Essay Abstract
Simple mathematical structures such as numbers or elementary geometry are directly tied to physical observations. Wigner pondered the existence of similar one-to-one correspondences between more advanced mathematical concepts, such as algebras, and the actual world. The compilation of such a list of "maps" is in itself a formidable research project en route to finding limits of the interplay between mathematics and physics. In this essay we will study the weighing problem, an example given in the 1930s to illustrate the idea of "complex experiments", and construct step by step the underlying group Z2xZ2 and its representations. The concepts involved are advanced enough to highlight a non-trivial link between mathematics and physics without losing the idea midway through the formalism.
Author Bio
I am doing my PhD at the Institute for Quantum Computing, developing novel interferometers and entangled photon sources to test the foundations of quantum mechanics with satellites. I completed a Bachelor of Science in Economics and a Bachelor of Science in Physics at the University of Bonn, Germany, in 2011 and 2012, respectively, and obtained a Master of Science in Quantum Technologies from the University of Leeds, UK, in 2013. Following that, I worked as a research assistant at the Centre for Quantum Technologies, Singapore, and the Max Planck Institute for the Science of Light in Erlangen,
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