They also moved Captain Christopher from sitting to standing and back again. It's not as showy as doing a mid-beam kidney transplant or whatever, but it's probably about as difficult considering how many things still have to line up after you start moving them around.
Very much to the contrary, I'd argue it's inherent in the way the machine always works.
On two levels, really. In the studio, the trick always involves "beaming out" an actor holding one pose and "beaming in" the same actor holding a different pose. It's physically impossible for him or her to hold a truly identical pose, so we have to accept that the fictional machine allows for activities to take place during the transport process.
Which is only to be expected: the heart ought to continue to beat, or if the process somehow slows down time and/or only involves a split second, nevertheless the molecules ought to continue to hold together, in what is a dynamic rather than static process. Turning matter into phased matter doesn't stop it from working - which we concretely and macroscopically see in those instances where people change pose between A and B, or hold an ongoing conversation while beamed, or indeed are directly witnessed moving about and doing stuff while explicitly phased like Barclay in "Realm of Fear".
The system may gently nudge Kirk's foot to ensure he lands standing
on uneven terrain, not
in it. It may more robustly force Christopher from sitting to standing position. But this is macroscopic manipulation, achieved by techniques comparable to beaming a manservant along with the transportee and having him go "If you just let me lift your leg a bit, Sir" during the process. As witnessed on screen, transporting is little different from walking, except you happen to be phased to another realm of existence between steps. Doing surgery between those steps is still a feat not comparable to lifting a leg or spitting out a phrase.
There was a portable transporter that did pretty much the same thing as the pip-sized device in NEM in Voyager's "Non Sequitur" and "Concerning Flight," the latter case ruling out tapping into a "real" transporter system, except that device was hand-held.
Umm, not really. In "Concerning Flight", the device wasn't portable: it remained right where Janeway activated it. Sure, it had a handheld control unit of alien design instead of a pulpit bolted to the floor, but in the end, it was no different from a transporter room being operated on site-to-site mode.
That the "system" apparently was the size of a fridge (that is, it was the pedestal on which the control unit rested) doesn't appear remarkable. We don't know how large "real" transporters are, but we do know they can be accommodated aboard rather small shuttlecraft. This may be the standard size for UFP tech; heck, it could even
be UFP tech, for the ease with which Janeway recognizes it at sight, stolen from another Caretaker victim or other Alpha wanderer.
The control unit from "Non Sequitur" is of course portable, moving with Alternate Tom. But Tom's surroundings have no shortage of fridge-sized machinery of assured UFP origin. Earth ought to have a public transporter network - and a non-public one, so it takes a bit of illegal accessing to get Tom to a Starfleet facility with that system. The remote might thus be a nonstandard, that is, non-public one, a lockpick rather than a key. It need not be a portable transporter machine, though.
Could be the "prototype" part was just that it was tiny enough for Data to keep it in one of his smuggling compartments, instead of the old fist-sized units.
Quite possibly. Or then there's a functionality to it that was missing from the previous Swiss Army Commbadges of comparable size. Or a couple of superfluous functionalities removed vis-á-vis the previous models. In the end, we're left with a device that achieves no more than an ordinary commbadge would. (A bit less, really, considering it doesn't allow Data to say "Two to beam up" while setting his phaser to explode against Shinzon's diabolical device.)
I'd like to stick to the James Bond analogy here. Not all of the Scotch gentleman's doodads defy the laws of physics or the real state of the art. But even those that don't have every excuse of really being the very cutting edge, just like S31 may have tiny communicators cleverly hidden in ornaments back when nobody else does. The regular guys don't bother with cutting edge, generally because keeping the edge sharp in field conditions is more trouble than worth. But every now and then, they may tap into something from the upper shelf, such as a super-tiny transporter beacon. Or, say, a silent and sparkless transporter with eye movement control, even though they generally dismiss such as worthless parlor tricks!
Timo Saloniemi