Why is E=MC^2 such a neat and simple formula?

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The discussion centers on the simplicity and elegance of the equation E=MC², emphasizing that the squared term arises from the need for unit consistency rather than arbitrary fitting. Participants noted that while the equation expresses the equivalence between mass and energy, it does not account for the energy required to convert rest mass into free energy. The conversation also delved into modern interpretations involving the Higgs field and the nature of quanta, suggesting that the equation's structure reflects deeper physical principles rather than mere mathematical convenience.

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OK.. my question I've pondered in the past.. why is E=MC2 such a nice and clean formula.. with no corrections or " x .00003845" etc.

Was metric based on the universe (physics) or is the universe somehow based on metric?
 
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No, it is not. The c^2 is there because the units are not "fitted" for this formula. With properly selected units it could be just E=m.
 
nasu said:
No, it is not. The c^2 is there because the units are not "fitted" for this formula. With properly selected units it could be just E=m.
squared is pretty neat though.. why not E=MC2.01867378432783794847384 etc.

Might be a silly question but it bugs me :)
 
What if it were? You could ask why 2.018... and not 2.019...:smile:
 
Yes. But 2.018 I could live with. but exactly 2? Either metric is based on energy/mass or the other way around. seems fishy. ;)
 
In metric units c is 299792458... Meter/sec. That's where the messy is.
 
gmax137 said:
In metric units c is 299798... Whatever. That's where the messy is.

ah.. that's a good point of view.. I hadn't thought of that.
 
Slyster said:
squared is pretty neat though.. why not E=MC2.01867378432783794847384 etc.

Might be a silly question but it bugs me :)
The squaring follows from the derivation and the units, just like with kinetic energy.
 
Slyster, I understand your curiosity about the formula. Indeed, it is confusing.

First, the formula expresses the equivalence between mass and free energy (quanta). Nevertheless, the formula don’t describe the energy we need to transform a particle with rest mass into free energy. The formula only shows the energy representation of mass. So C^2 is a constant to get the right outcome. The equation is classic physics (beginning of the 20th century) and probably Wikipedia will show you the original derivation.

Nevertheless, after nearly a century, our concept about the micro cosmos has changed. So let us try to explain the equation by modern understanding.

Rest mass is a local deformation of the flat Higgs field (scalar field). So the vector field (electromagnetic field) “absorbs” energy from the Higgs field and this amount of energy represents a certain number of quanta (E = n x h).
The “back ground” vector field – the carrier of quanta – isn’t a smooth field. It is turbulent space and the turbulence is perceptible as electromagnetic waves. These electromagnetic waves are not the whole vector field: we only can detect “the long ripples”. In fact, the turbulence is quanta. And the velocity of all these quanta is the speed of light.
So when we want to return the energy of the rest mass to the Higgs field, we have to “free” the enclosed quanta of the particle and spread it out into the environment. As a result, the local Higgs field will become flat again and the particle don’t exist anymore.

Spatial fields have a structure. Therefore, every spatial field has a volume and a surface area. Just like the bricks in a wall. The transfer of energy between 2 spatial fields is the transfer of local volume at the cost of local surface area and vice versa (combined spatial fields have a topological structure otherwise there is no conservation of energy). Unfortunately, we don’t express mass with the help of volume (n^3). So we have to translate mass into the surface area of individual quanta with the help of C^2.
Suppose science had expressed mass with the help of volume. Then the famous equation of Einstein has to be: E = m/c.
 

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