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Term papers due at Final: December 11, 1:30 pm

The Anthropic Principle

B. Carter, in Confrontation of Cosmological Theories with Observation, M.S. Longair, ed. The Anthropic Cosmological Principle, J. D. Barrow and F. J. Tipler

Consider this statement:

"It is not only that man is adapted to the universe. The universe is adapted to man." J. A. Wheeler, 1985.

Wheeler does not claim it to be a religious statement, although perhaps it is. What is he saying, then?

The question is "Why are we here?"

The underlying fact: Human beings exist. From that we can draw some conclusions about the history of the universe, just as we can from the observation of anything else (a supernova, a diamond…).

Philosophical complication: If we search for supernovas or magnetic monopoles or little black holes, we might fail to find them. However, non-observation of us is not a possible outcome of our observations.

So we are going to have to exercise a special caution in trying to draw any conclusion from our own existence.

In the words of statistics, there's a (whopping) selection bias.

A background story:

Suppose we measure the chemical composition of the Earth’s atmosphere. We will find it to be 21% oxygen. There is no significant ammonia. This isn’t the state of affairs on other planets and moons. Is that surprising?

One can give two answers. The first is yes. It is an amazing coincidence that conditions on the Earth are exactly what are required to sustain life. A small change in the numerical values of temperature, atmospheric contents, etc would render life as we know it impossible.

The second answer is no. If the physical parameters that describe our environment weren’t suitable for life, then we wouldn’t be here to observe it. Thus, our presence guarantees the results we get.

An uninteresting fact:

All the physical constants have to have precisely the values we observe in order for humans to evolve, since biology is very sensitive to chemistry, and chemistry is very sensitive to those constants. However, we can imagine slightly different values, giving rise to different creatures, who might then wonder how it was that the universe was set up so carefully for themselves.

So what we are really interested in is what conditions are necessary for the evolution of any creature capable of asking this question.

Non-observation of observers is not a possible outcome of any observations

A more interesting fact

A fairly large number of physical constants, not currently constrained by any established theory, probably have to have values close to those that we observe in order for any life to evolve. E.g.:

1. W: a dense universe would collapse before anything could evolve. A sparse universe wouldn't form galaxies, 2cd generation stars, elements with interesting chemistry…

2. The strength of the attractive nuclear force has to fall within a fairly narrow range (a factor of about 1.5) to make deuterium stable, but not diprotons. Outside that range, there's no apparent way to form heavy elements.

3.There's a particular excited state of the carbon nucleus whose energy just matches up with the rest mass of three helium nuclei. This allows carbon to form, and hence the heavier elements. These energy levels have to be very fine-tuned. Maybe there are other possible tunings that would work, but it seems that in a random draw of the strengths of these interactions (near the current values) most results wouldn't allow heavy elements to form.

4. Various special properties of C, O, H, N, etc are needed for the formation of our form of life.

It is conceivable that something other than complex chemistry (for which 1-3 are prerequisites) could provide the combination of stability and complexity needed for a substrate for evolution of conscious creatures, but there are no remotely plausible reasons to presume that. (contrary to science fiction)

Let's discount (4)- the question isn't why us but why anybody, and we have no reason to doubt that a variety of detailed chemistries could give rise to life.

Many quite different ideas are grouped under the vague heading of "anthropic principle". Generally, those that find the match between us and our universe unsurprising are called the weak anthropic principle. Those that try to draw some further inferences about the universe from its suitability for us tend to be called the strong anthropic principle.

Here we will assume that the detailed match between our version of life and current conditions is explained by Darwin- but that leaves to be explained why the universe has those rather precise physical properties needed as a substrate for any evolution.

What must the universe look like just because we are here?

We are made of carbon and live on a planet that is mostly iron. This implies that our Sun must be a second generation star. Therefore, the universe must be at least several billion years old. The universe cannot be too dense (it would collapse too soon) or too tenuous (stars wouldn’t form). So, the large scale properties of the universe are, in some sense, required by our existence.

This is the weak anthropic principle (WAP). It is not very controversial. In fact, it is often criticized as being a truism.

One can argue that some quantities that are not predicted by the theory can be found by appealing to the WAP. E.g. in attempts to determine what the early Earth was like, life seems to predate the oldest surviving rocks. So life itself tells us some things not easily determined about the early atmosphere, temperature, etc. However, it doesn't seem that such reasoning has given us any genuine new ideas about anything more general or fundamental.

Two forms of weak anthropic principles:

Since our existence is a precondition for observations, and various physical facts are preconditions for our existence, there is no point in trying to explain those physical facts. They just have to be true.

I call this the counter-productive AP, since it simply leads to dropping research topics. In its extreme form, it means dropping questions about the origin of any physical properties, since if you change any, we wouldn't be here. In a milder, but still useless form, it means dropping any questions about the fundamental physical constants, since if they were much different, nobody would be anywhere. But there has already been a good deal of progress in reducing the number of separate parameters needed to describe the world (e.g. in the unifications of forces), so it doesn't make sense to drop that endeavor mid-stream. It now seems that W=1 may result from inflation- if that pans out, it would have been a shame not to have investigated just because it's needed to have W~1 for life.

Many Tries (sometimes considered a form of the Strong AP)

If the universe has some of the properties it has (e.g. strength of nuclear force) because it is self-selected THERE MUST HAVE BEEN SOME LARGER ENSEMBLE FROM WHICH IT WAS SELECTED

What sort of larger ensembles could we have in mind?

There are a variety of pictures of space-time which include distinct regions on which it is conceivable that the fundamental constants take on different values. (We don't know yet which parameters come from a deeper theory and which will still be able to take on any of some range of values.)

E.g. In one inflationary picture, islands of non-inflating space nucleate randomly in an ever-inflating background. An infinite number of such islands will be created, making it inevitable that all the parameters which can take on a variety of values can be found somewhere with just the needed values for life.

E.g. In many-worlds versions of QM, any parameters which were set by a quantum-mechanical process take on each possible value in some "world" residing in the overall phase-space.

As wacky as these ideas (esp. the 2cd) may sound, they both arise from an attempt to understand other physical problems, NOT as an attempt to solve the anthropic question. So their solution of the anthropic question would be an added confirmation of their validity- IF the theory reaches the point where these look like self-consistent theories.

The key question is which parameters are set by more fundamental theories, and which are free to fluctuate among domains.

Strong anthropic principles (SAP)

The universe must have those properties that allow life to develop. This has several variants:

Teleology. The universe was designed with the goal of generating intelligence. This is a tenet of most religion. In a particularly strong form, some assert that intelligence is a necessary (and permanent) outcome of our universe.
Participation. Observers are necessary to bring the universe into being. Berkeley’s idealism. Extreme versions of the Copenhagen interpretation. Some versions of postmodernism.
Many tries. (as above, where it was labeled a Weak AP)

The primary motivation for the SAP is the desire to explain why the numbers that describe the universe satisfy the amazing coincidences needed for the existence of consciousness. This kind of explanatory technique has a realm of applicability that shrinks as the power of more conventional theory expands. We just don't know whether it will shrink to zero or not, if and when a completely unified theory is developed.

The traditional view is that once the value of a parameter has been explained by some more fundamental theory, it no longer becomes relevant to consider it in the anthropic context. If, however, any form of multiple-domain theory works out, it is precisely the unconstrained parameters which are guaranteed to have the right values in some domain, and hence to require no explanation. If it turns out that some properties which are tightly constrained by underlying theory also are tightly constrained by the anthropic principle, then it would be a real miracle that those constrained values are just right to make life, and that would provide food for religious thought. (as discussed in a recent forum on campus) This outlook is in some sense the reverse of the traditional view.

Probabilistic interpretations of deductive argumentation: Consider a Modus Ponens (MP) style argument: 1) If x then y. 2) x, 3) therefore y The probabilistic interpretation of this is: 1) Pr(Y*X) is high, 2)X, 3) therefore Pr(Y) is high. Here Pr(Y*X) is the conditional probability of x given y. This is a valid probabilistic interpretation of MP. Now consider Modus Tollens: 1)If x then y, 2) not-y, 3) therefore not-x. The probabilistic interpretation of Modus Tollens is: 1) Pr(Y*X) is high 2) not-Y, 3) therefore Pr(not-X) is high. Equivalently, 1) Pr(not-Y*X) is low, 2) not-Y, 3) therefore Pr(not-X) is high. The latter two arguments are not valid. The key point is that if a hypothesis says that an observation is very improbable does not mean that the hypothesis is improbable.

Summary:

There are some apparently fine-tuned parameters which take on just the right values needed for the existence of life.

How to interpret that fact will depend on how the current laws of physics end up embedded in deeper laws, if that is accomplished.

If all the parameters are uniquely specified by the form of a deeper theory, that they're suitable for life is still a sort of miracle, but not one about which science will have anything to say.

If the deeper theory allows some latitude for some of those parameters, then the strong supposition will be that our particular values are self-selected from some sort of ensemble, which will support pre-existing efforts to find such ensembles either in the extended space-time of GR (or its quantized successor) or in the phase space of QM. Thus our existence may turn out to be useful evidence helping point the way toward one class of theories over another.

These speculations are at (or beyond) the borders of physics.

Other questions which often come up in this context:

Why is there anything?
Why does the universe make any mathematical sense?
Whatever the overall form of the theory turns out to be (if it's ever known), why that?

Perhaps it's conceivable that science may have something to say someday about (3).

As for (1) and (2), no one has proposed any way that science could even begin to have anything to say about them.