Physical interpretation of equations

In summary: Maxwell's equations, a little more complicated...In summary, the conversation discusses the concept of understanding mathematical formulas intuitively and physically. While some formulas, like average speed, are easily derived and understood, others, such as v^2 = u^2 + 2ax and e=mc^2, can be more complex and require multiple interpretations. It may also take time for the physical meaning of a formula to be determined, and different individuals may have conflicting views on its interpretation. Mathematicians may not always focus on the physical meaning when developing new math, but often physicists are able to apply it to physical situations. Examples of this include the Euler beta function and its connection to the strong nuclear force, as well as the use of mathematical
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Can all formulas be thought of intuitively/physically?

For example, average speed is change in distance over change in time, that is intuitive and can easily be derived

But when you have something like v^2 = u^2 + 2ax, or e=mc^2, how do you think of it intuitively? Specifically the squared part, what exactly does velocity and the speed of light squared mean physically?
 
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sure,sooner or later. Sometimes via multiple interpretations...like the Schrodinger Wave equation...it's meaning is STILL debated...

but it may take quite a while to get to that stage (of physical interpretation) since as you suggest some math is so complicated it's physical meaning may take years to determine. And different people may have opposing/contradictory views...like Hawking and Jacob Beckenstein regarding the entropy of black holes...Hawking (as I recall) thought Beckenstein was nutty...until he arrived at the same conclusion via a different mathematical approach.

And typically mathematicians are not all that interested in the physical meaning when they may develop some new math...often they develop math and physicists come along and use it in a physical situation. When some math appears we may not have any theory to go with it.

One example is the Euler beta function which was later seen to be an aspect of the strong nuclear force...and even caused people to stumble intio string theory! String theory started out as one subject and someone later realized the math included gravitons...and so it became what it is today. Another example is some of the mathematics black holes: frames of reference...and the solution(s) to Einstein's equation of General Relativty...Einstein had the equation, Schwarszchild, Kerr, to name two, figured out solutions (for non rotating and rotating black holes) ...and what they meant...what the equation said physically about black holes.

Similar situation regarding
 

1. What is the physical interpretation of equations?

The physical interpretation of equations refers to understanding the real-world meaning and implications of mathematical equations. It involves translating mathematical concepts and relationships into physical quantities and understanding how they relate to each other in a given system.

2. Why is physical interpretation important in science?

Physical interpretation is important in science because it helps us understand and explain the natural phenomena and processes that we observe in the world. By interpreting equations, we can make predictions, test hypotheses, and make informed decisions based on scientific evidence.

3. How do scientists determine the physical interpretation of equations?

Scientists determine the physical interpretation of equations through experimentation, observation, and mathematical analysis. They use data and observations to validate and refine their interpretations, and they also use mathematical models and simulations to understand complex systems and processes.

4. Can the physical interpretation of equations change?

Yes, the physical interpretation of equations can change as our understanding of a system or phenomenon evolves. New evidence and discoveries may lead to revisions or updates in our interpretation of equations, as we strive to improve our understanding of the natural world.

5. How does the physical interpretation of equations relate to scientific theories?

The physical interpretation of equations is an essential component of scientific theories. It helps us understand the underlying principles and mechanisms that govern a system or phenomenon and provides a framework for making predictions and testing hypotheses. The physical interpretation of equations is crucial in supporting and validating scientific theories.

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