Physics on Netflix

The Netflix series, 3-body Problem, features physics and physicists throughout. I am not a big fan of science fiction, but watched the first episode, to try and get a sense of why the series is attracting so much attention. The opening scene (in the video above) is rooted in history. It depicts a "struggle session" during the Cultural Revolution, featuring the denunciation and killing of a physics professor, who is the father of the main character in the series.

For some more on the intellectual and political background see

Organized criticism of Einstein and relativity in China, 1949–1989, by Danian Hu

Effective quantum field theories and hierarchial reality

 Over the last hundred years, there has been a fruitful cross-fertilisation of concepts and techniques between the theory of condensed matter and the quantum theory of elementary particles and fields. Examples include spontaneous symmetry breaking, renormalisation, and BCS theory. Sometimes, these efforts have occurred in parallel and only later did people realise that two different communities were doing essentially the same thing but using different language. Other times, one community adopted ideas or techniques from the other.

Central to condensed matter theory are ideas of emergence, a hierarchy of scales, and effective theories that are valid at a particular scale. Elementary particle theorists such as Steven Weinberg often distinguish themselves as reductionists with different goals and approaches. I only recently became aware that effective field theories have become a big thing in the elementary particle community, and Weinberg has been one of the leaders of this!

There is a helpful article in the CERN Courier, published just a year ago.

A theory of theories

Michèle Levi takes a tour through the past, present and future of Effective Field Theory, with applications ranging from LHC physics to cosmology.

The figure below, taken from the article, shows a hierarchy of energy scales and the corresponding effective field theories (EFTs).

n.b. Energy increases from bottom to top. [This may be confusing for condensed matter physicists, as we tend to put the high-energy theories at the bottom].

SM is the standard model

HQET is heavy quark effective theory in which the heavy quark degrees of freedom are integrated out.

EW breaking is Electro-Weak symmetry breaking which occurs on the scale of the Higgs boson.

The smallest energy scale in the figure is Lamda_QCD which is of the scale of the mass of the proton.

The standard model is now considered an effective field theory.

For the associated history and philosophy, I found this article helpful. Effective Field Theories, Reductionism and Scientific Explanation, by Stephan Hartmann

The decoupling theorem, proved by Appelquist and Carazzone in 1975, [cited 2,500 times] is central to EFTs and a hierarchy of scales. 

In its simplest case, this theorem demonstrates that for two coupled systems with different energy scales m1 and m2 (with m2 > m1) and described by a renormalisable theory, there is always a renormalisation condition according to which the effects of the physics at scale m2 can be effectively included in the theory with the smaller scale m1 by changing the parameters of the corresponding theory. The decoupling theorem implies the existence of an EFT at scale m1 which will, however, cease to be applicable once the energy gets close to m2.

There are two distinct approaches to finding effective theories at a particular scale, referred to as bottom-up and top-down approaches. 

Top-down requires one to have a theory at a higher energy scale and then integrate out the high energy degrees of freedom (fields and particles) to find the effective theory for the lower energy scale. This is what Wilson did in his RG approach to critical phenomena. Another example is how string theorists try to derive GR and the Standard Model starting with strings.

Bottom-up can always be done because one does not need to know the higher energy theory. One can often write down the Lagrangian for the EFT based on symmetry considerations and phenomenology. An example is Fermi's theory of beta decay and the weak interactions.

In a previous post, I considered Bei Lok Hu's discussion of these two different routes to developing a quantum theory of gravity.

A major outstanding challenge in the theory of elementary particles and fields is the hierarchy problem: the measured values of some masses and coupling constants are many orders of magnitude different from the "bare" values used in the Lagrangian.

The articles I have read about the role of effective field theories make no mention of the corresponding issues in condensed matter or how emergence is involved. Emergence occurs in systems where there are many interacting components. Here those components are the quantum fields and their components with different momenta/energy. Hence, I would say that emergence is at the heart of big questions in the theory of elementary particles and fields.

Is biology better at computing than supercomputers?

Stimulated by discussions about the physics of learning machines with Gerard Milburn, I have been wondering about biomolecular machines such as proteins that do the transcription and translation of DNA in protein synthesis. These are rather amazing machines.

I found an article which considers a problem that is simpler than learning, computation.

The thermodynamic efficiency of computations made in cells across the range of life

Christopher P. Kempes, David Wolpert, Zachary Cohen and Juan Pérez-Mercader

It considers the computation of translating a random set of 20 amino acids into a specific string for a specific protein. Actual thermodynamic values are compared to a generalised Landauer bound for computation. Below is the punchline. (page 9)

Given that the average protein length is about 325 amino acids for 20 unique amino acids, we have that p_i=p=1/20³²⁵=1.46×10⁻⁴²³, where there are 20³²⁵ states, such that the initial entropy is  , which gives the free energy change of kT(S_I−0)=4.03×10⁻¹⁸ (J) or 1.24×10⁻²⁰ (J per amino acid). This value provides a minimum for synthesizing a typical protein. 

We can also calculate the biological value from the fact that if four ATP equivalents are required to add one amino acid to the polymer chain with a standard free energy of 47.7 (kJ mol⁻¹) for ATP to ADP, then the efficiency is 1.03×10⁻¹⁶ (J) or 3.17×10⁻¹⁹ (J per amino acid).  

This value is about 26 times larger than the generalized Landauer bound.

These results illustrate that translation operates at an astonishingly high efficiency, even though it is still fairly far away from the Landauer bound. To put these results in context, it is interesting to note that the best supercomputers perform a bit operation at approximately 5.27×10⁻¹³ (J per bit). In other words, the cost of computation in supercomputers is about eight orders of magnitude worse than the Landauer bound of  (J) for a bit operation, which is about six orders of magnitude less efficient than biological translation when both are compared to the appropriate Landauer bound. Biology is beating our current engineered computational thermodynamic efficiencies by an astonishing degree.

Superconductors in Hollywood

 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.

A light conversation about condensed matter physics

Three weeks ago I did a local book launch for Condensed Matter Physics: A Very Short Introduction.

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.

Many thanks to all the friends who came.

Emergence and the stratification of physics into sub-fields

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.

An illusion of purpose in emergent phenomena?

 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.

A biologist Michael Levin discusses the issue of intelligence in very small and primitive biological systems in a recent article, Collective Intelligence of Morphogenesis as a Teleonomic Process

[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].

The emphasis on "as if" I have taken from Thomas Schelling in the opening chapter of his beautiful book, Micromotives and Macrobehaviour.

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?