Recently my wife and I watched the movie, Joe Versus the Volcano, starring Tom Hanks and Meg Ryan. What I did not expect was that making superconductors commercially viable was central to the (silly but amusing) plot.
The plot summary on Wikipedia says
a wealthy industrialist named Samuel Graynamore needs "bubaru", a mineral essential for manufacturing superconductors. There are deposits of it on the tiny Pacific island of Waponi Woo, but the resident Waponis will only let him mine it if he solves a problem for them...
Here is the relevant scene...
The movie was made in 1990, just after the discovery of cuprate superconductors and at that time there was a lot of hype about commercialisation. I wonder if the scriptwriters drew on that.
It was at a wonderful independent bookstore, Avid Reader, It is a vibrant part of the local community and has several author events every week.
I had a conversation about the book with my friend,Dr Christian Heim, an author, composer, and psychiatrist. My wife and daughter were surprised it was so funny. Most people loved it, but a couple of people thought it should have been more technical. I think that is not the point of such an event or of the Very Short Introduction series.
Here is a recording of the conversation, including the Q&A with the audience afterwards.
The concept of emergence is central to understanding sub-fields of physics and how they are related, and not related, to other sub-fields.
The table below shows a stratum of sub-disciplines of physics. For each strata there are a range of length, time, and energy scales that are relevant. There are distinct entities that are composed of the entities from lower strata. These composite entities interact with one another via effective interactions that arise due to the interactions present at lower strata and can be described by an effective theory. Each sub-discipline of physics is semi-autonomous. Collective phenomena associated with a single strata can be studied, described, and understood without reference to lower strata.
Table entries are not meant to be exhaustive but to illustrate how emergence is central to understanding sub-fields of physics and how they are related to one another.
What do you think of the table? Is it helpful? Have you seen something like this before?
I welcome suggestions about entries that I could add.
A characteristic of emergent phenomena in a system of many interacting parts is that they exhibit collective behaviour where it looks like the many parts are "dancing to the same tune". But who is playing the music, who chose it, and who conducts the orchestra?
Consider the following examples.
1. A large group of starlings move together in what appears to be a coherent fashion. Yet, no lead starling is telling all the starlings how and where to move, according to some clever flight plan to avoid a predator. Studies of flocking [murmuration] have shown that each of the starlings just moves according to the motion of a few of their nearest neighbours. Nevertheless, the flock does move in a coherent fashion "as if" there is a lead starling or air traffic controller making sure all the planes stick to their flight plan.
2. You can buy a freshly baked loaf of bread at a local bakery every day. Why? Thousands of economic agents, from farmers to truck drivers to accountants to the baker, make choices and act based on limited local information. Their interactions are largely determined by the mechanism of prices and commercial contracts. In a market economy, no director of national bread supplies who co-ordinates the actions of all of these agents. Nevertheless, you can be confident that each morning you will be able to buy the loaf you want. The whole system acts in a co-ordinated manner "as if" it has a purpose: to reliably supply affordable high-quality bread.
3. A slime mould spreads over a surface containing food supplies with spatial locations and sizes similar to that of the cities surrounding Tokyo. After a few hours, the spread of the mould has reorganised so that it is focussed on paths that are similar to the routes of the Tokyo rail network. Moulds have no brain or computer chip but they can solve optimisation problems, such as finding the shortest path through a complex maze. In nature, this problem-solving ability has the advantage that it allows them to efficiently locate sources of food and nutrients. Slime moulds act "as if" they have a brain.
[I first became aware of Levin's work through a podcast episode brought to my attention by Gerard Milburn. The relevant discussion starts around 36 minutes].
He also mentions the example of Fermat's principle in optics: the path light takes as it travels between two spatially separated points is the path for which the travel time is an extremum [usually a minimum]. The light travels "as if" it has the purpose of finding this extremum.
[Aside: according to Wikipedia,
"Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature. Not until the 19th century was it understood that nature's ability to test alternative paths is merely a fundamental property of waves."
Similar issues of knowledge/intent/purpose arise when considering the motion of a classical particle moving between two spatial points. It takes the path for which the value of the action [time integral of the Lagrangian along a path] has an extremal value relative to all possible paths. I suspect that the path integral formulation of quantum theory is required to solve the "as if" problem. Any alternative suggestions?
