morenopo2012 said:It´s not a technical question, is about why the classic mechanics and even quantum mechanics equations are first or second order? ¿Exist any model with up order derivates?
If the statements there about stability are correct (pity there are no examples given) then we can apply the anthropic principle to argue that an intelligent life form is only likely to arise in a universe with second order physical laws.Ray Vickson said:See
https://www.quora.com/Why-dont-differential-equations-of-physics-go-beyond-the-second-order
for some useful results/discussions.
Modeling nature using derivatives is important because it allows us to understand and predict the behavior of natural phenomena. The first derivative represents the rate of change of a system, while the second derivative represents the rate of change of that rate of change. By studying these derivatives, we can gain insights into the underlying processes and dynamics of nature.
While higher order derivatives may provide more detailed information, they are often more complex and difficult to interpret. The first and second derivatives are often sufficient for making accurate predictions and understanding the general behavior of natural systems. Additionally, using higher order derivatives can lead to overfitting, where the model is too closely tailored to the specific data and does not accurately represent the overall trend.
The use of derivatives to model nature is based on the fundamental laws of physics, such as Newton's laws of motion and conservation of energy. These laws demonstrate that the behavior of natural systems can be described and predicted using derivatives. Additionally, empirical evidence from numerous scientific studies has shown that the 1st and 2nd derivatives are sufficient for modeling many natural phenomena.
While derivatives can provide valuable insights into the behavior of natural systems, they are not always applicable. For example, some systems may exhibit chaotic behavior that cannot be accurately described using derivatives. Additionally, there may be other factors at play that cannot be captured by derivatives alone, such as external influences or random events.
No, there are certainly aspects of nature that cannot be fully explained or predicted using derivatives. For example, human behavior and emotions are highly complex and cannot be reduced to a simple derivative equation. Additionally, phenomena at the quantum level may not follow the same laws that govern larger systems, making it difficult to accurately model using derivatives.