My experience is very difficult to explain as it was more a feeling than a measurable quantifiable experience, it is a feeling that was shared with another who also felt it and confirmed it at the time.
I was in my mid 20s, almost 20 years ago, that I met my then girlfriend of 1 year in Greece, as she was travelling around europe, we had very strong feelings for each other and, having been apart for several months, were very emotional about seeing each other.
She was extremely beautiful, not only externally but also within, in fact I have never met such a gentle soul since, we were perfectly matched, both easy going and perfectly at home with who we were, we were truely in love, I felt it with my whole body like it was an entity living inside me.
We shared a day sunbathing around the pool at our small apartment complex where we were staying, sleeping, listening to music and reading just like any other couple. We'd take a walk along the beach at dusk frolicking and messing around and then I'd give her a piggy back up the steep hill to where we were staying, I never wanted it to end.
It was after a hot day like this on the quiet Greek island that we returned to our apartment where we rested on our beds, separately as we were given a twin room and it was too hot to spend the nights in each others arms without any aircon.
It was then that I felt that my soul/spirit (whatever you'd like to call it) meet with hers somewhere in the air between us, I am by no means religious being a science graduate, the feeling was profound and had such an affect on me that there is not a day that goes by that I do not think about it.
I looked over to my girlfriend with shock and awe on my face and asked "did you feel that?'" she confirmed with an equal look of bewilderment that she had, but also could not explain it except for an overwhelming feeling of shared love.
I may not believe in a supreme being but there is so much about the universe that we do not understand, particularly the nature of existence and self awareness that makes us who we are, just recallling the event fills me with sadness of a lost love and a soulmate (in the real sense) that I let slip through my fingers.