The Block Universe: Examining the Rietdijk-Putnam Argument

[Dale]

I must not understand what is meant by Cauchy surface. How can any theory which is not a theory of everything have a Cauchy surface? I thought that having a Cauchy surface meant that given a complete initial condition the future and past were uniquely determined. But unless you have a theory of everything I don't see how that could ever be true.

 

[atyy]

I must not understand what is meant by Cauchy surface. How can any theory which is not a theory of everything have a Cauchy surface? I thought that having a Cauchy surface meant that given a complete initial condition the future and past were uniquely determined. But unless you have a theory of everything I don't see how that could ever be true.

In my understanding, we are just assuming its existence without evidence, for convenience in model building. It's a bit like assuming the topology of our universe is "space X time". It's just a property of all models in the model class we are restricting ourselves to by convention, even though we don't know which model in the model class is the best fit to the data.

martinbn mentioned the strong cosmic censorship conjecture, which is related to global hyperbolicity. Wuthrich's thesis http://philosophyfaculty.ucsd.edu/faculty/wuthrich/pub/WuthrichChristianPhD2006Final.pdf discusses many of these issues, and he writes "The strong version of this conjecture claims that no singularity—except a possible initial singularity—can ever emanate causal signals to any observer living in a physically realistic spacetime. In other words, the strong cosmic censorship conjecture demands that all physically realistic spacetimes be globally hyperbolic.".

Interestingly, he also writes "Although no proof or disproof of the conjecture has so far been forthcoming in spite of vast efforts, there is evidence that it may be violated, even in its weak form, in nongeneric situations of highly symmetric gravitational collapse. Simultaneously, the corpus of evidence suggesting that the conjecture, at least in its weak form, may be true for generic physically realistic spacetimes has significantly grown over the last years. The violation of either or both of the cosmic censorship hypotheses has consequences for the validity of determinism."

 

[PeterDonis]

I thought that having a Cauchy surface meant that given a complete initial condition the future and past were uniquely determined.

AFAIK the term "Cauchy surface" is particular to GR; it's not a general term used in various physical theories. Given initial conditions on a Cauchy surface, the *spacetime geometry* everywhere in the spacetime is uniquely determined. That would also uniquely determine the stress-energy tensor everywhere in the spacetime, via the EFE. But it would not uniquely determine anything else that was not uniquely determined by the spacetime geometry or the SET. (For example, it wouldn't uniquely determine quantum states everywhere, since there can be multiple quantum states with the same classical SET as their best classical approximation.)

 

[atyy]

Would it be correct that there is no contradiction in "believing" in the "block universe" as well as the idea that only things in the past light cone are "real" or "fixed and certain"? For example, I usually consider the Newtonian universe a block universe, just because it is deterministic. However, I also acknowledge that the past and future seem different. These can both be true. At the microscopic level, fine grained entropy does not increase and the future is as determined as the past. At the coarse grained (thermodynamic and/or psychological) level, entropy increases, and the future is more uncertain than the past.

In GR, we can have the block universe by assumption (I agree the argument from simultaneity is silly, so let's just tautologically assume it by virtue of our chosen model class - deterministic globally hyperbolic models of classical GR), and we can also have thermodynamic time and psychological time, and psychological time coincides with the assignment of events in the past light cone as fixed and certain.

http://fqxi.org/community/forum/topic/259
Hrvoje Nikolic, Block time: Why many physicists still don't accept it?

http://www.cpt.univ-mrs.fr/~rovelli/book.pdf
Carlo Rovelli, Quantum Gravity (see section 2.4.4)

 

[PAllen]

I draw a distinction between a deterministic theory and a block universe interpretation (philosophy). A theory (deterministic or not) can have many predictions confirmed or falsified, while a block universe interpretation can never be falsified, nor confirmed (over a a more parsimonious interpretation of the same theory).

I have never considered Newtonian physics as requiring a block universe interpretation, nor SR, nor GR, though all are deterministic as classical theories.

To me, the most natural non-block universe interpretation of Newtonian physics relies on the shared division into past and future of all observers at a given position and time, irrespective of motion and past. Then, the past is considered to have already happened, the future not so, irrespective of whether it is determined by the past.

In SR/GR, simultaneity surfaces are not shared by all observers at an event, and there is no preferred such surface for non-inertial observers, and no preferred such surface globally in GR for any observer. However, all observers at an event do share a fundamental surface - the past light cone. To me, this is the unique natural generalization to SR/GR of the Newtonian past/future boundary. It shares with the Newtonian boundary that it is unaffected by observer state of motion, and is not dependent on any convention. That this boundary differs for non-colocated observers in SR/GR is just something to accept about the these theories as distinct from Newtonian physics.

 

[PeterDonis]

Would it be correct that there is no contradiction in "believing" in the "block universe" as well as the idea that only things in the past light cone are "real" or "fixed and certain"?

It depends on what you mean by "block universe". The meaning of that term that I have been assuming in this thread (because it's the one used by the people I was arguing against in those previous threads I referred to in the OP) is that "block universe" means "all events in 4-d spacetime are fixed and certain". This is obviously inconsistent with believing that only events in the past light cone are fixed and certain.

But of course the term "block universe" could have other meanings which are not inconsistent with the belief that only events in the past light cone are fixed and certain. For example, if all you mean by "block universe" is "our models of the universe are deterministic", then obviously there is no inconsistency, since determinism only leads to all events in 4-d spacetime being fixed and certain if you have initial data on an entire Cauchy surface, which the past light cone is not (as I noted in a previous post).

 

[bahamagreen]

It depends on what you mean by "block universe". The meaning of that term that I have been assuming in this thread (because it's the one used by the people I was arguing against in those previous threads I referred to in the OP) is that "block universe" means "all events in 4-d spacetime are fixed and certain". This is obviously inconsistent with believing that only events in the past light cone are fixed and certain.

But of course the term "block universe" could have other meanings which are not inconsistent with the belief that only events in the past light cone are fixed and certain. For example, if all you mean by "block universe" is "our models of the universe are deterministic", then obviously there is no inconsistency, since determinism only leads to all events in 4-d spacetime being fixed and certain if you have initial data on an entire Cauchy surface, which the past light cone is not (as I noted in a previous post).

Are not the past light cones of ALL events fixed and certain?
Are there events that do not fall within the past light cone of any other event?

 

[PeterDonis]

Are there events that do not fall within the past light cone of any other event?

I'll answer this second question first: not in any spacetime that's globally hyperbolic, which means any spacetime we're interested in here. (I think the sufficient condition to make your statement true may actually be more general, but I don't have time to dig out my copy of Hawking & Ellis for review right now. )

Are not the past light cones of ALL events fixed and certain?

"Fixed and certain" is relative; it depends on which event you, the person trying to decide what is "real", are at, at the instant of your personal proper time when you are trying to decide.

More precisely, the interpretation I have just given is just as consistent, logically, with relativity as the interpretation implied by what I quoted from you (which is just the "block universe" interpretation, in the strong version I have been using that term to denote). So it is not valid to claim that the strong interpretation (all events are fixed and certain) is *required* by relativity. That is the claim I was arguing against in the OP.

 

[atyy]

Are not the past light cones of ALL events fixed and certain?
Are there events that do not fall within the past light cone of any other event?

I offered a "eat your cake and have it" interpretation in post #39, which is a redefinition of "block universe" as correctly understood by PAllen in #41 and Peter Donis in #42. In this point of view, the block universe is fundamental by postulation of the model class and has no fundamental arrow of time. But we allow initial conditions and a coarse graining so that there is an emergent arrow of time, and a further coarse graining so that there are emergent observers each with a sense of self. Furthermore, I pick out a special observer which is me in the model. Then "fixed and certain" is the subjective description by me of particular events, which by definition of its subjectivity and common sense in everyday life are only those events in my past light cone. And straightaway you can see this is really an emergent approximate description since I am not really a point in spacetime at the fundamental level, and there are some things like death and taxes which I believe to also be fixed and certain, though they are not yet labels I can assign to specific events.

 

[bahamagreen]

Second question's answer seems fine.

First question's answer is the issue. "Fixed and certain" is relative to the observer, in that each will have a different past light cone within which to map this F&C region with respect the the observer's event.
To the degree that an observer's past light cone falls entirely within a second observer's past light cone, I'm not seeing how the first observer avoids abstracting the inference that some regions of his future light cone fall within the second observer's past light cone, and that all events in the first observers' future light cone must fall within the past light cones of other observers.

How does the first observer not avoid the conclusion that if his future light cone is F&C for others it must also be so for himself (not observationally, but geometrically logically)?

The observer does not positively know his future LC is F&C or not. But if the observer doesn't know, yet other observers do know, then doesn't the certain and consistent knowledge by others that one's FLC is F&C trump one's lack of certainty, by this abstraction?

If there are people in the room who know how many marbles are in the bag, but I don't know, then it is true that this knowledge is relative to we observers in the room. But someone showing up and asking, "Show of hands, how many are certain of the number of marbles in the bag?" seeing any hands raised in response is going to conclude that the number is F&C, despite my not knowing. If I trust all the others, I must abstract and conclude that the number of marbles in the bag is F&C.

 

[PeterDonis]

"Fixed and certain" is relative to the observer, in that each will have a different past light cone within which to map this F&C region with respect the the observer's event.

A more correct statement is: "Fixed and certain" is relative to the observer, *and* to the particular event on the observer's worldline that we choose as "the present".

To the degree that an observer's past light cone falls entirely within a second observer's past light cone

More correctly: that an observer's past light cone, at a given event on that observer's worldline (call that event O), falls entirely within a second observer's past light cone, at some event on the second observer's worldline (call that event S).

You are correct that this will only happen if event S is in the future light cone of event O. But for that very reason, the first observer, at event O, will not view event S as a "present" event for the second observer--i.e., he will not, at event O, view the past light cone of event S as fixed and certain for the second observer (and therefore he won't for himself either). The only events on the second observer's worldline that the first observer must view as fixed and certain, at event O, are those in the intersection of the second observer's worldline and the past light cone of event O. Event S is not such an event; so as far as the first observer is concerned, at event O, event S is in the second observer's future, just as it is in his own (the first observer's) future.

How does the first observer not avoid the conclusion that if his future light cone is F&C for others it must also be so for himself (not observationally, but geometrically logically)?

Because light cones are properties of events, and because, as above, the only events on the second observer's worldline that the first observer must view as fixed and certain are those in the past light cone of event O (i.e., of whatever event on the first observer's worldline is viewed as "the present"). No event on the second observer's worldline can both be in the past light cone of event O, *and* have a past light cone that contains entirely the past light cone of event O.

if the observer doesn't know, yet other observers do know

"Know" is relative to events, just as "past light cone" is. See above.

If there are people in the room who know how many marbles are in the bag, but I don't know, then it is true that this knowledge is relative to we observers in the room. But someone showing up and asking, "Show of hands, how many are certain of the number of marbles in the bag?" seeing any hands raised in response is going to conclude that the number is F&C, despite my not knowing. If I trust all the others, I must abstract and conclude that the number of marbles in the bag is F&C.

And at the event on your worldline at which you have all this information, all of the events in question, the events at which other observers displayed knowledge of the number of marbles in the bag, are in your past light cone. So you never need to attribute "knowledge" to other observers at events outside your past light cone.

 

[bahamagreen]

Peter, thank you; you are very gracious to bear with me and make the detailed reply.

The part about O and S helps a lot. I'm still struggling, but I think you have identified my misconception about the light cones with - "...he will not, at event O, view the past light cone of event S as fixed and certain for the second observer (and therefore he won't for himself either)."

That is a "stronger" form of saying "Fixed and certain is relative to the observer"; my misconception was using a "weak" sense of it thinking that observers would view trivially different but always consistent F&C... I did not extend this strongly to realize that observers would disagree about F&C.

I'm still working to figure out how to grasp this, but this was a missing piece. I don't understand it yet, but I agree this makes the second premise a real issue.