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

[rasp]

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?

Thread is contained in the summary.

 

[Vanadium 50]

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?

 

[dsaun777]

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.

 

[gleem]

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.