About applicability of singularities in Physics

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SUMMARY

The discussion centers on the applicability of singularities, specifically higher derivatives of functions, in physics. Participants clarify that while singularities can refer to poles and zeros in functions, the original inquiry may pertain more to discontinuities, which can indeed occur in higher order derivatives. A notable example provided is shock waves, which illustrate how discontinuities manifest in physical phenomena. The conversation suggests that understanding these concepts could contribute to theories unifying large and small scale physics.

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  • Understanding of higher order derivatives in calculus
  • Familiarity with singularities in mathematical functions
  • Basic knowledge of shock waves in physics
  • Concepts of poles and zeros in polynomial functions
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  • Study shock wave dynamics and their mathematical representations
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rajesh_d
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Hello, I am new here and this is my first post. Kindly let me know if my post is off topic.

My question is about the applicability of singularities of a function in Physics. By singularity I mean one of the higher derivatives (>2) of a function jumping at a point. Is there any conceptual use of such singularities in a physical theory. Could they be used to represent the subatomic particles. Can this be helpful for a unified theory (of large and small scale)? I'd be glad to hear some discussion on it.
 
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I wonder why there isn't any response/reply.
 
Hi rajesh_d,

Poles and zeros for certain functions (which occur often in polynomials when working with such things as filters for example) might be considered singularities.

But it sounds as though you mean discontinuities rather than singularities. If so, Yes, higher order derivatives can be discontinuous. One physical example is a shock wave.

http://en.wikipedia.org/wiki/Shocks_and_Discontinuities_(MHD)
 

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