Anthony Aguirre at Big Questions Online discusses the two theories of time. His discussion is difficult to follow unless one is familiar with quantum mechanics and relativity theory, but he does give a clear explanation of the two basic theories on offer. What he calls below the "Unitary Block" theory is sometimes referred to as the B-Theory of time. What he calls the "Experienced World" is the A-Theory.
When we step back, we thus seem to have two rather different and contrary views of time’s nature. In one, the ‘Unitary Block’, spacetime and quantum states are laid out ‘all at once’, specified once and for all by some set of boundary conditions. Everything at any time is uniquely determined by — and thus implicitly contained in — any other time, and the world exhibits no distinction between past and future.His arguments for considering the Experienced World (A-Theory) to be fundamental can be read at the link. One might wonder why scientists even think there is a Unitary Block. The answer has to do with Einstein's discoveries about relativity:
At the same time, the ‘Experienced World’ we actually inhabit and observe has a very clear distinction between past, present, and future, produces entropy, and allows branching between a single present reality and several possible future realities.
Among knowledgeable and thoughtful people, there seem to be three basic views of this paradox:
1.The Unitary Block is the fundamental, and by implication more true description; things such as the arrow of time, definite experimental outcomes, etc., are emergent phenomena that, if we only could make precise enough computations, could be reduced to ‘nothing but’ the fundamental description.
2.The Unitary Block is wrong in some essential way. A more correct view would be much more like — and much more readily reconciled with — the Experienced World.
3.The Experienced World is more fundamental than the Unitary Block, which is just the correct description of regularities in the Experienced World in very particular regimes.
View 1 is by far the most common amongst my theoretical physicist colleagues, but I’ll make three arguments as to why we should think carefully before embracing it.
Right now, this second, an old man is exhaling his last breath. Elsewhere, two young lovers exchange their first kiss. Farther afield, two asteroids silently collide. Sunrise comes to a planet orbiting a neighboring star. This very second, a supernova detonates in a faraway galaxy.It's all very fascinating stuff with fascinating implications. For example, if the Unitary Block theory is correct I'm not sure what sense it makes to talk about the age of the universe. Every moment of time would have come into being at the instant that the universe was created. If that's so, then what does it mean to say that the universe is 14 billion years old?
And yet ‘this very second’ across the universe apparently does not really exist! Our best fundamental theory of space-time, Einstein’s Relativity, expressly precludes a single, objective definition of simultaneity. Events occurring ‘now’ by one observer’s estimation can — with equal validity — be said to occur at different times according to another observer who is far away and/or in motion relative to the first.
We don’t notice this issue much here on Earth, but it becomes very obvious for example in cosmology, where how one defines ‘now’ can determine whether the universe looks uniform or not, and even if it is finite or infinite!