I have been sporadically writing a series on a recent article by Sean Carroll. This is taking me several posts to respond to it fully, so I am going one section at a time. My first post gave an introduction to the topic, and covered Carroll's own introduction. My second post discussed his first main section, where he established his definitions and described the scope of his discussion. My third post discussed the definitions of "something" and "nothing". Carroll was a bit more reasonable here than many of his fellow atheists, who managed to get something out of nothing only by redefining the word "Nothing" to mean "Something." The fourth post discussed whether the universe could come into existence without something causing it, or could continue indefinitely. Carroll argued that both were plausible, and this is where his article started going wrong.
Now we come to the next section, entitled "Why this particular universe?" Even if we conclude that the universe could simply be, we are still tempted to ask why the universe is arranged as it is. Why this set of laws rather than another? Why this particular distribution of matter, anti-matter, and dark matter? This is probably at the heart of the current debate between those who argue that contemporary physics supports religious views, and those who say that it doesn't necessarily do so. I'm thinking in particular of the fine-tuning of the various physical constants.
Our current knowledge of fundamental physics can be reduced to a small number of underlying principles:
- It is a quantum field theory.
- It is constrained by various discrete features, such as the number of space and time dimensions and the geometry and topology of space/time.
- It is further constrained by various symmetries.
- It is constrained by a number of continuous parameters, which control (for example) the masses of the particles and the strength of the forces.
The first three of these conditions are of a different nature to the last. Firstly because they relate to the structure of the laws, while the last point to the finer details. Secondly, because these points are in principle easier to justify. One senses that one could explain them (or at least some of them) from general philosophical principles. The constants, however, as real quantities, and thus it is much harder to see how they could be predicted from first principles. They can only be induced from experiment.
There is no obvious logical reason (to the scientist with no interest in metaphysics) why any of these should be the case. The only guide he has is the demand for self-consistency. Experiment can show which theory is correct, but not explain why it is that way. Classical theories are just as self-consistent as quantum theories, and there might well be other options which are neither classical nor quantum. It is just as easy to construct theories which have different symmetries from the standard model, or which lack (for example) local gauge invariance. There is no logical reason why there has to be three space and one time dimensions (and obviously some candidate quantum gravity theories claim that there aren't). Or why it isn't represented by the Euclidean geometry used by Galileo and Newton rather than the Reimann geometry recognised since Einstein. These questions, are, I think very important, and I will discuss them again shortly.
But the biggest interest in recent times has been over these parameters. We are not discussing dimensional parameters such as the speed of light, whose numerical value will depend on whether you measure it in meters per second or furlongs per Jovian year. Instead these refer to dimensionless parameters, which have the same values no matter which units you use. One example is the fine structure constant, which controls the strength of the electromagnetic force. Another is the coupling between the scalar field and first family of lepton fields, which controls the electron mass. So we keep the quantum nature, symmetries, and geometry as they are in our universe, and start fiddling around with the values of these parameters.
There are about thirty of these numbers in total, most from the standard model of particle physics, and a few from cosmology. I say about thirty, because there is still some uncertainty. There might be a few more if (for example) there are some additional particles whose masses are too large or couplings to the currently known particles too small to have been measured in the experiments so far. There might be fewer if some of them are actually dependent on the others, for example if some of the cosmological parameters in practice can be deduced from the standard model parameters, or the standard model parameters are linked together through some unified theory we don't yet know about. Scientists deduce the values of these parameters through a process of deduction and comparison. They generally can't be measured directly, but we can calculate the values of quantities we can measure which depend on them. So we take an observable, calculate its value as a function of these parameters, measure what value it actually is, and use that to constrain the parameters. The system is very much over-determined, since there about thirty parameters, and a vast number of possible measurements that could be made.
So we have the ability to calculate many of the observable properties of the universe based on the basic theoretical structure (the symmetries and so on) and the values of these constants. That's why we are so confident in the theory. Thirty measurements are needed to constrain the parameters. Predicting the results of the tens of thousands of experiments after that is some considerable achievement. But just as we can calculate what the universe is like given the actual values of these parameters, we can also calculate what the universe would be like if they were slightly different.
And what we find is that the universe would be vastly different. Tweak one parameter a bit, and stars immediately collapse. Tweak another parameter, and atoms don't form. Tweak another parameter, and the most exciting molecule you can get is hydrogen. There are thirty parameters, but over a hundred conditions that need to be satisfied for chemists to have anything more than a handful of molecules to play around with. Of course, there wouldn't be any chemists in that case. Life requires the storage and transmission of complex information. While I don't see why this has to be provided through the DNA and RNA molecules, you will still need something of similar potentiality if you are to have life. Good luck doing that if all you have to build it out of is the hydrogen atom.
The universe would be consistent if these parameters had any real number. Only a tiny region in that space prevents the catastrophe (for us). It so happens that we are right in the middle of that region. Change any of the parameters by a small amount, and you break at least one of the conditions. Try to compensate for this by changing another parameter and you break something else. Of course, it may be that we don't live on the only island of order in this vast sea of chaos, but if there are any other regions which might allow the complexity needed for life, they are just as unlikely as the one we find ourselves in, were we to select the parameters at random (according to some sensible distribution). These are known as the anthropic coincidences, a name which is a little too human centred for my taste and thus obscures the point. It's not about our existence. It is about the existence of carbon and thus complex chemistry.
The possibility for these parameters to be just right for us is too small for it to be chance, not when there is any other possible option. And there are other options. The first is design, which those who accept God have immediately seized on. The second is large numbers; if we suppose that ours is not the only universe, but there is a vast number sampling every possible value of these constants, and we happen to be lucky enough to be in the one which has complex chemistry (although luck is the wrong word; we are in this universe because we couldn't be in any other). (A third option, which I have seen from some people such as Victor Stenger, is to try to deny the problem; but this is just wishful thinking and poor reasoning against an overwhelming weight of evidence.)
Carroll makes a couple of points in his discussion of this:
For other parameters, however, this anthropic expectation predicts something very different from the real universe. An obvious example is the low entropy of the early universe, which is many orders of magnitude smaller than what it would need to be in order for life to exist. More generally, the universe simply seems to have far more stuff in it than any reasonable anthropic criterion would imply; there are more than a trillion galaxies, with of order a hundred billion stars and planets in each of them, none of which is necessary for our existence here.
The first of these examples is clearly missing the point. True, the early universe was not suitable for life. But equally clearly, as the universe evolved under the second law, entropy increased until it became a value where life could be supported. God's need was for a universe that could support rational creatures. But God is timeless. If the time when those rational creatures exist is only a tiny interval when compared to the lifetime of the universe, then God has still achieved His goal; just as our planet (and the few others that might be like it) are only a tiny specks in the vastness of space; but that it exists at some point is nonetheless enough for God to achieve His goal. As for the vastness of space, even if it is true that this is independent of the fundamental parameters under consideration, it makes no difference to the argument. There is no obvious reason why God would prefer a small universe to a big one. God is not like a man who ought to conserve limited resources at every turn.
The second point he makes is more substantial. The problem is we don't know how to sample these parameters. We say that the chances of these parameters taking the values that they do is improbable because they could practically take any value from zero to infinity and lead to a self-consistent physics, but only a tiny region (or a number of tiny regions) are such that life can emerge. But to express this unlikelihood as a probability we need to know how probable it is that whatever mechanism it is that churns out these parameters would select one particular value. The value given to that probability distribution will depend on one's underlying model. All probability depends on one's assumptions. Those who believe in a God who wants to create a rational creature will peak the distribution around that region which supports life, because that's what their assumption demands. Those who deny God need an alternative way of predicting the distribution of parameters, one which isn't biased towards that small region. Which means that we need an atheistic theory of the origin, not of the universe, but of the emergence of physical law. Once we have that theory, then we can at least draw some ideas about how the parameters might be expected to be distributed if that version of atheism is true. But atheists don't have that to enough detail or certainty. In the lack of any certainty, we usually select a uniform distribution, but that doesn't work because a uniform distribution cannot be used over an infinite range. We can map the infinite range to a finite range by using, for example, an inverse tangent function, and select a uniform range over the inverse tangent of the parameters. That's now mathematically consistent, but why an inverse tangent rather than some other function? We have introduced a degree of arbitrariness such that whichever choice we make cannot be justified ahead of the other possibilities.
This problem is particular acute for those atheists such as Carroll who regard the universe as a brute fact -- something which could be otherwise but happens to be what it is, and it is impossible to give a further explanation. To calculate the chances of the parameters having the values that they do requires some theory generating them. But Carroll says that not only do we not know what that theory is but we cannot know what that theory is. His very philosophy denies us the possibility of getting philosophical guidance on how to sample the landscape of possible universes. Yet the question still remains: theism can explain why the parameters take the value that they do, while Carroll can't. Yet he still wants to maintain that his model has fewer assumptions (and is simpler) than theism. [Theists maintain that God is simple and thus cannot be other than what He is, and thus have just one constant to explain. Carroll has to pick one universe out of infinity without justification.]
The laws themselves
So that brings me to the other problem. Beyond the issue of these parameters, we have the further issue of whether we can explain the structure of physical law in terms of some more fundamental principle. This is, of course, of particular interest to me, since it is the topic of my book, where I argue that we can explain why modern physics is what it is if we assume classical theism. I claim that the axioms behind physics can be drawn from the conclusions of theism.
So the problem is that there is a vast (possibly infinite) number of different ways one can construct a self-consistent quantum theory, and many more if one also allows non-quantum theories. So why is the universe governed by this particular set of laws, rather than another? After correctly stating the problem, and saying that it seems hopeless, Carroll offers a thought. He presents the idea that the universe is governed the most simple or most elegant form of the laws.
One justification for this could be the trajectory of physics over the course of centuries. We started by considering a wide range of phenomena, astronomy, dynamics, gravity, electricity, light, heat, magnetism, fluids, gases, solids, hardness, brittleness, and so on. Gradually, starting from Newton's laws, these have been unified, and we are down to two theories, the standard model of particle physics (or some extension of it), and the standard model of cosmology. It is hoped soon that a theory of quantum gravity will be established unifying these.
However, this doesn't really answer the question. Many possible members of the landscape of laws equally reduce to a single principle. So we have no reason to prefer ours over those from a principle of simplicity. Are the laws that measure our universe simpler or more elegant than others? To answer this, we need to have an objective measure of simplicity and elegance, but such concepts are often used subjectively. What is elegant to one generation need not be to the next. If simplicity is to be defined in terms of the number of free fields, our universe couldn't be said to be that. Even within quantum field theory, one has the phi4 theory, the simplest possible field theory (in the sense that it has the fewest fields) or quantum electrodynamics, as the simplest gauge field theory. Even with the gauge structure we have, the weak interaction sector of the standard model is very messy, treating left and right handed particles differently. It would be far more elegant if it were an SU(2) version of QCD. Others might disagree: but that's my main point. The opinions of the last paragraph are just based on my own subjective ideas of simplicity and elegance. They don't count for anything in reality.
Or what about string theory? Could it be that our low energy messiness emerges from some elegant high energy theory? Calling string theory (or loop quantum gravity, or ...) elegant is a matter of opinion, not fact. And even if it was objectively elegant, why does that prove it to be true? There is no evidence, as Carroll states, for suggesting that the underlying laws are as simple as possible. And there is no known good reason that they should be.
So Carroll raises an important problem, but offers no real hope of a resolution in this section. The criteria of simplicity and elegance has no objective measure and no rational justification. The existence of intelligent observers is, to him, no more a solution.
The safest tentative conclusion to draw is that the properties of our particular universe cannot be solely attributed to the fact that intelligent observers exist within it, even if some particular properties may be.
This, statement of course, seems to have the direction of causality (in the sense of the sequence of explanation) the wrong way round. It is not the presence of intelligent observers that causes the universe to be what it is, but the nature of the universe that allows the possibility of intelligent observes. Unless, of course, we assign some purpose or design to the nature of the universe, which would mean going down the path towards God.
So what alternatives did Carroll miss? The most obvious one to me is that the structure of the universe can be deduced from underlying metaphysical principles. Indeed, I believe that philosophers should focus on doing this: figuring out what implications their philosophy has for physics, and then drawing up a list of physical axioms deduced from their philosophy which can be compared against our best theories. This would turn philosophy from random hand-waving to a genuine science. Of course, this might not resolve the underlying problem, but only push it down a level: why this philosophical system, rather than another? But at least then we move the question to the study where it belongs; and maybe here we might be able to reduce the number of degrees of freedom to just a handful, compared against the vast possibilities that physicists have to contend with. The problem Carroll faces is that we are reaching the limit of what can be explained through physics. But that doesn't mean that we have reached the limit of what it is possible to explain. It just means that we have to move beyond physics.
If physics had lead to a situation where we could say that that was the only self-consistent way in which the universe could work, then there would be (some, not complete) justification for seeking ultimate explanations in the natural science, as naturalists such as the new atheists demand. But that isn't what has happened. Instead, contemporary physics is demanding that we look beyond science for a more fundamental explanation. Atheists cannot argue that no explanation is possible, because theists have already provided one, which fits all the facts. The burden is on atheists to step up to the challenge.
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