Since the beginning of time humanity has been looking at the surrounding world as a book of nature and continually trying to study it through different views and approaches, which later in time, developed into sciences like mathematics, physics and chemistry etc. Over time, many scientific discoveries were made and many theories aiming to explain these scientific advances emerged.
Why should we care?
It is important to note that the cluster of classical sciences is deeply interconnected and one theory in physics echoes accompanying theories in mathematics and chemistry. If modern technology presents data that disproves theory in one field of scientific studies, then the other fields, in light of the latest discoveries, are being revised as well.
This whole discussion started on January 12, 2012. I also remember this day for it was the first cold day of rain and wind in January! I was referred by Nathan Schiller, my colleague, to the article “Annals of Mathematics Manifold Destiny: A legendary problem and the battle over who solved it” written by Sylvia Nasar and David Gruber. The article’s main topic is revolving around Poincare conjecture and its proof. This article focused my attention on the Poincare question itself. Poincare questioned whether a 3-manifold with the homology of a 3-sphere and also trivial fundamental group had to be a 3-sphere. Poincare’s new condition, also known as trivial fundamental group, “can be restated as every loop can be shrunk to a point” (http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture).
Furthmore, in differential geometry and topology, a manifold is a “topological space that, on a small enough scale, resembles the Euclidean space of a specific dimension, called the dimension of the manifold. Thus, a line and a circle are one-dimensional manifolds, a plane and sphere (the surface of a ball) are two-dimensional manifolds, and so on into high-dimensional space […] The concept of manifolds is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be expressed and understood in terms of the relatively well-understood properties of simpler spaces. For example, a manifold is typically endowed with a differentiable structure that allows one to do calculus and a Riemannian metric that allows one to measure distances and angles. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model space-time in general relativity” (http://en.wikipedia.org/wiki/Manifold).
However, recent discoveries made by OPERA (Oscillation Project with Emulsion-Tracking Apparatus) uncover facts about fundamental particles known as neutrinos which can travel faster than light (Geoff Brumfiel, 2011). This recent announcement spanned dozens of studies all aiming into exploration of this question whose answer could shake the foundations of physics: What if this anomaly is real? “That might seem impossible, given the universal speed limit set by Albert Einstein’s long-standing and well-tested special theory of relativity, but neutrinos have proved chock full of surprises over the years” (Choi, 2011, p.1). “The discovery of superluminal neutrinos present the biggest revolution to fundamental physics in about a century. A multitude of studies have already popped up to address the OPERA results, including some that suggest new physics to explain the findings” (Geoff Brumfiel, 2011; Charles Q. Choi, 2011).
Overall, the big picture presents that we may never be able to grasp that reality. The universe and its ingredients may be impossible to describe unambiguously. Over a few more years we will see a great example of science in action. “It is either a fantastic discovery which seemingly cannot but have huge and as yet unknown consequences or it is a mistake” (Choi, C, 2011). For certain, there will be deliberations of new unique physical theories which would require new mathematical theories to be built in order to support these physical theories. In my next post I will be commenting on streaming shifts that occur in mathematical field regarding new challenges in the unfolding great drama of life. Stay tuned!
Nasar, S., Gruber, D. (2006). Annals of Mathematics Manifold Destiny: A legendary problem and the battle over who solved it. The New Yorker. Retrieved from: http://www.newyorker.com/archive/2006/08/28/060828fa_fact2
Poincare Conjecture. Retrieved from: http://en.wikipedia.org/wiki/Poincar%C3%A9_conjecture
Manifold. Retrieved from: http://en.wikipedia.org/wiki/Manifold
Brumfiel, G. (2011). Particles Found to Travel Faster Than Speed of Light Neutrino results challenge a cornerstone of Albert Einstein’s special theory of relativity, which itself forms the foundation of modern physics. Scientific American, Nature magazine. Retrieved from: http://www.scientificamerican.com/article.cfm?id=particles-found-to-travel
Choi, C. Q. (2011). Leading Light: What Would Faster-Than-Light Neutrinos Mean for Physics? Most physicists are betting against the idea that neutrinos can pierce the cosmic speed limit, but that has not stopped some researchers from exploring the implications. Scientific American. Retrieved from: http://www.scientificamerican.com/article.cfm?id=ftl-neutrinos-new-physics-implicationsShare