thisismeamir / mathematicallimitsonworld

The Undergraduate physics project at the university of Teheran concerning mathematical limitations and the measurement problem

Mathematical Limits on the world

This is the project of my undergraduate physics studies repository. In here I gathered drafts and notes + reading materials that I found useful during the work on the project.

About the proposal

In the proposal I worked through mathematical and philosophical concepts that considered science and in specific physics. Showing were the empiricallity and the scientific method came from and forming the mathematical boundaries of physics. Then considering the limits of mathematics for itself one can assume that those limits can set boundaries on science and physics itself. If the resulting boundaries can imply lack of mathematical models for a physical process, one can argue that there would be physical concepts without any mathematical mdoel behind them. To put it more clearly we would interact with notions that requier randomized processes, of which is the notion of measurement in quantum physics. This process would let us ask ourselves, is there anyway to make a mathematical model of measurement and if not what is then the task of science and philosophy ro make our understanding of the world reacher?

In the way we start the journey by considering pure philosophical concepts, such as, empiricism and philosophy of science, then the mathematical part would be considered by looking at Shannon's information theory, Godels completeness and incompleteness theorem and Alan Turing thesis of computations. Later on we would review the foundation of quantum mechanics and it's mathematical and philosophical implications. At the end we would consider the part of quantum theory that includes the most peculiarity of it, measurement. We try to review the mathematical models that has been posed by different physicists and how they seem to be inconsistent with the measurement, at the end we approach quantum mechanical framework philosophically, looking at different interpretation and giving our ow interpretation as a consequence of the journey through mathemtical and philosophy.

Outline of Drafts

Epistemology

In the first draft we considered epistemology, what is knowing, knowledge and how do we know after all. These seem to be important ground work of the whole investigation. We would consider Justification and evidentialism and at the end we have a short review of empiricism. Since the later would come in the next chapter

Scientific Method

In this draft we investigate the general concept of science and scientific method, trying to reach the middle ground for the later chapters. This requires to define what is the knowledge that sciece seeks and what is the way science aquires that through.