Emergent Properties and Physics

©Fernando Caracena 2014

Most of what you see in our world are emergent properties that spring into existence from a deeper level of reality than we apparently are able to experience using the methods of natural science. We gain some appreciation for how that level of reality operates, indirectly by abstracting that information from well tested theories of physics.

Emergent property--

any unique property that "emerges" when component objects are joined together in constraining relations to "construct" a higher-level aggregate object, a novel property that unpredictably comes from a combination of two simpler constituents.

For example, the familiar taste of salt [NaCl] is an emergent property with respect to the sodium [Na] and chlorine [Cl] of which it is composed. [Both sodium and chlorine are caustic and toxic, but NaCl is essential to human life.]


Physics grew out of our experience in the material world, out of the impressions of  our five senses, but raised to a higher level of abstraction using Mathematics. In past posts, such as, Grokking Galileo’s Physics I and Grokking Galileo’s Physics part II, I have tried to demonstrate the flavor of this process as intuitively as possible. Indeed, the zeal with which physicists have pursued mathematical abstractions of patterns of physical processes has lead to the development of branches of pure mathematics. For example, Newton and Leibniz developed Calculus (see, Grokking Calculus and Grokking Calculus–Integral Calculus ).

In the process of mathematical abstracting, physicists have hit upon physical quantities that appear to be more fundamental than others. The more fundamental quantities fit into theories that are not only simpler and more compact, but appear to be more fundamental than others. Energy and momentum, for example, appear to be very fundamental to physics. It did not always appear to be so. Initially they were defined for convenience in terms of what were then considered to be more fundamental quantities, such as mass, length and time. The kinetic energy of a moving object of mass, m, and velocity, v, was defined as

KE = ½ m v2


v2 = v12+v22+v32  .(see,The Concepts of Energy and Momentum Conservation)

Note that here the three components of velocity along three mutually orthogonal axes are represented by v1, v2, v3.

In the precess of defining energy for convenience, the mathematical necessity emerged of considering total energy as being positive for unbound motion, zero for transitional states, and negative for bound systems. Some physicists still regard this as a bookkeeping convention. But again mathematical necessity of the theories of physics demands more than just bookkeeping. Positive and negative aspects of energy have a real correspondence with the types of motion they describe.

Mass as an Emergent Property

In classical physics, mass is considered a fundamental, intrinsic property of matter. Along with it, length and time are considered fundamental characteristics of physical existence. The fundamental units of physics are defined as measures of mass, length and time from which all other units of measure are derived.

Over the last few decades, physicists have developed a keen interest in cosmology as a test for elementary, high energy physics. The reason is that there is a great puzzle here about how the universe could originate in a point like structure and expand to its present size, which is much larger than the visible universe that extends about 13.8 billion light years in all directions from our location on planet Earth.

The Big Bang

The theory of creation of the universe is called the Big Bang Theory. It pictures the universe expanding from a very hot dense state concentrated in a point-like structure much smaller than the size of a proton[, a whimsical summary is given in song and video by the introduction to the popular TV show named after the subject of this section].

The degree of heat of an object in physics was originally measured in physics by temperature, which turned out later to be associated with the average kinetic energy contained by each degree of freedom of the constituents of a substance, ie., the atoms and molecules, in the case of matter. Very hot means that the constituents are on the average moving at very high energies, or at high kinetic energies. The interest here is that the average energy of the components of the Big Bang were far beyond the reach of any particle accelerator that we can build today. The Big Bang was the ultimate particle accelerator, and therefore is the place to test theories of elementary particel physics.

Cosmic Inflation

The other aspect of the Big Bang Theory, gained by applying more modern developments, is that the very high energy processes associated with it, were cut off abruptly by the phenomenon called Cosmic Inflation at about 10-35 seconds after the Big Bang, which over an incredibly small time interval rapidly cooled the very hot proto-matter. The modern version of the Big Bang Theory of creation is summarized succinctly in an online article, here. Cosmic inflation is a feature that came out of Einstein's General Theory of Relativity, in which any concentration of positive energy and momentum exerts a force of gravitational attraction. Change the sign of the energy-momentum to negative, and instead you get gravitational repulsion, which leads rapid expansion of space.

The universe was created with zero total energy. During the expansion out of the microscopic universe, a lot of negative energy was created, which produced a vast vacuum-filled space that was in a conditional unstable energy state. This "false" vacuum transitioned rapidly into a new vacuum through a process of symmetry breaking that differentiated the the electo-weak interactions into the weak nuclear force and the ordinary electromagnetic force. In the process, the new vacuum was filled with the presence of what is called the Higgs field, which endowed some of the elementary particles of physics with a rest mass; and therefore, inertial properties. Before  the transition to a background Higgs field, all quanta existed as radiation streaming at the speed of light that could not be slowed down without being destroyed. That means that the world that we are familiar with, which is dominated by inertial effects, could not emerge until the Higgs field appeared. The Higgs is an invisible ocean, from which our "reality emerges, and in which all our sense of reality swims. Mass is an emergent property of matter.

For related ideas, read my blog entry, "Holistic vs Redutionist Ideas in Physics" and Localization of Quantum Events". Another blog that touches on these issues is "Perception of Physical Reality". Also, look at Nature's Ultimate Joke.

Until only recently, I only half believed in the Higgs field and Higgs boson. I had encountered something like it in doing research for my PhD thesis, "The Electrodynamics of Vector Bosons". Basically, I found that the best theory of Vector Bosons [gauge theory] in terms of their electrodynamics is one that combines the interaction of photons and vector bosons in an interaction that looks the same for all of them. The odd thing about the theory was that the heavy rest mass neutral vector boson interacted the same way as zero rest mass photons.

I was forced to consider the validity of the Higgs theory by the recent discovery of the Higgs particle in the Large Hadron Collider.

Since I am also very interested in the philosophical implications of physics, I was forced to conclude that the aspects of the physical world, initially considered as fundamental, are really emergent properties. I describe some of the implications of this turn of affairs in an earlier blog entry, Nature's Ultimate Joke. Also, I recommend watching the NOVA video, "The illusion of time."

A possible route to a more fundamental physics is perhaps the work of Stephen Wolfram which he describes in a TED video.

Dr. Erik Verlinde has developed a new theory of gravity that goes beyond Enstein's General Theory of Relativity, which explains gravity as an emergent phenomena involving quantum information and entanglement. For a description of his theory see his video, "A New View on Gravity and the Dark Side of the Cosmos".








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