E = mc^2 (Why not E = mc^42 )?

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In summary, energy equals mass times the speed of light squared, which is a simple consequence of Noether and the relativistic free particle Lagrangian. This is a result of frame invariance and defines mass as k/c. This is why it is not considered a flat planar thing and why it cannot be defined as k/c^42.
  • #1
rootone
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"Energy equals mass times the speed of light squared."
OK, but why is it considered to be a flat planar thing?
Why not cubed or any dimension you fancy/
Why not E = mc^42 ?
 
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  • #2
rootone said:
"Energy equals mass times the speed of light squared."
OK, but why is it considered to be a flat planar thing?

It's not considered to be a flat planar thing.

You need the exponent of 2 to make the units come out right.
 
  • #3
Study the derivation of Special Relativity and you’ll see it’s got a connection to E=1/2 m v^2 of classical physics.
 
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  • #4
rootone said:
"Energy equals mass times the speed of light squared."
OK, but why is it considered to be a flat planar thing?
Why not cubed or any dimension you fancy/
Why not E = mc^42 ?
What are the units of E and what are the units of mc^42

I have no idea what you mean by “flat planar thing”
 
  • #5
Its a simple consequence of Noether and the only reasonable relativistic free particle Lagrangian k*dτ where τ is the proper time and k is a constant to be determined. By definition mass, m, is defined as k/c so the Lagrangian is mcdτ. Apply Noether and you get E = mc^2.

Relativity is strange like that - frame invariance is very constraining.

Why not define m as k/c^42? Try it - you will see that classical mechanics is not correct in the low speed limit.

Thanks
Bill
 
Last edited:
  • #6
Thanks for the replies.
Working on it.
 

1. Why is the equation written as E = mc^2 instead of E = mc^42?

The equation E = mc^2 is a result of Einstein's famous theory of special relativity, which states that the energy (E) of an object is equal to its mass (m) multiplied by the speed of light (c) squared. This equation has been extensively tested and proven to accurately describe the relationship between energy and mass. The exponent of 2 in the equation is a fundamental part of the theory and cannot be changed to a different value.

2. What does the equation E = mc^2 mean?

The equation E = mc^2 is a mathematical representation of the relationship between energy and mass in Einstein's theory of special relativity. It states that the energy of an object is equal to its mass multiplied by the speed of light squared. This means that even a small amount of mass can contain a large amount of energy, and that energy and mass are interchangeable.

3. Can E = mc^2 be applied to all types of energy?

Yes, E = mc^2 can be applied to all types of energy, including potential energy, kinetic energy, and thermal energy. However, it is most commonly used in the context of nuclear reactions and the conversion of mass into energy.

4. Is E = mc^2 the same as the law of conservation of energy?

No, E = mc^2 is not the same as the law of conservation of energy. The law of conservation of energy states that energy cannot be created or destroyed, but can only be transformed from one form to another. E = mc^2, on the other hand, shows the relationship between energy and mass and how they are interchangeable.

5. Can E = mc^2 be used to calculate the exact amount of energy in an object?

No, E = mc^2 cannot be used to calculate the exact amount of energy in an object. This equation only gives the relationship between energy and mass, but in order to calculate the exact amount of energy, other factors such as velocity and position must also be considered.

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