Twin Paradox and the Logical Foundation of Relativity Theory

[chronon]

I just noticed the following on the Philsci archive.

Judit, X. Madárasz and István, Németi and Gergely, Székely (2005) Twin Paradox and the Logical Foundation of Relativity Theory.
http://philsci-archive.pitt.edu/archive/00002358/

They seem to be saying that inertial frames can be dealt with using algebraic numbers, which allows a 1st order axiomatization. However accelerated frames require further axioms, equivalent to moving to the real numbers (I'm not sure whether this means higher order axioms). This seems reasonable to me, since acceleration means differential equations, which means going beyond the algebraic numbers.

I'd be interested to hear other people's opinions on this.

 

[CrankFan]

Most of mathematics (ordinary mathematics) can be formalized in ZFC.

The limitation they're talking about in that paper is due to the language of a particular first order theory rather than a limitation of first order theories in general.

Herb Enderton comments on that specific issue here:

http://groups-beta.google.com/group/sci.logic/msg/6d623f53af0e2580?dmode=source&hl=en

 

[tacman]

The Twin Paradox is a classic thought experiment in the theory of relativity that presents a paradoxical situation where one twin ages significantly less than the other due to traveling at high speeds. This paradox has been a source of debate and discussion in the scientific community for many years, and the paper by Madárasz, Németi, and Székely adds an interesting perspective to the discussion.

Their argument that the logical foundation of relativity theory can be understood through algebraic numbers is intriguing. It suggests that the principles of relativity can be axiomatized in a first-order system, which is a significant development in our understanding of this theory. However, the authors also point out that this approach is limited to inertial frames and that acceleration requires additional axioms, which may involve higher order mathematics.

This raises an important question about the nature of space and time and how they are related to mathematical concepts. Is the use of algebraic numbers sufficient to describe inertial frames because they are based on a discrete structure, while acceleration requires the use of real numbers because it involves continuous changes? This could have significant implications for our understanding of the physical world and the role of mathematics in describing it.

Overall, this paper offers a thought-provoking perspective on the Twin Paradox and the logical foundations of relativity theory. It highlights the importance of carefully examining the mathematical foundations of scientific theories and how they relate to the physical world. I believe this is a topic that warrants further discussion and exploration, and I look forward to seeing how this argument develops in the future.