How can I open MTS video files to iPhone's photostream so applications can use them?

My goal is to have the MTS files in PhotoStream so that all of my iPhone applications such as video collage creator apps can use them. MTS video files are files created by Sony Nex 3N camera that are downloaded to OSX and DropBox. Error msg.

How can I open MTS video files in iPhone in a way that video editing apps are able to use them?

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Update

1. comment to iskra's Handbrake: when I select the AVCHD thing, it says "No valid source found" -- how can I get the AVCHD into Handbrake?

and instructions

Needs clarification: Is handbrake really a solution to this? Or should I use Handbrake Alternative to get the ACHD videos to iPhone?