Follow us on twitter for updates and helpful hints! @physics_journal
P. W. Anderson (1972). More Is Different. Science, New Series, Vol. 177, No. 4047, pp. 393-396
Below are some of the best summaries sent in by students across the world. Well done to all students who submitted their summaries, there were some exceptional answers. A special congratulations goes to the students of Queen Elizabeth's Grammar School, Derbyshire, who were the school with the most students sending in summaries for us to read.
1. Why do you think Anderson chose to call the piece “More Is Different”?
Anderson wrote about ‘the arrogance of particle physicists’ who claimed among others that the only fundamental scientists are those studying systems and behaviours at the fundamental level (creating the fundamental laws), because these laws and concepts can be extrapolated to govern everything else we come across. Anderson’s main point is that new properties and/or behaviours can be observed at different levels of complexity, so the study of complex macroscopic systems (often named extensive research), is intensive in its own right as it brings with it new science that cannot be determined from the viewpoint of another alone. Therefore, systems with more complexity show differences to systems with less complexity at the fundamental level – more is different.
2. How would you summarise this paper in one paragraph?
Anderson’s paper explains the assertion that it is impossible to extrapolate our observations on a small scale, simply involving a few particles, once we have increased the scale and begin to look at larger groups of particles or systems. He sets out to examine the reductionist hypothesis, arguing that instead of the existence of “intensive” and “extensive” research - based on whether the research concerns fundamental laws (as suggested by Weisskopf) - each area of study is significant and can be viewed as fundamental, since each level of the ostensible hierarchy of the sciences requires “entirely new laws, concepts and generalizations”. Anderson then goes on to explore the idea of broken symmetries that appear in molecules on a larger scale - that is, the new properties that appear when the scale is changed. The article is concluded with a criticism of the conceit of “the particle physicist and his intensive research”, and the idea that the sciences are needed by each other to provide important alternative perspectives. The closing quote, from Fitzgerald and Hemingway, may serve to emphasise that the differences in importance between the sciences in the supposed hierarchy are somewhat superficial.
3. How would you summarise this paper in one sentence?
A complex system comprised of individual components will have less symmetry than its separate parts and will also exhibit behaviour that differs from predictions made by simply extrapolating the fundamental laws governing those parts, such that at each level of complexity, new concepts arise.
4. Do you have any criticisms of this article?
Until we have a complete understanding of everything in the universe, it would be impossible to concretely know for certain that all matter is completely governed by fundamental laws. For example, the existence of ‘dark matter’ suggests that the universe is not homogenous. The ‘dark matter’ is very different from observed matter, set apart most notably by its lack of interaction with light. Our understanding of is it severely lacking, as it appears to be under the control of laws currently outside our understanding. Therefore, it seems likely that there is not one set of laws for all matter and that different types of matter obey different laws, which are, consequently, not fundamental.
The answers to the rest of the questions can be downloaded as a completed Cornell notes template here.
- (P1, C1) What is the reductionist hypothesis?
- That we can reduce science to the study of the most fundamental ideas.
- (P1, C1&2) What areas of physics would you consider to be ‘intensive research’ and which would be ‘extensive research’? Why?
Intensive: particle physics, some aspects of theoretical physics, cosmology, nuclear physics.
Extensive: materials science (an application of quantum mechanics), you could argue that chemistry is the application of quantum mechanics to systems of many atoms (but chemists will frown at you). You can go right through the hierarchy of science and say anything that is not intensive, by definition, is extensive.
- (P1, C2) What is the constructionist hypothesis?
- That we can start from the fundamental laws and construct the universe.
- (P1, C3) According to the hierarchy presented in the third column of the first page, what would be the ‘most’ and ‘least’ fundamental areas of study?
Most: elementary particle physics
Least: social sciences
- (P1, C3) Why might the constructionist hypothesis not be valid?
- Because the behaviour of complex systems is not simply an extrapolation of the behaviour of simpler sub units. Molecules don’t behave as if they are simply a few atoms together, but have properties that couldn’t simply be extrapolated from an atom alone.
- (P2, C1) What laws govern the universe on the cosmological scale and what laws govern the universe on the atomic scale?
- General relativity on the cosmological scale and quantum mechanics on the atomic scale.
- (P2, C1) What is the chemical formula for ammonia?
- (P2, C1) Why does Anderson say that the Nitrogen in Ammonia is negatively charged and the Hydrogens in Ammonia are positively charged?
- Because Ammonia is covalently bonded, the Hydrogen atoms are sharing their electron with the Nitrogen, this means that there are more electrons in the vicinity of the Nitrogen nucleus that Nitrogen has protons, making that region of the molecule negatively charged. Equally, from Hydrogen’s point of view, by sharing its electron, the region around the Hydrogen nucleus has less electrons than there are protons in the nucleus, leading to a positive charge. This is a polar molecule for this reason.
- (P2, C1) What is an electric dipole moment?
- A measure of the separation of positive and negative charges.
- (P2, C1&2) Why is it said that there’s no such thing as an electric dipole moment in a stationary system of ammonia?
- A stationary system is an average of the states that the system can take. As the dipole of ammonia is inverted (due to the Nitrogen tunnelling through the triangle of Hydrogen atoms) very frequently between a pyramid (negative N on top, positive Hs on bottom) and a reversed pyramid (negative N on bottom, positive Hs on top), the average of this is zero.
- (P2, C2) What does Anderson mean by symmetry when discussing ammonia?
- He’s discussing parity – the equivalence of left- and right-handed states. In the case of ammonia, he means that the pyramid and the inverted pyramid are equally likely and therefore the system is symmetrical.
- (P2, C2&3) Why does Anderson say that sugar breaks the parity symmetry?
- Because it is a complex molecule of 40 atoms, and nature makes them in one orientation of spiral (clockwise or anticlockwise) and not the other. There’s no way to simply invert it to the other orientation of spiral.
- (P2, C3) What is different about sugar molecules that are produced by humans?
Human-made sugar molecules have no preference for the orientation of their spiral, we see an equal mix of both. Only nature has a preference for one ‘handedness’ of sugar molecule.
- (P2, C3) What is Anderson’s definition of symmetry?
- Viewpoints from which a system appears the same.
- (P2, C3) What is Anderson trying to explain in the last paragraph on P2?
- That the fundamental laws of physics alone can’t be built up to predict the complex behaviour of larger systems. If we put one nitrogen atom and three hydrogen atoms through the fundamental laws of physics, it won’t spit out a pyramid structure. But once we know it does have a pyramid structure, the laws do fit with this idea.
- (P3, C1) Draw a diagram of an atom (a circle) and a molecule (two circles joined by a line) to prove that a ‘crystal’ has less symmetry than the underlying structure.
- A circle has infinite lines of symmetry, but two circles joined by a line only has two (in 2D).
- (P3, C2) New properties come, according to Anderson, from broken symmetries. What macroscopic examples does he give?
- Superconductivity, superfluidity, antiferromagnetism, ferroelectricity.
- (P4, C1) Why does decreasing symmetry imply increasing complication? Are they synonymous?
- With more symmetry, rules tend to be simpler. For example kicking a football is a fairly simple process and very easily predictable, owing to the symmetry of the ball. But kicking a rugby ball is much more complicated, as the ball is less symmetrical, and kicking a rugby ball can have many different outcomes depending on whereabouts on the ball you kick it.
- (P4, C2) Given the first few paragraphs of the article, why does Anderson talk of the ‘arrogance of the particle physicist’?
- As they study the fundamental laws, which from a constructionist point of view would allow them to say that they can explain everything above them in the hierarchy.
Remember, reading a paper isn't like reading a piece of fiction or a newspaper article. Don't get frustrated if it doesn't immediately make sense - you might need to do a little research of your own to understand some of the ideas.
Each question refers to a specific part of the paper e.g. Page 2, Column 3 is written as (P2, C3).
Next week, we'll publish solutions to the questions and the best submitted summaries from students across the country.
Next week's article will be about the discovery of gravitational waves. As a taster, you might want to watch some of the following videos.
An 5min introduction by the scientists involved:
A very simple visual explanation of gravitational waves by Amber Stuver:
A demonstration of gravitational waves by Steve Mould: