"IT WORKED" means THEY STOPPED THE LOOP by Paola C.

"IT WORKED" means THEY STOPPED THE LOOP...

The sideway timeline is the result of the bomb explosion.
When they detonated the bomb at the end of season 5,
they actually changed the events. However, they didn't
change their current self past, as they are doubles in this timeline,
they just changed the future of those

(including their baby-selves already existing outside and inside the island)
living in 1977.
This new changed future is the sideway timeline we are seeing in this season 6 episodes.
For all those 70's survivors, infact, there will be no hatch, no desmond failing to hit the numbers, no flight crash... No misery after Jacob's touch.
No more people on the island cause all the survivors will leave for the dangerous radiation and the higher sea level after the explosion.
Daniel faraday will be free
to become a musician after what his mom Eloise found out, little Ben and Ethan will be sent back to the real world where they will grow up as to become the doctor
and the teacher of the 2004 parallel reality we've seen and so on...

ANd of course there will be no Time-flashes, hence NO LOOP anymore.

At this point, you're probably wondering: 'Yes, but why would Jacob accept this?
After all he could still be in time to go to the real world where they're kids,
touch them again and bring'em on the island again.
Well, my answer is, since the losties have changed a main event and stopped the loop, Jacob lost the game against MIB and so the power.
...And it makes sense if we consider Jacob as the destiny and MIB as the free will.

For the losties' current self version, instead, since past has already happened and it cannot be changed,
("Whatever happened, happened"), everything will continue untill the announced final battle,
infact right before the bomb explosion they're timeflashed....