"There was a fragmentation in America," Davidson remembered. "We were fogged in, so to speak, and Los Angeles was just emerging as a place."
But for unknown reasons, Esquire never published Davidson's images and they remained largely unseen for decades.
Last week, Davidson spoke with CNN about the images he captured in L.A. in 1964, and what the times represented for American culture.
"To go from Birmingham to Los Angeles was quite a jump," he said.
The struggle to win equal rights for African-Americans was getting bloodier, while the world tried to process the unthinkable assassination of a President that occurred less than a year earlier.
Also, people were starting to worry about a civil war in a faraway place called Vietnam.
Signals of oncoming social change surfaced in music, movies and the news. An old-school crooner named Dean Martin shared the Top 40 with four new upstarts called the Beatles. Moviegoers flocked to see a 30-year-old story called "My Fair Lady" along with a groundbreaking Cold War comedy called "Dr. Strangelove."
As Davidson's airliner touched down at LAX, he found a city that was smoggy, gray and alienated.
"There was a certain beauty in that grayness and that smog," said the Midwestern native. "It wasn't always smoggy, but I was taken by it. All that vitality spurred me on."
The jet's wheels hadn't even rolled to a stop yet before he pointed his camera out a window and started snapping palm trees in a parking lot surrounding the airport's iconic, futuristic Theme Building.
The city was about to undergo a cultural transformation driven by a Baby Boomer generation that was coming of age. In fact, 1964 was the opening year for West Hollywood's world-famous Whisky a Go Go -- one of the many Sunset Strip clubs that fueled the rise of counterculture bands like Buffalo Springfield, the Byrds and the Doors.
As a 30-something photographer, "I didn't know L.A. very well at the time," he remembered. "But there was something about the street and what the street gave me. That became my calling."
So Davidson hit the streets. But not by car, as you'd expect in L.A. Instead, he moved around on foot.
A stroll down a sidewalk revealed a big-finned, drop-top Cadillac and a woman walking in high heels.
With his camera, Davidson captured a moment in time when "just the point of her shoe was slammed against the concrete sidewalk. That was a moment I cherish," he said. "Somehow I was ready for it."
Years earlier, Davidson had studied in France with iconic photographer Henri Cartier-Bresson.
Two of Cartier-Bresson's most important lessons, Davidson said, were "to be patient and alert because those moments are fleeting, and to have a certain discipline to allow you to be focused as you walk down the street."
Davidson's photo shoot also took him to a classic drive-in diner called Tiny Naylor's.
The picture shows a man in sunglasses hanging out a car window with a microphone in his hand, trying to order food.
"There was something gross about someone ordering food over a microphone," Davidson said.
Another image shows a bus station where passengers made connections to Disneyland, Marineland and Venice Beach, where he found bodybuilders showing off their work.
"Everything was sort of like flesh and blood," Davidson said. "There were so many things going on in Venice at that time. One only had to walk around with his eyes open and mouth shut and his camera ready."
Esquire had sent Davidson to California with the idea that his photos would accompany an article written by someone like Tom Wolfe -- someone who represented an unconventional non-fiction writing style that was being called New Journalism.
"The L.A. I came back with was an L.A. that had a sharp point on it," Davidson said.
His photographs showed an L.A. that was "emotionally cold." The city Davidson experienced felt alienated, and he expressed that in his images. As he put it, the photographs "were pretty raw."
That wasn't quite what Esquire expected.
"They looked at the pictures and they said: 'What is this about? How come there aren't any bathing beauties? Where's the swimming pool?' " Davidson said. "They didn't understand the pictures. They didn't understand the alienation."
The assignment never came to fruition. Only now are the photos getting widespread exposure.
Recently, Davidson returned to photograph a very different Los Angeles. He found it more alive, more in tune and cleaner, he said. In many ways, you can look back at America before 1964 and after -- and see two very different eras.
With a unique perspective, Davidson was able to capture a moment in time before so much of America began to change.