# God and Time III: General Relativity

Imagine if somebody said that only one height exists at once—whichever elevation you happen to be in at the moment, only things at that elevation really existThe moles in the ground are can be asserted to be "below", but that just means that they used to exist when you were in your basement.  And the birds in the trees are "above" you, but that just means that they will exist after you indulge your habit of climbing to the attic.

(Unlike the case of time, I can go either up or down, but who cares?  Time may flow like a river, but space flies like a bumblebee, wobbling around in random directions.)

This is clearly uncommonly silly, and there are several retorts one might make to it.  If the ground beneath us doesn't exist, then what on earth is holding us up and supporting us?

Also, there is no such thing as a perfectly flat human being.  Your brain occupies several different planes of elevation at once, and there is no good reason to think that any horizontal slice of your brain would be capable of thinking, independently of all the other slices.

Another possible retort would be to critique the language, and say that there is really no meaning to it.  If I say that the birds will exist after I go into the attic, I am implicitly and illegitimately assuming that my attic exists, and that I can therefore go up to it.  But if I really took my philosophy completely seriously, I would have to believe that the attic doesn't exist either.  To say that up exists upwards is a circular definition, which can hardly console us if things that are up do not exist in the first place.

But if none of these "philosophical" arguments are persuasive, I can always crack out the "Argument from Geophysics".  Our most advanced scientific theories suggest that the world is in fact round.  It turns out that up and down are relative concepts, you see.  In Australia, they fall in a different direction than we do.  What they call down is different from what we call down.  The actual laws of physics are rotationally symmetric.  There is a symmetry which mixes up the up-down axis with the right-left axis and the forwards-backwards axis.  We can call "down" the direction which points to the Earth, but the earth is a contingent object which might not have existed.  Out in space, there is no reason to adopt a geocentric coordinate system.

And certainly, if we start doing theology, it would be presumptuous to think that the God who created the whole universe, all the stars and galaxies, is confined to existing at some particular elevation.  Whatever limitations we may ascribe to created beings, we should not ascribe them to the unlimited Creator, who made them all out of nothing.

(Some ideas, e.g. the idea that God is a really old man with a long white beard who lives in the sky, really do become ridiculous when you consider the size and proportions of the Universe as discovered by modern Science.  But garden variety Internet Atheists are always trying to manufacture this feeling artificially, in situations where it's a non sequitur.  If you can't tell the difference between Classical Theism and belief in a sky-fairy or an invisible garage dragon, that shows your intellectual limitations, not mine.)

This analogy summarizes the previous posts in this series, only I was talking about Time instead of Height:

It turns out that there is also a "rotational symmetry" so to speak (called a Lorentz boost) which mixes Space and Time.  It works a little bit differently from a regular rotation, since it involves rotating along hyperbolas instead of circles.  Mathematically, it's just a matter of throwing in a minus sign.  A result of this is that there is a lightcone which is unaffected by the symmetry transformation.  Some pairs of points are timelike separated (one point can affect the other) and others are spacelike separated (neither can affect the other), but there is no such thing any more as simultaneity.  From the perspective of somebody who is stationary, time goes slower for somebody who is moving; this is called "time dilation".

But in General Relativity, things get more wild, since space and time can themselves be affected by the behavior of matter.  Thus the distances and durations become a function of where and when you are.  Time runs slightly slower near the earth than it does in outer space.  (Believe it or not, this is why things fall down.  An object in free-fall always takes the path which maximizes the amount of time to get from point A to point B.  This is a compromise between SR and GR time dilation effects.)

In Special Relativity, space and time are a unity, but they have a fixed geometry.  The distances and the times are the same regardless of what matter does.  They are unaffected, and therefore they might possibly (by a Materialist, not by a Classical Theist) be taken to be a fundamental, necessary, and immutable feature of reality, which limits other entities but is not itself affected by them.

In General Relativity, by contrast, the spacetime metric $g_{ab}$ not only affects matter, it is in turn affected by matter.  This implies that the causal structure  (which tells you which points can affect which other points by signals) is itself causally affected by stuff.  So we learn that the particular geometry of spacetime is a contingent, mutable feature of reality.

From a philosophical point of view, the Absolute Spacetime of Newton (or Special Relativity) was never very satisfying.  Even if it is Absolute, an empty Spacetime can hardly itself be the source of all that is real.  Thus there must also be some other principles besides those of space and time, threatening an unparsimonius proliferation of fixed principles.  It has seemingly arbitrary features, and yet if it is really immutable and necessary it is difficult to explain it in terms of other things, other than just God's will.  Many philosophers such as St. Leibnitz and Mach rejected absolute spacetime, and tried to reduce it to the status of merely relative data relating various material objects.  Newton and his followers, on the other hand, tried to identify Space and Time with the necessary attributes of God, his Immensity and Eternity, but this doesn't work very well theologically.

Einstein was influenced by Mach in the creation of GR, but it doesn't really meet Mach's original aspirations since spacetime is still a reality independent of matter in his theory.  Mach would have said that spacetime has no independent reality; that it is just a way of keeping track of the relationships between material objects.  (He thought that the water would run to the sides of a rotating bucket only because the bucket was rotating compared to the distant stars).  But in GR, it is possible to have a geometry apart from any matter, e.g. empty Minkowski space, or a spacetime with gravitational waves.

There is indeed a sense in which the curved spacetime of GR is relational—there is no absolute fixed coordinate system to measure everything else by.  Thus it is only meaningful to  measure the locations and times and velocities of objects relative to other objects, indeed unlike SR we must even specify a specific path through spacetime between the two objects, in order to meaningfully compare them.  But, even though GR is relational, the spacetime metric $g_{ab}$ is itself one of the entities which may be used to construct relational observables.

Thus I would say that Spacetime in GR is neither absolute in the Newtonian sense (more fundamental than matter), nor relative in the Leibnitz/Machian sense (less fundamental than matter), but rather has the same status as matter.  It is real in the same concrete, tangible way that a rock or a tree is real.  It is one of several different fields in Nature, all with equal status, all capable of affecting and being affected.

As some physicist I can't track down right now (Carlo Rovelli?) once said, if an intense gravity wave passed by and destroyed your house, you would think of it as being just as real as any other kind of matter.

Now, if Spacetime (and therefore Time) is real in the same sense that a rock or a tree are real, that meas that it is also a contingent, created being.  Time is just one of the many things that God has created.  But the Creator, blessed be he, is not dependent on rocks or trees for his existence.  He is not measured or parcelled out by units of space, therefore he is also not measured by time.  Time is just something he created, which need not have existed.  Before they were created, and afterwards, he exists just the same as he ever was.  He is the Absolute, the Fundamental Reality which everything else depends on, but which does not itself depend on anything.  God's divine attributes (his necessity, eternity, and unity) imply that he cannot change with time, nor can he consist of distinct parts at each time.  He is the Alpha and the Omega, the Beginning and the End!

But I digress, since I was planning to discuss the Scriptures in the next post.  This one is supposed to be about how GR makes it even harder to say that God is in Time.  I've already talked about the contingency of the spacetime geometry.  Now let's talk about the arbitrariness of selecting what you mean by a single moment of time.

In SR, there is still a preferred notion of "simultaneity" if you pick a particular reference frame.  I drew a picture of that in the previous post:

Here Sue and Martha don't agree on whether $p$ or $q$ came first.  But maybe Sue is objectively right and Martha objectively wrong?  Somebody could still argue that there is a special inertial frame of reference with respect to which God happens to exist.  In other words, God has no position, and yet he has a velocity?  He is not an idol, a piece of wood or stone carved into an anthropomorphic form.  Why should he be limited in this way.

But in GR, spacetime is curved, and there are no inertial coordinate systems defined on the whole spacetime.  You can divide Spacetime into Space and Time in any way you like, using wiggly surfaces (although one might want to restrict to surfaces which are everywhere spacelike).  For example, the relationship between 2 coordinate systems could look like this:

In GR is not always any particular connection between a given coordinate system and a given observer, so I have not drawn Sue and Martha in this picture, but I have still drawn the spacelike separated points $p$ and $q$ which are in an ambiguous time relation.  (Since spacetime is 4 dimensional, the time slices I've drawn actually represent 3 dimensional surfaces.)

Of course, nothing stops you from choosing a funky coordinate system in Newtonian mechanics or SR either.  For example, it is often convenient to choose a rotating frame of reference to follow a rotating body such as the Earth.  Or a coordinate system which tracks an accelerating observer.  (Many pop descriptions of GR give the false impression that you need GR to describe accelerating coordinate systems; this is obviously false since objects can accelerate even in Newtonian mechanics, and nobody can prevent you to choosing coordinates however you like no matter what the correct theory of physics is.)

The difference in GR is that none of the coordinate choices are particularly nice or special.  It looks from the picture above like the gray coordinate system is nicer than the apricot one, but that's just because your computer screen is flat.  On a typical curved spacetime, all time slices are bent in one place or another.  Thus, instead of having a 3 parameter family of "nice" time slices, we have an infinite dimensional family.  (The details depend on which particular curved spacetime we have.)

Do we really want to say that God's experience of time depends on making an arbitrary choice about how to respond to the gravitational field of each and every star?  An choice which, from the perspective of physics, is a completely meaningless choice of coordinate system?  God's perspective on the universe should not be more provincial and limited than the perspective of a mere physicist such as myself.  The Glory of Israel does not change, so why does he need a time coordinate?

Now it is true that on some specially nice spacetimes, there is a naturally nice choice of time coordinate.  For example in an FRW expanding universe, there is a "cosmic time" coordinate which tracks the overall size (the "redshift factor") of the universe.  Some philosophers, such as St. William Lane Craig, have suggested that God's "time" might simply be this "cosmic time".

But this is a misunderstanding of the physics of our universe.  The FRW metric is a just an approximation to reality.  It describes a universe which is completely uniform (the same in everywhere) and isotropic (the same in every direction).  This is a very good approximation on large distance scales (billions of light years), but on shorter distance scales (e.g. the solar system, or the milky way, or your living room) you may have noticed that matter is not distributed uniformly.  It comes in clumps, and each of these clumps has a gravitational field which distorts the spacetime metric, making the FRW metric no longer correct.  On a lumpy spacetime, the notion of "cosmic time" is not well-defined.

With sufficient effort, one might be able to define a different time coordinate which is well defined.  Perhaps the maximum proper time since the Big Bang, or something.  But reformulating GR in a way that makes special reference to such quantities spoils the beauty of Einstein's theory.  It is ugly.  As for a blind and lame theory like that, I hate it in my soul.  Why should our physical theory describing gravitation get uglier when we describe how it relates to God?

The closest thing I know about to an elegant reformulation of GR with a special time coordinate is called "shape dynamics".  (I say know about, since I don't understand it).  Apparently this is equivalent to GR in a coordinate system where you pick your time slices to be CMC ("constant mean curvature") slices.  I won't explain that right now, except to say that the soap films in your bubble bath are also CMC surfaces.  But given a GR spacetime metric, there might be many possible choices of CMC slicings, or none.  So the equivalence to GR is not complete.

It is of course always possible that a new theory of physics (such as Hořava gravity) might reimpose something like absolute time.  But I wouldn't count on it.

I think this is a good illustration of the point I made in Models and Metaphysics:

But it seems to me that the correct view is in the middle, that Physics has some bearing on Metaphysics but it doesn't fully determine it.

There are always going to be ways to force physics into being compatible with an A-theory metaphysics of time, but it doesn't look elegant or pretty.  The B-theory seems to fit much more naturally.  Physics can't usually rule out metaphysical ideas, but it can make them look a lot clunkier.

But in this case, physics isn't telling us anything we couldn't have learned from good philosophical theology.  Or from scriptural exegesis—which will be the subject of my next post in this series.

I am a Lecturer in Theoretical Physics at the University of Cambridge. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my postdocs at UC Santa Barbara, the Institute for Advanced Study in Princeton, and Stanford. The views expressed on this blog are my own, and should not be attributed to any of these fine institutions.
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### 30 Responses to God and Time III: General Relativity

1. Bob Kurland says:

Nice article, and I especially like your two preceding ones on the metaphysics of time and special relativity, which I hadn't read. Let me ask another question. If you think of special relativity and a block universe, then there is a predetermined future. Now what would be the equivalent of that taking general relativity--a block universe with squiggly world lines, or do you have unambiguous world lines with general relativity? And, further, I didn't read your article about free will, but it seems to me that a predetermined block universe pretty well destroys any non-compatibilist (sp?) notion of free will. The only way I would see to get around this would be to combine Molina's Middle Knowledge for God and a many world/many minds interpretation of quantum mechanics. By the way, there's an interesting argument about block universes between Christopher Isham and John Polkinghorne in "Quantum Cosmology and the Laws of Nature"...see http://www.ctns.org/books.html
click on the icon for "Quantum Cosmology..." and then on the chapter in the list on the right.

2. Aron Wall says:

Bob,
Thanks for your comments. (Also, it's nice to see a fellow blogger who is a physicist and a Christian.)

I do believe in libertarian free will, and I don't beleive in Molinism. Yet I don't believe that this is in any way contradicted by the hypothesis that the future exists (which you call the "block universe", but I think that is a misleading metaphor). I had free will in the past, I have it in the present, and I will have it in the future. Saying that the future and the past both exist, just as much as the present does, does not in any way contradict the previous sentence. Indeed it agrees with it. There is nothing to reconcile.

"Predetermined" is not the right word to use here. "Pre" refers to a time sequence. What, specifically, do you think would determine my free decisions, in such a way that I am not free? Note that, every decision is fixed after it is made, but that does not imply that it was made unfreely at the time. On my view of time, all spacetime events are like that, always.

In general relativity, point particles travel along timelike (or lightlike) worldlines. In the absence of other forces, they follow geodesics, which are the equivalent of "straight lines" in a curved spacetime. But if you allow for forces, they may wiggle around.

3. Bob Kurland says:

Thanks Aron for your explanation. What I mean by "predetermined" is that there are no choices, no alternatives for one to make. If the future is "there", then one's choice is determined--one may believe that one is making a free choice, but how can that be unless there are multiple futures for one to choose from, options each of which is possible? The type of free will I think you're maintaining is what I guess the professional philosophers call a compatibilist (sp?) free will. Or maybe not..enlighten me.
See
http://plato.stanford.edu/entries/compatibilism/
PS--I may have mentioned this in a previous comment. My son attended St. John's (Annapolis) and while his interests are in English, not science or math, he is proud that he knows what Maxwell's equations are and understands them.

How about describing God as an entity or a background independent of space-time or for that matter not having any properties or quantum numbers? All physics will be superimposed on that background.

5. Robert Childress says:

Hey Bob,

The claim that future decisions will be made doesn't impinge on the fact that such choices could be made with some degree of freedom. To say that the future is real is not to say that the future is now (which you seem to recognize by referring to the future as "there" (though perhaps it would be better to call it "then"?)).

But if we follow it out that the future is not now, then from our perspective at time "now" we do have different futures that could come to be. Obviously, only one future ultimately will exist as a "now" when we get "then," and that future will be (at least partially) determined by the free decisions we make along the way.

So, any decision I make "now" I make freely. That a decision exists in the past does not entail that I was not free to choose otherwise at that time. It just so happens that I freely made that decision then, so that specific decision is that which is recorded in time. That a decision exists in the future does not entail that I will be unable to choose differently at that time. It just means that at that time, I will freely make that decision. But the making of that future decision isn't set in stone "now," it's something that will happen in the future.

Clear as mud?

6. Calvin Marshall says:

Dr. Wall -- Thank you for this post and two previous ones on this topic. I've been reading through Lee Smolin's book 'The Trouble with Physics' and came across the quote below. I would be interested in your thoughts on this.

"All the theories that triumphed had consequences for experiment that were simple to work out and could be tested within a few years...Whatever else one says about string theory, loop quantum gravity, and other approaches, they have not delivered on that front...I believe there is something basic we are all missing, some wrong assumption we are all making...More and more, I have the feeling that quantum theory and general relativity are both deeply wrong about the nature of time. It is not enough to combine them. There is a deeper problem, perhaps going back to the origin of physics...Around the beginning of the seventeenth century, Descartes and Galileo both made a most wonderful discovery: You could draw a graph, with one axis being space and the other being time. A motion through space then becomes a curve on the graph. In this way, time is represented as if it were another dimension of space. Motion is frozen, and a whole history of constant motion and change is presented to us as something static and unchanging. If I had to guess (and guessing is what I do for a living), this is the scene of the crime. We have to find a way to unfreeze time -- to represent time without turning it into space. I have no idea how to do this. I can't even conceive of a mathematics that doesn't represent a world as if it were frozen in eternity...One thing I do know about the question of how to represent time without its turning into a dimension of space is that it comes up in other fields, from theoretical biology to computer science to law. In an effort to shake free some new ideas, the philosopher Roberto Mangabeira Unger and I recently organized a small workshop at Perimeter bringing together visionaries in each of these fields to talk about time. Those two days were the most exciting I've spent in years." (Lee Smolin. 'The Trouble with Physics'. pp. 256-58).

7. Bob Kurland says:

To Aron and Robert: I understand what you are saying, and it is, I think, a representation of the compatibilist (sp? again!) notion of Free Will. If I can give a picture, then the options between which one might choose are there, but the only one that is "real" is the option that you will choose. Which, as far as I can see, means there aren't several options in fact, but only one, and that the requirement for Free Will, that there be alternatives to choose from, isn't really there. Or maybe I'm being muddled. If so, I'd greatly appreciate being cleared up.
By the way, Aron or Robert: do you have any strong feelings pro or con for the Many Worlds/Many Minds interpretation of quantum mechanics?

8. Scott Church says:

Calvin,

Thanks for the quote from Lee Smolin's book... I hadn't thought of that possibility before! My gut is that he may be onto something. But I for one have no idea what sort of breakthrough would "unfreeze" time in a manner that reduces to the GR and quantum limits we observe. But then again, I suppose that if the path to real breakthroughs were even remotely obvious they'd be happening a lot more frequently. I haven't gotten around to reading Smolin's book yet. Perhaps I should... especially since I just finished my current book this morning.

But that said...

9. Scott Church says:

Bob,

Even if no such breakthrough occurs and time remains "frozen" in our view of the universe, here are a couple observations you might find helpful...

First, free will can be understood in the context of causality--specifically, our ability to act freely in the present (time t) as causal agents to bring about future events at time t + dt. In this context meaningful causality requires only two things: A timelike worldline connecting two events A and B, and a time asymmetry along it. Note that neither of these requires time to be dynamic ("unfrozen"). This implies that there is no inconsistency to our free choices as causal agents affecting future events, even if those events are in some sense "already there" before we "flow" into them.

Second, it can be (and has been) argued that quantum indeterminacy leaves room for human free will. Not that it is the source of free will per se, but that the resulting lack of determinism leaves room for the action of rational agents to make free choices, however that happens (Aron has explored some of the implications of this here and here as well as in the previous posts in this series). The choices we make in the present (free or otherwise) can be understood in a quantum context as "collapsing" the wave function of the universe. Per Bell's Theorem (or the EPR effect) these collapses must be "non-local"--that is, they happen everywhere "at once" (this is one of the reasons Einstein objected to quantum mechanics--from a relativistic perspective this sort of "action at a distance" was anathema to him). Given that space and time are joined at the hip in GR, it makes little sense to exclude action at distant times from this.

So... there's a sense in which our choices here and now collapse the wave function of the universe there and then as well. The history of the universe may be thought of as resulting from the collective superposition (or decoherence of every quantum "measurement" in its history. Thus, even if time is frozen, the future you will roll into isn't what it is independent of the choices you make in the present! It's all static... and what we choose along our own worldlines helps shape it! [As always Aron, if I missed anything feel free to correct me.]

I hope this helps! :-)

10. Robert Childress says:

Hey Bob,

The following response may or may not be helpful... The answer to whether what I believe about free will falls into a compatibilist or incompatibilist camp will be based chiefly on the answers to two questions:

1) Are human actions deterministic?
2) What is free will?

By deterministic, I mean that the details of any event within a system is entirely calculable in a mechanistic/algorithmic sense provided that we possess a complete understanding of the entire circumstances of the system at some given point in time.

If I believe that the future is deterministic, I could be a compatibilist or an incompatibilist. That is, I could believe that such a future is compatible with free will or I could believe that such a future is incompatible with free will, and such a distinction would hinge on my definition of free will. Of course, if the future isn't deterministic, then the question might not have much practical significance at all. As Scott pointed out, quantum indeterminacy rules out a strictly deterministic future. In that case, it doesn't matter whether someone is a compatibilist or not -- the future isn't deterministic, so there's no need to find some kind of compatibility.

Of course, some people will argue that even though a system isn't strictly deterministic, indeterminacy on a quantum level doesn't necessarily rule out determinism at a higher level - for example, at some kind of psychological level. I don't really buy into that, but I'll set it aside for the moment to prevent myself from spiraling out of control.

Compatibilists would argue that the capacity to act freely can be conjoined with the truth of determinism. Alfred R. Mele provides the following example as an illustration (which is not to say he is a compatibilist - I don't know if he is - it's just an example). Imagine a conversation:

Ann: Stan gave \$20 to a homeless man today.
Bill: Why? Did he hold a gun to Stan's head?
Ann: No, Stan freely gave him the money.

In this sense, even if Stan gave the money because of deterministic causal processes, it could still be argued that he did it without being compelled to do so. I don't find this particularly satisfying because it seems like too weak of a definition of free will. I would probably argue that free will has something to do with possessing the capacity to choose between a range of possible actions without compulsion. Is this definition compatible with determinism?

I don't think it is. I think determinism rules out any true sense of having a range of possible actions from which to choose. So in that sense, I think I would fall into an incompatibilist camp. To push it further, though, I actually do believe people have the capacity to choose between a range of possible actions without compulsion. That probably sticks me in the libertarianism camp.

And just to bring it around full-circle, I also think that the b-theory of time does not entail determinism and I think it does not rule out free will (as I defined it above). I think the confusion seeps in when we think of time from a timeless perspective, but then attribute to that timeless perspective a sense of "before-ness." Even if my future choices are real, that doesn't mean they were forced to be that way in some pre-determined sense.

And to completely obfuscate things, I'm not entirely settled on the b-theory of time. I'm still holding out for a C theory!

Does that help us reach some shared misunderstandings? :)

11. Andy says:

12. Andrew says:

I think this is my favourite post yet, good job bro.

13. Scott Church says:

Andy,

The 19th Century preacher Charles Haddon Spurgeon once said,

"Defend the Bible? I'd sooner defend a hungry lion!

His point wasn't that we shouldn't be ready to give an account of the hope that's within us (1 Peter 3:15), but that the Bible can damn well take care of itself. And he was right! Having been a believer for 41 years now, I've been challenged about my faith countless times by countless atheists, often in just the way you describe. In virtually every case I found that their views of the Gospel (and religion in general) were based on nothing more than a handful of "just so" stories, none of which had even been questioned much less fact-checked.

IMHO, the best thing you can do for your college-bound kids is to expose them to atheist agendas. Don't avoid the Dawkins' and Krauses in academia... seek them out! Expose their views to the light of reason, evidence, and scripture, and teach your kids to do the same. In my experience such folks will beat their chests about religion, but ask them for properly thought-through arguments and due diligence and invariably they become evasive. Press the point and they'll turn into cornered animals. Help your kids develop inquiring minds, and critical thinking and scholarship skills, and I guarantee you... atheist agendas will need protection from them, not the other way around! :-)

Blessings.

PS - To that end, I would recommend Nancy Pearcey's book Finding Truth: 5 Principles for Unmasking Atheism, Secularism, and Other God Substitutes. It's a great place to start.

14. TY says:

Dr Wall,

Fine article and trying to digest it.

You say: "Now, if Spacetime (and therefore Time) is real in the same sense that a rock or a tree are real, that meas that it is also a contingent, created being. Time is just one of the many things that God has created. But the Creator, blessed be he, is not dependent on rocks or trees for his existence. He is not measured or parcelled out by units of space, therefore he is also not measured by time. Time is just something he created, which need not have existed. Before they were created, and afterwards, he exists just the same as he ever was."

Does the above imply that time had a finite beginning, at the very point of creation? God being timeless, He existed before he created this real thing called time and all matter..

Stephen Hawking did a Lecture "The Beginning of Tine" and concluded: "The conclusion of this lecture is that the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago. The beginning of real time, would have been a singularity, at which the laws of physics would have broken down." http://www.hawking.org.uk/the-beginning-of-time.html

Love to have your comment, as usual,

Thanks.

15. Bob Kurland says:

TY, St. Augustine said the same thing some 1500 years ago about the creation of time as did Aron:
"There was no time, therefore, when thou hadst not made anything, because thou hadst made time itself. And there are no times that are coeternal with thee, because thou dost abide forever; but if times should abide, they would not be times." Confessions, Chapter XIV:7

and without knowing anything about GR!

16. Daniel says:

Aron and Bob and Robert discussed this statement by Aron: "every decision is fixed after it is made, but that does not imply that it was made unfreely at the time" and Robert put forword the idea that "free choice is meant-- free to choose between alternatives"
Was that sentence determined and free? Were there two determiners? Were there two free choosers?
I think so. But in a non contradictory sense: independently freely determined to be truly free BY eternal wisdom not force; AND dependently freely determined by force not eternal wisdom.
Are we confusing dependence = non-true freedom so that only God the independent can be a truly free chooser between alternatives?
I wrote because I just had to tell the three of you men how grateful I am for your kind discussion. I am so grateful that our God and Savior has created such a splendid world of mathematical and logical relationships for us to discover with physicists and thinkers in it like you men. Thanks to God and to you. Now to be grateful to both God, for Him and you, and to be thankful to you at the same time, makes me suspect that God is the primary independently free chooser of truly free dependent choosers and therefore God is the free chooser of each of my dependent freely chosen choices.... so thanks are due and owing to the the Triune God and to His free choosing dependent creatures. And I have so much to learn, so much to be grateful for, especially for the grace of God shown to the free choosers who freely caused His Son to die (as much as if we were the fore-ordained free choosers who drove the nails in His hands).
So, Thanks to both of you and to Robert for your musings on whether determinism and free will are compatible/non-contradictory. I do think they are non-contradictory, and I am grateful for the intellect God gave you men to discuss the physics and the theology of it all in such an UNDIVIDED way. It will be exciting to see more in Heaven... all because of God the Son stepped into time as one of us at the Incarnation. Physics and Theology are mind-blowing and heart-humbling.
Grateful,
Daniel

17. TY says:

Thank you Bob (Kurland)

I recognise St Aron wasn't the first to make that statement although I have to credit him for a lot of originality and freshness in his writings (laughs!). What I wanted to know, Bob, is whether the statement that time had a beginning is identical to saying that space, or this universe, had a beginning. Even if one says there was something before this universe, and so on backwards in time, there was an absolute beginning at time t=0. As you know, it is not a settled question in cosmology as the whether there was a beginning. Please see Aron recent series: Did the Universe Begin?

Thanks

18. Bob Kurland says:

I'll have to answer your question, TY, that I don't know enough to respond to your question/comment. Special Relativity, General Relativity and cosmology are not my areas of expertise in physics. I haven't read "St." Aron's series, but am starting to do so now--it looks mighty interesting.

19. Charlie says:

Aron so you don't need GR to describe accelerated reference frames, but doesn't Einstein have a description of gravity in terms of accelerated objects that wasn't there pre-GR physics?

20. Aron Wall says:

In addition to St. Augustine, the idea that God is outside of time is also in St. Boethius' Consolation of Philosophy. Plotinus (a 1st century Hellenistic Jew), who was before Augustine, also wrote that God created time when he created the universe.

Bob,
I'm anti-MWI, although the other interpretations of QM also leave a lot to be desired. But I think that the correct interpretation of QM should be nondeterministic.

I'm not a compatibilist. A compatibilist is somebody who believes in both free will and determinism. I believe in free will, and I don't believe in determinism. And I don't think that determinism is implied by the B-theory either.

As St. Robert said,

And just to bring it around full-circle, I also think that the b-theory of time does not entail determinism and I think it does not rule out free will (as I defined it above). I think the confusion seeps in when we think of time from a timeless perspective, but then attribute to that timeless perspective a sense of "before-ness." Even if my future choices are real, that doesn't mean they were forced to be that way in some pre-determined sense.

Precisely so. Only the choice you choose is actually real, but you could have chosen a different choice, and then that other timeline would be the one that is real.

kashyap,
God is indeed indepedent of spacetime and has no quantum numbers. But presumably that is not the only thing we wish to say about God...

Calvin,
That quote from Smolin seems kind of nutty to me. It's hard to imagine what a theory where you couldn't graph time on a space axis would even look like. I mean, I suppose you could play it as a movie instead, but that would just represent time by time.

If you are an A-theorist, I guess that first you could do physics by drawing the history of the universe on a graph, and then you put on your "metaphysics" hat and say a bunch of additional words about what time is really like!

TY,

Does the above imply that time had a finite beginning, at the very point of creation? God being timeless, He existed before he created this real thing called time and all matter.

No, I don't think it necessarily implies that time had a finite beginning. Even if time went back infinitely (back to $t = -\infty$), it would still be true that God existed "before" all time. And even if time lasts forever to the future, God would exist "after" all time as well. He is the Alpha and the Omega, the Beginning and the End.

The word "before" is being used here in a bit of a nonliteral way, since of course strictly speaking there was no "time" before time was created. What we are really saying is that God is eternal, that his existence is ontologically prior to, and does not in any way depend on, space or time.

I discussed this a little bit in Metaphors in the Nicene Creed II.

Scott,

In this context meaningful causality requires only two things: A timelike worldline connecting two events A and B, and a time asymmetry along it.

While this is almost certainly part of the story it seems incomplete. What kind of time asymmetry? (Presumably one related to the 2nd law of thermodynamics). And surely, just because one could send a signal to a particular spacetime point, doesn't mean one actually does do so.

And while you're welcome to try to make sense of free will in terms of discussion of "wavefunction collapse", I'm not sufficiently confident in anything like the Copenhagen interpretation to endorse any of the details. But I suspect there is some relationship between free will and the nondeterminism of QM.

Charlie,
There's the Equivalence Principle, which is the statement that locally, gravity looks just like an accelerated coordinate system.

Thanks for your compliments, Daniel, Andrew, and Andy.

21. Scott Church says:

Aron, yes... by "time asymmetry" I was referring to the Second Law. The point being that given two events along a common world line, such an asymmetry allows us to discriminate Cause from Effect (although the the order would depend on one's choice of an arrow of time). You are right, of course... those two constraints may be necessary, but by themselves they aren't sufficient to determine causality. My point was simply that they comprise the lowest common denominator in which we can meaningfully speak of it, and both exist within B-Theory. And you're right about wave function "collapse" too. I chose that term because frankly, given the context I couldn't come up with a better one (I meant to use it loosely... which is why I did so with quotes). Maybe I should have stuck to "measurement..." That would have more clearly accommodated other quantum interpretations than Copenhagen. But at the time it seemed too vague for the point I wanted to make, and a discussion of decoherence probably would've muddled things thoroughly.

I suppose the idea of introducing causality and quantum measurement into a discussion of free will seems a little strange. I did so with a couple things in mind...

First, if the idea free will is to have any teeth it must involve empowered agency. That is, we are free, and responsible for our actions to the extent that we are causal agents, able to affect change in the world through our choices. Your web and database servers are now in a different state because my free choice to post this comment causally altered them. An HTTP Get request for this page's URL now returns content that differs from yesterday's. This might seem obvious, but some have argued that a B-Theory of time renders the notion of causality superfluous. Events, these folks claim, are strung along world lines like beads on a necklace. Some of them may occur in a sequence that implies inter-relatedness but these are just patterns, and speaking of them as causal relationships is a category error (Hume argued for this, although without bringing any B-Theory ideas into it). Showing that the necessary conditions for meaningful efficient causality apply here as much as in A-Theory demonstrates that this is not the case.

Second, I think the biggest reason many folks struggle with the notion of free will in a B-Theory universe is that it's difficult to envision how our choices here and now meaningfully determine a future that "already exists" there and then. It is true that in the present we generally aren't constrained to make the choices we do. We could have done otherwise... at least in principle. But... In The Empire Strikes Back, Luke Skywalker chooses to embark on a mission to rescue Han Solo and Princess Leia. He was free to do otherwise (and in fact did so against Yoda's counsel). However, the movie film already contained that choice before the camera projected it, along with the rest of Luke's choices throughout the movie.

From the perspective of the story it's easy to see how in the moment Luke freely chose his destiny. But at the same time also it's easy to see how one might struggle to wrap their head around the idea of an empowered agent meaningfully determining his/her destiny on a roll of film that exists as a whole, and all of his/her choices were "pre-recorded" before the movie began. This certainly was my biggest struggle with it, and judging from most of the comments in the God and Time series I gather it is for others as well.

Now it seems to me that quantum measurement (whatever that means) might help us understand this. To wit, if our choices are acts of causal agency, then in principle they can be described in terms of one or more quantum "measurements." If so, we can say that quantum nondeterminism creates a space in which the mystery of free will can occur. But, I think we can say more than that. Regardless of how they happen or how we interpret them, quantum measurements are non-local (Bell's Theorem), which by my lights means spacio-temporily non-local. It follows that in principle, our causal agency in the present could contribute to a future that is "already there" before we come to it. What if, to some extent at least, each frame of the movie film contributes to all others, and the whole is the sum (superposition?) of the parts? Maybe the choices I make in this frame impact the "pre-recorded" ones in my future before the projector reaches them.

As this thread and previous ones have shown, it isn't necessary to involve these ideas in a discussion of free will. But for me at least, they makes it easier to imagine how our free choices shape destiny in the context of a static, "pre-existing" B-Theory future.

I hope this helps... :-)

22. paul says:

Please forgive me if you mentioned this and I missed it. But what is your take on simultaneous causation? Is this is a legitimate concept in physics? It seems to me that casual signals cannot go faster than light so causal relations cannot be simultaneous. Is this right?

23. Aron Wall says:

paul,
Certain kinds of theories in physics, called "gauge theories" (including Maxwell's equations and General Relativity) have relationships called "constraint equations", which restrict the valid field configurations at a single moment of time.

For example, in Maxwell's equations, the Gauss Law says that the number of electric field lines coming out of a region is proportional to the charge in that region. You could, if you like, this of this as a form of "simultaneous causation", although obviously if you mean that in a Deep Philosophical Sense it could be a rather controversial statement.

The reason this does not allow you to send signals faster than light, is that charge is automatically conserved in a gauge theory. This prevents you from just creating or destroying it at whim and then have distant observers notice a change in the electric field elsewhere.

Something very similar happens in General Relativity, except instead of electric charge, the constraints involve energy-momentum, which is also conserved. (Energy is just momentum in the time direction; it's a 4-dimensional vector.) Although in this case the definition of the total energy of a spacetime can be more subtle.

24. paul says:

Hi
Aron thanks you for your reply. I find it amazing how often you reply to comments on this. Something i really commend you on.
The case you give , you said may be implied to imply simultaneous causation but even that is controversial. So Im sorry If Im still a little confused about the status of simultaneous causation in physics. is is something where the isa consensus position that its accepted, not accepted, not discussed or other?
Perhaps I could clarify with the case that is most often quoted from Immanuel Kant of a ball resting on a cushion. Its argued the depression caused by the ball is simultaneous with its effect. But it seems to me that the ball is causing the depression through forces that are transmitted at the speed of light and so this case which is argued to be a definite case of simultaenous causation is in fact not. Am I correct?

On a different question. You seem to imply that your paper on the singularity in the GSl is an extension of the Penrose theorem which if I understand correctly assumes the universe is infinite in size. Is that also true for your GSl singularity or is the proof independent of the size of the universe?

25. Aron Wall says:

paul,
Among physicists, questions like these are "not discussed". Arguing about which things "really" count as causation is more something philosophers do, than something physicists do. If you asked philosophers of science, I would expect it to be controversial (given that everything involving attributing "causation" to the world is controversial!)

In the case of the ball on the cushion, the repulsive force comes through a combination of electrical field forces and the Pauli exclusion principle. It's quite true that no signals travel faster than light, but QM the wavefunctions of the cushion electrons and the ball electrons actually overlap, so it's not completely obvious what we should say here. Just thinking of a bunch of point particles exerting forces on each other with a "delay" is not actually the right model; you really have to think about it in field theory terms if you want to include the effects of finite light speed. But then even identifying clearly what you mean by the "ball" and what you mean by the "cushion" is going to be difficult. Out of respect for the complexities of the situation, I think I won't commit to an answer to this question right now.

(And even if I did come up with an answer based on field theory, someone could then come along and say that things are completely different if we think about the ball and the cushion in a quantum gravity model! Because space and time are discrete, or fuzzy, or whatever...)

I suppose someone could say, it doesn't matter whether a ball-cushion has simultaneous causation in the real world, it's just a thought experiment to show we can think about simultaneous causation without logical contradiction. Whether that's a good answer or not depends on how one is trying to use the thought experiment.

A quick google search suggests that people are primarily using the concept `simultaneous causation' to argue about things like the kalam argument and whether it makes sense for God to have created the universe. This seems wrong-headed to me. God's creation of the universe is, in any case, not parallel to the power of any individual being. Only God can create in the true sense of the word, all other beings simply exercise the finite powers which they have been given. God is outside of time, while created beings (at least those we can experience), are are in time. The idea that God's creation would become more or less plausible based on how cushions and balls behave seems a bit misguided to me. God is the author of the story, not one of the "forces" in the story.

Yes, the classical Penrose singularity theorem assumes that the universe is infinite in size (when applied in a cosmological setting; when applying it to an isolated system like a black hole, since the black hole is much smaller than the whole universe, presumably it is "as if" the universe is spatially infinite). Except for the fact that one can include some effects due to quantum fields, my proof based on the GSL is no better than the classical proof, so in particular it does not imply a singularity if the universe is spatially finite. A good example is the maximally extended de Sitter spacetime, which (in one particular foliation into space + time) looks like a sphere which shrinks down from arbitrarily large size to a finite size, and then grows back to infinity again.

Actually, there is one situation in which you can apply the Penrose singularity theorem even in a finite universe, and that is if space has nontrivial topology. [Attempts an explanation which may or may not be comprehensible:] For example, imagine if space at one time were a cube, but if you go off one edge of the cube you reappear on the opposite edge (like wrapping around the screen in certain video games). We call this a "3-torus" topology (because the 2 dimensional version of what I just said, where you use a square, is topologically the same as the surface of a doughnut, i.e. a torus). You can think of this topology as being like flat Euclidean space, but with certain points "identified" so that the exact same matter structures are repeated over and over again, every time you move an integer number of units in the x, y, or z directions. In this case, we call Euclidean space the "universal cover" of the torus space. Then, since the Penrose singularity theorem applies to infinite Euclidean space, it also applies to the torus geometry. Since classical physics can't tell the difference between a 3-torus, and a plane where everything repeats, the Penrose theorem applies to both.

But quantum physics can tell the difference between a torical and infinite geometry; for example, there is a Casimir effect which gives a small negative energy due to the universe being finite in size. So the argument based on the GSL would not apply to a 3-torus universe.

26. paul says:

Thank you, i really appreciate you taking the time to answer.

27. Scott Church says:

Fascinating discussion Aron... thank you!

Interestingly causality, as understood by St. Thomas Aquinas and the Scholastics, was simultaneous. Today the traditional "unmoved mover" argument attributed to Aristotle and St. Thomas Aquinas is usually presented as a sort of "pinball causality" proof. A was caused by B; B was caused by C; etc... all the way back (in time) to a First Cause identified as God. As such, responses to it typically involve attempts to show that there's nothing implausible about a past-infinite regress of efficient causes. However, contrary to popular belief this is not the argument either of them made! St. Aquinas had no problem with a past-infinite universe, and Gen. 1:1 notwithstanding he was open to the idea that it was. His argument, like Aristotle's, actually postulated a chain of inter-related causes (material, formal, efficient and final) simultaneously present behind every actuality (as opposed to potentiality)--not unlike the ball on the cushion. According to St. Aquinas (and Aristotle), infinite or otherwise, it is logically impossible for such a chain to exist in the present moment without at least one causal factor whose actuality was not realized from a corresponding potentiality... in other words, an Unmoved Mover. ["Move" and "mover" were much broader terms in Aristotle and Aquinas than they are today and connoted change as well as movement, which is why in this context the idea of an "unmoved mover" sounds a little strange to our ears.] This is precisely why they presented the Unmoved Mover as a formal proof for God's existence rather than something derived from experience or evidence of any unfolding causal chains as we understand them.

The argument is formulated today in "pinball causality" terms because after the Enlightenment the world came to be seen as a great machine--Paley's master "clock" with moving parts--and that's our framework for understanding all causality. The notions of formal and final causality have been dispensed with (Sean Carroll assumed this very point in his debate with St. Craig!). As you know, I've struggled myself with the idea of causality vis 'a vis B-theory time. But from this perspective, much of our confusion regarding God "causing" the universe--at t=0 or whenever--is a philosophical problem we've largely made for ourselves, and I'm starting to rethink all of the things that to date have troubled me in this regard. I just finished St. Feser's book The Last Superstition and enjoyed it very much. He goes into great length about all of this, including the history of the misunderstandings. I don't find all of his conclusions convincing (particularly many details as to how all of this works out in real-world situations), and I'm not prepared to call myself a Thomist just yet, much less an Aristotelian. :-) But the concepts of formal and final causality make a lot more sense to me now than they used to, and all of this strikes me as having a great deal to say regarding the Kalam argument and other questions about God, creation, and causality.

Thoughts...?

{PS - The idea of a finite universe having a Casimir effect is completely new to me! Does this imply that finding one would demonstrate that the universe isn't infinite? If so, that seems like it would be quite a discovery... has anyone tried to look for it?]

28. Aron Wall says:

Scott,
That sounds accurate, although I think "St. Aquinas had no problem with a past-infinite universe" in the sense that he thought it was logically possible, but that Gen 1:1 and other texts implied that as a matter of revealed fact, the universe was created a finite time in the past.

If you liked The Last Superstition, you could try Scholastic Metaphysics to get more of the details of his system. However, I was also not convinced by a lot of the arguments. You could also try his book on Aquinas, but I haven't read that one.

Dimensional analysis says that the Casimir effect in a (static, for simplicity) torical universe of length scale $L = 10$ billion light years would be of order

That energy would be uniformly distributed throughout the universe, so if you want the energy density you need to divide this number by the cube of 10 billion light years. Good luck with that!

29. Scott Church says:

Aron, thanks for the book recommends. I've been considering both actually, although I wish they had Kindle versions... But at the moment I'm even more intrigued by his book Philosophy of Mind (A Beginner's Guide) which from a philosophical perspective explores the inability of materialism to account for consciousness, reason, and free-will.

As for cosmology with the Casimir effect... ugh! You know, even as I typed that question to you, a still small voice in the back of my mind was whispering, "Scott... you do realize don't you, that if it were that easy to pin down the size and large-scale topology of the universe someone would have a Nobel by now for having done so...?" :-)

30. mstair says:

“Truly, truly, I say to you, he who hears my word and believes him who sent me, has eternal life; he does not come into judgment, but has passed from death to life.
John 5: 24 (RSV)

This is a direct quote from Jesus. Notice the verb word-salad he chooses in the last verse, “he who hears my word and believes him who sent me, has eternal life; he does not come into judgment, but has passed from death to life.”
Hearing and believing are in the present tense (the hearers and believers in the action of hearing and believing). In the same sentence, however, Jesus says that as that is done, they have eternal life (past possessive tense), will not be (and are not even considered for) coming into judgement (future tense) and have already passed from death to life (past active tense). This is the kind of paradox we see when a timeless being explains His unique perspective of being able to perceive both an entropic, timeline, existence – simultaneously with – a divine, timeless one.”

Excerpt From: Mike Stair. “On Earth As It Is In Heaven.” iBooks. https://itun.es/us/DZeA8.l