Application of Calculus in Non Continuous Physical Systems

[Phynite]

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 ?

 

[SteamKing]

Which matter is discontinuous? Do you have specific examples in mind?

 

[Phynite]

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.

 

[SteamKing]

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.

 

[PJC01]

While it is true that the basic principles of Calculus require a continuous system or function, its application in physics goes beyond just the mathematical framework. Calculus is a powerful tool for analyzing and predicting the behavior of physical systems, and its applications have been extensively tested and validated through experiments and observations.

In fact, the concept of limits in Calculus allows us to approximate the behavior of non-continuous systems by breaking them down into smaller, continuous parts. This approach has been successfully applied in various fields of physics, such as mechanics, electromagnetism, and thermodynamics.

Moreover, the laws and principles of physics, such as Newton's laws of motion and the laws of thermodynamics, are formulated using Calculus. These laws have been extensively tested and found to accurately describe the behavior of physical systems, even those that are non-continuous.

While there may be instances where the use of Calculus in non-continuous systems may lead to some errors, these can be minimized through careful analysis and consideration of the limitations of the model being used. Additionally, advancements in mathematical techniques, such as numerical methods and differential equations, have further improved the accuracy of using Calculus in non-continuous systems.

In conclusion, while the basic principles of Calculus require continuity, its applications in physics have been extensively validated and have proven to be a valuable tool for understanding and predicting the behavior of non-continuous physical systems. Its continued use in physics is a testament to its effectiveness and reliability in this field.