A Universe from Nothing?

by Aron Wall Posted on December 7, 2012

Today I went to a talk by Lawrence Krauss entitled “A Universe from Nothing”, which had the following abstract:

The question, "Why is there something rather than nothing?" has been asked for millenia by people who speculate on the need for a creator of our Universe.  Today, exciting scientific advances provide new insight into this cosmological mystery: Not only can something arise from nothing, something will always arise from nothing.  Lawrence Krauss will present a mind-bending trip back to the beginning of the beginning and the end of the end, reviewing the remarkable developments in cosmology and particle physics over the past 20 years that have revolutionized our picture of the origin of the universe, and of its future, and which have literally revolutionized our understanding of both nothing, and something.  In the process, it has become clear that not only can our universe naturally arise from nothing, without supernatural shenanigans, but that it probably did.

In the first 45 minutes, he provided an animated and reasonably clear explanation of concordance cosmology, the current version of the Big Bang model, dating from the discovery in 1998 that the expansion of the universe is accelerating (rather than decelerating as one would expect from the attractive gravity of ordinary matter).  This is exciting but now well-established work, which I've heard about a hundred times before, but was probably new to many of the people in the audience.  It was peppered with occasional off-hand sneers at Republicans, Theology, and Young Earth Creationism, but for the most part it was a pretty valiant stab at popularizing an important set of 20th century discoveries.

The real reason I was there, of course, was to listen to his claims in the last 15 minutes that modern cosmology somehow points to the nonexistence of a Creator.  His claim was that there is evidence that the universe came from "Nothing" according to physical processes, and this apparently is supposed to undermine the religious view that God created the world supernaturally.  There were so many things wrong with this part of his talk, both a physics and a philosophical perspective, that I'm not entirely sure where to begin.  But let's try anyway.

His Slam on Theology.  Krauss said that Theology wasn't based on empirical evidence, so therefore he didn't believe it.  That was it.  He didn't seem to take any particular theological ideas seriously enough to even try to define them, let alone refute them.  There was no indication that Religion had any other origin besides a bunch of clueless dudes sitting around asking "Why is there Something rather than Nothing?"  (In the case of Christianity, I thought it had more to do with a guy claiming to be God, doing miracles, and dozens of people saying that they saw him alive after he was killed.  But what do I know?)

But let's get back to cosmology, since that was the subject of his talk.  It used to be that Christians believed that the world was created a finite time ago, out of Nothing.  Although some of them, like St. Thomas Aquinas, said that God could have created a universe with an infinitely long past.  Atheists had (and have) a diversity of opinions, but most of them thought that things would make more sense if the universe were around forever, since then maybe you wouldn't have to explain where it came from.  Then Big Bang cosmology came along, and it now seems—provisionally speaking—like the Universe really did have a beginning.  Now some atheists think they can refute the Christian view that God created the Universe from Nothing by arguing that the world did emerge from Nothing.  The role-reversal here is a little strange.

What Christians mean by creation ex nihilo is that God created the Universe, but that he didn't make it out of any pre-existing stuff that was lying around.  Thus, while the universe didn't come "out of" anything, it still comes from God.

What Krauss seems to mean is something quite different, namely that there's some specific entity we can talk about called "Nothing", which has suitable properties for generating our universe.

But the universe can only come from nothing if you define a certain kind of something as being "Nothing".  Duh, because any explanation by its very nature must explain one thing in terms of some other thing!  This other thing must be taken for granted for purposes of the explanation.  Now, Krauss actually referred to 3 different ideas which he called "Nothing #1, #2, and #3":

Nothing #1: an "empty" spacetime a.k.a. the vacuum.  In ordinary non-speculative quantum field theory (QFT), the "vacuum state" (the configuration of fields with the lowest energy) is actually filled with so-called virtual particles which can affect physics in various ways.  At least, that's what the popularized physics books say; if one actually studies quantum field theory rigorously, people tend to use somewhat different language since the notion of "virtual particle" can be difficult to define.  But let's spot him the terminology since he was talking to a popular audience.

Krauss claimed that if you start with an empty space which has no virtual particles in it, virtual particles will appear, and this is "something" coming from "nothing".  This is bosh, since strictly speaking, there's no such thing in QFT as a state with no virtual particles.  (If there were, it would be infinitely different from the vacuum state, and would therefore have an infinitely large energy.  That's not nothing at all!)  If anything can colloquially be called "Nothing" in QFT, it is the vacuum state.  But this state already has all those virtual particles in it.  And as time passes, this vacuum evolves to....wait for it....itself!  That's right, if you agree to call the vacuum state Nothing, then Nothing comes out of it.  (He seemed to think this story might change once you take gravity into account, due to negative energies, but I didn't really understand this suggestion so I won't comment on it.)

The QFT vacuum isn't nothing.  Of course, from a strict philosophical point of view, the vacuum state of QFT is not Nothing since it's filled with all those virtual particles, and even aside from that, there's the space and time geometry, which is not Nothing.  To fix this he started taking up a different kind of nothing:

Nothing #2: the absence of any space or time.  This actually connects to an interesting quantum gravity idea known as the "Hartle-Hawking state" or the "no-boundary boundary condition".   (Jim Hartle is on my floor at UCSB, by the way.)  The suggestion is that the laws of physics not only tell you how the universe at one time evolves to a later time, they also tell you what the initial state of the universe is.

In some sense, one can think of this state as emerging out of Nothing #2.  However, the sense in which this is true is subtle.  There's another sense in which the Hartle-Hawking state does not emerge from Nothing; rather it has existed for an infinite amount of time— the popular physics articles never mention this, for some reason!  This is an interesting and important idea, but I think it deserves to be in it's own post, after I've explained QFT better.  The important thing to know is the following:

The crucial physics here is totally speculative!  It was entirely based on speculative ideas about quantum gravity which anyone working in the field would admit are not proven.  This is because we currently have no experimentally testable theory of quantum gravity!  (Nor do we even know how to formulate a consistent theory of quantum gravity mathematically, except perhaps in some special situations that probably don't apply to the beginning of our universe)

I mentioned this in the Q&A afterwards.  My comment seemed to aggravate him a little, since he thought he'd been sufficiently clear about this.  But I discovered that at least one member of the audience was still unclear on which parts were speculative, and which weren't, at the end of the lecture.  In my experience, one has to be crystal clear about this sort of thing when speaking to a popular audience, or they tend to walk away thinking that "Science" has proven things when it hasn't.

Atheists such as Krauss scorn theology as being completely non-empirical.  They claim it is not based on evidence of any sort.  I find it extremely ironic when this sort of atheist thinks that speculative quantum gravity ideas are just the right thing to further bolster their atheism.  Suppose you think that Science is better than Religion because it is based on evidence, and suppose you also want to refute Religion by using Science.  Here's a little hint: consistency would suggest using a branch of Science that actually has some experimental data!

The universe has zero energy.  Krauss thinks that the universe coming out of Nothing has been made more plausible by cosmology.  To understand his terminology, you have to know that (roughly speaking) a closed universe means that space at one time is finite in volume, and shaped kind of like a sphere, so that if you travel around the universe far enough you come back to where you started.  On the other hand, in a flat universe, space at one moment of time is shaped like ordinary Euclidean geometry, and is infinitely large.  Current observations indicate that the universe is flat.  As far as I could tell, Krauss' argument can be translated into these terms:

  1. The total energy of a closed universe is zero.  (It's tricky to define energy in general relativity, but according to one commonly used definition, this is true.)
  2. Conservation of energy suggests that if the universe came from Nothing, it should have zero energy.
  3. If there was a period of extremely rapid expansion at the beginning of the universe (as evidence suggests there was—this is called inflation), then whether or not the universe started out closed, it should look flat today.
  4. But the universe does look flat,
  5. Therefore Science suggests that the universe was created out of Nothing,
  6. Therefore there is no need for God.

Perhaps I'm missing some crucial steps in his argument.  But there seem to be several enormous leaps of logic in there.

The Hartle-Hawking state isn't Nothing either.  Strictly speaking, even the Hartle-Hawking idea doesn't strictly get the universe out of Nothing, since it says that the initial state of the universe depends on the laws of physics.  Now the laws of physics aren't nothing.  So if, for example, you are wondering if there is any role left for the Creator, then one might say he picked the laws of nature.

Now, there's all sorts of difficult philosophical issues involved in what's called the Cosmological Argument for the existence of God.  But it's hard to get into them with someone like Krauss who is so dismissive of Philosophy.  The trouble with people like that is that it isn't possible to just find things out using Science instead of Philosophy.  That's because you have to do Philosophy to know what is or is not implied by Science.  People who dismiss Philosophy still end up doing it; they just do it badly, without a critical examination of their premises.

Nothing #3: the string theory multiverse.  Krauss acknowledges that the laws of phyiscs themselves might seem to call  for an explanation.  Especially since the various constants of Nature seem to be "fine-tuned" to allow the existence of life (I'll go into this in much more depth later).  On the face of it, this seems to be at least some mild evidence for the existence of God, but Krauss would never admit such a thing.

He suggests that we can explain this fine-tuning if string theory turns out to be true.  That's because string theory has an enormous number of different possible configurations, that look like universes with different laws of physics.  Some people have suggested that if there's a gazillion different universes (known as the "multiverse"), each with its own laws of physics, that it's not surprising that one of those universes should support life.  Krauss admitted that there was some dispute as to whether this idea counts as "Science", what with it being totally speculative and arguably untestable.  But what I want to know is, why the $@#& would we ever refer to an infinite number of universes, governed by the principles of string theory, as a Nothing?

I should say that this review is based entirely on Krauss' talk.  I have not read his book, but I have read this negative review by philosopher St. Feser.

[Update 7/21/20: added two paragraphs to the text, beginning "What Christians mean..." to make the argument a little clearer.]

Posted in Reviews | 18 Comments

Pillar of Science VI: Community Examination

by Aron Wall Posted on December 5, 2012

Scientific Results are Examined Collaboratively.

Scientists do not work alone, but in a particular kind of community.  The last stage of a research project is publishing and explaining the results.  Assuming these results get noticed, this begins the process of further review, critique, confirmation and rebuttal by other scientists.  No one person is smart enough to see things from all angles.  We need help from others to look in a clearer, less fragmented way.  Perhaps one could call this undivided looking?

Science is not just a set of facts, or an abstract procedure for testing ideas.  It is an ethical, truth-seeking community.  The love of truth is embodied in the alliance of particular, fallible humans, united by a common geeky interest in finding something out.  Together we create a public deposit of information which can be used to find new things out.

Because the community as a whole is truth-seeking, in the long run it reduces the need to trust the competency and ethics of the original researchers.  If someone fakes an experiment (or else just makes an innocent mistake), other people will be unable to replicate the result, and eventually the truth will come out.

Healthy scientific collaboration encourages reasonable dissent.   Otherwise group-think can insulate the community from effective criticism of accepted ideas.  Some people say that scientists should proportion their beliefs to the evidence.  However, there's also some value in diversity of opinion, because it permits subgroups to work on unpopular hypotheses.  I suppose things work best when the scientific community taken as a whole proportions its research work to the evidence.

One might argue that collaboration is not strictly necessary to Science.  Imagine a solo scientist doing careful experiments in secret, and drawing the correct conclusions from them.  (Even in this case the scientist would be drawing on public ideas which had gone before, "standing on the shoulders of giants", as the saying goes.)  But in practice, the benefits of discussion are so great that it's hard to imagine a successful modern scientist working completely alone.  Hence the symbiosis of Science with the Academy.

Individuals who think they can revolutionize Science all by themselves are almost always crackpots, the sort of crazy person I described one pillar ago.  If you want to see clearly, you have to expose yourself to the light.

Posted in Scientific Method | 1 Comment

Geometry is a Field

by Aron Wall Posted on November 26, 2012

In Time as the Fourth Dimension?, I explained how to calculate the distance (or duration) squared between any two points of spacetime, using a spin-off of the Pythagorean theorem:

s^2= (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - (\Delta t)^2.

Then I explained the Ten Symmetries of Spacetime, i.e. ways to shift or rotate the coordinate system (t,\,x,\,y,\,z) that don't change the formula for s^2.

Well, it turns out that I lied.  The formula isn't actually true, except in the special case that there is nothing in the universe.  A significant reservation, I know.  Instead, what's true is that the geometry of space is a field, meaning that it varies from place to place, depending on where you are!  However, if you zoom in really close at any particular point, it looks similar to the formula I told you.

The field that says what geometry is like at any given place and time is called (brace yourself) the gravitational field.  In order to describe it, we use something called the metric, which indicates what the geometry of spacetime looks like at any given point.  The way this works is, suppose we have two points p and q which are very close to each other.  Suppose we want to know the distance between these points.

Since the points are really close to each other, we call the distance between them ds, where the d is just a reminder that we're using Calculus to study infinitesimal quantities.  If you don't know Calculus, just pretend these are really small numbers.  We want to figure out what ds is, if we know the infinitesimal coordinate differences (dx,\, dy,\,dz,\,dt).  The way we do this is by generalizing the heck out of the Pythagorean theorem.  I'll write it down, and then explain what it means:

(ds)^2 = g_{xx}\,(dx)^2 + g_{yy}\,(dy)^2 + g_{zz}\,(dz)^2 + g_{tt} \,(dt)^2 + \\ 2[ g_{xy}\,dx\,dy + g_{xz}\,dx\,dz + g_{xt}\,dx\,dt + g_{yz}\,dy\,dz + g_{yt}\,dy\,dt + g_{zt}\,dz\,dt].

The right-hand side of the equation consists of every possible way of multiplying two of the coordinate distances (dx,\, dy,\,dz,\,dt).  There are 4 different ways to pick the first (dx,\, dy,\,dz,\,dt), and 4 different ways to pick the second, which gives 4 \times 4 = 16 possible combinations in all.  However, multiplication is commutative so e.g. dx\,dy = dy\,dx.  So I added terms like that together; that's where the factor of 2 came from.  Taking that into account, there's 10 terms in all.

The funny g things with subscripts are just functions of spacetime, i.e. they are just numbers that depend on where you are, i.e. they are fields.  In the special case where we pick these numbers to be g_{xx} = g_{yy} = g_{zz} = +1,\,g_{tt} = -1 and the rest zero, we get the geometry I told you about, which goes by the aliases "Minkowski space", "flat spacetime", and "Special Relativity".  In all other cases we have what is colloquially called "curved spacetime" which is the province of "General Relativity".

The formula above looks kind of ugly, but we can prettify it by choosing good notation.  We collectively refer to all ten of these gravitational fields as the metric, denoted g_{ab}, where subscripts like a and b can refer to any of the four coordinate labels.  (People often call these labels (0,\,1,\,2,\,3) instead of (x,\,y,\,z,\,t) to avoid confusion, since the metric itself says which of the coordinate directions behave more like space, and which behave more like time, and this can vary from place to place!)  Then we write the four coordinate differences (dx,\, dy,\,dz,\,dt) collectively as dx^a, where the superscript says which of the four it is.  Finally, we make up a rule called the Einstein summation convention, that if we ever see the same letter as both a subscript and as a superscript, we add up all of the four possible ways for them to be the same (i.e. both 0, both 1, both 2, or both 3).  These are just changes in how we write things, not substantive changes, but they let us rewrite that long ugly equation like this:

ds^2 = g_{ab}\,dx^a\,dx^b.

There, isn't that much prettier?

Suppose we want to find the distance (or duration) between two points which are NOT infinitesimally close to each other.  In that case, we have to choose a path between the two points, since the amount of distance (or duration) depends on which path you choose, and in a curved spacetime there's not necessarily one "best" path.  This shouldn't seem that strange, since even in everyday life we know perfectly well that the distance between San Francisco and L.A. depends on which highway you take, and the distance between Tokyo and New York depends on which way around the globe you fly.  (It's totally intuitive for distances, but when the duration depends on the route you take through spacetime, people call it the Twin Paradox and act all shocked!)

So this is the first main idea of General Relativity: the geometry of spacetime is a field which varies from place to place.  This field affects matter by determining the paths that things take through space and time, but it also is affected by matter—we call this gravity.  The second main idea is that coordinates are an arbitrary choice; I'll tell you about this later.  The third main idea is the Einstein equation which says how matter affects the metric.  I haven't told you anything about this equation yet, but once I do, you would in principle be able to calculate everything about the gravitational field from that one equation.

There can also be distortions of the spacetime geometry which exist independently of matter.  These gravity waves are to gravity what light is to electromagnetism, ripples in the field which travel through empty space, and can be emitted and absorbed.  The propagation of these waves is also determined by the Einstein equation.  Since gravity comes from massive objects, gravity waves are emitted when extremely large masses oscillate, for example when two neutron stars orbit each other.  We know gravity waves are there, but we haven't detected them directly.  However, we hope to detect them soon with the LIGO experiment.

UPDATE: I realized that I never said how you would calculate the distance between two points, once you choose a path.  The answer is that you chop the path into lots of tiny little line segments, and find the length of each line segment using the metric.  Then you add them all up.  If you know Calculus, this can be done using an integral.

Posted in Physics | 6 Comments

Email Subscription Added

by Aron Wall Posted on November 24, 2012

It is now possible to subscribe by email by clicking on the subscribe link, located at the bottom of the "meta" menu on the right side-bar.  Undivided Looking can send you an email notification every time there is a new post.  (Your email address will not be used for any purposes unrelated to the blog, because that would be a sin.)

The emails may sometimes be delayed by anywhere up to a few hours, due to issues with our ISP.  If you want quicker results, you may prefer using the RSS feed, also in the right-hand side bar.

 

Posted in Blog | Leave a comment

Giving Thanks

by Aron Wall Posted on November 22, 2012

Today is Thanksgiving Day (in the United States), a day set aside for us all to remember the things in life we are grateful for.   Fortunately, Nicole and I started the process of gratitude earlier this week when we finished writing and mailing our thank-you notes for the useful and beautiful presents we got by agreeing to spend the rest of our lives together.

All of us have been supported by other people in many ways, or we would not be alive.  All of us should be grateful more often for those things.  Those of us who believe in God have the privilege of also having someone to thank for the blessings of life that don't come from other human beings, such as the sun and moon, stars and trees, happy coincidences, good health and harvests, etc.  Even when the good things come from other people, we can still accept it as ultimately coming from the hand of God, who has, after all, provided those other people with the ability and conscience to help us.

But what about when bad things happen?  Is it consistent to attribute everything good that happens to God, but then turn around and say that God has no responsibility for any of the bad things that happen?  Should we blame God for the bad as we praise him for the good? If religious folk thank God even for the indirect results of God's providence, that are mediated through human choices, why should we not take the same attitude for bad things caused indirectly by God?

Some people say: God does not cause evil, he only permits it.  This idea can be comforting to those who have suffered greatly, because then they don't have to deal with resentment towards a God who inflicts suffering as well as joy.  Others may find this a pedantic distinction, saying that God is equally responsible for the evils he permits.

The Bible, on the other hand, doesn't seem to refrain from attributing sorrowful events to God:

When disaster comes to a city, has not the Lord caused it?  (Amos 3:6)

When the evil comes from other people, this is in one sense a violation of God's will, who has most definitely commanded us to love our neighbors (Lev. 19:18), strangers (Lev. 19:34), and enemies (Ex. 23:4-5, Prov. 24:17-18, 25:21), and who has set a day of judgement in which wrongdoers will be punished.  When a woman is raped, this horrible crime arises not because God approves of rape, but because God allows the will of wicked men to affect other people.

Nevertheless, God does allow it, and the Bible is not shy about describing such things as being (in another sense) God's decision and will.  When the righteous St. Job loses everything, including his children, to a combination of "natural" disasters and bandit attacks, what does he do?

At this, Job got up and tore his robe and shaved his head. Then he fell to the ground in worship and said:

“Naked I came from my mother’s womb,
and naked I will depart.
The Lord gave and the Lord has taken away;
may the name of the Lord be praised.”

In all this, Job did not sin by charging God with wrongdoing.  (Job 1:20-22)

Job attributes the disaster to God's "taking away", but he does not blame God by charging him with "wrongdoing".  What gives?  How is it possible for God to do something evil without being evil?  The key is what the patriarch St. Joseph says to his brothers, when he forgives them after they had sold him into slavery:

“Don’t be afraid.  Am I in the place of God?  You intended to harm me, but God intended it for good to accomplish what is now being done, the saving of many lives.” (Genesis 50:20)

One and the same act can be both evil and good, depending on whose intentions we consider.  The selling of Joseph into slavery is evil as done by his brothers, because they intended to harm him.  It is good as done by God, because God's intentions were different: God did it in order to save lives.  (I am not trying to make any comment about free will here; presumably if Joseph's brothers had freely chosen not to sell him into slavery, then God would also have chosen something different.)  Thus God can condemn what people do, while simultaneously using it for his good plan.

That must be why, after the Apostles were flogged for teaching about Jesus, they were

The apostles left the Sanhedrin, rejoicing because they had been counted worthy of suffering disgrace for the Name.  (Acts 5:41)

Why on earth did they take this attitude?  St. Paul explains it like this:

We also rejoice in our sufferings, because we know that suffering produces perseverance; perseverance, character; and character, hope.  And hope does not disappoint us, because God has poured out his love into our hearts by the Holy Spirit, whom he has given us.  (Romans 5:3-5)

And we know that in all things God works for the good of those who love him, who have been called according to his purpose.  (Romans 8:28)

The idea that God does not cause bad things to happen is a superficial teaching.  It evades the cross and forgets the gospel message that we are to rejoice and thank God for everything that happens to us.  That is why St. James tells us to

Consider it pure joy, my brothers, whenever you face trials of many kinds, because you know that the testing of your faith develops perseverance.  Perseverance must finish its work so that you may be mature and complete, not lacking anything.(James 1:2-4)

But perhaps James was just copying his brother's idea:

“Blessed are you when people insult you, persecute you and falsely say all kinds of evil against you because of me.  Rejoice and be glad, because great is your reward in heaven, for in the same way they persecuted the prophets who were before you.” (Matt. 5:11-12)

In conclusion, it doesn't make any sense to thank God for the good things in life and absolve him for the bad things.  No, we should also credit the bad things to God, and give thanks for them as well.  Not because the evil is imaginary, but because he intends to use it to build us up into more loving people, for the sake of the salvation of the world.

But perhaps your last year was actually quite pleasant, as mine was.  In that case, let's not forget to thank him for the obvious blessings as well.

Posted in Theology | 9 Comments