[Physicist Paul] Davies is saying here that the flow of time is an illusion like the apparent movement of the sun across the sky is an illusion. It's we who are moving, not the sun. Likewise, on Davies' view, sometimes called the static view of time, every moment of time, every event, past, present, and future exists now, and somehow our consciousness moves from one to the next.Suppose for a moment that this is true. It would seem then that time does not exist "out there" but is rather somehow an internal feature of our minds. Time is a word we use to describe the way our minds apprehend events. Our minds create the illusion of temporality.
On this view, the universe is like a movie that has been instantaneously burned onto a DVD. Every event in the movie exists simultaneously with every other event, but the characters in the movie, and even the person viewing the movie, perceive those events as happening sequentially.
Immanuel Kant declared that "time, apart from the subject [i.e. the perceiver], is nothing". In other words, Kant is saying that time is not an objective reality but rather a structure of the human mind that enables us to experience the world. If Kant is correct then it follows that if there were no minds there'd be no time. There might be events like the events in the movie that's been impressed onto the DVD, but they wouldn't occur in any time unless they were experienced by a mind.
If we take this a step further it makes moot the questions of the age of the universe or the age of the earth. Since there were no minds (if we bracket out the mind of God) to perceive the unfolding of the universe then from the original "Big Bang" to the appearance of minds the events would have all occurred instantly or simultaneously, like "burning" an entire movie instantly onto a DVD.
Eventually, when observers with minds appeared they looked back at the evidence of cosmic history and concluded that, had a human observer been watching this "movie" it would have taken about 13.5 billion years, but since we're assuming there were no observers, no minds, it didn't take any time at all.
In other words, when human beings look back at the history of cosmic evolution - the expansion of the universe, the birth and death of stars, radioactive disintegrations, etc. - it's like popping the DVD into the player and watching the movie. Until the movie is played and observed it's just a bunch of pits in a disc. There's no time on the disc. Nothing on the disc has any meaning until it's put in the player and apprehended by a mind.
If Kant's view that time is part of the structure of our minds is correct then if the human race, or at least all creatures with minds structured to experience time, were to disappear, time itself would disappear. Just as there would be no pain or sound or color if there were no organisms with senses structured to experience these sensations, likewise there'd be no time if there were no minds to experience it.
This seems astonishingly counter-intuitive, but then Galileo's view that it was the earth, not the celestial bodies, that was moving was also counter-intuitive. The more we learn about the universe the stranger it seems. Indeed, it's quite possible that the world we experience is in reality not at all as it appears to us to be.
It's also quite possible that the only way to hold onto the belief that there is an objective time - that time would continue to exist even if human beings and other minds were extinguished from the earth - is to believe that time exists because an omnipresent mind, the mind of God, observes every event in the universe.