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What Is “Fundamental”
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It From Bit or Bit From It
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Which of Our Basic Physical Assumptions Are Wrong?
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Lyla Taylor: on 9/12/19 at 12:41pm UTC, wrote More than times, students are not solve some subjects problems and face...

Nathan William: on 9/10/19 at 7:15am UTC, wrote Statistics is one of the most difficult subjects that are taught in the...

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FQXi FORUM
October 16, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: How to faithfully map a mathematical structure to an experimental situation by Sascha Agne [refresh]
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Author Sascha Agne wrote on Mar. 11, 2015 @ 19:49 GMT
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,

Download Essay PDF File

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Author Sascha Agne wrote on Mar. 25, 2015 @ 00:30 GMT
I don't mean to be disrespectful either but what has your reply to do with my essay? As for your "theorem" I don't get it.

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Joe Fisher wrote on Apr. 9, 2015 @ 16:01 GMT
Dear Sascha,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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Gary D. Simpson wrote on Apr. 16, 2015 @ 21:56 GMT
Sascha,

This was a very clearly written essay. I am an engineer and have worked in chemical plants in the past. I was sent to some training on a topic called experimental design. The objective was to be able to conduct plant tests by performing as few measurements as possible. That training was similar to what you present. The statistical objective was to structure the tests such that the variance would remain as small as possible. The problem in a chemical plant though is that there are so many variances and they are not necessarily constant.

There is another application of what you discuss. In surveying, they always try to use the same datum. Also, in machine shops, the locations of holes and edges are always with respect to the same datum.

This is very practical stuff. Well done.

Best Regards and Good Luck,

Gary Simpson

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Armin Nikkhah Shirazi wrote on Apr. 17, 2015 @ 09:13 GMT
Dear Sascha,

Of all the essays I have read so far, yours is unique in pointing out a deep relationship between mathematics and optimal experimental design. Of course, one might have already guessed that such relationships exist, but your example illustrates beautifully that these can sometimes be far from obvious.

I think a possible beneficial side effect for the theoretical side is that examples like the one you gave may help us build intuitions for understanding abstract mathematical structures in more concrete terms. I personally believe that one of the neglected areas in fundamental theoretical physics is in the area of deducing novel physical insights from the "meaning" of abstract representations, and work like yours may facilitate such endeavors.

I hope you will keep a notebook in which you collect examples like the one in your paper and will consider compiling these into a book. It would make unique and valuable contribution both for the experimental and the theoretical side.

Best wishes,

Armin

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Louise Hart wrote on May. 1, 2019 @ 07:09 GMT
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