In my earlier post Every Now and Then I explained why I think the most plausible explanation for our perception of the now being different from the past and the future is due to the ability of our brains to store memory. I thus believe in the 'block universe' in which there is nothing special about the now, and the past and the future exists in the same way as the present moment.
Nevertheless, I want to point out this isn't more than a believe of mine that I personally find plausible. Especially, I do not think it follows from Special Relativity, as some comments indicated - and as also Petkov argues in his paper. Here, I want to explain why I don't think his argument holds. I will pick around on Petkov's paper not because I dislike it so much, but because it is actually a useful summary that also contains a brief historical introduction on the previous work on the issue, most notably the Rietdijk-Putnam argument [1,2].
Please note that the following does not take into account quantum mechanics, with which everything becomes much more complicated.
The following should be familiar to everybody who has opened a textbook on Special Relativity (SR), so excuse me for being somewhat brief with the basics. In SR one can construct the surface of simultaneity of an inertial observer, Bob, in a straight-forward way. One puts two lights in equal distances into the restframe of the observer (meaning their relative velocities vanishes). If Bob measures signals from both lights to arrive at his worldline at the same time, he says they were emitted simultaneously. Doing this for lights of all possible distances creates a surface, called the 'surface of simultaneity' on which all events lie that happen at the same time according to Bob. One can repeat this for all instances on the world-line of the observer, which gives a slicing of simultaneity. For the observer in rest, these are just parallels to the x-axis in Minkowski-space.
If one considers a second observer (Alice) moving with a relative velocity to Bob, she can do the same construction. It turns out however, her notion of simultaneity is a different one, and her slices of equal time are not identical to those of Bob. The reason for this is that the speed of light is constant in SR and the same for all observers. If Alice's and Bob's world lines cross at one point (e.g. the origin), the events they consider simultaneous with this meeting are on two different lines that form an X.
This is illustrated very nicely in this figure from the Wiki-commons. Here, event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame.
The argument then goes as follows: if everything exists that Bob calls simultaneous but there is nothing special about Bob, then everything that Alice calls simultaneous exists the same way. You can repeat this for all observers that cross either of these already existing surfaces anywhere and you'll fill up the whole space. Thus, everything in the four-dimensional plane exists, because everything lies on somebodies surface of simultaneity.
There was a criticism of this argument by Stein  which I didn't read so I can only tell you what Petkov says about it. Apparently Stein's criticism is that the notion of present but distant events does not make sense, since one can not say anything about the 'now' that is not also 'here', so one should talk only about the 'here-now'. To reformulate this into Bee-speech, I'd say the argument is you can't have information about the 'existence' of anything that is not (yet) causally connected to you, like everything on your space-like slice is. Thus, concluding it 'exists' just because you measure it later is not possible. (This is probably a very fanciful interpretation of mine about a paper I didn't read, apologies.)
Petkov wants to show that
1) The block universe view, in which the universe is regarded as a timelessly existing four-dimensional world, is the only one that is consistent with Special Relativity.
2) Special Relativity alone can resolve the debate on whether the world is three-dimensional or four-dimensional.
I will in the following argue that 1) is wrong and 2) is correct. For being able to conclude anything at all, I will start with explaining what I am talking about. There is a possibility I am not using the terms as your philosopher next door does, but at least you know what I am talking about
- a) The block universe is a 3+1 dimensional space time with Lorentzian signature in which there is no present moment that is special in some regard.
- b) Presentism means there is a notion of 'now' and it is only the 'now' that exists. This can be further sub-divided in to categories
- b1) Presentism in which time is a parameter.
- b2) Presentism in which time is not a parameter.
For maximal carefulness I want to point out that another assumption which also goes into the argument is
A) Time is either a parameter or a dimension and there is no other possibility.
If that wasn't the case one could never make a claim like 'is the only option consistent with' as done in 1). To call upon the Principle of Finite Imagination, one should however keep in mind that this is an unproved assumption and an alternative option can't be outruled. I will understand SR as the relativity of all observations in all inertial frames. Sorry for nitpicking, but I want to throw out all merely philosophical baggage that isn't observable - you'll see later why.
In Media Res
For the reader who has taken a class in SR the rest of the argument is now actually trivial.
Let us start with claim 2): We know that time can't be a universal parameter because we have experimental prove the passage of time depends on the state of motion and path of an object. Thus, presentism b2) is falsified, which means with A) time is a dimension. It follows 2) is correct.
Now to claim 1): The first observation is that one should be skeptical about this claim because it involves the notion of 'existence' which doesn't appear in SR altogether. So how can one possibly say whether some sort of 'existence' is compatible with SR?
I'll give you an analogy. I could ask you whether my invisible friend is compatible with complex analysis. At the very best, you could say the question doesn't make sense, or to make it sound somewhat more sophisticated, it is ill-defined. Unless I tell you something about my invisible friend, there is nothing incompatible because in complex analysis there are no invisible friends. If I now told you my invisible friend is an entire function that is bounded but not constant, you could go and prove this is incompatible with complex analysis (via Liouville's theorem).
So how come Petkov as Rietdijk and Putnam can and do say anything about claim 1)? Well, the reason is that they don't actually explain anything about 'existence'. Instead, they say the 'now' does 'exist', thereby exporting 'existence' into a concept that can be defined in SR: the 'now'. Since I do not want to define 'existence' either, I too want to export it into the 'now'. This then however doesn't allow us solve the problem addressed in 1), for there is no reason why the 'existence' should be bound to the 'now' in the way one can define it in SR.
Let me make that more precise. The 'now' in SR can be constructed using surfaces of simultaneity in the usual way as mentioned in the prelimiaries. This is a definition of now. It doesn't say anything about existence. If you however use this definition of now, and say what is 'now' according to this definition 'exists', then you suddenly have a definition for existence. Cool, eh?
However, this is a definition and not a conclusion, as you can't say anything about whether something exists on your surface of simultaneity elsewhere, you can only say something exists if it's not only 'now' but also 'here'.
That, so I gather was also the argument by Stein mentioned above.
So, the flaw in the argument is that you can very well have a notion of a 'now' that 'exists' that is not in disagreement with any measurements confirming SR because there is no reason to define 'presently existing' with the surfaces of simultaneity in SR. In fact, everything that can be said about 'existence' in SR is a completely empty statement.
To see this, put an 'existence - slicing' with a time parameter τ on Minkowski-space  and say for each τ it is only the respective slice that 'exists', or is 'now' - according to this definition of 'now'. This can't be in conflict with experiment, for you never measure 'existence' anywhere than where you are. What you measure are signals from elsewhere and/or elsewhen. Yet on which 'now' slice these signals sat with you at emission is completely irrelevant. All that matters is that the propagation takes place according to the laws of SR because that's what we have measured. This is not a block-universe because it has a notion of a present moment, but is not in disagreement with any predictions by SR.
Thus, 1) is wrong.
Below an illustration to this.
There is however two more things to be said here:
One is that this option is compatible with all our measurements, but it does of course break observer-independence as a matter of principle for singling out some slicing means singling out preferred restframes.
The other one is that this option is compatible with Special Relativity and all measurements because it doesn't have any observables whatsoever and is not falsifiable. To make this an interesting scenario, you'd have to tie some observables to the 'existence-slicing' (if you think GR that could e.g. be the restframe of the CMB).
 Rietdijk, C.W. A Rigorous Proof of Determinism Derived from the Special Theory of Relativity, Philosophy of Science, 33 (1966) pp. 341-344
 Putnam, H. (1967) Time and Physical Geometry, Journal of Philosophy, 64, (1967) pp. 240-247
 Stein, H. On Einstein-Minkowski Space-Time, Journal of Philosophy, 65, (1968) pp. 5-23
 You would want to make sure it fulfils some nice-ness features of slicing like that the slices don't cross, are space-like, and cover all of space etc.
TAGS: PHYSICS, SPECIAL RELATIVITY, BLOCK UNIVERSE, PHILOSOPHY, TIME, PRESENTISM