No Time at All
Julian Barbour's view is that time does not exist. How then are we to account for impression that time exists and all the wealth of evidence to support that impression? His proposal is that we should consider the universe to be formed of a vast collection of something like snapshot or holograms, fully three dimensional but with no movement. Each snapshot is not literally a recording onto a media, it is in itself the nature of that moment, that 'Now' as he would call it. The snapshots are mathematical structures he describes as Platonic forms. He proposes that they co-exist in a higher dimensional realm: eternal and unchanging, each a single possible state of the universe. Barbour writes: "I am getting ever more Platonic (or Pythagorean) and am prepared to identify the physical world with the realm of ideals."
When first trying to grasp his idea, one might expect these snapshots to be organised like frames on a movie film, but their relationship is more complex.There is no single order in which they can be placed, this is a form of Many Worlds cosmology. Barbour describes a range of increasingly subtle ways to order the snapshots starting with the simple distinction that follows from the expansion of the universe, we will find a variation of the density of matter, next we can look for the distribution of matter and how it locally curves space-time. Where two snapshots closely resemble each other, but differ in someway, we can consider these to be equivalent to consecutive moments in time. Finally we can look into the detail of the matter where we will sometimes find signs that one snapshot precedes another. In any snapshot that contains our Earth for example, its rich texture shows its history. These ordering processes give a structure resembling time yet still are not.
Barbour's ideas were in part inspired from the Wheeler DeWitt equation, an early attempt to formulate quantum gravity that produced an equation of state for the universe with no time variable. This equation specifies a wave function for the universe and sets it constant. Most physicists dismiss it as a mistake, citing the obvious reason that the universe does change over time, it expands, and so its wave function must change too. Others raise a more subtle objection to the equation arguing that it is impossible in principle to construct a wave function for the entire universe as quantum mechanics is an inherently dualistic theory separating the subject matter under observation and the measuring instruments used to make the observation. With the whole universe under study, the observer would need to be outside the universe to make an observation. This might sound like splitting hairs but it is not. The measuring instruments are always treated in a different way, they are considered to be classical objects that have definite states with no uncertainty, where as a state defined by a wave function intrinsically has uncertainty. Normally the measurements are being made on incredibly small things, quanta, and the problem does not arise. It only becomes apparent when quantum mechanics is stretched to the largest scale.
There are other other cosmologist who accept the Wheeler DeWitt equation but they do not agree that time does not exist at all. It can be argued that the universe tunneled out of some other time independent state of being. Like all explanations for the Big Bang, this is speculation. Barbour clearly defends his provocative position brilliantly as his ideas have gained him great respect, he is very frequently cited and has inspired others. Lee Smolin, one of the fiercest critics of the state of physics today does not agree with Barbour about the non existence of time but considers him as being a philosophical mentor.
Barbour's radical position does not automatically make time travel possible. He considers time travel unlikely, but as Einstein found , ideas may have implications that their creators do not wish to consider. Powerful ideas live a life of their own. Barbour's ideas are certainly powerful and his theory may prove relevant.