Proof of the Fundamental Theorem of Calculus

Click For Summary

Discussion Overview

The discussion revolves around the proof of the Fundamental Theorem of Calculus, with a focus on time dilation in the context of special relativity. Participants explore various mathematical formulations and interpretations related to time dilation, light waves, and Lorentz transformations, while attempting to clarify their reasoning and assumptions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants discuss the relationship between time dilation and light waves, proposing formulas such as t' = t(1 - V/C) and t' = γ.t(1 - V/C), while others express confusion over these derivations.
  • One participant suggests that the time dilation calculated in frame A may not represent true time dilation without considering Lorentz transformations.
  • There are claims about the difficulty in understanding the original proof and the need for clearer communication of mathematical ideas, particularly for those less familiar with formal proofs.
  • Some participants express uncertainty about the meaning of certain terms and formulas, such as "lesser time" and the interpretation of V/C.
  • A participant reflects on their background in mathematics and their struggle to grasp the language and concepts of physics, particularly in relation to relativity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the proposed proofs or the clarity of the explanations. Multiple competing views and interpretations remain, leading to ongoing debate and confusion.

Contextual Notes

There are indications of missing assumptions and unclear definitions, particularly regarding the relationship between time dilation and light waves. The discussion also highlights the challenges of communicating complex mathematical ideas across different levels of understanding.

Who May Find This Useful

This discussion may be of interest to those studying special relativity, mathematical proofs, or the Fundamental Theorem of Calculus, particularly individuals seeking to understand the nuances of time dilation and its implications in physics.

  • #61


DaleSpam said:
It seems OK to me except for one small detail:I would not say that B travels with the lightwave since the light wave travels at c and B does not. I would say that B travels with the source of the lightwave. The v used in the Doppler shift formula is the relative velocity between the source and the detector. B detects no shift because B travels with the same speed v of the source.

If you want to talk about the speed wrt the lightwave, that is always c.

Hi DaleSpam. As usual you are right, one have to carefully compose his/her sentences in physics. Excellent, this topic is now fully analysed. I have learned a lot from you, I will read my books much easier now because of the basic understandings of time dilation (just nature). Slowly I will place links in my other 2 topics to this topic as the final end, one per day :smile:
 

Similar threads

Undergrad Missing proof of the Shell theorem in General Relativity
  • · Replies 34 ·
2
Replies
34
Views
2K
Graduate Assumptions of Hawking-Penrose 1970 Singularity Theorem
  • · Replies 35 ·
2
Replies
35
Views
4K
High School Question about the fundamental theorem of calculus
  • · Replies 2 ·
Replies
2
Views
3K
High School A proof of the fundamental theorem of calculus
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Fundamental theorem of arithmetic from Jordan-Hölder theorem
  • · Replies 5 ·
Replies
5
Views
3K
Insights A Numerical Insight for the Fundamental Theorem of Calculus - Comments
  • · Replies 8 ·
Replies
8
Views
3K
Differentiate the given integral
  • · Replies 15 ·
Replies
15
Views
2K
Insights A Short Proof of Birkhoff's Theorem - Comments
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Analysis of functions of a single variable via multivariable calculus?
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Parallel transport of a 1-form aound a closed loop
  • · Replies 8 ·
Replies
8
Views
2K