Complexity is the study of the phenomena which emerge from a collection of interacting objects. The main idea behind a complex system is that the behaviour involved is such that the sum of information in the overall system is greater than the sum of information from each of its parts.  A complex system is one in  which large networks of components with no central control give rise to collective behaviour. Analysis of this behaviour provides an understanding of the emergent phenomena of the system. Emergence in a complex system being, when complex patterns arise out of a multiplicity of relatively simple interactions.

[A system simply means a collection of items which usually interact. A collection of photons in a box can be an example of a quantum system, whilst the collection of items in your kitchen is an example of a classical system!]

Complexity can be seen broadly across nature, birds flying in V formations, ants marching in mass congregation, individual neutrons coming together to produce consciousness however this post (and in general) I shall stick mainly with physics. The cooperative physics of overlapping systems can display fundamentally new behaviour,  otherwise not apparent in the properties of the ‘individual units’ that make up the many-body system. The standard particle model illustrates this. It divides matter into elementary subatomic particles and their various components which then interact through the electromagnetic, weak and strong forces and mediate the dynamics. Helium is comprised of two protons, neutrons and electrons. As individual entities the components have their properties such  as mass, charge, spin. Bring them together and due to these properties a complex system is formed. The strong force holds the protons and neutrons together in the nucleus, with a certain nuclear binding energy, whilst the electromagnetic force causes electrons to orbit the nucleus at discrete energy levels. The atom illustrates the most basic, complex system. – A rich complexity found as a consequence of individual properties of components interacting on mass.

Results from quantum mechanics often require we shed our intuition from sensory experience and draw conclusions from the unexpected ‘collective effects’. Indeed there is an intimate relation between quantum information and complexity science. Quantum systems acquire a higher complexity than that of classical Newtonian systems, where the properties of the system often result in the creation of a macroscopic state with what is known as – quantum mechanical coherence. The systems have these emergent properties as we said before. This means, the behaviour can be described by considering the collective interactions of many quantum mechanical objects but it is so complex that one would not have been able to predict the existence beforehand by studying the behaviour of the individual particles alone.

A particular experiment which illustrates the features of complexity is the Double Slit experiment. In this experiment, a beam of light is shone on a barrier in which two slits have been cut. The light that passes through the barrier is then recorded on a photographic plate. When firing single photons, if both slits are open a wave interference pattern occurs, commonly only produced by a wave front. However if one slit is closed a single line on the screen will be observed. This illustrates the feature of non-linearity in the system. The effect of the changing the slits from one to two is not simply proportional to the change in outcome we may expect. Conventionally we would expect two lines to appear on the screen in accordance with the slits, however instead we see a much more complex wave-like product, representing an interference pattern.  Here we clearly see the extremely strong interdependency between the components of the system in the nature of the overall outcome. An entirely new phenomenon that arises, only when, the components of the system act together in bulk.

The complexity of a particular system is also interpreted as the degree of difficulty in predicting the properties of the system- given the properties of the system’s parts alone. This is entirely what makes Quantum physics so complex. In Classical Mechanics if we know all there is to know about about the components i.e. how heavy the javelin is, how strong the athlete is, how hard the wind is blowing, we can predict with absolute certainty how far the javelin will travel. However this is the entirely unachievable with Quantum Mechanics …the outcome of experiments cannot be quantised, no singular outcome is achievable, and no accurate prediction can be formed as a result of analysing the system’s parts alone. The system is inherently complex. All we can deduce, armed with as much information as humanly possible, is the probability of a certain outcome…

A post on the fundamental differences between a classical system and a quantum system coming soon!