I just finished reading “dreams of a final theory” by Steven Weinberg. The book is somewhat less technical than I had expected. Despite having a chapter titled “Against Philosophy”, Weinberg deals with several issues that have more to do with the methodology of science than with its content, such as reductionism, “aesthetics” in science, positivism, belief in God etc. Overall, the book is quite enjoyable. I am interested in developing a better understanding of several of the issues Weinberg discusses, so this book has given me a lot of starting material.
To me, the most interesting arguement that Weinberg makes is that “aesthetics” has played a significant role in the formulation as well as the acceptance of several of the theories that have been developed in the last century. I had encountered similar claims before but had not taken them very seriously. But Weinberg makes his case quite convincingly. He argues that validating a theory by means of experiment is not as simple as it may seem. There can be any number of reasons for an anomaly in experimenal results. In judging whether a theory may be valid, whether it is worth trying to validate, physicists necessarily rely on “aesthetic” judgements. As an example, he argues that physicists were more or less certain of Einstein’s theory of general relativity before it was conclusively validated by experiment. As another example, he argues that physicists were sceptical of the theory of quantum electro-dynamics although it was in agreement with experimental results because some calculations based on it involved “ugly” infinities in intermediate steps. He writes that part of this “beauty” lies in simplicity – not the simplicity of the equations but of ideas. Another part of this beauty lies in what he calls logical isolation or rigidity. For example, he writes that no one has yet found a way to make a small modification in the principles of quantum mechanics without destroying the theory altogether. It would make little difference in Newton’s inverse square law of gravitational force if the exponent were changed to 2.01 instead of 2, but even the introduction of a small non-linear term in the linear equations of quantum mechanics produces nonsensical results. Such a theory does not explains why it should be correct but it explains why it cannot be just a little wrong. Concluding a chapter titled “Beautiful Theories” Weinberg writes
We believe that, if we ask why the world is the way it is and then ask why that answer is the way it is, at the end of this chain of explanations we shall find a few simple principles of compelling beauty… the beauty of present theories is an anticipation, a premonition, of the beauty of the final theory. And in any case, we would not accept any theory as final unless it were beautiful. (emphasis mine)
The last sentence in that excerpt sums up most of what Weinberg is saying about beauty. If one keeps asking why as Weinberg does, there will come a point where one will have to stop. How does one decide what that point is? For Weinberg that point will have been reached when we have a simple and logically isolated theory that “explains” everything including the values of what we call universal constants.
In my next post in this series, I will try to present my own thoughts on what it means for a theory to explain something and on beauty.