The Character of Physical Law

The threads of laws and nature

Richard Feynman delivered a wonderful lecture series in 1964 called The Character of Physical Law, introducing listeners to several fundamental topics in physics. From Newtonian motion to Heisenberg’s uncertainty principle, Feynman dazzles us with the beauty and peculiarities of nature along the way.

His lecture series made it clear to me why Bill Gates had referred to Feynman as the “best teacher [he] never had”. One cannot help but appreciate the care and joy that Feynman takes with language and teaching. We might have a few more students in science today if we could bring more of his magic into the classroom.

This post will summarise the key lessons that I took from Feynman’s lectures, focusing more on his thinking methods and reflections than on the physics itself. This will range from the interconnection of ideas to the art of scientific inquiry. But you should, if you have the time and inclination, watch or read his lectures in full. You’ll be all the worldlier for it.

What is the character of our physical laws? To Feynman, physical laws describe the rhythms and patterns that we observe in our universe. These laws are often simple but universal in their description. And while they’re typically mathematical in expression, they’re rarely exact.

Feynman describes an “edge of mystery” that pertains to our description of reality. If we attack every idea with a ‘why’, we’ll soon find ourselves up against the boundaries of theory and evidence. We don’t yet have explanations for the machinery that underly nature’s most fundamental phenomena. Some of this mystery may or may not be a property of nature itself.

So, what makes a good theory or physical law? In A Brief History of Time, Stephen Hawking specified some requirements: First, without too many arbitrary elements, it should describe many classes of observations. Second, it should make specific predictions about the results of future observations that we can falsify through observation and experiment.

Feynman shared the same sentiments but observed how great models tend to lead to new discoveries in neighbouring domains. He described for example how the laws of gravitation and a study of Jupiter’s satellites allowed scientists to determine the speed of light.

Powerful ideas seem to contain basic principles that enable us to derive a whole basket of insights. So, it’s sometimes fruitful and fun to stretch these theories to extremes or impossible consequences. Not only does it test the limitations of our ideas, it may reveal something new about our assumptions, models and understanding of the world.

Hierarchies and interconnections

“You have to learn the tricks; it is just a series of rules that people have found out that are very useful for such a thing.”
Richard Feynman, The Character of Physical Law, 1964

There are many complicated laws for us to think about when studying the physical sciences. These include the laws for gravitation, electromagnetism, nuclear interactions and so on. Feynman likes to think of them as different rules or descriptions to the same underlying puzzle. We know in thermodynamics for example that temperature is referring to the speed of jiggling atoms in an object or system.

Feynman likens discoveries to nodes on a web of interconnections, as opposed to branches on a unidirectional tree. And if reasoning rests on this interconnected web, then logic can flow and follow in many directions. Feynman’s point is that there are many possible and reasonable places to start in the journey of discovery.

To manage our cumulative knowledge, we like to organise ideas into interconnected hierarchies. From the chemistry of water, to the behaviour of storms, we subdivide and specialise. The interconnections are strong in some areas, and weak in others. But all have areas for progress. We simply add, remove and reposition our pieces of understanding until the jigsaw of knowledge makes a little more sense.

Feynman says it isn’t “sensible for the ones who specialize at one end, and the ones who specialize at the other end, to have such disregard for each other”. This applies not only to science, but to the humanities and creative arts as well. We’re all “connecting one step to another”, “both from working at the ends and working in the middle, and in that way, we are gradually understanding this tremendous world of interconnecting hierarchies.”

“There seem to be a lot of unrelated concepts; but with a more profound understanding of the various principles, there appear deep interconnections between the concepts, each one implying others in some way.”
Richard Feynman, The Character of Physical Law, 1964

The equivalency of new ideas

While certain ideas are scientifically and mathematically equivalent, they can differ in philosophy and psychology. For example, Feynman describes how we can state the law of gravitation in three different but equivalent ways: (1) Newton’s law (action at a distance); (2) the field method (potential at the centre); and (3) the minimum principle (path of least action). Each of the three makes us think about gravity in slightly different ways.

This is important because the philosophy and psychology of ideas shape the guesses we make in the future. Their similarities and differences provide clues towards future laws. The Newtonian description for example was eventually found to be inadequate. Einstein had formulated his special and general theory of relativity on the basis that objects with positive rest mass could not travel faster than the speed of light. But Einstein’s ideas (and overwhelming evidence) are difficult to accept if we’re unable to abandon our Newtonian worldview and ‘common sense’.

“Philosophically, you like them or do not like them; and training is the only way to beat that disease… As long as physics is incomplete, and we are trying to understand the other laws, then the different possible formulations may give clues about what might happen in other circumstances”.
Richard Feynman, The Character of Physical Law, 1964

Scientific prejudice and certainty

Here, there is the distinction between scientific prejudice and absolute certainty. The former is a bias, based on your sense of what is more and less likely. If your bias is incorrect, then an accumulation of experiments should reshape your views and beliefs. But if we hold a precondition with absolute certainty, then we can never change or update our views.

As Feynman puts it, “it is necessary for the very existence of science that minds exist which do not allow that nature must satisfy some preconceived conditions”. You’ll see Feynman for instance qualify various statements with “I think”, “as far as we know” and “to our knowledge”.

“Psychologically, we must keep all the theories in our heads, and every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics. He knows that they are all equivalent, and that nobody is ever going to be able to decide which one is right at that level, but he keeps them in his head, hoping that they will give him different ideas for guessing.”
Richard Feynman, The Character of Physical Law, 1964

The Babylonian tradition

To uncover the mystery of nature and models for mathematics, Feynman distinguishes between two schools of thought: (1) Babylonian tradition; and (2) Greek tradition. Babylonian schools focused on producing large quantities of examples and relations to derive a general rule. By contrast, the Euclidean or Greek tradition focused on a set of axioms that contain the consequences that follow.

If we have no idea on where to start, then the axiomatic approach is unlikely to be efficient. In any case, how does one even know what the best axioms are? So, Feynman tends to err towards the Babylonian tradition.

“We must always keep all the alternative ways of looking at a thing in our heads; so physicists do Babylonian mathematics, and pay but little attention to the precise reasoning from fixed axioms”.
Richard Feynman, The Character of Physical Law, 1964

Traversing the deep unknown

“If you thought science was certain – well, that is just an error on your part”.
Richard Feynman, The Character of Physical Law, 1964

In his third lecture, Feynman raises an interesting question: how can we “extend our laws into regions we are not sure about?”. His answer: sometimes we just have “to stick our necks out”. We wouldn’t make any predictions if all the laws or theories we develop are based solely on the results we’ve observed.

Similarly, Feynman says “if we take the derivation too seriously, and feel that one [theory] is only valid because another is valid, then we cannot understand the interconnections of the different branches of physics.” We have to use our incomplete knowledge to guess new laws and theories that “extend beyond the proof”.

For instance, Feynman describes how the Newtonian description of gravitation lead to the derivation of the law of conservation of angular momentum. While we know today that Newton’s laws were incomplete descriptions, the conservation of angular momentum (to our knowledge) remains a valid and universal principle.

Science has an element of uncertainty. And if you’re making predictions that extend beyond your observable range, then there must be some uncertainty. However, like the conservation of energy, there are principles we’ve observed to be true, as far as we know at least. This gives us the confidence and opportunity to make incremental progress in our quest for understanding.

Additionally, while we can disprove a theory, we can never prove it right. Some observation in the future could debunk what we think we know. Vague theories are also less useful to us, given we can neither prove it right or wrong. And those with emotional interests in these theories are more likely to rationalise new evidence to their liking. So, it helps to specify how we might be wrong, prior to the observation or experiment itself.

Guessing new laws

“If science is to progress, what we need is the ability to experiment, honesty in reporting results,… [and] the intelligence to interpret the results.”
Richard Feynman, The Character of Physical Law, 1964

Feynman says there are really three steps to developing new laws and theories: (1) guesses; (2) computation of consequences; and (3) comparing consequences to nature, experience and/or experiment. Sometimes, we’ll start at (2) or (3), out of curiosity or accident, leading us back to (1). And if our guesses disagree with observation, then the law is wrong, no matter how beautiful or elegant it seems.

But it’s not always obvious why we’re wrong when we’re wrong. It could be in our guess, computation and/or comparison. It takes skill to reflect and improve upon our incorrectness. The even bigger challenge is finding what we should substitute in its place. As Feynman puts it, “to guess what to keep and what to throw away takes considerable skill. Actually, it is probably merely a matter of luck, but it looks as if it takes considerable skill”.

Feynman also disagrees with those that think that “guessing is a dumb man’s job”. He thinks it’s quite the opposite. Often, when all the known principles and knowledge of a system are taken together, we find inconsistencies. And it often takes a subtle change or substitute to make the pieces of the puzzle work. Furthermore, there are infinite ways to guess at something. A blind machine alone is unlikely to arrive at the right answer.

And for those that believe that the only theories that matter are those that agree with experiment, Feynman asks whether they’re indifferent between Mayan astronomy and our modern understanding of planetary motion. Even if they’re computationally equivalent, different ideas offer different philosophical and psychological value. And most of us derive some joy from understanding than calculating nature’s machinery.

The art of natural lawmaking

“It is not unscientific to make a guess… It is scientific only to say what is more likely and what less likely, and not to be proving all the time the possible and impossible”.
Richard Feynman, The Character of Physical Law, 1964

Feynman says there’s an art to guessing nature’s laws. And if we wish to learn this art, we might look at history first. He points out how Isaac Newton combined an incomplete knowledge with observational results to ‘guess’ the laws of gravitation. Similarly, James Clerk Maxwell discovered the laws of electricity and magnetism by gathering all the known laws at the time, studying their inconsistencies and adjusting accordingly. Maxwell imagined a model of idler wheels and gears. While this model was not a description of reality, the equations that came from it were consistent with observations.

Accumulative paradoxes

There’s a running theme here of accumulating inconsistencies. Albert Einstein ‘guessed’ the general theory of relativity after thinking about the “accumulation of paradoxes” from the known laws. This was particularly difficult because Newton’s laws were so reliable and engrained. But to explain minor discrepancies in Newtonian predictions (e.g. Mercury’s orbit) required a transformation in our understanding of space and time itself. The philosophy of ideas can change enormously when we try to account for tiny variations in our observations and experiments.

Feynman also points out how two physicists discovered quantum mechanics, independently and very differently. Like relativity, there was an accumulation of paradoxes that we could not explain with the laws were known. According to Feynman, Erwin Schrodinger ‘guessed’ at the equation, while Werner Heisenberg analysed the measurable. Differences in the philosophy of ideas and approaches can lead to the same discovery. This speaks again to the hierarchies and interconnections of ideas.

Filling pigeonholes

We also exhibit a habit for organising and categorising what we know. This process to reduce complexity, in combination with known rules, can help us to guess at the unknown. For instance, when Dmitri Mendeleev arranged the elements by atomic number, electron configuration and chemical properties, the gaps in his periodic table made predictions about new elements that we’d discover in the decades ahead.

Strait-jacket imagination

“It always turns out that the greatest discoveries abstract away from the model and the model never does any good”.
Richard Feynman, The Character of Physical Law, 1964

Unfortunately, the craft of natural lawmaking faces a big challenge. Feynman says “history does not help us much” with solving the next major mystery. When we get really stuck, it’s because “the methods we are using are just like the ones we have used before”. He believes how each new discovery or model is likely to bring about something entirely different. “What we need is imagination, but imagination in a terrible strait-jacket”.

Nature’s grand tapestry

“Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organisation of the entire tapestry.”
Richard Feynman, The Character of Physical Law, 1964

Feynman reminds us that we’re lucky to live in a time where we have the opportunity to make discoveries. Each discovery happens only once. And that special day will never happen again. That’s what makes science, at least to Feynman, very exciting. He likens the process of discovery to a wonderful jigsaw puzzle. It’s a large puzzle with many different and proliferating pieces. Some pieces fit together, others don’t. While we can’t know for sure if a complete picture exists, Feynman says we can draw encouragement from the “common characteristics of several pieces” we’ve seen so far (e.g. the principles of conservation). There appears a grand tapestry in nature for us to uncover.

“What is it about nature that lets this happen, that it is possible to guess from one part what the rest is going to do? That is an unscientific question: I do not know how to answer it, and therefore I am going to give an unscientific answer. I think it is because nature has a simplicity and therefore a great beauty.”
Richard Feynman, The Character of Physical Law, 1964

References

Richard Feynman. (1965). The Character of Physical Law. Available at <https://www.youtube.com/watch?v=j3mhkYbznBk> and <http://people.virginia.edu/~ecd3m/1110/Fall2014/The_Character_of_Physical_Law.pdf>
Stephen Hawking. (1988). A Brief History of Time: From the Big Bang to Black Holes. More at <http://www.hawking.org.uk/publications.html>