This is an interesting video brought to my attention by What is Enlightenment Magazine. I have experienced this bliss momentarily before myself. The most vivid experience I had of it did not come from a formal meditation but from a process called "image streaming" where you verbally describe your mental imagery. It is a good mental workout that is supposed to synchronize the brain's hemispheres.
We are constantly worrying even when we don't know what we are worrying about. This is an important apparatus for our survival as it keeps us wary and it drives us towards innovation and preparation for perceived or imagined threats. But this process exist even when we feel like we are not worrying there is a continuous loop of time mapping/identity formulating/ future speculation/danger monitering of the environment that goes on behind the scenes and keeps us in a tense state. When the input is overridden it is shockingly freeing (as was the case with the woman's stroke).
We are constantly seeking this experience in various forms of entertainment, fantasy, drugs, etc... We know we can over-ride that neural circuit, but for most of us it only happens in degrees and only rarely. Some people can train themselves to do it at will, but it is so far not possible to know whether this is a genetic trait that only some are capable of or all of us can do. I strongly believe only a few are capable of it, in the same way that only 1 in 50 million people (a guess) can throw a 98mph fastball for a strike. You are either born with the potential or not.
I believe that this state of peace is one of the primary rewards in the reward/punishment system that nature uses to funnel humans down to specific behaviors. When everything is right with the world (we have our sex, status, and protection of our offspring) we are at ease. And being at ease makes us appear even more attractive because others see us as successful. When we don't have these things, we live in a more tense state which is our body's way of telling us "you will not get the reward of freedom and peace until you figure out a way to aquire sex, status and protection of your offspring".
Drugs, fantasy, meditation, spirituality are ways to tap the reward without aquiring the darwinian currency. We were designed by nature to be obsessive worriers. Our ancestors who were not, did not survive long enough to breed as much as those who were. (Hitchens comes to mind here-"created sick by Gawd and commanded to be well"- an indictment not only of the Abrahamic religions but also of Buddhism which exists under the same complete lack of acknowledgement of human evolution).
Even the Dalai Lama has speculated about a future technology that could induce this state. Even just a taste of it made available for everyone on a regular basis could change the world more than a trillion prayers, sermons or holy books. Just a specific electrical current in the brain (imagining this were safely possible with some device) could truly be the next big advancement in human technology (a new paradigm larger than the computer, the atom bomb, or the microscope).
I suspect that such a device would be unfathomably difficult to construct due to the variation in human neuroanatomy, but it is without doubt theoretically possible.