# Einstein's potential energy equation

• einsteinian77
In summary, the 1/2 in the classical potential energy equation does not appear in Einstein's potential energy equation because it is already accounted for in the rest energy term, E=mc^2. This is due to the derivation of the equation using the Lorentz factor and the inclusion of kinetic energy. Therefore, the half does not need to be explicitly included in the equation.
einsteinian77
What happened to the 1/2 in the transformation of classical potential energy equation to Einstein's potential energy equation. Is it dropped because giving off all rest energy would require annhilation of a particle pair thereof 1/2mv2+1/2mv2=1mv2 gets rid of the half?

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Originally posted by einsteinian77
What happened to the 1/2 in the transformation of classical potential energy equation to Einstein's potential energy equation. Is it dropped because giving off all rest energy would require annhilation of a particle pair thereof 1/2mv2+1/2mv2=1mv2 gets rid of the half?

What do you mean by "Einstein's potential energy equation"? I don't understand the question. Do you mean to compare mc^2 with (1/2)mv^2? Apples and oranges?

Potential energy doesn't equal 1/2mv^2(that's kinetic energy) it equals mgh

I think you are asking about the energy E = mc^2 equation relating to classical systems.

First E = mc^2 is only for stationary objects. The actual equation is E = mc^2/[1-((v^2)/(c^2))]^1/2(you see now why when discussing it in general people assume v = 0)

Einstein's equation deals with the total energy of an object at any speed. and the derivation can be found in most Modern Physics books( a convineince for me because I don't remember it off the top of my head)

kinetic energy from Einstein

E=mc2/(1-(v/c)2)1/2
where m is rest mass.
Expand Lorentz term in power series:
(1-(v/c)2)-1/2=1+(v/c)2/2+...
Net result:
E=mc2+mv2/2+...
The first 2 terms are the energy due to rest mass and the kinetic energy.

whats so difficult about my question krab all i was asking was how come there is no half in the rest energy equation.

Well, then it's been competently answered by Mathman and VBPhysics.

## 1. What is Einstein's potential energy equation?

Einstein's potential energy equation, also known as the mass-energy equivalence equation, is E=mc². It represents the relationship between mass and energy, stating that mass and energy are two forms of the same thing and can be converted into each other.

## 2. Who came up with the equation?

The equation was derived by Albert Einstein in 1905 as part of his special theory of relativity.

## 3. How is the equation used in science?

The equation is used in various fields of science, including nuclear physics, particle physics, and astrophysics. It helps in understanding the relationship between mass and energy and has also been used in the development of nuclear energy and atomic bombs.

## 4. Can the equation be applied to everyday situations?

Yes, the equation has practical applications in everyday situations, such as in medical imaging technologies like PET scans, where it is used to convert between mass and energy to create detailed images of the body.

## 5. Is the equation still relevant today?

Absolutely! The equation is still considered one of the most significant and groundbreaking equations in physics and is the foundation of many modern scientific theories and technologies. It continues to be studied and applied in various fields of science.

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