Interesting Coincidence with Classical/Modern View of Mass and Energy

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Discussion Overview

The discussion revolves around the relationship between mass and energy in both classical and modern physics, particularly focusing on the implications of unit analysis and the mass-energy equivalence expressed in E=mc². Participants explore whether the mathematical relationships observed in classical physics inadvertently hint at deeper connections in modern physics.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant notes that energy can be expressed as a scalar multiple of mass using the formula for joules, suggesting a potential connection to mass-energy equivalence.
  • Another participant expresses surprise at the coincidence of units in physical formulas, implying a deeper significance.
  • A third participant comments on the relationship between mass and energy in relativity, stating that setting the speed of light to 1 leads to mass and energy having the same units, which they argue is not coincidental.
  • One participant speculates on alternative forms of kinetic energy and their implications for rest energy, questioning the meaningfulness of such formulations.

Areas of Agreement / Disagreement

Participants express varying degrees of surprise and intrigue regarding the relationships between mass and energy, with some suggesting deeper connections while others focus on the coincidence of units. The discussion does not reach a consensus on the implications of these observations.

Contextual Notes

Participants do not fully explore the assumptions underlying their claims, such as the definitions of energy and mass in different contexts, nor do they resolve the implications of alternative formulations of kinetic energy.

Cadaei
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Has anyone ever noticed that, even in classical physics, energy is shown as a scalar multiple of mass?

For example, consider the joule;

1 J = 1 kg*(m/s)^2

If you consider the units of motion (m/s) to be a vector quantity, then squaring such a vector would be interpreted as a dot product that produces a scalar.

1 J (energy) = [mass in kg]*[scalar speed]

Which is eerily similar to E=MC^2. Thus, whether anyone in the past realized it or not, did they inadvertently stumble on the mass-energy equivalence just by dealing with these units?
 
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The units in a physical formula actually do work out? What a coincidence!
 
Creepy! :bugeye:
 
If you set the speed of light to 1, mass and energy have the same units. This is not a coincidence, and shows that the concepts are related in relativity.

If, for some strange reason, nonrelativistic kinetic energy would be something like mv^3, the rest energy of objects should be something like mc^3. But I do not think this would give meaningful physics.
 

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