The Name

A reader named Ken Murphy asks:

In Ps. 110:4 the word LORD is spelled in all capitals. Why?

It stands for YHWH, the proper name of God which was revealed to Moses at the Burning Bush (Exodus 3:14-15), which is in turn short for the divine proclamation I AM WHO I AM.  This title declares God's eternal self-existence.

Thus, the words "the Lord" are not actually a translation, rather it is a substitution performed throughout translations of the Old Testament in order to avoid writing the Sacred Name.  In some of these translations, the word LORD is placed in all capital letters so that you know when this was done.  (In some Jewish versions of the Bible, they instead substitute HaShem (which means "the Name").  There is another Hebrew word "Adoni" which actually means a lord (this word could be used of a human ruler as well as of God), so that way you can tell which word is being used.  (These types of things can be learned by reading the "translator's preface" in the uninspired pages of your Bible located before Genesis 1:1.)

In the first verse of Psalm 110, we actually have both types of "Lord" appearing together.  King David prophesies of a greater king than himself when he says:

YHWH said to my Lord, sit at my right hand until I make your enemies a footstool for your feet. (Psalm 110:1)

Since Hebrew was written at the time written with consonants only, the vowels in between these four letters are unknown, but modern Hebrew scholars tend to think it was pronounced something like "Yahweh".  The old-fashioned pronunciation "Jehovah" was based on inserting the vowels in "Adonai".

The Third Commandment says "You shall not misuse the name of YHWH your God, for YHWH will not hold anyone guiltless who misuses his name." (Ex. 20:7).  God made himself more tangibly present to the Israelites by giving them his Name, but in doing so he opened up the possibility that his Name could be abused and used flippantly or as a curse, instead of as a blessing.  For this reason, God commanded that his Name, which made the Israelites holy, must be held with respect.  Vulnerability is the flip side of intimacy.  As it is written:

I will walk among you; I will be your God, and you will be my people. (Lev 26:12)

Some people might think that misuse of God's name can't really matter very much, but that would mean that using it doesn't matter either.  If reverent use of the Name sanctifies God's people, then irreverent use will, conversely, coarsen and corrupt the sense of being dedicated to God.  For this reason Jesus taught us to pray, "Hallowed be your Name" (Matt. 6:9).

This is one of several ways in which the Torah says that placed aspects of himself among the Israelites, others being the Holy Spirit, the Shekhinah [Glory Cloud], and the Temple.  Somewhat surprisingly, the Temple is often referred to as the place where God's Name dwells.  For example, when God promises King David that he will have a descendent who will reign forever, he says:

He is the one who will build a house for my Name, and I will establish the throne of his kingdom forever.  (2 Samuel 7:13)

Here "my Name" is a metonymy: it stands for the presence of the God whose Name it is.  As it is written:

Then I will dwell among the Israelites and be their God.  They will know that I am YHWH their God, who brought them out of Egypt so that I might dwell among them.  I am YHWH their God.  (Ex 29:43)

It was always part of God's plan to find a place to rest on the Earth.  Not that he can really be confined to a Temple built with human hands, for as Solomon says:

But will God really dwell on earth?  The heavens, even the highest heaven, cannot contain you. How much less this temple I have built!  Yet give attention to your servant’s prayer and his plea for mercy, Lord my God.  Hear the cry and the prayer that your servant is praying in your presence this day.  May your eyes be open toward this temple night and day, this place of which you said, ‘My Name shall be there,’ so that you will hear the prayer your servant prays toward this place.  Hear the supplication of your servant and of your people Israel when they pray toward this place.  Hear from heaven, your dwelling place, and when you hear, forgive.  (1 Kings 8:27-30)

Nevertheless, his Name can be spoken, and in this way he can be honored or dishonored.

At first, the Jews freely used the name YHWH to refer to God, even in ordinary conversation, as can be seen from the Old Testament.  However, as time went on, this came to be regarded as unsafe and presumptuous.  Eventually, the rabbis decided that the best way to satisfy the Third Commandment was never to say the Name at all.  That way there would be no chance of accidental blasphemy.  The High Priest could use the Name on Yom Kippur [The Day of Atonement], but that was it.  After the Temple was destroyed, the Name was never spoken again by halakha-compliant Jews.

This was the opposite mistake from careless or flippant use of the Name.  Instead they played it so safe that God may as well not have revealed the Name in the first place.  God had put himself on a first name basis with Israel, so to speak, and they declined to exercise the privilege.

So what did God do?  Did he rectify this situation by telling people they were missing out?  Did he put things back the way they were before?  No, instead, in his divine wisdom he had a completely different plan.  As it is written:

Shout and be glad, Daughter Zion. For I am coming, and I will live among you,” declares YHWH. “Many nations will be joined with YHWH in that day and will become my people.  I will live among you and you will know that YHWH Sabaoth has sent me to you.  YHWH will inherit Judah as his portion in the holy land and will again choose Jerusalem.  Be still before the Lord, all mankind, because he has roused himself from his holy dwelling.” (Zech. 2:10-13)

Rather than restore the old intimacies, God gave new ones.  He himself came and lived among us.  Greater intimacy implies greater vulnerability.  The new name he has given us to speak aloud is the name of "Jesus",

Who, being in very nature God,
did not consider equality with God something to be used to his own advantage;
rather, he made himself nothing
by taking the very nature of a servant,
being made in human likeness.
And being found in appearance as a man,
he humbled himself
by becoming obedient to death—
even death on a cross!
Therefore God exalted him to the highest place
and gave him the name that is above every name,
that at the name of Jesus every knee should bow,
in heaven and on earth and under the earth,
and every tongue acknowledge that Jesus Christ is Lord,
to the glory of God the Father.  (Phil. 2:6-11)

When Paul says that God gave to Jesus "the name that is above every name", there is only one Name which a first century rabbinically educated Jew could have in mind.  The first century Christians might not have ever spoken the name YHWH, but in passages like this there is an implicit allusion to the Name of God.

When you see the name Lord in the New Testament, this is the Greek word kyrios.  In principle, this word, like Adoni, could itself refer to an ordinary human being.  However, the New Testament writers continually quote from the Greek Septuagint, which uses kyrios as its substitution for YHWH.  This puts an important overtone into the word.

People argue about whether the New Testament really refers to Jesus as God.  What they don't realize is that in the Greek linguistic context, calling Jesus theos is actually a surprisingly ambiguous statement of Jesus' divinity (and many of the passages calling Jesus theos can be explained away).  What is quite unambiguous is calling Jesus kyrios and then applying to him Old Testament passages in which kyrios is a substitution for YHWH.  For example "Everyone who calls on the name of the Lord will be saved (Rom 10:13)"

To those of my readers who are baptized, remember that you have been dedicated into "the name of the Father, the Son, and the Holy Spirit"!   What name is this?  It is a singular name.  "The Father, the Son, and the Holy Spirit" is grammatically plural, not singular.  So the "name" must refer to some unmentioned name which belongs to all three persons equally.  The mystery of our faith is that all three persons are one YHWH, the eternal existence.  This passage is another example of an implicit reference to that Name which no first century Jew would ever say.

This is the Name into which you were baptized, making you into God's Temple.  If you defile this Temple, you also dishonor the Name which God placed in you.   But if you honor him, he will honor you, by coming to live with you.

Posted in Theology | 10 Comments

Did the Universe Begin? IV: Quantum Eternity Theorem

Having pointed out that the BVG theorem presupposes the existence of a classical spacetime, Carroll goes on to cite some evidence that the universe did not have a beginning, based on quantum mechanics (QM):

If you need to invoke a theorem, because that’s what you like to do rather than building models, I would suggest the quantum eternity theorem. If you have a universe that obeys the conventional rules of quantum mechanics, has a non-zero energy, and the individual laws of physics are themselves not changing with time, that universe is necessarily eternal. The time parameter in Schrödinger’s equation, telling you how the universe evolves, goes from minus infinity to infinity. Now this might not be the definitive answer to the real world because you could always violate the assumptions of the theorem but because it takes quantum mechanics seriously it’s a much more likely starting point for analyzing the history of the universe. But again, I will keep reiterating that what matters are the models, not the abstract principles.

First of all, some background.  In QM, there's a gizmo called the wavefunction \Psi.  This is the thing that tells you what are the probabilities for any particular thing to be happening, at any given moment.  It involves specifying a complex number z = a + bi for each possible configuration of the universe.  Complex numbers are two-dimensional, so they have both an absolute value (or magnitude) |z| = \sqrt{a^2 + b^2} and a phase (or direction) in the two dimensional plane.  The square of the absolute value |z|^2 gives you the probability to be in that state, while the phase (or direction) of the complex number is an additional weird extra piece of information which is special to QM.  (There's some deep conceptual issues about what the wavefunction "really" means, but let's not get into that here.)

In ordinary QM, the wavefunction of the universe changes with time.  If you want to work out how it changes with time, you need to know the formula for the total energy of the universe, written out as a function of the positions and momenta of all the particles or fields.  Once you know what H is, you can then use Schrödinger's equation:

H \Psi = i \hbar \frac{d}{dt} \Psi.

This equation tells you that if your state \Psi is in a state with a specific energy H \Psi = E \Psi (this is called an energy eigenstate), then its phase just spins around and around, at a rate proportional to the energy E divided by Planck's constant \hbar.  That's rather boring, since it would mean that none of the probabilities actually change at all.  On the other hand, if you have a state where the energy has quantum uncertainty (meaning that it is actually a superposition of states with definite energy) then more interesting things can happen due to interference patterns between the different energy eigenstates.

So, if you know what H is (that specifies the dynamics of your theory) and you know what the wavefunction \Psi is at some specific time t_1, and if you assume that this theory is valid at all moments of time, then you can work out what \Psi is at any other moment of time, past or future.  And it particular, you know what it would have been at a time t_2 which is arbitrarily earlier than t_1 is.  Hence—so Carroll's argument goes—the universe cannot have had a beginning.

That's all the Quantum Eternity Theorem (QET) says.  It's a little bombastic for Carroll to even refer to this as a "theorem", since it's just an elementary restatement of one of the most basic principles of QM.   As Carroll said in his post-debate reflections:

For convenience I quoted my own paper as a reference, although I’m surely not the first to figure it out; it’s a fairly trivial result once you think about it.

You could still imagine that God miraculously created the universe at a given moment of time t = 0, and that the laws of physics only apply after that moment of time.  Then physics as such would have nothing to say about the actual Beginning, but only what happens after that.  There's no logical contradiction in saying that, but it might make some people uncomfortable if—so far as we can tell from Science—the universe has to have lasted forever.  In some ways, this is the position Christians were in prior to Modern Science, when the study of the heavens seemed to indicate that the universe just kept going on and on, like a clock that never needs winding up.  Back then, Christians mostly believed there was a Beginning for philosophical reasons, or else because it said so in the Bible.  We now know that the Universe developed from a simpler form, and that it has only existed in its currently observable form for about 13.8 billion years.  The scientific case for a Beginning is certainly much more conclusive now than it was then, since back then there wasn't much of a scientific case at all!

But if Carroll's QET does apply, then no matter how many fireworks there were at the "Big Bang", it could only really have been the universe passing from one form to another.  So is he right?

Probably not.  Carroll himself states the important loophole in his reasoning, although he does it in a kind of a cryptic way so that only another physicist like me knows what it really means.  Let's have it again:

If you have a universe that obeys the conventional rules of quantum mechanics, has a non-zero energy, and the individual laws of physics are themselves not changing with time, that universe is necessarily eternal.

What Carroll neglected to say during the debate, is that there's very good reason to believe that the energy of the universe is zero (if it is defined at all).

It's actually rather tricky to make precise the concept of "energy" in General Relativity.  The reason is that energy is defined with respect to how things change with time, and time is a rather slippery concept in GR.  There isn't just one notion of time, but rather any choice of "t" coordinate you might choose is equally valid.  If there's no well-defined concept of time, then there's also no well-defined concept of energy, and the QET won't apply.

So when people do refer to energy in GR, they need to be some type of special situation that allows them to invoke the concept.  Here are the cases people talk about most often:

  1. If we zoom in close to one point, we can adopt a particular local inertial reference frame and define the energy of an object using that local coordinate system.  But Special Relativity tells us there are several equally good notions of time , and even those are only good in the neighborhood of a single point, so this won't work for the QET.
  2. If you have a spacetime which is approximately unchanging with respect to some special time coordinate "t", you can define the energy of objects with respect to that time coordinate, as long as their gravitational field is small.  This is called the Killing energy, but this is also inapplicable in cosmology since the universe is not anywhere close to static (it is expanding).
  3. If you have a system of objects sitting by themselves inside an otherwise empty infinite space, then you can use the notion of time defined by a clock which is very far away from the system.  This is called the ADM energy, and it tells you the effective gravitational mass of the system as measured from far away.  But this is also inapplicable to cosmological settings, since so far as we know the universe is not a clump of matter in an empty space.
  4. Finally, if you have a closed universe (one with no boundary) then there is an unambiguous notion of energy associated with the gravitational Hamiltonian H.  However, it is exactly zero for all physically allowed states: H = 0!

The conventional view of researchers in quantum gravity—with, apparently, the exception of Carroll himself—is that the same thing is likely to be true in quantum gravity.  That is, instead of the usual Schrödinger's equation, the dynamics of the theory are encoded in the Wheeler-DeWitt equation:

H \Psi = 0.

Now since H tells us how \Psi changes with time, the Wheeler-DeWitt equation tells us that the quantum state does not change with time at all!  That's weird, since we all know that things do change with time.

Does that mean that Zeno was right and time is an illusion?  Well, we have to be very careful with interpretation here.  The real reason why this happens in gravitational theories is because the choice of spacetime coordinates is arbitrary—you are free to label your spacetime points with any (x,y,z,t) coordinates you like: there is not one "best" way to do it.  (Although I've been focusing on General Relativity, physicists expect similar issues to pop up in almost any decent theory of gravity.  So long as it does not reintroduce a notion of absolute Newtonian time, there will necessarily be a "Hamiltonian constraint" saying that the only physically allowed states of a closed universe are those for which H = 0.)

So when we say that the wavefunction doesn't change with time, what this really means is that the choice of time coordinate is arbitrary.  "Time" needs to be measured relative to some physical clock.  There is no absolute "t" coordinate relative to which everything else moves,  So, I think I would say that in this case, the QET "applies", but in a totally trivial way, and when you unpack its real meaning, it doesn't tell us anything about whether or not there was any time before the Big Bang.  Thus the formalism of ordinary QM is not applicable.

To summarize, in a closed cosmology, the energy is zero, and in an open cosmology it might not even be defined.  Thus Carroll's appeal to the QET probably doesn't make sense.

As I said to Carroll in the comments to his post-debate reflections:

Regarding the QET, to my mind the most conservative belief about quantum gravity is that it is—like GR—governed by a Hamiltonian constraint rather than an ordinary Hamiltonian (as in standard QM). In this setup, it’s not obvious that the QET applies.

What’s more, since there is no “absolute time” in GR, there are lots of different, inequivalent ways to evolve space forwards in time. As Wheeler put it, time is many fingered. This concept of time evolution will be much more subtle to quantize, and it’s far from obvious (to me, at any rate) that it’s forbidden for time to begin or end. In any case, this is quantum gravity, so none of us really know what we’re talking about!

And he replied:

Aron– That’s certainly a respectable point of view. It’s basically choosing the option that the energy is zero, which is definitely a possibility. And if that does turn out to be the case, time can certainly “end,” but in a very funny sense, since “time” was only emergent to begin with.

But the other option, that the energy is not zero and the ordinary time-dependent Schrödinger equation applies, is at the very least equally reasonable (perhaps more so). Our best-understood example of quantum gravity is the AdS/CFT correspondence, where the theory is most carefully defined in terms of the Hamiltonian of the boundary theory — in which perfectly conventional Schrödinger evolution applies. My suspicion is that quantum gravity will work similarly in other cases as well. But as you say, it’s quantum gravity, so we’re allowed to speculate but not allowed to act like we know the answer.

AdS/CFT is a famous duality between an ordinary QM theory (the CFT) and a gravitational (string) theory with a negative cosmological constant.  In this case, there is a well-defined nonzero H, but that is because you have a bunch of matter sitting in an otherwise empty AdS space, so you can use the ADM definition of the Hamiltonian.  (This duality tells us very interesting things about general aspects of quantum gravity, but it probably doesn't apply directly to our own universe, which has a positive cosmological constant, among other considerations.)

GR predicts (A) that H \ne 0 for matter sitting in empty AdS space, and (B) that H = 0 for closed universes.  It doesn't make any sense to me to say that because string theory agrees with GR about (A), it probably disagrees with GR about (B).  To me, the most conservative thing to say is that both of these facts continue to be true.  Furthermore, case (B) is far more likely to describe the real universe than (A) is.A

Although, as we both said to each other, no one really knows for sure how the correct theory of quantum gravity is going to be formulated.  Of course, there is nothing wrong with Carroll putting forward his personal opinion in the debate—I can hardly complain about that after Craig put forward my opinions!  But I think he could have been more clear that it was his personal opinion, and that, given more "conventional" beliefs about quantum gravity, the QET probably can't be applied in cosmological settings.

[9/22/14: a few minor wording changes—AW]

Posted in Physics, Reviews | 2 Comments

Did the Universe Begin? III: BGV Theorem

There is a theorem due to Borde, Guth, and Vilenkin which might be taken as evidence for a beginning of time.

Roughly speaking, this theorem says that in any expanding cosmology, spacetime has to be incomplete to the past.  In other words, the BGV theorem tells us that while there might be an "eternal inflation" scenario where inflation lasts forever to the future, inflation still has to have had some type of beginning in the past.  BGV show that "nearly all" geodesics hit some type of beginning of the spacetime, although there may be some which can be extended infinitely far back to the past.

If we assume that the universe was always expanding, so that the BGV theorem applies, then presumably there must have been some type of initial singularity.

The fine-print (some readers may wish to skip this section):
[BGV do not need to assume that the universe is homogeneous (the same everywhere on average) or isotropic (the same in each direction on average).  Although the universe does seem to be homogeneous and isotropic so far as we can tell, they don't use this assumption.

More precisely, let H be the Hubble constant which says how rapidly the universe is expanding.  In general this is not a fully coordinate-invariant notion, but BGV get around that by imagining a bunch of "comoving observers", one at each spatial position, and defining the Hubble constant by the rate at which these observers are expanding away from each other.  The comoving observers are assumed to follow the path of geodesics, i.e. paths through spacetime which are as straight as possible, that is without any acceleration.

Now let us consider a different type of geodesic—the path taken by a lightray through spacetime.  Now if the average value H_\mathrm{avg} along some lightlike geodesic is positive, then BGV prove that it must reach a boundary of the expanding region in a finite amount of time.  In other words, these lightlike geodesics reach all the way back to some type of "beginning of time" (or at least the beginning of the expanding region of spacetime which we are considering).

We can also consider timelike geodesics, describing the motion of particles travelling at less than the speed of light.  For nearly all timelike geodesics, if H_\mathrm{avg} > 0 then that geodesic also begins at a beginning of time.  However, the theorem only applies to geodesics which are moving at a finite velocity with respect to the original geodesics which we used to define H_\mathrm{avg}.  The original set of observers is allowed to extend back infinitely far back in time.

As an example of this, one can consider a spacetime metric of the following form:

ds^2 = dt^2 - a(t)^2 (dx^2 + dy^2 + dz^2).

If we set the "scale factor" to be exponentially inflating:

a(t) = e^{Ht},

then such a universe extends infinitely far to the past from the perspective of an observer who remains at a fixed value of (x,\,y,\,z).  But nevertheless, observers travelling at a finite velocity relative to those hit a beginning of time (or else exit the region of spacetime where this metric is valid).

Since the BGV theorem only refers to the average value of the expansion, it applies even to cosmologies which cyclically oscillate between expanding and contracting phases, so long as there is more expansion (during the expanding phases) then there is contraction (during the contracting phases).

On the other hand, in certain cases even an expanding cosmology may have 0 average expansion, due to the fact that we are averaging over an infinite amount of time.  So the BGV theorem does not rule out e.g. a universe where the scale factor a(t) approaches some constant value in the distant past.]
The fine print is now over.

All right, everyone who skipped the details section is back, yes?

The BGV theorem is sometimes referred to as a "singularity theorem", but it is not really very closely connected to the others, because it doesn't use an energy condition or any other substantive physical assumption.  It's really just a mathematical statement that all possible expanding geometries have this property of not being complete.

Carroll correctly observes that the BGV theorem relies on spacetime being classical:

So I’d like to talk about the Borde-Guth-Vilenkin theorem since Dr. Craig emphasizes it. The rough translation is that in some universes, not all, the space-time description that we have as a classical space-time breaks down at some point in the past. Where Dr. Craig says that the Borde-Guth-Vilenkin theorem implies the universe had a beginning, that is false. That is not what it says. What it says is that our ability to describe the universe classically, that is to say, not including the effects of quantum mechanics, gives out. That may be because there’s a beginning or it may be because the universe is eternal, either because the assumptions of the theorem were violated or because quantum mechanics becomes important.

It is quite true that the BGV theorem is proven only for classical metrics, although I see no particular reason to believe that its conclusion (if the universe is always expanding, than it had an edge) breaks down for quantum spacetimes.

However, Carroll's secondary point that the assumptions of the theorem might not hold seems even more devastating.  It says that there must be a beginning if the universe is always expanding.  So maybe have it contract first, and then expand.  That's an easy way around the BGV theorem, and (as Carroll points out) there are a number of models like that.  On this point I agree with Carroll that the BGV theorem is not by itself particularly strong evidence for a beginning.

Posted in Physics, Reviews | 26 Comments

Did the Universe Begin? II: Singularity Theorems

Our best theory of gravity is classical General Relativity.  "Classical" is physics-speak for not taking into account quantum mechanics.  So we know that classical GR has to break down during the Planck era, if not later.

Classical Big Bang cosmology predicts that there is an initial singularity at the first moment of time.  In fact, there are some theorems to that effect.  These are the Penrose and Hawking singularity theorems, which will be the subject of this post.

In GR, attractive gravity is caused by the energy or pressure of matter.  Tension (which is negative pressure) produces antigravity (repulsion rather than attraction).

Very crudely speaking, the singularity theorems say that if you assume that matter obeys some energy condition restricting the amount of energy and/or pressure, then you can deduce that under certain conditions there has to be a place where your spacetime has an edge and cannot be extended any further.  This we call a singularity.  Typically, some component of the curvature becomes infinite at the singularity.

There are several different singularity theorems, pioneered by Hawking and Penrose.  One of them says that singularity theorem says that all expanding cosmologies like our own have to begin with a singularity.  Roughly speaking, it says that if there is only gravity and no antigravity, then tracing the universe backwards in time there is no way to stop it from crunching down to zero size.   Hence there must exist an initial singularity (at least somewhere, perhaps everywhere).

However, this Hawking-Penrose theorem uses something called strong energy condition, which says that the repulsive antigravity from tension is not allowed to be greater than the gravity from energy.  It turns out that the strong energy condition can be violated by lots of different types of otherwise reasonable physics theories.  In particular, it was violated during inflation, and it is violated by the cosmological constant today.  So no one really takes this theorem very seriously anymore.

There is another singularity theorem (proven originally by Penrose) which is better, because it only uses the null energy condition, which says that nearby lightrays are always focused by gravity.  This turns out to be a much weaker condition, which is satisfied by most respectable classical matter theories (although it is violated quantum mechanically).  However the Penrose singularity theorem only says that there has to be a singularity if space at one time is infinite.

If space at one time is finite in size (for example, if it is shaped like a 3-sphere) then there might be a "bounce" where the universe contracts to a small size and then starts expanding again.  The de Sitter cosmology is an example of this, although there are also examples of finite cosmologies that begin with singularities.  We don't really know whether space is finite or infinite, since inflation stretched it out so much that even if it were a giant sphere, the radius is so large that it seems flat today.

A few years ago I wrote an article in which I argued that the conclusions of the Penrose singularity theorem should continue to hold in quantum gravitational situations.  Even though the null energy condition can be violated by quantum fields, it turns out that you can get the same conclusions if you instead assume something called the "Generalized Second Law" (GSL), which says that the Second Law of thermodynamics applies to black holes and similar types of horizons.

(I described the application of this result to time travel in a  recent Scientific American blog post.  Technically, you have to use the time-reverse of the GSL, which I mentioned in the comments here, but if the GSL is true, its time-reverse should also be.  This may seem weird because normally we think of the Second Law as something which only works in one time direction, but I promise you that one can make sense of it.)

The advantage of using the GSL is that it makes it more plausible that the conclusions of the Penrose singularity theorem apply even in fully quantum-gravitational situations, e.g. during the Planck era.  In my article, I showed that the results apply "semiclassically", meaning when the quantum corrections to spacetime are small but still taken into account.   I then argued (and not everyone would find this part of my article persuasive) that under certain assumptions one might expect the result to hold even in full quantum gravity, when these quantum fluctuations are large.  But remember, all statements about quantum gravity are speculative.

I am a little reluctant to even bring up my own work, since personally I think it is more persuasive that clearly established (but incomplete) physics predicts a beginning, than that speculative new physics says this.  I think of it more as laying the groundwork for a possible future understanding, then a totally conclusive result.  Still, I think that the Penrose theorem is connected to enough other deep principles of physics that something like it will probably be true and important in the final theory of physics.  Other physicists think that singularities are so disturbing that any "complete" theory of physics should eliminate them.

Funny story.  One time I was arguing with an atheist grad student about God and the question of the universe's beginning came up.  I mentioned my own work (and I am quite sure that I put in some caveats about the potential limitations, since I always do this).  A few weeks later I found him posting on some atheist website cocky statements along the lines of "Theists believe that the universe had a beginning because of the GSL, but this is silly for the following reasons...".  And this at a time when practically no one else had even heard of my work!  So just in case it isn't clear: many smart people believed in God before I came along, and the case for Theism is hardly dependent on my tiny contributions to physics!

In conclusion, to the extent that the singularity theorems are relevant, they tend to point to a Beginning, although it might be possible to evade this conclusion either by (a) having space be finite, or else (b) through quantum gravity effects, if my speculative arguments for a quantum singularity theorem are wrong.

Posted in Physics, Reviews | 4 Comments

Did the Universe Begin? I: Big Bang Cosmology

The next topic from the Carroll-Craig debate which I wish to discuss is what Science has to say about whether or not there was a beginning.  Was there a first moment of time, before which the universe did not exist?  What does Modern Cosmology have to say about this question?

I think that Modern Cosmology gives a fairly clear answer: probably, but not almost certainly.  But, rather than try to argue only for one particular conclusion, I will instead try to provide the evidence in both directions, on which my opinions are based.

The reason why I say probably is that, given our current best theories of the universe, there are some decent reasons to think that the universe had some type of beginning at the so-called "Big Bang".  However, once you get to an early enough moment of time, we don't really understand anything anymore, so really anything might have happened.  That is why the term "Big Bang Model" refers to the (very well-confirmed) theory of the expansion of the universe after the Big Bang, rather than to the Big Bang singularity itself.

Given our current best understanding of particle physics, we think we can describe fairly well the history of the universe starting at around 10^{-6} seconds after the Big Bang.  We're certainly on-base in the period from about 10 seconds to 20 minutes, since this is when Big Bang nucleosythesis occurred (creating the first atomic nuclei), and we can check that the current abundances of H, He, and Li atoms are in agreement with what our theory of nucleosynthesis predicts.

Inflation (which would have happened at a much earlier time) is somewhat less certain, but it makes pretty good predictions so almost everyone believes in it these days.  The recent BICEP2 results indicate that the energy scale of inflation was just a couple orders of magnitude below the Planck scale.  This is a much higher energy scale than anything else we can measure in physics, although it is comparable to the GUT scale (where most particle physicists, but not I, believe that the forces probably unify into one force).  During the inflation era, the universe grew in an extremely rapid way, stretching out and diluting any information about what the universe was like before inflation.

The Planck era was approximately the first 10^{-43} "seconds after" the "Big Bang".  This is the era where strong quantum gravity effects become important.  In other words, the quantum uncertainty in concepts of "space" and "time" become so large that our classical concepts break down.  That's why I put scare-quotes around things in this paragraph—we no longer know what on earth (or in the heavens) we are talking about.  This is the point when everything is pretty much up for grabs.

So, even if we can say there appears to have been a beginning based on an extrapolation of the Big Bang Model to early times, there are also reasons why we can't be completely sure, so long as we don't completely understand quantum spacetime (or the initial conditions for inflation).  Certainly the universe as we know it began, but we cannot completely eliminate the possibility of a pre-Big-Bang stage.

Nevertheless, in the next few posts I will discuss the limited evidence which we do have, especially those points which were mentioned in the debate.  In particular I will cover singularity theorems, the BGV theorem, the 2nd Law of Thermodynamics, the quantum eternity theorem.  Oh, and the Hartle-Hawking no-boundary proposal.  That too.

Posted in Physics, Reviews | 4 Comments

Time Machines and Event Horizons

I've written a pop-article about Time Machines and Event Horizons, which has appeared on the Scientific American blog Critical Opalescence.  George Musser, my host, is an editor at Scientific American, and kindly gave me this opportunity to talk about some of my ideas in my article, The Generalized Second Law implies a Quantum Singularity Theorem.

If you have any questions about the physics in the article, please feel free to leave comments on this post here.  (Questions left on the Scientific American website will be answered in the comments to this post, if anywhere.)

Posted in Links, Physics | 15 Comments

Gaps at the Dinner Table

Speaking of the God of the Gaps™, I was myself accused of believing it just the other day.  I was at dinner with Raphael Bousso, Eva Silverstein, Ori Ganor, and some other physicists, and they were discussing fine-tuning and questions involving the precise way in the Multiverse is supposed to explain it.

Well, eventually I got tired of remaining in the closet, and I asserted: "Given that I believe in God for other reasons, I think it's most likely that God chose the Laws of Nature to be conducive to life".  Well, this got everyone pretty worked up (in a friendly way) and Raphael tried to apply that ominous phrase: the God of the Gaps™.

Well, it isn't.  In my comment, it was completely manifest that I did not believe in a God whose sole purpose was to fill the fine-tuning "gap".  I believe in God primarily for other (good, evidence-driven) reasons.   Once you already believe in God, it is seems totally natural (supernatural?) that he should pick laws of Nature which support life.  Theism isn't an ad hoc hypothesis invented solely to fix the problem of fine-tuning.   Whereas the Multiverse is, so I guess I should have made a counter-accusation regarding the Multiverse-of-the-Gaps!

Or perhaps it should be called Naturalism-of-the-Gaps, that touching faith that Naturalism can explain away the apparent meaning and purpose of the Universe (something which is perfectly obvious to many ordinary people, who haven't been trained out of this intuition by a Naturalist worldview masquerading as "Science").

Of course, for all I know God did create gazillions of other universes besides ours, and this is the explanation for the fine-tuning of our universe.  But I'm certainly not required to believe that the laws of physics are ultimately due to blind processes which don't care about us.  Without that premise, a fine-tuned universe just doesn't seem like as big of a problem.  Hence there is no need to fill the gap with elaborate new physics.

(But don't worry, if I think of a wonderful physical explanation with experimental consequences, I'll still be perfectly happy to publish it and collect my Nobel prize... just because I am open to supernatural explanations, does not mean my mind is closed to natural ones.)

The other thing the dinner conversation made clear is that some physicists get seriously nervous about the fact that God can't be described by equations, and is therefore (in their eyes) ill-defined.  I'll have something to say about this later, in response to Sean Carroll's debate comments.  For now I'll just say that it seemed rather insular to me—there are only a small number of people who are capable of using equations to describe the world, yet everybody else manages somehow.  As they say, if all you have is a hammer, everything starts to look like a nail.  It is our job as physicists to describe the world as completely as we can using equations, but it does not follow that there are no other ways of gaining knowledge about the world.

Perhaps I should have asked whether any of them had ever had a mystical experience.

On the other hand, somebody else (I think it was Ori) pointed out that Monotheism is the ultimate example of a unification hypothesis—explaining diverse things in Nature based on the operation of a single principle.  The elegance of Monotheism seemed to have some appeal to him.

It's a funny thing.   These days, the Multiverse is taken seriously by theoretical physicists, yet God isn't.  (Although the more old-fashioned types attack both concepts as equally unscientific.)  And yet, there is at least some observational evidence for the existence of God (in the way of claimed miracles and visions and so on).  On the other hand, there is no observational evidence for the existence of the Multiverse.

Apart from fine-tuning itself, the best that can be said about the Multiverse is that certain types of speculative new physics (such as string theory) might also predict multiple universes with different laws of physics (depending on certain other factors).  But it's not like there's any actual experimental evidence for other universes, or for any specific theory which predicts them.  It's almost as if people care more about whether an idea has the flavor of Science (or science-fiction) than if there is any actual evidence for it.  The most important aspect of Science is always observational support!

(It's important for people like me who study quantum gravity to remind ourselves of this point from time to time.  It's always especially ironic when people in my field dismiss concepts for lack of observational evidence, since there isn't much in the way of quantum gravity experiments.  10^{-35} meters is just way too tiny to see!)

Posted in Theological Method | 26 Comments

God of the Gaps

Then there is the phrase "The God of the Gaps"™.  In any long discussion on "Science and Religion", this phrase must eventually be deployed by one or the other party, either by the skeptic (with a triumphal tone as of one finally deploying his most powerful weapon) or else by the articulate and educated defender of a modern faith, showing his sophisticated ability to rise above primitive superstitions: "But that's the God of the Gaps™!" they say in response to a proposed act of the Deity, "We can't possibly believe in that!"

In the debate between Carroll and St. Craig, both participants had their obligatory five seconds of hate towards this idea.  Craig:

This is not to make some sort of naïve claim that contemporary cosmology proves the existence of God. There is no God-of-the-gaps reasoning here. Rather I’m saying that contemporary cosmology provides significant evidence in support of premises in philosophical arguments for conclusions having theological significance.


It is certainly a true issue that we don’t know why the early universe had a low entropy and entropy has ever been increasing. That’s a good challenge for cosmology. To imagine the cosmologist cannot answer that question without somehow invoking God is a classic god-of-the-gaps move. I know that Dr. Craig says that is not what he’s doing but then he does it.

It is difficult to fight against a slogan delivered so frequently and with such conviction, especially when for some perverse reason educated and intelligent people on both sides insist on attacking the same strawman.  But it is worth pointing out, that if the detractors of an idea could be defeat it simply by labeling it with a silly-sounding alliterative phrase, we wouldn't be able to believe in the “Big Bang” theory either.

As Carroll quotes the philosopher David Lewis as saying:

I do not know how to refute an incredulous stare.

These references to the God of the Gaps™ often function as a similar incredulous stare, not any kind of actual argument.  (Mind you, the incredulous stares Lewis got were because of his belief in modal realism, i.e. every single logically possible world is equally real.  Perhaps those incredulous stares just meant that ideas which flagrantly violate common sense should be assigned a tiny prior probability?)

Anyway, if the God of the Gaps™ is a fallacy, it's a very strange one.  It is not any one of the standard textbook logical fallacies, and it is only ever brought up in theological contexts.   On the surface, it sounds awfully like claiming that inference to the best explanation is a fallacy.  Let me pull out some home truths here, and make the following bold statement:

Any time we ever believe in anything rationally, we do so because there is some kind of "gap" in our understanding of how the universe works, which is filled by postulating the existence of that thing.

In other words, all valid arguments that something exists are based on Of-the-Gaps type reasoning.  This is just how reasoning (scientific or otherwise) works.

This is not to say, of course, that all gaps are best filled by postulating specific divine intervention.  Of course not.  Admittedly, Monotheists do believe the following:

All phenomena which occur in Nature do so because God sustains the world in being, thus (at least indirectly) causing everything.

But this hardly implies that all phenomena make equally good evidence for God's existence.

To the best of my knowledge, no Christian apologist has ever made the following argument: 1) Science cannot explain high temperature superconductivity [a puzzling phenomenon in condensed matter physics], 2) therefore an intelligent designer must have caused it, 3) therefore God exists.  The reason is that it is obvious in this case that there should exist in principle an ordinary scientific explanation for this phenomenon.  Superconductors involve complicated, messy physics and there is no particularly good reason to be surprised that we don't understand them fully yet.

(When an Intelligent Design theorist such as St. Behe argues that: 1) there exist phenomena in Nature such as bacterial flagellum which could not plausibly have evolved naturally because they have irreducible complexity, 2) therefore they must have been created by an intelligent designer, he is not committing any type of logical fallacy, let alone God of the Gaps™.  The problem with his argument is that biologists have shown that his premise (1) is false, but it's a perfectly good type of argument, if its premises were really true.)

In other cases, such as the seeming low-entropy beginning of the Universe, or the fine-tuning of the constants of Nature to permit life, or why certain forms of life have conscious experiences, or why murder is wrong, or for that matter why there is a material Universe at all, it is at the very least not completely obvious that there will exist a natural explanation of the usual scientific type.  There is a reason that theistic philosophers (not being totally stupid) latch onto these types of "big" or "fundamental" questions rather than questions about superconductivity.

It's actually the exact same reason why many atheistic philosophers will deny that these are meaningful questions to which one has a right to expect an answer.  (Carroll does this in the debate, regarding the question of why the Universe came into existence.  Assuming for the sake of argument that it did, he argues that this is not the sort of thing one needs an explanation for.)  One could imagine a hypothetical physics which is in one sense a complete system of equations, and yet fails to answer some or all of these questions.  In that case the Naturalist will (because of his conviction that Science is the only ultimate path to truth) deny that the questions are meaningful, while any person who feels unable to swallow this will have for themselves an argument for the existence of God.

Other, more optimistic Naturalists may hold to the belief that "Science will one day explain that".  Since data about what Science will do in the future is sadly unobtainable, this type typically appeals to one of those historical just-so stories I mentioned in my previous post.  To rephrase it once more (note that I do not accuse Carroll of making the following argument in all particulars; as I said I am using the debate as a springboard to talk about larger issues):

"Our superstitious ancestors thought that nearly all natural phenomena—the rising of the sun, the growth of the crops, etc. were attributable to numerous supernatural beings. Science has discredited nearly all of these ideas, but of course Science is not yet complete. The modern day defenders of religious traditions, therefore, although their original motivation for belief is gone, cling to these holes in our understanding as keeping a place for the divine activity. If only evolution or Big Bang cosmology or something leaves a place for God's activity, these religious types argue, then we have some role for Religion. But as Science continues to discover more and more, the gaps get smaller and smaller, and eventually these claims will disappear as well. To cling to this sort of Religion is worthless."

This type of reasoning (which is quite common, although I phrase it in my own words) tends to glide imperceptibly from popular pagan polytheists (who thought there was a divinity for every major or minor phenomenon) to the Hebrew monotheists (who resisted this trend as superstitious and wrong).

It was perfectly obvious to any pagan philosopher or early Christian that Nature proceeds according to orderly laws, and natural processes. Modern Science can take credit for unifying the description of many phenomena into common mathematical frameworks, but to act as though the existence of order in Nature is a modern discovery is simply absurd. It is true that this fact is in considerable tension with certain forms of Animism or Nature Polytheism. But certainly almost any astute monotheist living in the last two thousand years, is going to admit that God causes most things to happen, not through whim but through the operation of certain natural processes, which can be understood to some extent by human reason.

In this sense, Naturalism and Monotheism have a shared (and highly successful) common heritage.  Both of them imply that the material world is not to be understood as divine, and that therefore it is fair game for impersonal study and observation.  To act as though the fruits of this shared common presupposition is some type of falsification of one of these two positions is completely unfair.

So then, everyone should stop using this phrase, God of the Gaps™.  In addition to being confusing and condescending, and not really a logical fallacy, it almost always indicates the presence of a strawman opponent.  Very few religious people believe that God exists only to fill gaps in our understanding of Science.  Let's argue against the real positions on the table.

Posted in Reviews, Theological Method | 5 Comments