The common argument for the “block universe” comes in several forms, all logically equivalent; the one I’ll use here is the “Andromeda paradox”:
That Wikipedia entry quotes from Roger Penrose in The Emperor’s New Mind, which is where I first encountered the argument many years ago. Here’s what Penrose says:
[P]eople pass each other on the street [on Earth]; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already ‘fixed’?
We might summarize this argument in a single sentence as: relativity of simultaneity implies the block universe (i.e., it implies that all of 4-D spacetime must be fixed).
However, as just stated, the argument is not complete; we need an additional premise. Penrose gets at it indirectly when he says “according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past”. In other words, Penrose is implicitly claiming that every observer, at a given event, divides the universe into the “uncertain future” and the “certain past”, based on his “surface of simultaneity” through that event. “Surface of simultaneity” is a long phrase to type, but several posters in the PF threads I referred to above have used a shorter term, “3D world”, which I’ll use henceforth. The added premise then becomes: events to the past of any observer’s “3D world” at a given event are fixed and certain.
With the added premise, we can now see the argument more clearly. At any given event, there can be observers moving on any timelike worldline through that event. The 3D worlds of all these observers are “tilted” with respect to each other because of relativity of simultaneity. But if events to the past of any observer’s 3D world are fixed and certain, then the entire region of spacetime which is spacelike separated from the given event must be fixed and certain.
As you can probably see, the above argument at a single event is not enough to show us that *all* of 4D spacetime is fixed and certain; it’s only enough to show us that the region of spacetime which is spacelike separated from our chosen event is fixed and certain. In order to extend that to all of 4D spacetime, we need an additional premise: that the above argument holds at *any* event. In the Andromeda paradox, for example, we could run the argument from the Andromedan’s perspective: two Andromedans passing each other on the street will have 3D worlds passing through events on Earth’s worldline that may be separated by years. By the above argument, all events on Earth’s worldline that are spacelike separated from the chosen event on Andromeda’s worldline must be fixed and certain. But, since those events include events in the future light cone of the event we originally chose on Earth (where two people passing on the street disagree on whether the Andromedan space fleet has been launched), we can see that extending the argument to any event forces us to conclude that all of 4D spacetime, including our causal future as well as the region spacelike separated from us, is fixed and certain.
So we can summarize the Andromeda paradox argument as follows:
(1) Relativity of simultaneity + all observers’ 3D worlds are real at every event = block universe
(I’ve used the word “real” here because that’s the word that block universe proponents often use; but note that it’s really shorthand for “events to the past of any observer’s 3D world at any event are fixed and certain”.)
Now, in those PF threads I referred to on this topic, a lot of electronic ink was spilled in arguing for proposition (1). However, all of that was really a waste of time, because I already agree with proposition (1)! (And so, I suspect, do others who posted in those threads expressing similar objections to mine.) Proposition (1), in itself, is not the problem. Nobody needs to be convinced that, given its premises, the conclusion of proposition (1) is true. The problem is the premises, specifically the second one.
Most block universe proponents spend no time at all on the second premise, apparently because they think it’s so obvious that it doesn’t need justification or argument. But, as the above shows, simply assuming the second premise is tantamount to assuming the conclusion! (Strictly speaking, you still need the first premise as well, but everybody also agrees on the first premise; relativity of simultaneity is an accepted fact. So the second premise is the one that’s doing all the work.) In other words, if your argument for the block universe basically consists of helping yourself to the second premise, you’ve avoided the real issue.
In a couple of those PF threads, when challenged on the second premise, block universe proponents did offer two proposed justifications for it:
(2-1) The only alternative to the second premise is solipsism (only my present event is real).
(2-2) 3D worlds can be directly observed.
Proposition (2-1) is false, because there is another alternative to the second premise that accounts for all of our observations:
(3) All events in the past light cone of a given event are real (i.e., fixed and certain) for an observer at that event.
The reason this accounts for all of our observations is that information can’t travel faster than light, so anything we observe at a given event can only give information about the past light cone of that event. (More on this below.) Also, note that proposition (3) is obviously consistent with relativistic causality, whereas Penrose’s assumption that 3D worlds are what divide the universe into “the uncertain future” and “the certain past” is not. (It’s rather ironic, btw, that Penrose himself gives a good explanation of relativistic causality in the same book in which the above argument appears: he even has a diagram showing the division of spacetime into causal past, causal future, and “elsewhere”, the spacelike separated region. Our intuitions don’t really know how to deal with “elsewhere”; it’s neither fixed and certain, since we can’t predict what happens there with certainty based only on the data in our past light cone, nor changeable, since we can’t causally affect what happens there; we can only causally affect events in our future light cone. Yet, even though Penrose explains all this, he appears to forget it when making the Andromeda paradox argument. This is an instructive example of why arguments from authority should not be given weight; you should always check up.)
Given the above, proposition (2-2) is obviously false as well; we can’t directly observe a 3D world because of the finite speed of light. (As a side note, this proposition has been agreed to be false repeatedly by block universe proponents; but in later threads they forget they agreed and again present this invalid argument.) What we directly observe is our past light cone; 3D worlds are constructions from the data in our past light cones. But there is nothing requiring us to accept constructions from our data as fixed and certain, and there is at least one good reason not to: our constructions may end up being wrong, because our information is incomplete.
When I raised this last objection in PF threads, (that 3D worlds are constructions from the data, which may turn out to be wrong), an argument against that was advanced:
(4) People can communicate the experimental results that show relativity of simultaneity (as Penrose has the two people on Earth doing when they later make telescopic observations of the Andromedan fleet); this amounts to communicating their knowledge of 3D worlds, which therefore must be real.
However, this is also false, because, as I noted above, the information in our observations can only travel at the speed of light; and furthermore, in order to communicate, people must exchange information about their observations, which of course can only be done at the speed of light. So by the time the people have information about all the events that show relativity of simultaneity, all of those events are in their past light cones, so there is no need to postulate entire 3D worlds in order to explain the observations; simply accepting their past light cones as real is enough.
So in summary: a common argument for the “block universe” view, based on proposition (1), is invalid; but it’s invalid not because the conclusion doesn’t follow from the premises (it does), but because the second premise is not established. Block universe proponents gloss over this by simply assuming the second premise; but when challenged, they are unable to give any cogent justification for doing so. So the block universe view is not established by this argument, and one should not take at face value pop science books and TV shows that imply that it is.