# What is the actual equation of e=mc^2?

• alchemist
In summary: Anderson, 2003In summary, the actual equation for E=mc^2 is E = m0c2/sqrt[1-(v/c)2]. This equation relates the mass of a tardyon particle to its free-particle energy. It can also be rewritten as E2 - (pc)2 = (m0c2)2.

#### alchemist

what is the actual equation of e=mc^2? this is only the simplified equation, and i have forgotten the actual one already...

You probably mean

E2 = p2c2 + m2c4

- Warren

what does the P stand for? and is that equation homogenous?

It's a lowercase p, and it stands for (linear) momentum. I don't know what you mean by "homogenous."

- Warren

It all depends on whether you are a massist or an energist.

------

A massist is willing to attribute mass values to anything, in any state of motion. For a massist, this m is really m0, a mass attributed to something in its rest frame of reference. For a massist

E2 = p2c2 + m02c4
p = mv

are always true in any inertial frame. For light quanta,

E = pc
p = mc

, because m0 = 0 for light quanta. But m = p/c = E/c2, a mass value dependent upon total energy of a quantum.
So E = mc2 is true for a light quantum as well as a particle with a non-zero rest mass.

------

An energist is willing to attribute energy values to anything, in any state of motion. For an energist, m can only be attributed to something in its rest frame, so the subscript 0 is never needed. For an energist,

p2 = E2/c2 - m2c2

is always true in any inertial frame. The energy E must come from other physics. For light quanta, p = E/c is a given, so

p2 = p2 - m2c2

, so

m2c2 = 0

. Since c > 0,

m = 0 for a light quantum.
So, E = mc2/(1 - v2/c2)1/2 only in the case of a particle with non-zero rest mass.

------

Most modern day physicists, especially high-energy physicists, tend to be energists rather than massists.

I said:

So, E = mc2/(1 - v2/c2)1/2 only in the case of a particle with non-zero rest mass.

I should have said:

So, E = mc2/(1 - v2/c2)1/2 only in the case of a particle with non-zero mass.

Originally posted by alchemist
what is the actual equation of e=mc^2? this is only the simplified equation, and i have forgotten the actual one already...

The equation E = mc2 is the mass-energy equation relating the mass m of a particle to the free-particle energy E. The proof can be found here

www.geocities.com/physics_world/sr/mass_energy_equiv.htm

If the particle is a tardyon (i.e. a particle which travels at speeds less than light) then

m = m0/sqrt[1-(v/c)2]

Multiply both sides by c2

mc2 = m0c2/sqrt[1-(v/c)2]

Substitute in E = mc2 to get

E = m0c2/sqrt[1-(v/c)2]

This equation can be rewritten as

E2 - (pc)2 = (m0c2)2

Pete

## 1. What does the equation e=mc^2 mean?

The equation e=mc^2 represents the relationship between mass and energy, stating that energy (e) is equal to the mass (m) of an object multiplied by the speed of light (c) squared.

## 2. Who came up with the equation e=mc^2?

The equation e=mc^2 was developed by Albert Einstein as part of his theory of special relativity in 1905.

## 3. How is the equation e=mc^2 used in science?

The equation e=mc^2 has been used in various scientific fields, such as nuclear physics, cosmology, and energy production. It is also a fundamental equation in understanding the relationship between matter and energy.

## 4. What is the significance of the speed of light in the equation e=mc^2?

The speed of light (c) is a constant in the equation e=mc^2, meaning that it remains the same regardless of the frame of reference. This constant allows us to relate mass and energy, and it also shows that energy and mass are interchangeable.

## 5. Can e=mc^2 be applied to all objects?

Yes, the equation e=mc^2 can be applied to all objects, including subatomic particles, atoms, and even larger objects. However, the effects of this equation are most noticeable in objects with large amounts of mass and/or moving at high speeds.

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