- #1
DeadCat_86
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In the mass-energy equivalent equation, E=mc^2, why is it related to the speed of light?
Exploring the Connection Between E=mc^2 and the Speed of Light
- Thread starter DeadCat_86
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In summary: So in summary, the mass-energy equivalent equation, E=mc^2, is related to the speed of light because it is the only non-arbitrary velocity that can provide the correct conversion factor for energy, which has dimensions of L2/T2. This follows from the postulates of Special Relativity, which state that the laws of physics are the same in all inertial frames and the speed of light is constant.
- #2
espen180
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That is the formula for rest energy predicted by Special Relativity.
From the postulates of SR (Invariance of c, physical laws are the same in all inertial frames) one can derive the equations describing energy:
[tex]E_{tot}=\gamma mc^2[/tex]
[tex]E_k=(\gamma -1)mc^2[/tex]
which lead to the conclusion that a mass has a rest energy [tex]E_0=mc^2[/tex] which is called the mass-energy equivalence.
So the the short answer is that it follows from the postulates of SR.
For a more in depth description detailing how the equation is derived, see
http://en.wikipedia.org/wiki/Mass-energy_equivalence#Background
From the postulates of SR (Invariance of c, physical laws are the same in all inertial frames) one can derive the equations describing energy:
[tex]E_{tot}=\gamma mc^2[/tex]
[tex]E_k=(\gamma -1)mc^2[/tex]
which lead to the conclusion that a mass has a rest energy [tex]E_0=mc^2[/tex] which is called the mass-energy equivalence.
So the the short answer is that it follows from the postulates of SR.
For a more in depth description detailing how the equation is derived, see
http://en.wikipedia.org/wiki/Mass-energy_equivalence#Background
- #3
tiny-tim
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Merry Christmas!
He DeadCat_86! Have a bouncy Christmas!
e is energy, which is ML2/T2, while m is of course just M,
so the conversion factor must have dimensions of L2/T2, ie it has to be a velocity squared …
and c is the only non-arbitrary velocity for such a general equation!
DeadCat_86 said:
He DeadCat_86! Have a bouncy Christmas!
e is energy, which is ML2/T2, while m is of course just M,
so the conversion factor must have dimensions of L2/T2, ie it has to be a velocity squared …
and c is the only non-arbitrary velocity for such a general equation!
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Nabeshin
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tiny-tim said:He DeadCat_86! Have a bouncy Christmas!
e is energy, which is ML2/T2, while m is of course just M,
so the conversion factor must have dimensions of L2/T2, ie it has to be a velocity squared …
and c is the only non-arbitrary velocity for such a general equation!
Dimensional analysis saves the day yet again!
FAQ: Exploring the Connection Between E=mc^2 and the Speed of Light
Why is the speed of light (c) used in the equation E=mc^2?
The speed of light (c) is used in the equation E=mc^2 because it represents a fundamental constant in the universe. It is the maximum speed at which all forms of matter and energy can travel, according to the theory of relativity. As such, it plays a crucial role in understanding the relationship between mass and energy.
What does the "c" in E=mc^2 stand for?
The "c" in E=mc^2 stands for the speed of light, which is approximately 299,792,458 meters per second. This value is a constant in the equation and is used to convert mass (m) into energy (E).
How did Einstein come up with the equation E=mc^2?
Einstein arrived at the equation E=mc^2 through his theory of special relativity. In this theory, he proposed that the mass and energy of an object are related and can be converted into one another. By manipulating mathematical equations and incorporating the constant speed of light, he was able to derive the famous formula.
Can E=mc^2 be applied to all forms of energy?
Yes, E=mc^2 can be applied to all forms of energy, as it is a general formula that relates mass to energy. It has been successfully used in various fields, such as nuclear physics and astrophysics, to calculate the amount of energy released in different processes.
Does E=mc^2 only apply to objects moving at the speed of light?
No, E=mc^2 applies to all objects, regardless of their speed, as long as they have mass. However, the equation becomes more significant when dealing with objects that are moving at or close to the speed of light, as it demonstrates the immense amount of energy that can be released from a small amount of mass at high velocities.