The most interesting thing about a personal transporter is that it transports itself, so it manages rematerialisation while dematerialised. Impressive. Most impressive.
How so? Regular transporters don't require a pad at the other end, be it for beaming down or up. So the badge could pretend to be beaming up from the padless end, taking itself along as payload. No, I have no bloody idea how the padless part works, but it could be a simple "cheat", a reversing of a process that isn't one-way in temporal coordinates.
As bullshit as it admittedly seems I guess they're just following the direction of travel seen when Janeway and Leonardo Da Vinci beamed themselves to safety with that drinks flask-sized personal transporter and the combadge-sized one from Nemesis.
...Ah, the da Vinci thing didn't self-transport. Janeway had a remote; the device itself was the doodad the remote was resting on, and didn't go anywhere.
The Nemesis one might have been a transporter. Or then a transponder, to help compensate for whatever was broken by Shinzon aboard the
Enterprise. Remember that the sparkles on LaForge's console took down
all the transporters of the E-E, thus apparently hitting a centralized, shared resource. Might have been a sensor rather than a pattern buffer or an antenna (since the latter two come in multiple examples on the ship).
Transporters often break their self-made rules. But explaining it away is usually pretty trivial, and even the writers are getting the hang of this technobabble. I have no problem with the devices being magic wands from our perspective in the dramatic sense. But mobile phones would have been that to Jimmy Maxwell, so we still have the option of believing in these things for real. I mean, we really can't claim the opposite even with the expertise of Maxwell, because even he knew that science is always wrong, often fundamentally so.
Timo Saloniemi