What do these words mean? These ideas in philosophy try to answer the question(s)
whether the past and/or the future exist.Now, presentism claims that only the present exists while eternalism (also called "The Block Universe paradigm") claims that the whole spacetime including the past and future exists as well.
Who is right?
It is not hard to see that both opinions are textbook examples of unfalsifiable statements. How are you supposed to decide that the past doesn't (or didn't) exist? Clearly, this question depends on the definition of the word "exist" in a particular context. This word was not designed to settle similar ill-defined questions.
It was invented for people to be able to say whether a mammoth could be found somewhere in their local forest before they die of hunger. They didn't care whether they would find the animal in 5 minutes or 10 minutes but it had to take place before they starved to death. Later, people tried to give the verb a more accurate definition but it doesn't mean that they succeeded.
Analogously, the sentence "is the world three-dimensional or four-dimensional?" is a canonical example of sloppy formulations. The answer depends on whether "the world" in the sentence means a "slice of spacetime" or the "spacetime" itself. Both concepts, the slice as well as the spacetime, "exist" in the space of concepts. A priori, we can mean both things. Why the hell do some people find it important to answer questions that are clearly (and perhaps deliberately) ambiguously formulated?
So I find it kind of mind-boggling (it not mind-blogging) that the very same people who like to say that statements in science must be falsifiable - and who even enjoy to lead their impressionable readers to the completely wrong conclusion that even very accurate, quantitative, and a priori incredibly strong scientific statements are not falsifiable - are usually the very same people who are absolutely excited about meaningless philosophical babbling about questions that can be given no operational meaning. Suddenly, they can't even think of the idea that these pet theories of theirs could be unfalsifiable, that they could be vacuous piles of crap.
The same thing can be said about Lee Smolin. He has written thousands of pages defending outdated and bizarre philosophical dogmas about relationism. There exists no scientific reason why "relationism" should be generally true.
Moreover, this concept is generally ill-defined. In specific contexts, its more concrete mutations - such as Mach's principle - can be shown incorrect. More generally, these hypotheses can be shown contrived and unlikely because they make too strong, unjustified assumptions about the laws of physics. Once the correct laws are actually found by the scientific method (e.g. general relativity as the right classical theory of gravity and inertia), we can see why the old philosophical statements were mostly wrong and almost universally ill-defined.
But certain people still mentally live in the 12th century scholasticism when concepts were ill-defined, statements involving these statements were both ill-defined and unsubstantiated, but the "scholars of good faith" wanted these statements to control the thinking of all people.
The presentism vs eternalism debate is another great example. What experiment can I do - even in principle - that would prove that the past doesn't exist or that the future does exist? Even though the question can't be sharply answered in science, we can still talk about the relationships between the presentism vs eternalism debate and science.
Early humans and the existence of spacetime
Most animals don't remember too much. In the past, people tended to forget things, too. They had to struggle to survive every day and sometimes every minute. Their immediate present was what was controlling their emotions and what they cared about. That's why by the "existence", they meant the existence "at the same moment" only. Sometimes they would be thinking about the past and the future as well. But these concepts were mysterious and "unreal". The realm of the past and the realm of the future was full of gods and dragons.
As the people were getting better in remembering and archiving the past, the past was becoming "more real" for them. And as they were getting better in predicting the future, the future was becoming "more real" as well. Moreover, the past and the future should be treated in a similar way as soon as you accept the existence of positive and negative real numbers.
Saint Augustine and Saint Thomas Aquinas were two early figures who began to promote eternalism. Because the cutting-edge cosmological model of their era involved God who created the world, they were saying that the world was created including the time. God is above time. There's no way to ask what was before the world was created because the word "before" only works inside God's creation i.e. inside the spacetime.
Now, these theological ideas couldn't change the fact that people were primarily perceiving their present and they cared about it. But it is fair to say that the perspective of the two Gentlemen was closer to the spirit of Einstein's relativity.
Presentism and relativity
Once we understand relativity, we find one obvious problem about presentism. If we want to say that only the "present 3D slice of spacetime exists", we are obliged to clarify the proposition by choosing a reference frame. In the blogosphere, there exists a preferred reference frame but in the real world, there doesn't.
The old-fashioned presentism seems to be in trouble. If we want the word "exist" to have a universal meaning that the 6.5 billions of people on Earth could agree with, there are actually many ways to define the verb - one for each reference frame. In special relativity, we could argue that only the inertial ones are legitimate. But in general relativity, we can say even that each (generally curved) spacelike slice through spacetime produces a new definition of presentism. Does it mean that no form of interpersonal presentism can survive in relativity?
Actually, there is a natural relativitistic counterpart of presentism. You may say that not only the other moments of spacetime are unreal: the other places in space are unreal as well. Only the particular point (or small region) in spacetime where you live "exists". Such a definition of "local presentism" is Lorentz-covariant. In fact, it follows the usual thinking in mechanics and field theory.
In mechanics, the degrees of freedom are viewed as functions of the variable "t", the time. In relativistic field theory, the degrees of freedom (fields) are functions of "t,x,y,z" (plus six or seven extra coordinates). In mechanics, "x,y,z" could have been degrees of freedom (positions of particles) that become operators in quantum mechanics but in field theory, they are just variables that are treated on equal footing with "t". Integrals over "t" in mechanics (such as the action) are replaced by integrals over "t,x,y,z" (of the Lagrangian density).
So the "local presentism" is a natural relativistic version of the old "presentism". Our ability to construct this framework shows that the presentism vs eternalism debate cannot be really solved forever by the arguments based on the Lorentz invariance only.
In reality, we don't live at a "point" of spacetime. We occupy a region of spacetime. Even our brains do. It is not just a technical limitation caused by a low density of our brains; the holographic principle implies that nonzero information must always occupy a non-infinitesimal region whose surface can't be smaller than the information inside (in Planck units). So these are new subtleties.
Even though I have written a lot of words by now, it is important to emphasize again that neither of these questions has any real impact on anything. If you use a curved, non-canonical slice to define the word "exist", it may be ugly but this ugliness doesn't influence any phenomena. Phenomena are not influenced by things that are defined to "exist". Instead, they are influenced by the other phenomena in their past light cone and by the probabilistic laws of physics.
If you ask a more accurate question than the question "What exists?" - for example the question "what degrees of freedom must be taken into account when you predict the event XY" - you may obtain a much more accurate answer.
And even if you win the silly battle for the meaning of the ambiguous verb "exist", the answer to the more meaningful question is not necessarily identical to the answer to the question "what exists?". For example, the brain activity depends on various processes and the signals propagate by subluminal speeds. Whether we define the word "exist" in one way or another has no impact on the question what information our brains can actually process. These are very different issues; the meaning of the word "exist" is a purely linguistic exercise without any impact on physics, neurobiology, or other sciences and without any impact on our ability to manipulate with information about the Universe.
Higher-dimensional geometry = new definitions
There are many other relativistically well-behaved definitions that an observer could adopt for the "existence". He may say that only his past light cone exists, both light cone exists, whole spacetime exists, only the space-like-separated region exists, and so forth. ;-) Once again, neither of these linguistic choices has any physical impact on anything.
And if a physicist wants to avoid confusion, there is a simple recipe. Instead of using the word "exist", he may say "exist in spacetime" or "exist in the past light cone of XY". Or he may say whatever he means. The ambiguity of the word "exist" (without additional specifications) is man-made and it is easy to fix it: simply use a more accurate language. And the fact that other people can use (and often do use) imprecise language doesn't mean that there "exists" any physical mystery to be solved. ;-)
Noam Chomsky, a linguist, asked in 1957 whether colorless green ideas sleep furiously. It was meaningless to answer such questions because the words were combined in a context that they were not designed for. No sane answer could exist at that time. Incidentally, in 2008, the answer to Chomsky's question is Yes because the largely homogenized (colorless) mobs of green activists are unable to think rationally (their ideas are sleeping). Their severe limitation can make us furious, indeed. But because the word "green" wasn't understood in this way in 1957, the question made no sense fifty years ago.
Is there an actual mystery surrounding the "existence" of the past and the future?
In fact, no mystery of this kind exists, neither on the present slice nor in spacetime! More precisely, this mystery existed in the past because people were silly and it also exists today because many people still can't distinguish vacuous verbal games from physical questions. It may also exist in the future if the people will be getting less sensible again or if the words will be given a different meaning. But the mystery shouldn't exist today if the people were thinking scientifically! ;-)
You may also say whether you conciousness is connected with a point in spacetime or a region. Obviously, it is a region and one can make various experiments - for example, to quickly burn a portion of your brain - to check whether your consciousness is affected. Disclaimer: you can only test it once. You might still say that these physiological tests don't tell you where (and when) the consciousness is "really" located. But even though the word "consciousness" is supposed to sound mysterious, the sensible scientist's approach is to accept the operational definition and to distrust theories about souls flying outside the body.
Human consciousness, despite its mysterious connotations, is linked with structures and processes in the brain. Less complex structures can also have some "consciousness" but they are unable to reliably manipulate with its products - namely with macroscopic amounts of the information.
Eternalism vs causality in quantum mechanics
While the presentism vs eternalism debate is pretty much vacuous, ambiguous, and confusing - and relativity adds some new twists that perhaps make the debate even more ambiguous - there exist related questions that are slightly more physical.
One of them is the question
What events influence the present - or a particular event at this moment?In classical mechanics, you needed to know all the degrees of freedom at some moment "t_0" and you could have calculated all the degrees of freedom at a different moment "t_1". Typically, you would choose "t_0" to occur before "t_1" but it wasn't strictly necessary. (Don't forget that retrodictions become exponentially difficult for complex systems due to the increasing entropy!)
At any rate, the future was determined by the past.
The same thing is true in field theory. If you know the value of all fields in space at "t_0", you may calculate their values at a different moment "t_1". But for relativistic, local field theories, there exists an additional choice. It is enough to know the degrees of freedom at "t_0" in some region "R" of space and you may still calculate something, namely all the degrees of freedom in the intersection of the future light cones of the points in the region "R".
Once again, relativity adds new ways how the information can be organized. Why? It is because it is adding new dimensions of spacetime that may be treated in analogy with time (even though they are spatial). And the four-dimensional geometry is richer and more interesting than the one-dimensional geometry of intervals on the "t" axis.
In quantum mechanics, only the probabilities may be predicted. If we know something about the past, the squared absolute values of some complex amplitudes determine the probabilities of various things in the future. Even though Sean Carroll can't get it, this procedure only follows these rules in the forward time direction: it depends on an intrinsic logical arrow of time. Retrodictions are calculated differently and they depend on priors; predictions in quantum mechanics don't need any priors.
Relativistic quantum field theory still preserves the causality of relativistic classical field theory: if you know everything about the region "R", you may still calculate everything - i.e. all probabilities of various outcomes of measurements - about the intersection of the future light cones of points in "R". This fact can be easily seen in the Heisenberg picture: the whole evolution in time is encoded in the Heisenberg field equations for the operators that are analogous and equally causal as they were in classical field theory.
However, one can show that the probabilistic character of quantum mechanics is no illusion - it can't be mimicked by hidden variables - as long as we accept the causality principle in the previous paragraph that is almost certainly inevitable in a Lorentz-invariant theory. And the Lorentz invariance is supported by an overwhelming body of evidence: a physicist certainly can't deny it completely because of some philosophical preconceptions and such heavily supported insights (principles of relativity) simply must be taken seriously when a scientist tries to answer some questions about space and time.
Free will theorem and presentism
John Conway and Simon Kochen have proven the free-will theorem that shows that if the experimenters have the free will to decide what buttons they are going to press (and they seem to have it, at least in some countries), the particles (and other objects) measured in their experiments must have the free will, too. This amusing statement means that the outcomes of the experiments can't be calculated as a function of some "hidden variables" in their past light cones, not even in principle.
This conclusion means that the spacetime including all the events that have actually happened - and that will happen - cannot be interpreted as a coherent block that obeys unambiguous laws. The "free will" they derive means that the outcome of an experiment done "now" is not a function of things in the past. In this sense, the results of these experiments are "really" decided now. They were not decided in the past. That's what the free will means. Conway and Kochen's theorem therefore supports presentism, at least morally.
And the future cannot exist now, either. The fate of the Universe (and its particles) in the future hasn't yet been decided. This statement is what the free will actually means. The spacetime may exist in some abstract sense but because the theorem literally says that the future events don't depend on things that exist "now" but also on random decisions that are invariably linked to the future points in spacetime, it is legitimate to say that the future "doesn't exist now". ;-)
We have to ask more accurate questions to decide whether the presentist or eternalist definition of the word "exist" is right in particular contexts. And in different contexts, the answers may be different. But if you are interested in my universal sentiments, I think that both perspectives are partially right. And it's true even in the context of the free will theorem. Conway and Kochen have shown that the humans and particles have the same kind or (qualitatively) the same degree of the free will but they haven't actually shown that both of them have the free will. In some sense, both humans as well as particles only have a partial free will which is also vaguely compatible with their theorem. However, I can't exactly tell you what this mysterious statement means.