Well, keep in mind that the magic ring of THE HOBBIT was retrofitted to an entirely new concept when Tolkien wrote THE LORD OF THE RINGS.

The One Ring (which Bilbo found) possessed all the powers of the other Rings, and the Seven and the Nine were originally intended to confer invisibility. But by "confer invisibility" Tolkien seems to mean some sort of transference of the physical body to the spiritual plane. i.e., the physical presence remained, but was somehow "faded" so that the Ring's wearer became aware and active in the incorporeal aspects of Ea.

It's not like an interdimensional shift or the bending of light rays which you find in science fiction or fantasy which has been influenced by science fiction. Rather, Tolkien seems to have envisioned the physical world as an aspect of the greater world, which also included the non-physical, spiritual, or unseen world.

Men are normally aware only of the physical world. They are spiritually blind (in fact, this closely resembles the Christian teaching that we are spiritually dead, and therefore cannot perceive matters of the spirit without help) and spiritually deaf. Men, in Tolkien, are totally insensate to disembodied spirits, unless those spirits are given some special power to make themselves known to the living, as the Nazgul, the Barrow-wights, and the Dead Men of Dunharrow possessed.

Or think of a Man's body simply as a glove fitting over the spirit. The Rings would permit a Man to sort of slip out of that glove, or to make the glove insubstantial enough that light would pass through it. People naturally want to analyze the phenomenon from a scientific point (worrying about conservation of mass and so forth), but the effect doesn't seem to have been derived from scientific principles.

On the other hand, some people have argued that the body was rendered transparent -- not eliminated, but physically altered -- while the Rings were worn. The ultimate fate of someone who wore these Rings would be that they'd lose their substance. The Nazgul were shapeless, according to Gandalf, without the special robes they wore when they were sent to hunt for the Ring, or to lead armies. The loss of substance was the fading Tolkien referred to.

The Seven, however, did not affect the Dwarves in this way because it was not in their nature to be reduced to wraiths. Aule made them differently from the way Elves and Men were made.

When Celebrimbor made the Three he didn't desire invisibility, so these powers were not bestowed upon those Rings (to render unseen the wearer, and to render unseen things visible).
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