Thor "Bifrost Vs Star Trek "Transporter"

[JamesStaley]

In one world it's called "Magic", in the other, "Technology". But wouldn't the Transporter in Star Trek be more or less the same thing as the Bifrost from the Thor movie & Norse mythology? The only difference between the two would be one of power and distance - how far you can go. The Bifrost is used to travel between worlds/realms/galaxys and is bigger and more powerful by necessity, while the Star Trek device known as the "Transporter" only has to carry you from a ship in orbit to the planet below or over to another nearby ship: it can't beam you from one planet to another one clear across the galaxy.
Watching the Thor movie, another difference (probably noted only by me?) is that the Bifrost doesn't break you down into your component parts the way ST's Transporter does. The Bifrost lets you travel quickly between worlds, but you do it intact and you're aware of the trip, Vs being just a beam of energy that has to be reassembled once you get to where you're going (and HOPEFULLY get there intact and put back together the way you're suposed to be!).
So, what would happen if by a 200-Trillion-to-One accident, the two accidentally intersected each other while in use, and Star Fleet personal end up in Asgard and Asgardians end up on a Federation starship

[The Romulan Republic]

The Bifrost definitely has more power, and as I recall from the first Thor film, can also be used as an energy weapon. Also, their exists only one. Its unique and, as far as I know, can be used for but one purpose at one time.

As to personnel switching places- which personnel, when, and where? Picard on Asgard during Thor One is very different from, say, Loki on DS9 during the Dominion War, just to pick two examples.

[Kojiro]

For what it's worth, the Bi-Frost appears to actually be two components. The beam that carries the travelers and a black 'portal' which appears to exist just outside Asgard and the target destinations, presumably created by the Bi-Frost. So in reality the Bi-Frost 'beam' isn't so long ranged, instead it relies on the portal doing the bulk of the distance work. Those in the beam are also themselves- able to look about, talk and otherwise behave normally.

What is clear is that the Bi-Frost beam is capable of immense power. Planet cracking if we're to believe dialogue. Transporters on the other hand are notoriously fickle things, upset by any number of plot saving disruptions. I would wager that should the beams cross the transporter beam would lose coherence (if they even interact). The Bi-Frost beam will shear through the front of a car on regular settings or outright destroy living matter in it's path (such as the unlucky raider Thor lands on in TDW). If they intersect I imagine the transporter just fails or perhaps at best dumps the person in the beam, to be deposited wherever it was going. On the upside this is likely Earth or Asgard so they should be ok.

What seems unlikely is that a transporter could ever pluck someone from the Bi-Frost. Between the sheer amount of power used to the incredibly small window a person would actually intersect with the beam it seems doubtful any firm lock could be established. That's assuming they remained in range long enough to do anything anyway.