A bewildering physics problem solved using 128 tennis balls
Here's an interesting physics problem for you. Imagine that you have 128 tennis balls, and can arrange them any way you want. How many arrangements are possible? You might ask why this is important, and does anyone care?
Actually, if you were to take the time to work out all the possible arrangements, changing systems and configurations, it would take several lifetimes and the number you would come up with would exceed the number of particles in the universe.
At least, this is what researchers at the University of Cambridge
came up with after developing a computer program that can answer the mind-numbing question.
The answer, by the way, is an astronomical figure, 10^250 (1 followed by 250 zeros). The number is referred to as ten unquadragintilliard and is so huge that it vastly exceeds the total number of particles in the universe. While the number is incomprehensible to most of us, the process used to find it has many applications.
The field of granular physics
The study provides us with a working example of how “configurational entropy” might be calculated. Basically, this gives scientists the means of measuring how disordered the particles within a system or structure are. For example, by being able to calculate configurational entropy, we would be able to predict the movement of avalanches or how shifting sand dunes might change the topography of a desert.
Granular physics deals with questions involving the behavior of substances such as snow, sand, and even soil, and their behavior under different conditions. Now, there are different versions of the same problem of calculating configurational entropy in other fields of study, including string theory, cosmology, machine learning, and various branches of mathematics.
This is what the Cambridge team finds so exciting. Science Daily
quotes Stefano Martiniani, a Benefactor Scholar at St John's College, University of Cambridge, who lead the study with colleagues in the Department of Chemistry.
He explained: "The problem is completely general. Granular materials themselves are the second most processed kind of material in the world after water and even the shape of the surface of the Earth is defined by how they behave."
What is entropy?
While predicting the course of an avalanche or the movement of a desert may be a long way off, the research done by the Cambridge team will end up being the basis for further development of mathematical programs. At the core of problems such as predicting movement of particles is something called "entropy."
Entropy describes how disordered the particles are in a system. In physics, a system is described as any collection of particles being studied. For example, we could study all the water particles in a lake or all the water molecules in an ice cube. However, granular physics deals with materials large enough to be seen by the naked eye, and not at the molecular level, reports Science Boundaries
In granular physics, it is difficult to predict changes in a system because there are additional outside factors involved, like temperature and the wind. In order to do so would require us to be able to measure changes in the structural disorder of all of the particles in a system, its configurational entropy.
And this is what the team was able to do after developing a computer model, taking a small sample (the tennis balls), of all possible configurations and working out the probability of the number of arrangements that would lead to those particular configurations appearing.
Martiniani says, “By answering the problem we are opening up uncharted territory. This methodology could be used anywhere that people are trying to work out how many possible solutions to a problem you can find.”
This fascinating study, "Turning intractable counting into sampling: computing the configurational entropy of three-dimensional jammed packings,"
was published in the journal Physical Review E
on January 26, 2016.