How to relate to math expressions that don’t have physical representations

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Discussion Overview

The discussion revolves around the use of mathematical expressions in physics that lack direct physical representations. Participants explore the implications of terms like c² in the context of relativity and the quantum wave equation, questioning how to reconcile these mathematical constructs with physical understanding.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the interpretation of c² as a speed, suggesting it conflicts with the understanding of the maximum speed of light.
  • Another participant emphasizes that describing rest energy as rest mass times the square of the speed of light does not violate the speed of light, framing it as a definition of energy.
  • A participant notes that understanding mathematical relationships in physics comes from the derivation of those relationships and the underlying assumptions and principles.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of mathematical terms in physics, particularly regarding c² and its implications. The discussion remains unresolved, with no consensus reached on how to relate these mathematical expressions to physical concepts.

Contextual Notes

Participants highlight the need for clarity on definitions and assumptions when discussing mathematical expressions that do not have direct physical meanings. The discussion reflects varying interpretations of these concepts.

rasp
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TL;DR
I’m wondering how to get comfortable in using math terms in physics equations that do not have physical meanings. I know the formulas work but what are we saying about the terms? For example, I’m thinking of i in quantum wave equation and c^2 in Relativity I mean as c is the highest speed possible, what is c^2. I understand speed ^2 satisfies the dimensions, but how can we employ a number which violates our understanding of the maximum speed?
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rasp said:
but how can we employ a number which violates our understanding of the maximum speed?

Why do you think c2 is a speed? Is an acre an length?
 
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rasp said:
Summary:: I’m wondering how to get comfortable in using math terms in physics equations that do not have physical meanings. I know the formulas work but what are we saying about the terms? For example, I’m thinking of i in quantum wave equation and c^2 in Relativity I mean as c is the highest speed possible, what is c^2. I understand speed ^2 satisfies the dimensions, but how can we employ a number which violates our understanding of the maximum speed?

Thread is contained in the summary.
Nothing is violating the speed of light when we describe rest energy as being equal to the rest mass times the square of the speed of light. This is just what energy is and how it is defined.
 
Your understanding and appreciation of a mathematical relationship of physical variables is obtained from the derivation of that relationship and the assumptions and physical principles that are required to develop it.
 

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