# God and Time II: Special Relativity

Despite what people seem to think, there are very few controversies in Theology where there is decisive evidence coming from Physics (leaving aside some real doozies such as Young Earth Creationism).  But the question of whether God is in Time is one of them.

In the previous post I argued that God must perceive Time as it really is.  But our conception of Time has been modified radically as a result of Einstein's theories of Relativity.  It starts out with Special Relativity, and becomes even more extreme with General Relativity.

The first thing to notice is that our usual division of time into Past, Present, and Future—which I tacitly accepted when discussing the metaphysical problems of the A-theory (a.k.a. Presentist) idea that only the Present really exists—seems to be totally wrong.  Instead you have to think about spacetime, and it is unclear what we even mean by referring to the "Present".  As I said in one of my earliest posts:

We're used to dividing up time into three parts relative to ourselves: past, present, and future. The present is just an infinitesimal sliver, so in a sense this division is into two parts: points to the past have $\Delta t < 0$ compared to you, while points to the future have $\Delta t > 0$ compared to you.

However, special relativity tells us you have to chop up spacetime in a more complicated way.  Bearing in mind that you each live in a particular place as well as a particular time, you can chop up spacetime into three different regions.  The future is points that are timelike separated to you and have $\Delta t > 0$; these are the points of spacetime that you can affect.  The past is points that are timelike but have $\Delta t < 0$; these are the points that can affect you.  Then there is elsewhere, the points that are spacelike separated.  These points can neither affect, nor be affected, by each other.  The three regions are separated by the "light cone", which consists of the points that you could send a lightray to (or from).  I'm too lazy to draw a picture right now, but you can see a pretty good explanation here

If we treat time as a metaphysically fundamental quality, and say that things at the present moment of time really exist, really we are saying that anything which is simultaneous to my present experience exists.  But the concept of "simultaneous" is rendered problematic in Special Relativity.

That is because there exists a symmetry of spacetime, called a Lorentz boost, which mixes up the time and space coordinates.  (The Lorentz boost corresponds to changing the speed of the "reference frame" in which you are viewing the system.  You can always transform to a frame in which a given object's center of mass is at rest.)

Here is an spacetime diagram of two frames of reference, one in which "Static Sue" is at rest, and the other in which "Mobile Martha" is at rest (despite their names, there's no actual objective fact about which one of them is moving):

Here the vertical axis is time and the horizontal axis is one of the dimensions of space.  The horizontal grey lines indicate Sue's notion of simultaneity, and the diagonal peach lines represent Martha's notion of simultaneity.  Their relative velocity is about half the speed of light, which would travel at approximately 45° had I drawn any light in this picture (I chose not to draw any light because, sadly, both ladies are blind).  Sue and Martha's reference frames do not agree about which of the two events $p$ or $q$ occurred first.

In particular, as long as two points $p$ and $q$ are spacelike separated, by acting with this symmetry you can always choose for their time coordinates to have any of the 3 temporal relations: $t(p) > t(q)$, $t(p) = t(q)$, or $t(p) < t(q)$.  Since nothing can travel faster than light, no causal signals can go between the points $p$ or $q$ anyway, so the order doesn't really matter.

(Nor can we say that if $p$ exists, everything spacelike separated to $q$ exists simultaneously.  For "simultaneous" is supposed to be a transitive relation.  If $p$ is simultaneous with $q$, and $q$ is simultaneous with $r$, then $p$ and $r$ should also coexist simultaneously.  But in Special Relativity every pair of spacetime points share a common point they are both spacelike to.  This idea would thus make all spacetime points simultaneous.)

And yet, for some reason, in the very same 20th century in which Physics got rid of the idea of the Present moment, some revisionist theologians decided to propose a more limited, anthropomorphic deity who changes with time, or who doesn't know the future.  Either because they wrongly believe divine foreknowledge conflicts with free will, or because they believe that the Bible teaches this, or because they subscribe to more radical process theology ideas...

But if:

1) God is omnipresent (so he does not pick out a particular point in space), and
2) The Lorentz boost is a valid symmetry of reality, then inevitably:
3) God is omnitemporal.

There are only a few possible rebuttals.  One is to hope that relativity turns out to be wrong in this respect.  There are a few very speculative quantum gravity ideas about this (e.g. Hořava gravity), but none of them are extremely promising.

A second is to say that God just breaks this symmetry, he "picks out a particular reference frame" and that's just that.  Well, in addition to being ugly to theoretical physicists such as me, it seems bizarre that God, who transcends the universe and created it, would need to break a law of nature of that he created just in order to relate to the universe.  (It's not like not we're talking about a miracle here, we're just talking about the way in which God coexists with the universe at every moment.) God relates to the universe by creating it as it is, and by knowing it as it is—which means that there should be no reason to break any symmetries in describing how God relates to the universe, if our best model of how the universe is preserves those symmetries.

A third approach might be to bite the bullet and say that God exists in space as well as time.  Maybe there is one version of God (or should I say "a god"?) existing at each spacetime point, and each god knows only the things in the past lightcone of that point.  So God can't send signals faster than light or know what's going on in the Andromeda Galaxy right now (for any reference frame's definition of "right now").  But what a needless limitation!  I could throw out a prooftext here, but I'm supposed to be saving the Scriptures for the next post.  Instead I will confine myself to pointing out that this view has serious issues concerning the divine unity as well as omniscience and omnipotence.  Is it really necessary for the Blessed Creator to chop himself up into pieces, just in order to create the spacetime continuum?  This seems to tend more towards a Pantheistic view in which the God creates the universe out of his body, then a Monotheistic view in which he creates freely like a novelist inventing a story.

One reader (who subscribes to the "Open Theism" view that God does not know the future) suggests that perhaps God exists in all reference frames.  But this makes no sense to me.  We cannot say that God exists in all reference frames simultaneously, since we need to first pick a reference frame to say what we mean by simultaneous!  Indeed, this view does not really give a well defined answer to the question of what knowledge God has access to at any given moment.  If I, sitting in a particular place and time, pray to God to intervene at some other point, which is spacelike separated to me, can he base his answer on things taking place in the Andromeda Galaxy, or not?  This model would imply that there are infinitely many versions of God at a single spacetime point, each with different knowledge and powers.  That's even more complicated than the previous supposal.  Which version of God gets to decide what happens at that point, and why can't they just all communicate with each other?  This view seems more problematic than any of the others.

So, to conclude, Special Relativity seems to strongly suggest that if God has no definite position in Space, he must also not be in Time.  Now we have Spacetime, and we ought to be able to translate what we say about God into that language somehow, unless we think that our theological expressions should be immune to progress in the Sciences.  But here it is traditional theology, not revisionist modern theology, which fits the data better.

(Although this raises certain questions about other theological entities, such as angels or heaven, which are often conceived of as being in time, but not space.  Or at least not in our space... but of course we don't really know much about what these entities are really like.  Although God transcends all understanding, in certain respects we know a lot less about these created entities than we know about God, because (a) there are no metaphysical arguments that they have to exist, and (b) we interact with them less frequently.)

I've decided to save General Relativity and other physics considerations for another post.

Next: General Relativity

## About Aron Wall

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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### 19 Responses to God and Time II: Special Relativity

1. Miloš says:

Thanks you for such illuminating posts about God, time and theory of relativity.

I am very interested in philosophy of time, especially in debate between A- and B- theory. I have one question form now: do you think that argument from theory of relativity is knock down argument against presentism (which is probably most popular version of A- theory of time)? Recently philosopher Bradley Monton publish article "Presentism and Quantum Gravity" where he argued that even if presentism is not compatible with special relativity it does not mean that it can not be reconciled with some more fundamental physical theory (quantum gravity).

My knowledge of physics is superficial at best but I am aware from philosophy of science that idea of fundamental physical theory is problematic or that we are far away from some plausible candidate for fundamental physical theory.

2. Eric says:

Aron wouldn't your argument assume Minkowski spacetime? What about Lorentzian? There seems to be some support for the latter from Karl Popper, Quentin Smith, and Tim Maudlin.

3. Robert Childress says:

Well, I'm about ready to accept something B-like, as the B-theory does seem to emerge. It fits super well with my theological understandings.

Looking forward to the next post!

4. Aron Wall says:

Eric,
Minkowski spacetime is a special case of a Lorentzian geometry, so it's not a question of one versus the other. In a Lorentzian geometry, the geometry is allowed to vary in space and time so long as locally, if you zoom in close to any given spacetime point, it looks like Minkowksi space.

Special Relativity is about Minkowski geometry; General Relativity is about Lorentzian geometry.

Miloš,
Well, it's hard to have a perfectly knock-down argument against anything in philosophy, and of course it is also true that our physical theories are provisional. However, I think that at the very least relativity provides strong evidence against presentism. It would be rather surprising if the final theory of physics involves undoing fundamental conceptual shifts required by previous theories, e.g. by reintroducing an absolute Newtonian time.

5. Thanks for the lucid sketch of A Theory & B Theory. You have a knack for writing about philosophical head-scratchers in plain English. I envy your students. (Consider something book-length. A Christian physicist should have no trouble finding an agent.)

We should add free will to the list of controversies in Theology where there is decisive evidence coming from Physics. Isn't the B Theory a stunning depiction of Divine Determinism? God creates this massive, amber-like slab of past, present, & future, all parts of which are equally “real.” How could any single detail have been otherwise unless God made it differently?

Far from being incompatible with Christian theology, this takes St. Paul at his word: Why does God hold us accountable and punish us if we have no free will? This is what Romans 9:19 is asking. St. Paul puts the question into the mouth of an imaginary disputant after stating that God has mercy on some (Moses and Jacob) and hardens others (Esau and Pharoah). His answer does not mention free will, middle knowledge, or allowing evil in the best possible world. The answer is the single most terrifying thing in any of the world's religions: Who are you to ask? God creates some men to be vessels of wrath, others to be vessels of mercy. The purpose is to demonstrate His power. Reality is not about us or our standards. We have no inalienable right to free will (only the Prime Mover has that). God, like a potter making different vessels for different reasons, has the absolute right to make whatever He wants for whatever reason He wants. (Ouch! This is so harsh, but there you have it.) https://www.biblegateway.com/verse/en/Romans%209:19

Note the explicit denial that moral responsibility requires the capacity to do otherwise. "Why does He still find fault? Who can resist His will?" = It's not fair that God judges us because we couldn't do otherwise! St. Paul's answer chills the blood. Damnation isn't about people abusing their free will; it's how God shows His power and mercy to the Elect (in the same way He demonstrated His power by hardening Pharoah's heart and then destroying him). Again, ouch, but that's what it says. For some, the appeal of Christianity is that it takes determinism seriously.

I await your book on physics & the B theory of time supporting the plain teaching of Romans 9. This would be a bestseller. ;o)

6. Miloš says:

Aron,

Sorry I was not precise enough. My questions is not primary concerned with adequate theory of time but with notion fundamental in arguments from physics for some philosophical thesis.

Here we have tension between one extremely successful physical theory (or alleged tension, there are philosophers which argue that there are not tension at all) and widespread philosophical view on time. Should we say that this tension is strong evidence against this theory or that maybe there is not tension with some more fundamental physical theory (I understand that Bradley Monton argue for such conclusion).

Similar question is raised against recent Christopher Weaver's argument from paper ''Fundamental Causation'' by philosopher Massimo Pigliucci (see one of the recent posts at Scientia and Veritas).

7. Robert Childress says:

Hey Petronius,

Leaving your scriptural references aside for a moment, are you suggesting that the B-theory on its own leaves no room for free will? Or do you just see it as some kind of difficulty?

I can understand how the B-theory would allow for God to be aware of what every decision is at every moment of time (or spacetime, or whatever), but I'm not sure that it implies God has eliminated free agency from the decisions. Is it not still us who are making those decisions at each moment of time? The future decisions are actual and real, but that's only because they are decision we will make. Likewise past decisions are actual and real, but only because they are decisions we have made. And so on.

Thanks,
Robert

8. Robert,

Why did you make decision X at time T? There were causal antecedents. If we could rewind Time back to T, how could X have been any different? Given the same circumstances, it would be the same choice. If not, what explains the discrepancy? Sure, YOU made the choice, but how could you have done otherwise? I'd like to see a flowchart of how libertarian free will works, how a contingent, created being activates its own thoughts and directs the course of its mind, how we hover ghost-like athwart the causal nexus when we make choices. We don't create our thoughts or actions ex nihilo. (Do we choose the thoughts which lead to our actions? That sounds bizarre, and the regress is a doozy: do we choose to choose them, etc.)

Whether the B theory and Special R entail determinism is championed by some, denied by others: http://www.informationphilosopher.com/freedom/special_relativity.html

9. Robert Childress says:

Hey Petronius,

If we could rewind time back to T, of course decision X would be the same. It's the decision that was actually made. That doesn't imply that the decision was not the result of an evaluation of external factors, an introspection of internal values, a consideration of potential options, and a choice that I freely made within that context. And no matter how many times you replay that same moment of time, I will choose to make the same choice over and over again.

That doesn't mean I didn't make the decision freely. I could have made any number of other possible decisions. If I had made a different decision, that is the decision that you would see replayed over and over again. Just because I didn't make a different decision doesn't mean I could not logically have made any other decision. But whatever decision I actually made is going to be the real and actual decision that exists in time.

And it's the same for all of my future decisions. Just because I will at some time T2 in the future make some decision Y doesn't mean I won't freely choose to make decision Y. Never the less, decision Y will be whatever decision Y actually is. Not because I had no choice but to make that decision, but because out of all the multitudinous possible choices I could have made I decided to make that choice.

I won't argue that the freedom of my will is obviously limited to some degree -- of course it is, and it seems to have significant limitations -- but within those limitations I certainly appear to act freely, and I haven't yet seen reason to believe I don't. The B theory doesn't seem to imply that we don't act freely, either. Unless I misunderstand something, in which case I'd freely will to be corrected.

Thanks.

10. And no matter how many times you replay that same moment of time, I will choose to make the same choice over and over again. That doesn't mean I didn't make the decision freely.

Then in what sense could you have done otherwise? What do you mean by “freely”? If you mean not coerced, that’s true but harmless. No one’s denying that.

I could have made any number of other possible decisions.

You’re asserting that you could have done otherwise after conceding that if we rewind Time you’ll always make the same decision. What tipped the balance in favor of decision X? That factor would need to be different for you to make a different decision.

Just because I didn't make a different decision doesn't mean I could not logically have made any other decision.

So this is all about logical possibility? Or is it that if some of the antecedents had been different you would have made a different choice? Again, what do we mean by “free”?

I won't argue that the freedom of my will is obviously limited to some degree -- of course it is, and it seems to have significant limitations -- but within those limitations I certainly appear to act freely, and I haven't yet seen reason to believe I don't.

In the same way, it feels like the earth is stationary, that I’m not composed of zillions of particles, that Time is not relative to anything else, etc.

The B theory doesn't seem to imply that we don't act freely, either.
If my future children are as “real” as the words I’m typing here, doesn’t it mean I’ll be getting lucky a few of these nights? In what meaningful sense can I do otherwise? (I don’t know if this is Determinism; it’s more like some new-fangled Fatalism.) An A theorist could say there’s a spotlight moving through the slab of Time, illuming me typing this, me getting lucky, and me with my future kids. A B theorist would deny there’s any spotlight. ALL of these things exist in the exact same fashion. If you want to throw the word “free” at it, I don’t see how that gives me any superpowers. I don't know what it means.

In an earlier post Dr. Wall writes “So at the end of the day, I fall back on my religion for deciding what to believe about Free Will.” http://www.wall.org/~aron/blog/free-will/

In his heart a man plans his course, but the LORD determines his steps. (Proverbs 16:9)

A man's steps are directed by the LORD. How then can anyone understand his own way? (Proverbs 20:24)

The king's heart is in the hand of the LORD; he directs it like a watercourse wherever he pleases. (Proverbs 21:1)

Man's days are determined; you have decreed the number of his months and have set limits he cannot exceed. (Job 14:5)

Now listen, you who say, "Today or tomorrow we will go to this or that city, spend a year there, carry on business and make money." Why, you do not even know what will happen tomorrow. What is your life? You are a mist that appears for a little while and then vanishes. Instead, you ought to say, "If it is the Lord's will, we will live and do this or that." (James 4:13-15)

Who can speak and have it happen if the Lord has not decreed it? Is it not from the mouth of the Most High that both calamities and good things come? (Lamentations 3:37-38)

And in Romans 9 St. Paul doesn’t deny free will; he takes a swing at us for asking.

11. Robert Childress says:

Hey Petronius,

Under the B-theory, the reason the decision is the same is because it's the only actual decision that exists. Under the A-theory, if you rewind time there is no future that actually exists, so perhaps there's a potential for a different decision under that theory? But I'm confused by the significance you seem to place on a decision remaining the same given the exact same universal context.

Perhaps you are suggesting that the only way an agent can demonstrate free will is if he behaves differently given the exact same set of circumstances. I disagree. I don't think that would demonstrate freedom of the will so much as madness.

What matters is the existence of a decision making process. A lack of compulsion is a crucial detail. Having some kind of conscious awareness is probably another. Having sufficient time to consider options before making the decision may also be important -- otherwise it's an instinctual reaction more than an intentional decision. If a person's decision making process arrives at the same conclusion given the exact same circumstances, it's a sign of rationality.

We do not always behave rationally, of course. And I doubt whether different circumstances are ever exactly the same. And there are a great deal of choices we make that do not include much or any of a decision making process. But I don't see how that invalidates those times when a decision making process does occur -- and sometimes it does.

I don't think your description of the A-theory is very accurate -- the spotlight thing. The A-theorist doesn't think there is a slab (at least, a presentist wouldn't, I don't think). Nevertheless, though, I think you're argument for a lack of free will has more to do with your religious beliefs than it does with the B-theory of time. I think the B-theory leaves it open ended as to whether or not any of our decisions were the result of a decision making process.

And the religious question is important. I appreciate the scripture references you've provided, and I hope you don't count it amiss that I'm going to avoid discussing them and your interpretations of them at this time. I haven't spent enough time thinking about the scriptural question to provide much of a meaningful exchange and I don't really want to take the time to dig into it right now, as I'm occupied with other thoughts.

Or perhaps I'm just mechanistically determined to avoid them at this moment of time? :)

Blessings,
Robert

12. Robert,

Under the B-theory, the reason the decision is the same is because it's the only actual decision that exists.

Then it's incompatible with Libertarian free will, which is the capacity to do otherwise. That's what the "free" refers to. It's not me who's putting the unique emphasis on this. Forests have been felled to supply paper for all the philosophical dialogues. (You're in the Compatibilist camp.) The problem with free will is that everyone agrees it's important but no one can agree what it is. It seems like we want an almost miraculous ability to pull ourselves out of the primordial swamp by the scalp (Nietzsche's disdainful expression), thereby assuming Total Authorship of all our deeds. Otherwise it seems wrong to be blamed or praised.

My religious beliefs are a work in progress. The Fire & Brimstone stuff beckons because it takes Determinism - fatalism seriously. (I didn't believe in free will when I was an atheist.) In candor, it also repels. On the one hand, God controls everything. On the other, we are held accountable (even for our thoughts!) On the one hand, God predestines some to mercy. On the other, He's just in damning those who aren't predestined. What the heck!? The fact that I don't reject this outright suggests some supernatural Agency is at work. That's the impression I have. I can't do otherwise. (Determinist jokes write themselves). ;)

Mechanistically Yours,
PJ

13. Robert Childress says:

Eh, I think it's reasonable to say that I could have done otherwise than make some decision X. But I didn't. I chose to make decision X and that is the decision that is recorded in time. That's all the B- theory seems to suggest.

I don't agree that free means without any boundaries at all, though. If that is what libertarian free-willers believe then it's immediately rendered incoherent. I think instead it's better defined as a lack of compulsion when selecting one possible option from many options. In effect, having the capacity to compel oneself to make a choice.

There's more to be argued about it for sure, such as within the philosophy of mind. This theory of time doesn't seem to diminish the freedom of my decisions though. The reality of our future decisions doesn't mean they're made "now" before we get there. It means when we get there those are the decisions we will choose to make (in my opinion, of our own volition).

14. Seth says:

I find it confusing but too often reiterated that if one could rewind time and a mind were to make the same decision then that proves there is no Free Will.
But what of the alternative? If a person makes different choices everytime then his choices must be completely independent of the actual circumstances and any kind of rational decision making. He's not actually exercising Free Will because his "choices" are independent of any kind of volition. Otherwise, a random number generator would be the penacle of Free Will instead of the opposite.
Free Will deniers who make this argument seemed to be confused that just because you can make a different choice that you will make a different choice. This doesn't follow.
In a B Theory view of time the timeline doesn't bar you from making different choices. Rather, the timeline exists the way it does specifically because even though you could make different choices, you won't.

15. Blair Reynolds says:

Interesting site. I did my dissertation on process pneumatology. Enjoy discussing process. Would encourage all to read more on what process is saying about SR. Some major points were overlooked here. But that's OK; it's a complicated issue.

16. Andy says:

Petro, I'm sorry I didn't see this before. I just read part 3 and came back to read the first 2. I believe you're saying that we're almost like robots and our decisions are based on past "input" so if you went back 100 times the decision would always be the same. Even decisions based on your mood at the time, etc. So depending on my circumstance, I may or may not believe in God. But then where does will power fit. Suppose I don't want to smoke and eventually smoke my last cigarette. Then cave, smoke another, and quit again after 3 months. I'm not sure outside input determines which time I smoke and when I quit. Or if I wake up at 4am and decide to pray about it. Also some decisions, picking up a nickel, changing the channel or just leaving it because the remote is 6" out of reach, going to the bathroom before bed or just going to bed because I'm too tired, etc, seem like they could go either way at any time. Also, your take on Paul and free will. Troubling indeed, but there's more to the story. The bible says that God wishes EVERY person to be saved. Do where does that leave us... perhaps God really is outside of time and knows the future, knew Pharoah would never accept Him, so chose him to make an example of. If God knows the future, there's no difference to Him if He punishes us before or after we sin. Its only problematic from our perspective, not His.

17. Calvin Marshall says:

Aron -- I recently came across the following from Rudolph Carnap's autobiography. In this place Carnap recounts a conversation with Einstein (in Princeton) where he expressed some ambivalence with respect to the implications of his own theories of relativity. Thought this would be of interest in light of the discussion on A-theory/B-theory.

“Once Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation…But Einstein thought that these scientific descriptions cannot possibly satisfy our human needs; that there is something essential about the Now which is just outside of the realm of science.”
Rorty, Ame. "Rudolph Carnap: Autobiography." The Many Faces of Philosophy: Reflections from Plato to Arendt. Oxford: Oxford UP, 2003. 443.

18. Scott Church says:

Hi Aron. I recently came across Lee Smolin's book Time Reborn. I haven't had a chance to read it yet or even digest any of the ideas he's proposing, but if I understand him correctly he's claiming that that the absence of absolute time in SR and GR (and all the attendant A vs. B theory issues) may be an artifact of our chosen mathematical frameworks--in other words, he thinks that time is physically real, and not treating it as such is blocking progress. He seems to draw heavily on "shape dynamics" and the work of Barbour et al. (2013) in which time is treated as physically real by replacing spacetime refoliation invariance with three-dimensional conformal invariance. Alan Lightman reviewed the book for the NYT here and he seems to like it, except for Smolin's theory of universe natural selection via black hole (which I also think is hand-waved and too speculative to be useful). Peter Woit took issue with much of the book, but as near as I can tell not in this area.

Again, I haven't had a chance to read it and I'm brand new to these ideas, so I don't know what to think. I'm considering getting the book but I'd love to get your take on it before I do. What do you think of all this? Is there anything to it, and if so, does it have the potential to change the whole A vs. B theory discussion? Best!

19. Mactoul says:

Aron,
You write
"our usual division of time into Past, Present, and Future—seems to be totally wrong. "

Do you hold that
"Past and future are symmetrical. There is no sense in which the past is determined and the future is not determined."

I have put the above in quotes since it is point (17) of the philosopher GEM Anscombe list of "Twenty opinions common among modern Anglo-American philosophers".