of the 4-dimensional object in 3D space. Perhaps an interaction with one orb/slice can influence the state of adjacent orbs/slices. Maybe the heat of a finger on one orb bleeds over to affect the other orbs that are also its adjacent slices in a way that is visual.
This would not necessarily involve high technology. The material of the orbs may simply react to changes in heat. They may not be made of matter at all as we know it, but rather be the influence of 4-dimensional displacement into our universe however that may manifest. This might help explain their resilience.
This would require acceptance of the idea that 4-dimensional objects can intersect our 3D space on a scale that people can experience. I'm not aware of any proof that that has actually happened in human experience, but absence of evidence is not evidence of absence.
If anything is allowed, the glass is some kind of piezoelectric material or a close relative that generates a signal when you touch or press it. This is then transferred to the other bowl which just projects it on the outside.
If you want the hands of the receiver to receive then you basically need a form of electrical braille. The sensation you receive from a particular form will tell you what letters make up the words.
A glass sphere is a perfectly fine lens. They make lenses for cameras that's basically a big glass ball attached to the end of your camera. Unlike a standard lens, these can take a nearly complete 360° image of your entire surroundings (excluding only the camera itself and anything directly behind it. So if you attach a suitably high megapixel camera to a spherical lens, you get a video-phone that captures the entire room.
(Due to limitations in typical camera technology, which are built for taking rectangular images, this ends up being lower quality than a typical panorama involving multiple shots taken from a camera rotated on a tripod, but if you designed the camera specifically optimized for this purpose, you could eliminate that limitation. Also, a regular panoramic camera isn't going to allow you to capture the whole room in real time, since you have to rotate it to get a full view. A spherical lens could give you that capability.)
Now for the receiver, well, you'd just need to attach a similar sphere to a high resolution projector, and you could project the same image from the sending sphere into the receiving sphere. Note that there may be technical challenges involved in allowing sending and receiving on the same sphere simultaneously, so you'd need 2 spheres to simplify that. Perhaps you could mount it to the back of the camera so that your sending sphere does not see the receiving sphere. Receiving sphere could be a frosted glass, so the image rear-projects directly onto the surface of the sphere, or it could work like a regular projector, beaming an image onto the walls around you. (You'd want to be in a completely featureless white-walled room to get the full effect. Better if the room is also spherical and the projector is in the center so you get a good consistent focus on the image.)
If both spheres are hollow, connect them via a taut wire. Tapping on one sphere will cause the tapping to be heard on the other, specially if they have a hole opposite to the point where the wire connects. No magic required, just wave physics.
You may be interested in a related question, for which I provided a similar answer: Could two smart phones work as an intercom on an alien planet?
Quantum entanglement: https://en.wikipedia.org/wiki/Quantum_entanglement
It is a mystery today and why do not be a mystery in your world? Like today, here, real world, it just occurs.
Do you know we - the whole humanity - don't know how electricity works exactly? We can make lots of things with it, but we don't know up to the certainty what an electric charge is.
Bonus: Einstein referring to it as "spooky action at a distance".
Your orbs just have this capacity naturally, no one knows why.
The spheres have a single quantumly entangled particle in the center, the glass magnifies the properties of this center particle. Spheres come in linked pairs that mirror each other over distance. if one orb is placed in your pocket, the other one grows hotter, if one is thrown in a snow drift the other sphere cools the air around it and fogs. The communication method relies on rotating the sphere in specific patterns similar to Morse code- Counter clockwise, clockwise, Shake, tap etc..