Outer Limits of Reason (55 page)

Emmy Noether (1882–1935) went further with these ideas. She focused on laws of physics called
conservation laws
. Such laws say that throughout a process or experiment a certain quantity does not change. Prominent examples include:

1.
Conservation of momentum
.  This says that the total momentum of all the objects in a system will always remain the same. We see this, for example, when “breaking” the billiard balls on a pool table. In the beginning only the white ball is moving very fast toward the other balls. After the other balls are hit, they scatter in all different directions and at all different speeds. Conservation of momentum says that the speeds and directions all add up to the speed and direction of the original white ball.

2.
Conservation of angular momentum
.  This law says that how and at what speed bodies spin must remain the same. A classic example of where such a conservation law is demonstrated is when an ice skater is spinning around and then brings her arms in toward her body. To preserve angular momentum, she will spin faster when her arms are pulled toward herself.

3.
Conservation of energy
.  In short, this says that the type of energy in a system can change but the amount of energy must stay the same. For example, when you press on your brakes, the energy of the car moving turns into heat within the brake pads. At a dam, water drops from a high height and can rotate a turbine, which makes electricity.

Noether showed that each of these conservation laws corresponds to a certain symmetry of the system. The above three conservation laws come from the following three symmetries respectively:

1.
Symmetry of place
.  This means that an experiment can be done in different places and the results will still be the same.

2.
Symmetry of orientation
.  Independent of how an experiment is oriented, the results of the experiment will be the same.

3.
Symmetry of time
.  Regardless of when an experiment is done, the results will be identical.

(We are not going to show how the conservation laws correspond to the symmetries.) Noether actually proved something far more general: she showed that
any
conservation law (of a certain type) will have a corresponding symmetry (of a certain type), and furthermore
any
symmetry (of a certain type) will have a corresponding conservation law (of a certain type).

Following Noether's theme, later researchers went further. Rather than looking for conservation laws, they looked for symmetries. This put symmetries at the center of their experiments and calculations. Physicists like John von Neumann (1903–1957) and Eugene Wigner formulated large parts of quantum mechanics in group theory, which is the mathematical language of symmetry. Many other branches of physics also use group theory in a fundamental way.

All these scientists are proposing that instead of humans seeing real structure in the universe, humans are acting as sieves. Scientists do not see the laws of physics; rather, what they select, they call science.

A modern exponent of these ideas is Victor J. Stenger. In a fascinating book titled
The Comprehensible Cosmos: Where Do the Laws of Physics Come From?
Stenger explains much of modern physics from the point of view of symmetry. He uses more sophisticated forms of symmetry than we have discussed to explain modern quantum mechanics, cosmology, quantum field theories, and all the other areas of contemporary physics. The book discusses local symmetries, global symmetries, gauge symmetries, and so on. All these different symmetries can be treated under the umbrella of something he calls
point of view invariance
. This notion says that regardless of how or when a phenomenon is observed, and regardless of how it is described, the laws of physics must be the same. Using these ideas as a sieve to determine the laws of physics, Stenger shows that the laws of physics are not “out there.” They are just the way we look at the universe. In the preface he summarizes: “The laws of physics are simply restrictions on the ways physicists may draw the models they use to represent the behavior of matter.” Again, what this means is the laws are those ways of describing the symmetries that we observe.

Probably the first to promote these ideas was Arthur Stanley Eddington. He was not only a world-class scientist but also a very deep philosopher. Some of his ideas also have an impact on several of the themes of this book.

Rather than just looking at the universe, Eddington turned to look at the scientist, asking “Who will observe the observers?”
⁵⁸
He became an epistemologist to see how a scientist learns about the universe. Eddington's concept of science is something he called
selective subjectivism
. The laws are not objectively out there. Rather, they are subjectively chosen. The scientist selects certain phenomena on the basis of their symmetry and then calls the recurrent rules that describe such phenomena
laws of nature
. The laws can be expressed in mathematical language because that is the way we view the external world. Or as he says, “The mathematics is not there till we put it there.” It is not the structure that we are looking at, rather it is the way we look at it the universe. Eddington finishes off his important book,
Space, Time and Gravitation
, with the following wonderful quote: “We have found a strange footprint on the shores of the unknown. We have devised profound theories, one after another, to account for its origins. At last, we have succeeded in reconstructing the creature that made the footprint. And lo! It is our own.”

Before we leave Eddington, let us consider a very profound thought that is relevant to the theme of this book. When we talk about the limits of scientific reasoning, we must keep in mind how we are observing the universe. Eddington presents a fantastic analogy about a scientist who studies fish (an ichthyologist):

Let us suppose that an ichthyologist is exploring the life of the ocean. He casts a net into the water and brings up a fishy assortment. Surveying his catch, he proceeds in the usual manner of a scientist to systematise what it reveals. He arrives at two generalisations:

(1) No sea-creature is less than two inches long.

(2) All sea-creatures have gills.

These are both true of his catch, and he assumes tentatively that they will remain true however often he repeats it.

In applying this analogy, the catch stands for the body of knowledge which constitutes physical science, and the net for the sensory and intellectual equipment which we use in obtaining it. The casting of the net corresponds to observation; for knowledge which has not been or could not be obtained by observation is not admitted into physical science.

An onlooker may object that the first generalisation is wrong. “There are plenty of sea-creatures under two inches long, only your net is not adapted to catch them.” The ichthyologist dismisses this objection contemptuously. “Anything uncatchable by my net is
ipso facto
outside the scope of ichthyological knowledge. In short, what my net can't catch isn't fish.” Or—to translate the analogy—“If you are not simply guessing, you are claiming a knowledge of the physical universe discovered in some other way than by the methods of physical science, and admittedly unverifiable by such methods. You are a metaphysician. Bah!”
⁵⁹

Eddington is stressing that we should look at the size of the net that we cast to obtain our observations. In other words, the way we look at the universe is the way it will present itself to us. He goes on to point out that by looking at the net we will see that the information determined in (1) is more fundamental than the information determined in (2). After all, if we are using a net with two-inch holes, we won't catch a fish that is one inch. In contrast, the fact that all the sea creatures have gills, could be an unwarranted generalization of the fish that we have seen. There might very well be fish without gills out there. Eddington concludes that we learn more from looking at the way we are observing the universe than from actually observing it.

One can only speculate about how our scientific method can be adjusted so that we can see more of the universe. Continuing with the analogy of the fish scientists, what type of fish would we find if we cast a net that has one-inch holes? What are we missing by looking at the universe the way we do? What is out there?
⁶⁰

There are some problems with this solution to the issues raised by the anthropic principle. For one thing, there is simply a feeling that there is an immense underlying structure “out there” that does not care if it is observed by human or conscious creatures. There are vast tracts of both space and time that do not seem to have human or any other observers. Are we really to believe that when a certain part of the cosmos comes into view, it also comes into existence? As for time, there were long eons before observers came into being. Are we really to believe that there was no structure then? The feeling is that the laws are out there and we are viewing them.

Another, related difficulty is that these ideas go against the central conception in all of physics. There have always been laws of physics and states of physics. The laws determine the states and we study the states to learn more about the laws. Here we are proposing that the state of physics—the way the observer is observing—affects the laws of physics. This is a radical change. How do states, which are formulated by laws, change the laws? Actually, the last few paragraphs have said something even deeper: there are no laws at all!

The last problem I will mention is that not all of what we see satisfies the symmetries that we expect in our laws. Many features of the physical universe were formulated by something called
symmetry breaking.
This is a seemingly random process that takes some law of physics that has good symmetry properties and changes it into some other law that has less symmetry. Why some forms of symmetry should be preserved and not others is beyond us (for now) and seems totally random. While the properties of symmetry might shed light on some of the structure, they do not explain all of it.

A few years ago these ideas finally hit me. After I had given a lecture on the basics of quantum mechanics and the central role that the complex numbers play in it, a student asked the following fundamental question: “Why does the universe follow the complex numbers?” The question is excellent in its simplicity. Why the strange complex numbers and not the real numbers that we are used to? It took me some time to formulate the response that really gets to the crux of the issues. The answer is that the universe does not follow complex numbers. Instead, the universe does what it does! Human beings use complex numbers to help them understand this part of the universe called quantum mechanics. If mathematicians had not invented complex numbers, then physicists would have had a harder time understanding the world. The Earth and the sun do not look up Newton's famous formula that describes the attractive force between two bodies and determine the force between them. Rather, the formula is used by humans to understand what is going on. Again, we must emphasize, the universe does not function using complex numbers, Newton's formula, or any other law of nature. Rather, the universe works the way it does. It is humans who use the tools they have to understand the world.

We Do Not Know (Yet)

There is one other response to our fine-tuned universe: we simply do not know (yet). Science has progressed at a breathtaking speed over the past few centuries and we expect a lot from science. Nevertheless, no one has said that science will provide the answers to
all
the questions. At the moment, all of the above answers have a science-fiction feel to them and none of them are really scientifically satisfying. Some new evidence may arise to show that one of the above explanations for the anthropic phenomena is correct. In the future, scientists may find better answers than the ones given. Another possibility is that there is an infinite chain of explanations, one deeper than the next. One explanation might work for a while and then a deeper one is found that explains the previous one, and this goes on for eternity.
⁶¹
However, we must also accept the possibility that there will never be a satisfying explanation for these overlapping questions. In that case, we simply will never know. It takes a touch of humility to say we don't know, and perhaps such humility is warranted.

Let us speculate on why it is so hard to find a legitimate answer to the anthropic principle. There is something inherently strange about all the possible explanations for this principle. For most questions that can be asked about a system, an answer can be found within the system. For example, “Why is it raining today?” Answer: “The clouds are full and the temperature is correct.” This is a question about the environment, with an answer
from
the environment. However, sometimes when a question is so fundamental, one must go outside the system to a deeper level. For instance, fundamental chemistry questions are answered within chemistry or at a deeper physics level. “Why does water boil?” Answer: “Because the fire under the pot increases the energy, etc.” This is a physics answer. Fundamental sociology questions like “Why did the people rebel?” can probably be answered at the deeper psychological level, etc. With our questions about the fine-tuned universe, we are asking fundamental questions that can only be answered by looking
outside
the universe. Why should the entire universe be a certain way? We are searching for an answer outside the universe. What is outside the universe? A deity? Many other universes? We are not used to answers that are outside the universe. Scientists want answers from within the universe and do not like traveling to regions beyond. Even for such fundamental questions about the entire universe, we like answers within the universe and are uncomfortable looking elsewhere. I suspect this discomfort will be with us for some time.