Rabbi Yosef Ber Soloveitchik said:
“When we pray and learn [Torah], we do not transcend into the Heavenly spheres. Rather, we bring the Divine into our midst, into our very being.” 
Yet, other Jewish authors give a seemingly different report:
“When we give ourselves up to the contemplation of G-d, our soul takes us into a region beyond our present physical world…We transcend, we go beyond the limitation of finite thought, and we draw therefrom power, strength and wisdom …If we have been nervous, tense or worried, we can, in a few minutes, cause ourselves to become calm…It is a deliberate and conscious change from our daily thinking to a communication with the infinite, through our soul…It has been said that we can experience union with something larger than ourselves, a sense of oneness with the power beyond…in that union, we shall find our greatest contentment and peace. That union we make and can experience only through our soul.” 
So which is it? Do we “transcend,” or do we “bring the Diving into our midst”?
Rabbi Joseph Gelberman used to say, “Never ‘instead of.’ Always ‘in addition to.’
So, perhaps it needn’t be one or the other: “transcend” vs. “bring the Divine into our midst…”
Perhaps it can be both.
Perhaps they are even the same thing.
Many times, we come to prayer with some vague concern on our mind or heart. It might not be dire. Just an unanswered question. Doubt about an outcome. Then, in the midst of prayer — it evaporates. Disappears. Not because the situation has changed. It’s our perspective that has changed. Suddenly, we just see things in a different way. Or see ourselves in a different way. And it changed with no effort on our own part.
It can happen at any point in the avodah — in the liturgy. It doesn’t matter what nusach you davven. It can happen regardless of whether your siddur is Orthodox, Reform, Conservative, etc. It might help if you use the same siddur consistently. But it’s not about the meaning of the words — although, you might experience it as a sudden, new insight into what you’re reading and saying, or a sudden, new sense of how it speaks to you individually, at that very moment.
We feel better. Less concern. Less doubt about ourselves or others. More accepting of a wider range of outcomes. Whatever — it will be alright.
In between the two moments — or, we could say, in the moment between concern and freedom-from-concern — we transcended.
“Transcending” isn’t a perplexing, mysterious experience. The room doesn’t disappear. We don’t feel as if we ourselves ceased to exist or went away anywhere. Actually, we barely notice it happening, if we notice it at all. We only know that something happened after it happened.
What happened? Our attention went beyond the information of our senses, beyond the chatter and clutter of our own minds, regardless of how rational, to “our inner Aleph” — to the perfect Peace that is the Source of our very existence.
It need take no more than an instant. It might not be a “clear experience” at all. Yet, it changes our mood. It changes our affect.
Transcending, we bring the Divine into the very midst of ourselves, while remaining ourselves. Only — happier, calmer selves.