Application of Calculus in Non Continuous Physical Systems

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Discussion Overview

The discussion centers on the application of calculus in physics, particularly in relation to non-continuous physical systems. Participants explore the implications of matter's discontinuity on the validity of calculus in various physical theories and applications.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the validity of applying calculus in physics due to the discontinuous nature of matter, suggesting that this could lead to erroneous results.
  • Another participant seeks clarification on which specific forms of matter are considered discontinuous and whether any forms of matter can be deemed continuous.
  • A different participant asserts that matter is inherently discrete and discontinuous, arguing that calculus is inappropriate for analyzing phenomena in gravitation, electromagnetism, and nuclear physics.
  • In response, another participant defends the successful application of calculus in these areas, challenging the assumption that calculus is limited to continuous systems and requesting examples of failures in its application.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of calculus in the context of discontinuous matter, with no consensus reached on the validity of its application in physics.

Contextual Notes

Participants have not provided specific examples of discontinuous matter or instances where calculus has led to erroneous results in physical applications, leaving these points unresolved.

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In the mathematics of Calculus, a basic requirement is that the system or function should be continuous. Until the discovery that matter is discontinuous, applying Calculus in Physics was reasonable. But why is it still applied almost everywhere in physics ? Won't such applications produce erroneous results ?
 
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Which matter is discontinuous? Do you have specific examples in mind?
 
SteamKing said:
Which matter is discontinuous? Do you have specific examples in mind?

Does it mean that some form of matter is continuous ? Matter, as we all know, is made up of atoms. So it is discrete and discontinuous. So I believe that application of Calculus is inappropriate in areas like Gravitation, Electromagnetism and Nuclear Physics.
 
Well, I can't argue with your beliefs, but I reject them. Application of the calculus to the problems you mention has been quite successful. You assume that atoms behave independently regardless of circumstances. Your assumption that the calculus can deal only with mathematically continuous systems is also faulty. You also have not provided any examples, according to your hypothesis, that application of the calculus has provided faulty results when used to analyze physical phenomena.
 

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