What is the meaning of squaring a number

  • Context: Undergrad 
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Discussion Overview

The discussion centers on the concept of squaring a number, particularly in the context of its physical meaning and implications in equations, such as the potential force in nuclear physics represented by V = Ze² / r. Participants explore the reasons behind squaring values in mathematical equations and its relationship to physical concepts.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that squaring a value means multiplying it by itself and seeks to understand the physical significance of this operation in equations like V = Ze² / r.
  • Another participant suggests that while there are various reasons for squaring in different equations, the fundamental understanding remains that it is simply a mathematical operation without deeper implications.
  • A different viewpoint emphasizes the relationship between mathematics and the physical world, suggesting that the question reflects on how well mathematics models physical phenomena.
  • One participant explains that squaring relates to dimensionality, stating that squaring a length results in an area, and connects this to the concept of kinetic energy as an integral of force times velocity.

Areas of Agreement / Disagreement

Participants express differing views on the significance of squaring in mathematical equations, with some seeing it as a straightforward operation and others exploring its deeper implications in physical contexts. The discussion remains unresolved regarding the broader meaning of squaring in relation to physical laws.

Contextual Notes

Some participants highlight the complexity of understanding the relationship between mathematical operations and their physical interpretations, indicating that the discussion may depend on individual perspectives on mathematics and physics.

Ross J
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Yes, I understand it means a value times itself. I want to know WHY you do it though, what is the physical meaning behind it.

For example in nuclear physics for a potential force,

V = Ze^2 / r

Where e is the electric charge unit, Z is the atomic number, and r is radius. Why is it squared? What is this telling me?
 
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Ross J said:
Yes, I understand it means a value times itself.
That's really all there is to it.
I want to know WHY you do it though, what is the physical meaning behind it.

For example in nuclear physics for a potential force,

V = Ze^2 / r

Where e is the electric charge unit, Z is the atomic number, and r is radius. Why is it squared? What is this telling me?
Every equation is different and while some share common reasons for doing things, there are many different reasons why an equation might include squaring something. There is no one answer because there really isn't anything to this other than the first answer you already know. It's not any more profound than why sometimes you add, subtract, multiply or divide. Knowing why that equation is what it is doesn't really provide an additional answer to the original question beyond the one you already know.

But the derivation of that equation can be found here:
http://dev.physicslab.org/Document.aspx?doctype=3&filename=AtomicNuclear_BohrModelDerivation.xml

In short, you're multiplying the charge of the proton(s) by the charge of the electon.
 
Thank you, that was more than I could have hoped for
 
Ross J said:
Yes, I understand it means a value times itself. I want to know WHY you do it though, what is the physical meaning behind it.

For example in nuclear physics for a potential force,

V = Ze^2 / r

Where e is the electric charge unit, Z is the atomic number, and r is radius. Why is it squared? What is this telling me?
That question is about how Maths seems to model the Physical World so well. After all, Maths is just 'in our heads'. Considering the nature of Mathematics can make your brain ache.
 
When you square something, you are turning a single dimension (length) into an area. Many physical quantities are integrals (the area under the curve) of some other quantity. For example, the kinetic energy = ½ m v2 is the integral of force times velocity ∫ F⋅v dt which goes to the fundamental definition of energy.
 

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