The time travel and multiplayer components of Pokemon Ranger: Tracks of Light are actually very closely related, because all the multiplayer missions take place in a temple in the past world(which will be revealed to you through multiple trips in the story). Once you've passed a certain point in the storyline, you can go back there anytime by touching the rock slab in Rainbow Island.
Below is the main hub room for the past world. In it you can go into the temple or change.level up your partner Pokemon. Ukulele Pichu cannot follow you, and you have your own sets of partners in that world. You start out with a Piplup and you gain more by completing missions.
The top screen is different...Your Styler level is reset for the past world, and your partners' power and recovery speed can be upgraded by using AP, another set of points different from Ranger Points. You gain them for each successful capture in missions and for completing it.
The tasks in each mission are simple at first...you capture a set number of Pokemon, or certain species of Pokemon and defeat a boss in a set time limit....Along the way you can break chests to gain extra time/Styler energy/ other powerups most multiplayer games have as standard items. Of course, I'd imagine with 4 people playing it'll be a race to see who gets the mission done first, and based off official trailers, you can help your partners capture Pokemon together. Below, screens of a mission, and the top screen while you're playing. The green boxes are treasure chests, and the red box is where you're headed(to beat the boss) after you've completed a task.
And then after that it's boss time.
After capturing the boss Pokemon you get your mission rank and probably a new unlocked partner. If you've captured certain species of Pokemon, rock slabs in the present world bearing that Pokemon's picture will break, opening up new paths.
By completing the multiplayer missions(you can do them solo if you want), you're rewarded when you go back. For instance, the rock slab thing I mentioned earlier, but more importantly, you get Celebi's Ranger Sign, which you can use at any time to summon the partner you had in the past world, any one of them! Cool feature there. Video for details.
