Oct. 24, 2012 -- It's dinnertime at the Alexander home, in Lynchburg, Va.

Holley Alexander is serving chicken curry, 14-year-old Bond is hungry after soccer and the dad, Dr. Eben Alexander, leads the family in prayer.

In this home, saying grace is different these days. This family has been touched by a medical miracle -- and maybe more.

"It was impossible after impossible after impossible that all these things happened," Alexander said in an interview with "Nightline" co-anchor Terry Moran.

Alexander, a Harvard neurosurgeon, nearly died four years ago when a ferocious E. coli meningitis infection attacked his brain and plunged him deep into a week-long coma. Brain scans showed his entire cortex -- the parts of the brain that give us consciousness, thought, memory and understanding -- was not functioning. Doctors gave him little chance to live and told his family that if he did survive he'd probably be brain-damaged for the rest of his life.

"Nurses would come in, and they would pull his eyelids back, shine in the flashlight, and his eyes were just off and cocked," Holley Andersen said. "It's just like no one was there."

Against all odds, Alexander woke up a week after being stricken. But he believes Holley was right: He wasn't there.

Deep in coma, his brain infected so badly only the most primitive parts were working, Alexander claimed he experienced something extraordinary: a journey to Heaven.

"In every sense, of the word that's what my experience showed me," Alexander said.

"My first memories from when I was deep inside: I had no language, all my earthly memories were gone," he said. "I had no body awareness at all. I was just a speck of awareness in kind of a dark, murky environment, in roots or vessels or something. And I seemed to be there for a very long time -- I would say years.

"I was rescued by this beautiful, spinning, white light that had a melody, an incredibly beautiful melody with it that opened up into a bright valley," he added, "an extremely verdant valley with blossoming flowers and a just incredible, rich, ultra-real world of indescribable complexity."

Alexander said there was a young woman who soared across time and space with him on a butterfly wing and gave him a message to take back from Heaven.

"She looked at me, and this was with no words, but the concepts came straight into mind: You are love; you are cherished; there's nothing you have to fear; there's nothing you can do wrong," he said.

God was there as a vast presence of love, Alexander said, and Alexander understood God through an orb of brilliant light.

"It was all of eternity and all of conscious existence," he said. "But it was this brilliant orb of light that was almost as necessary as a translator to bring in that message from the divine and the incredible."

After he recovered, Alexander, who was adopted, was shown a picture by his biological family of a sister he had never met or seen before. He recognized the sister as the young woman from Heaven.

"I looked up at that picture on my dresser that I had just got and I knew who my guardian angel was on the butterfly wing," he said. "It is the most profound experience I've ever had in this life."

Of course, many would call Alexander's experience a hallucination -- but not him.

"I know this is not a hallucination, not a dream, not what we call a confabulation," Alexander said. "I know that it really occurred, and it occurred outside of my brain."

It was a near-death experience -- like those reported by thousands of others. But Alexander was determined to prove scientifically that it happened.

In his new book, "Proof of Heaven," he raises and then strikes down various hypotheses on how his journey could not happen.

Alexander said he is scientifically certain that his stricken brain could never have produced the images and ideas he experienced -- or remembered them.

"If you would have asked me before my coma, How much will someone who is in coma for a week with a severe bacterial meningitis -- so severe that the sugar level ... around my brain, normally around 60-80 and in a bad meningitis maybe down to 20; in my case it went down to 1 -- to me, that's just one piece of evidence of how severe this was. If you'd ask me how much would that patient remember, I'd say nothing," he said. "They wouldn't remember a single thing. ...The severity of the meningitis would have prevented dreams, hallucinations, confabulations, because those things all require a fairly coordinated amount of cortex."

Alexander isn't fazed at all by the skeptics. He was one, too.

Now he has "proof of Heaven," he said.

"For me, it's become clear that the best way to look at it is to turn it around and realize that consciousness exists in a much richer form, free and independent of the brain, which has everything to do with the eternity of our souls and the fact that our awareness, our consciousness, our soul, our spirit, does not depend on the existence of the brain in the physical universe. In fact, it's freed up to a much richer knowing when we're outside."