The Block Universe: Examining the Rietdijk-Putnam Argument

[PeterDonis]

[Reposted from my PF blog]

The "block universe" interpretation of SR has come up repeatedly in threads here on PF. Rather than link to them, I want to summarize the key argument that is made for the "block universe" being necessary, and then summarize the arguments I made in those threads to show why I don't agree.

The key argument comes in several forms, all logically equivalent; the one I'll use here is the "Andromeda paradox":

http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument

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, 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: the key 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, and one should not take at face value pop science books and TV shows that imply that it is.

 

[atyy]

How about GR? We get all spacetime and matter in one go as a solution of the Einstein Field Equations.

 

[PAllen]

How about GR? We get all spacetime and matter in one go as a solution of the Einstein Field Equations.

Such a solution is a construction in Peter's sense. You only know the validity of such a construction within your past light cone. A moment later you might see evidence that your initial (or boundary) conditions weren't quite right and need to be adjusted to account for both what you knew before and what you know now.

 

[atyy]

Such a solution is a construction in Peter's sense. You only know the validity of such a construction within your past light cone. A moment later you might see evidence that your initial (or boundary) conditions weren't quite right and need to be adjusted to account for both what you knew before and what you know now.

The argument seems too powerful. If we accept it, then even the validity of GR in the future is unknown.

 

[atyy]

While I find it hard to argue against the block universe in any deterministic theory, there are some fascinating coments by Haag on this issue in quantum theory in his book "Local Quatum Physics" https://www.amazon.com/dp/3540610499/?tag=pfamazon01-20 p313

"Our question is rather: why should there be any difference between quantum physics and classical physics with respect to the status of irreversibility? A short answer is that quantum physics introduces an element of discreteness manifested in the existence of stable structures and the "indivisibility of a quantum process". This is closely tied to indeterminacy. The future is open, not precisely determined by the past. Though some remnant of time-reversal symmetry persists in quantum mechanics and quantum field theory, there is the asymmetry of the basic statements discussed at the end of section VII.1. In Bohr's view this "reminds us of the essential irreversibility inherent in the very concept of observation". In other words it is tied to the psychological arrow of time. But if we do not want to place the concept of observation into the center of physics we must ask ourselves: what would be the natural picture if we claim that there are discrete, real events, i.e., random, irreversible choices in nature?

Starting from this question we come almost unavoidably to an evolutionary picture of physics. There is an evolving pattern of events. At any stage the past consists of the part which has been realized, the future is open and allows possibilities for new events. Altogether we have a growing graph or, using aanother mathematical language, a growing category whose objects are the events and whose (directed) arrows are the causal links. ..."

 

[bahamagreen]

Interesting, but I can't tell quite what you are posing as the problem... I must be missing something about the nature of light cones?

I guess I've always thought that the block universe idea came from abstracting each event's past light cone of "certain past" to the geometric logical implication that every event in spacetime is within the past light cones of some other events' "certain and consistent pasts"... so the 2nd premise acts as the base case in a proof by mathematical induction...

If the second premise is "events to the past of any observer's "3D world" at a given event are fixed and certain", I'm not seeing why additional premises would be required.

Maybe more explanitory detail, but not additional premises...

"every event is in the past light cone of some other event(s)"
"an event in the past light cone of another event, being in the certain past of that event, must have some certainty in its future light cone"
"all events within an event's future light cone are also those for some other events for which the events in that future light cone fall within the past light cones of these other events"...

Are all those details true?

If so, it seems like these are just restating the geometry of spacetime that already contains these by construction. Or maybe I'm missing something about spacetime...?

I can't tell by your discussion if you are suggesting that the 2nd premise doesn't geometrically imply that all events are certain by virtue of all events being in the past lightcones of other events or not.

It does seems to me that bringing up observers, communication, data construction, and light speed confuses the question - the block universe implications look like they emerge beyond what's observable at single events and rather are abstracted through applying the 2nd premise to multiple events.

 

[stevendaryl]

While I find it hard to argue against the block universe in any deterministic theory, there are some fascinating coments by Haag on this issue in quantum theory in his book "Local Quatum Physics" https://www.amazon.com/dp/3540610499/?tag=pfamazon01-20 p313 ...

The interplay between quantum mechanics and SR is interesting, but to me, it doesn't conclusively point one way or the other. An argument from QM that sort of supports the idea of the block world is the question of the ontology of the wave function. Consider an EPR-type experiment where a twin pair of spin-1/2 particles is produced. Alice on Earth measures the spin of one of the particles, while Bob on Alpha Centauri measures the spin of the other. For simplicity, assume that they both measure spins in the same direction, so they should get opposite results. At the moment that Alice measures spin-up, she knows instantly that Bob will measure spin-down. But obviously (according to SR), her measurement result can't possibly affect Bob's measurement result. So it seems to me that the fact that Bob would measure spin-down must have been true (although unknown to Alice) BEFORE Alice made her measurement. To me, this suggests that Bob's result was pre-determined. And from Bob's point of view, Alice's result was pre-determined. So both results were pre-determined.

 

[Dale]

The argument seems too powerful. If we accept it, then even the validity of GR in the future is unknown.

It is true that the future validity of any scientific theory is unknown. However, that is not the point of the argument.

The point of the argument is that if you assume the validity of GR you cannot know the validity of the solution you derive for the EFE at any event outside of your past light cone. The solution depends on the distribution of matter (stress energy), and you do not know the distribution of matter outside of your past light cone.

 

[Geometry_dude]

You have to be very careful in these kind of arguments what exactly you mean. I have found it helpful to draw Minkowski diagrams to look at these questions, but other's might not agree.

I think we can all agree on the statement that if you are an observer (pointlike mass moving on a curve $\gamma$, whose influence on spacetime geometry can be neglected) at a spacetime point $\gamma(\tau) = q \in \mathcal Q$ at proper time $\tau$, then everything you see is your past lightcone. Since the measurement of how long a process takes or how long an object is, might differ for another observer not having the same spacetime position and (4-)velocity as you, it is convenient to define 'the present' at proper time $\tau$ as everyting you see at point $q=\gamma(\tau)$, that is everything on the past lightcone. Now this definition of the present strongly depends on the event $q$ or on the observer and due to the twin effect it is physically not meaningful to define a global notion of simultaneity that conceptually resembles the one you have in Newtonian mechanics (there do exist other ones).

Accordingly, we define the past as the collection of events in the past lightcone (not on it) and the future consisting at least of the collection of events in the future lightcone. I think we can also agree that everything in the past is 'already determined'.

Now, if you believe that all spacelike separated events from $q$ are 'already determined' in an ontological sense (of course, they come after our definition of present), then you can take a second such observer at $q'$, say lying almost on the future lightcone, and because you are just as "special" as him or her (here we reject solipsism), everything that is spacelike separated from $q'$ is 'already determined', that means also some events lying in the future lightcone of #q#. If you proceed with this reasoning you will find that "the entire universe" is 'already determined', thus leading you to the block universe picture, which by this argument must include determinism contrary to what others might say. However, there is no to contradiction to quantum theory on this level as quantum theory alone does not contradict determinism, also contrary to what some others might say (it depends on how you resolve the measurement problem).

Now, it's true that you can escape this argument by rejecting that all spacelike separated events from your current event are 'already determined', I mean why should you believe that, right?
But then you are again either faced with solipsism, that means in this case your 'current' spacetime position defines the global present as all the events on the past lightcone (note that you don't need determinism here), or you define a "global now", in mathematical terms that would be a foliation of a globally hyperbolic spacetime into spacelike $3$-leaves. But then you introduce something into your worldview that is unobservable in principle and defines what is "now" and "real". In addition, if you accept the existence of such a global, non-solipsisitic now, then you might still have trouble getting rid of determinism - and if you don't there's no reason to introduce such a global now to begin with. :-)

It is true though that if you stay within usual GR, then there's no global simultaneity, everything is deterministic and you get the block universe.

 

[Dale]

Now, if you believe that all spacelike separated events from $q$ are 'already determined' in an ontological sense ...

But then you introduce something into your worldview that is unobservable in principle

While this is a valid criticism, it is not a valid argument because the criticism applies equally to both positions being argued.

Also, the identification of a past light cone with a global present or even a local present is a little strange to say the least. I don't recall anyone else make that statement.

 

[Geometry_dude]

I fully agree. Solipsism it is then?

I always thought we moved past that point as a society. :P

 

[Dale]

I don't know why block universe advocates are so stuck on solipsism. Nobody ever brings it up but them. It is a nonsense connection.

As long as I believe that the events on my past light cone are external to me and not merely figments of my imagination then I am not a solipsist, regardless of what I may choose to assert or not assert about the structure of the universe outside of my past light cone.

 

[atyy]

I would like to understand this position better, so here is a paraphrase for those who don't support the block universe to comment on.

1) In a theory with a Cauchy surface, the past and future are determined by the state at anyone point in time. Here, not assuming the block universe means we accept determinism, but we don't accept the reality of the certain future. In special relativity, this is equivalent to postulating an aether, since there is a privileged time with which time evolution occurs.

2a) In a theory without a Cauchy surface, then the future or some large section of the manifold is not determined by any smaller subset of the manifold, and the undetermined section is therefore considered not real.

2b) Does the LCDM model have a Cauchy surface? What are the physically important solutions of GR that do not have a Cauchy surface?

 

[atyy]

I don't know why block universe advocates are so stuck on solipsism. Nobody ever brings it up but them. It is a nonsense connection.

As long as I believe that the events on my past light cone are external to me and not merely figments of my imagination then I am not a solipsist, regardless of what I may choose to assert or not assert about the structure of the universe outside of my past light cone.

It seems close to solipsism, because it means that in an EPR experiment, if I am Alice and Bob is at spacelike separation, then Bob is not in my past when I get a result. So Bob does not exist, if I understand Peter Donis's position correctly. This is one of the ways of denying that a loophole free experimental violation of the Bell inequality implies nonlocality - denying the independent reality of distant results. It is not accepted that this implies solipsism, but it is close enough that views that are close to this usually try to explicitly defend against it. For example, http://arxiv.org/abs/1301.3274 (preprint version of Rev. Mod. Phys. 85, 1693)

 

[Dale]

It seems close to solipsism

It is nowhere near solipsism. I can believe that I am some "chosen" being and that my past light cone uniquely defines what "really actually exists" and still believe that those events are external to me. (note, I am not claiming that I am a "chosen" being nor do I believe that Peter Donis is claiming that, but I am trying to show how far you can push this idea without being a solipsist)

It is nothing more than philosophical name calling or at least trying to imply some sort of "guilt by association". Solipsism is a very specific philosophical position, not merely a broad category which includes any philosophical position with a privileged observer.

 

[atyy]

The interplay between quantum mechanics and SR is interesting, but to me, it doesn't conclusively point one way or the other. An argument from QM that sort of supports the idea of the block world is the question of the ontology of the wave function. Consider an EPR-type experiment where a twin pair of spin-1/2 particles is produced. Alice on Earth measures the spin of one of the particles, while Bob on Alpha Centauri measures the spin of the other. For simplicity, assume that they both measure spins in the same direction, so they should get opposite results. At the moment that Alice measures spin-up, she knows instantly that Bob will measure spin-down. But obviously (according to SR), her measurement result can't possibly affect Bob's measurement result. So it seems to me that the fact that Bob would measure spin-down must have been true (although unknown to Alice) BEFORE Alice made her measurement. To me, this suggests that Bob's result was pre-determined. And from Bob's point of view, Alice's result was pre-determined. So both results were pre-determined.

Yes. I think it's a bit more plausible in QM if we take the Copenhagen interpretation, because although the entire universe may be determined, it isn't in our theory, since we don't have a wave function of the universe. I think what you are saying is that superdeterminism could be true, which we all agree on, but it is not useful to us. On the other hand, in GR, even if it were true that the future is undetermined, and maybe GR will even fail in the future, within the theory itself, no such failure is predicted.

 

[martinbn]

I would like to understand this position better, so here is a paraphrase for those who don't support the block universe to comment on.

1) In a theory with a Cauchy surface, the past and future are determined by the state at anyone point in time. Here, not assuming the block universe means we accept determinism, but we don't accept the reality of the certain future. In special relativity, this is equivalent to postulating an aether, since there is a privileged time with which time evolution occurs.

I don't understand this implication. The existence of a Cauchy surface and a time function is not unique. Why would there be a privileged time?

2a) In a theory without a Cauchy surface, then the future or some large section of the manifold is not determined by any smaller subset of the manifold, and the undetermined section is therefore considered not real.

Why would it be considered not real?

2b) Does the LCDM model have a Cauchy surface? What are the physically important solutions of GR that do not have a Cauchy surface?

LCDM has.

If you think strong cosmic censorship is true and that most of the solutions are globally hyperbolic (i.e. have a Cauchy surface) then I guess the answer is none.

 

[atyy]

It is nowhere near solipsism. I can believe that I am some "chosen" being and that my past light cone uniquely defines what "really actually exists" and still believe that those events are external to me. (note, I am not claiming that I am a "chosen" being nor do I believe that Peter Donis is claiming that, but I am trying to show how far you can push this idea without being a solipsist)

It is nothing more than philosophical name calling or at least trying to imply some sort of "guilt by association". Solipsism is a very specific philosophical position, not merely a broad category which includes any philosophical position with a privileged observer.

But is correct to say that the position advocated in the OP is that events at spacelike separation from me now do not exist?

 

[Dale]

Does GR have any Cauchy surface? GR doesn't have a theory of matter, so I cannot see how it would have any Cauchy surfaces ever.

 

[Dale]

But is correct to say that the position advocated in the OP is that events at spacelike separation from me now do not exist?

I don't think that the OP advocated any position, merely showed the error in the argument of the block universe advocates.

 

[atyy]

I don't understand this implication. The existence of a Cauchy surface and a time function is not unique. Why would there be a privileged time?

Why would it be considered not real?

I'm not sure, I'm trying to paraphrase in more technical language what I think might be the position advocated in the OP.

LCDM has.

If you think strong cosmic censorship is true and that most of the solutions are globally hyperbolic (i.e. have a Cauchy surface) then I guess the answer is none.

If I understand you correctly, then all physically important solutions have a Cauchy surface. If so, then does the position advocated in the OP amount to denying the existence of a Cauchy surface? Or is it something subtler?

 

[atyy]

I don't think that the OP advocated any position, merely showed the error in the argument of the block universe advocates.

Hmmm, I thought the block universe is quite harmless. I think it is naive, but just about as naive as what we need to use the Copenhagen interpretation.

Isn't the block universe just saying our universe is a solution of the Einstein field equations? It is true we may not know which one of the solutions we are actually in, but doesn't the assumption that our universe is a solution of the EFE immediately assume the existence of the solution, ie. the block universe?

 

[atyy]

Does GR have any Cauchy surface? GR doesn't have a theory of matter, so I cannot see how it would have any Cauchy surfaces ever.

Global hyperbolicity (which martinbn mentioned) is equivalent (I think) to the existence of a Cauchy surface in GR. I believe LQG's starting point assumes a version of GR in which solutions must be globally hyperbolic - the point is not that LQG is correct, but that I have not seen this assumption criticized, so I think most people believe that the assumption of global hyperbolicity isn't too restrictive.

 

[martinbn]

If I understand you correctly, then all physically important solutions have a Cauchy surface. If so, then does the position advocated in the OP amount to denying the existence of a Cauchy surface? Or is it something subtler?

I don't see how this is related. His comment is applicable for Minkowski spacetime, which is globally hyperbolic. So, no, he is not denying the existnace of Cauchy surfaces.

 

[martinbn]

I'm not sure, I'm trying to paraphrase in more technical language what I think might be the position advocated in the OP.

But I think his position is clear, and I think that everyone agrees with him. The only difference between people might be that some would say that the second part of the premise is natural and should be accepted.

 

[Dale]

Hmmm, I thought the block universe is quite harmless. I think it is naive, but just about as naive as what we need to use the Copenhagen interpretation.

The issue isn't the block universe interpretation. The issue is the validity of the arguments used to assert that the block universe is the "one true" interpretation of SR.

Personally, the block universe is my preferred interpretation. However I recognize that as a personal preference and not some unavoidable logical implication of SR. If people want to use the block universe interpretation then they are welcome to do so. They are even welcome to explain why they personally prefer the block universe interpretation over other interpretations.

However, when they try to argue that the block universe is logically implied by SR to the exclusion of any other interpretation then their arguments must be sound. They are not sound, as shown by the OP and many other threads on this topic.

 

[Dale]

Global hyperbolicity (which martinbn mentioned) is equivalent (I think) to the existence of a Cauchy surface in GR. I believe LQG's starting point assumes a version of GR in which solutions must be globally hyperbolic - the point is not that LQG is correct, but that I have not seen this assumption criticized, so I think most people believe that the assumption of global hyperbolicity isn't too restrictive.

Using GR alone you cannot predict whether a star will go nova or not, so you cannot determine the spacetime describing that star without some additional theory of matter that will describe if the star explodes or not. I.e., GR does not include any state equations for the matter distribution that would allow you to determine the future from a given initial condition.

 

[Geometry_dude]

Yes, DaleSpam, I agree with you that solipsism is a bit too much in this case, which your counter-example shows excellently. Also, I wasn't advocating the block universe, just stating implications.

The past lightcone is the events you see at a fixed proper time of your worldline, so it makes sense to define this as "your present".

As should be clear to everyone, one has to distinguish between what GR says and "the real world", which we model with GR. The question then is whether we want to believe what GR says about the fundamental nature of time and determinism or whether we do not want to believe it for some other metaphysical reasons. All you can do is check whether your particular position is compatible with the phenomena.

Personally, I agree with Smolin that GR alone fails to capture "the essence of time" and it appears to me that if we only accept the fundamental model of spacetime in GR even without the Einstein equations, then we have to introduce a direction in time and to me it appears that the most natural way to do this is to fix a global complete timelike vector field, which has a complete timelike flow, i.e. a "flow of time". This way there is no need to fix a Cauchy surface (assuming the spacetime is globally hyperbolic and not, e.g. vicious) and no contradiction with the twin effect. Whether this has any predictive benefit and whether this vector field can be found is of course another question.

DaleSpam, that's an excellent remark. In principle one could have a probabilistic theory of matter and then look how the spacetime would behave in each case. The only problem I see is that such a theory of matter is usually dependent on the metric.

 

[atyy]

The issue isn't the block universe interpretation. The issue is the validity of the arguments used to assert that the block universe is the "one true" interpretation of SR.

Personally, the block universe is my preferred interpretation. However I recognize that as a personal preference and not some unavoidable logical implication of SR. If people want to use the block universe interpretation then they are welcome to do so. They are even welcome to explain why they personally prefer the block universe interpretation over other interpretations.

However, when they try to argue that the block universe is logically implied by SR to the exclusion of any other interpretation then their arguments must be sound. They are not sound, as shown by the OP and many other threads on this topic.

Ok, I think that makes sense. As I understand, in SR and GR one doesn't argue for the block universe. One simply assumes it: ie. we assume that the universe is a solution of a set of globally hyperbolic equations.

Using GR alone you cannot predict whether a star will go nova or not, so you cannot determine the spacetime describing that star without some additional theory of matter that will describe if the star explodes or not. I.e., GR does not include any state equations for the matter distribution that would allow you to determine the future from a given initial condition.

Yes. I think the assumption of global hyperbolicity is just that the equations exist. I think it is also assumed that we don't know the initial data well enough to know which solution we are in exactly, but that the solutions are well behaved enough that we can make coarse grained predictions about the future based on our limited data.

 

[atyy]

I don't see how this is related. His comment is applicable for Minkowski spacetime, which is globally hyperbolic. So, no, he is not denying the existnace of Cauchy surfaces.

How about in GR - is there a Cauchy surface that lies entirely within the past light cone of a single observer (for all physically important solutions)?

 

[martinbn]

How about in GR - is there a Cauchy surface that lies entirely within the past light cone of a single observer (for all physically important solutions)?

Of course not, but why do you ask about this?

 

[atyy]

Of course not, but why do you ask about this?

I guess that if only events in the past light cone are real, then since the Cauchy surface doesn't lie entirely within the past light cone, then the Cauchy surface is not real, which would seem like a good argument that the future is not determined.

 

[martinbn]

I guess that if only events in the past light cone are real, then since the Cauchy surface doesn't lie entirely within the past light cone, then the Cauchy surface is not real, which would seem like a good argument that the future is not determined.

The future is determined by the data on the Cauchy surface, and a Cauchy surface exists through every point in the spacetime. Being real is different.

 

[PeterDonis]

Wow, lots of good discussion! Rather than try to respond individually, let me clarify a few points that I think will address the main questions that have been raised in the discussion.

(1) As DaleSpam noted, in the OP I am not, strictly speaking, advocating any particular positive viewpoint. I am only trying to show that a particular claim, that the observed fact of relativity of simultaneity is sufficient to *require* the block universe interpretation of SR, is not valid. (A quick note: I said "SR" in the OP, but I don't see how the logic would be changed at all if we extended the argument to cover any spacetime that was a solution of the EFE--or perhaps any spacetime with a Cauchy surface; more on that below. SR, as far as the argument in the OP goes, can really be considered as just one particular solution of the EFE, Minkowski spacetime; none of the key features of the argument rely on properties that are particular to that spacetime, like global flatness.)

That said, I do, of course, have a positive viewpoint, and I might as well give it. In our ordinary thinking about what is "real", we do draw a key distinction between "past" and "future": we view the "past" as fixed and certain, unchangeable, whereas we view the "future" as not yet certain, changeable. So we view the "past" as "real" in a way that the "future" is not. (Note that the block universe argument I describe in the OP implicitly adopts this view as well; the quote from Penrose I gave, that states the argument, draws a distinction between events which are "fixed and certain" and events which are not. More on that below.)

However, as I noted in the OP, that view is based on Newtonian, non-relativistic physics. Once we admit relativity into our worldview, we have to admit the existence of a third category, "elsewhere", consisting of events that are neither "past" nor "future" in our usual senses of those terms. The question then becomes, what is the "reality category", so to speak, of events that are in the "elsewhere" region? The argument that block universe proponents make, the claim that relativity of simultaneity requires the block universe interpretation, implicitly assumes that events in "elsewhere" must be put in the same "reality category" as events in the "past" (i.e., events in our past light cone). My argument in the OP is simply that that assumption is not logically required--its truth is consistent with relativity, but so is its falsity--and without it, the argument that relativity of simultaneity requires the block universe interpretation does not go through. But my own view is that the assumption is just plain false: if push comes to shove and we have to choose, we should put "elsewhere" events in the same "reality category" as "future" events (i.e., events in our future light cone). (My actual preference would be to just admit that there are three separate categories, not two, and leave it at that. But many people's intuitions can't seem to find room for that.)

(2) Just as a note, if you're looking for a quick summary of the point of view I was arguing in the OP, this quote gives it:

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.

In other words, I'm not saying that the *argument* I described in the OP, that block universe proponents give, is invalid, logically speaking. I'm saying that one of its *premises* is not established. And I'm focusing attention on that particular premise because *that* is where the real argument is; block universe proponents seem to want to just gloss over that premise as too obvious to need justification, but it isn't--it's the crux of the issue.

(3) I think it's important to distinguish our models of reality from reality itself. Any 4-dimensional spacetime, any solution of the EFE (including Minkowski spacetime), is a *model* of reality. In the model, of course the entire 4-d spacetime is determined; within the model, there is no reason to pick out any particular portion of the 4-d spacetime as being "more real" than any other. But the *reason* for that is that, within the model, the initial conditions are determined--or, more generally, the conditions on some Cauchy surface of the spacetime (assuming there is one--but the main spacetimes that get lots of practical use, Schwarzschild, Kerr, FRW, etc., and Minkowski of course, all have Cauchy surfaces) are determined, and of course it's a theorem that determining the conditions everywhere on one Cauchy surface is sufficient to determine the entire spacetime.

But in reality, we never know the conditions on an entire Cauchy surface. We only know the conditions in our past light cone, which does not completely cover any Cauchy surface. So we can never be sure that any given model, any given 4-d spacetime, exactly matches reality, *except* in our past light cone. There will always be multiple 4-d spacetimes (strictly speaking, an infinite number of them) that are consistent with the data in our past light cone. We can talk about some being more probable than others--a spacetime in which the Sun is exploding "right now", i.e., in a surface of simultaneity passing through Earth at this instant, is just as consistent with our past light cone data as one in which the Sun continues to shine normally, but I think most would agree that the former is much less probable. But we can never be *sure* which model is correct, for a given region of spacetime, until we have all the data from that region--until we actually *see* the Sun still shining normally, eight minutes from now, and thereby verify that it didn't explode. And at that point, the relevant events are in our past light cone; so we can never be forced to view any events outside our past light cone as "real" in the way we are forced to view events within our past light cone as "real".

Note, btw, that I have said "our" past light cone above. Surely, we are tempted to say, events outside our past light cone (like events happening in the Andromeda galaxy "right now") are in the past light cone of some other event in 4-d spacetime? But that is simply making the same error that I described above: confusing the model with reality. Yes, in our current *model* of 4-d spacetime that describes the universe, there are plenty of events which have, in their past light cone, events happening "right now" in the Andromeda galaxy. But that's the model, not reality.

To put it another way: if we're going to admit any distinction at all between different "categories of reality", the only sound basis on which to draw the distinction is our current past light cone, given our particular current location in spacetime, according to our best current model of it. If we refuse to admit any such distinction, then of course we can say that all events are "equally real", as block universe proponents want to say: but that's not an argument, it's just assuming the conclusion.

(4) I confess I am as confused as DaleSpam is by the repeated assertions about solipsism. It particularly confuses me in response to the OP in this thread, since I specifically addressed precisely that question:

(2-1) The only alternative to the second premise is solipsism (only my present event is real).

...

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.

In other words, the key issue is not "does anything exist besides me at the present moment?"--*nobody* is taking the solipsist viewpoint that the answer to that question is "no". The question is whether we are justified in considering any events outside our past light cone as fixed and certain, the way we consider "past" events (events in our past light cone) to be fixed and certain. My answer to that is "no", but that's a long, long way from solipsism.

Note, also, that I am carefully not using the word "exist" at all, and I'm putting the word "real" in scare-quotes whenever I can, and I'm trying to use the term "fixed and certain" as a better way of describing the distinction that's at issue. The question is not whether, say, there are "real" events happening in the Andromeda galaxy "right now"; the word "real" is simply too imprecise and too charged with different connotations to different people to be a useful one in this connection. But asking whether there are events happening in the Andromeda galaxy "right now" that we, here on Earth right now, can view as being fixed and certain, is much more precise and admits of a much more definite and useful answer: no, there aren't, because any such events would be outside our past light cone, here on Earth right now. We won't know for sure that any such events happened, much less exactly what happened at them, for another couple million years, when they move inside our past light cone.

Btw, I am also *not* saying that events in our past light cone are "present" events. Of course they're not: they're past events. The word "present" is another of those words that, while useful in a colloquial sense, breaks down when you try to push it too far. Strictly speaking, from the viewpoint of a given spacetime model, the "present" of any given observer is just a single event--more precisely, once you pick a particular event on a particular observer's worldline, you are *defining* that single event as that observer's "present" for the purpose of whatever problem you are analyzing. What we actually perceive as the "present", in our everyday lives, is really a small segment of our past light cone, since it takes time for our sensory apparatus to send signals to our brains and for our brains to process those signals and produce our conscious experience. So the "present" we perceive is, from the viewpoint of a spacetime model, a kind of illusion. But that's probably getting into areas like cognitive science that are out of scope for this forum.

 

[PeterDonis]

Global hyperbolicity (which martinbn mentioned) is equivalent (I think) to the existence of a Cauchy surface in GR.

Yes, it is. I believe this is shown in Hawking & Ellis.