# What in the world does E =mc2 mean?

Matthias765
What in the world does E =mc2 mean? (Einstein's equation.)

Related Special and General Relativity News on Phys.org
Staff Emeritus
Gold Member
Dearly Missed
The amount of energy that could be obtained by completely annihilating a mass m Kg is equal to m Kg multiplied by $$9X10^{16} meters^2/second^2$$. The units come out right for an energy.

Last edited:
dextercioby
Homework Helper
SA, you mean ~9 times 10 to the power of 16, right? :uhh:

Daniel.

Staff Emeritus
Gold Member
Dearly Missed
dextercioby said:
SA, you mean ~9 times 10 to the power of 16, right? :uhh:

Daniel.
Eek! I put in the value for the wrong length! It's changed now.

dextercioby
Homework Helper
You had put the number for "cgs", instead of "mKs" but left out the all important "centi".

Daniel.

Matthias765
ok, thanks for the anwser.

Phobos
Staff Emeritus
Gold Member
Matthias765 said:
What in the world does E =mc2 mean? (Einstein's equation.)
mass and energy are two sides of the same coin
you can convert one to the other
the conversion factor is c-squared
a little matter is made of a lot of energy

But what's energy here? The energy of gamma rays (high energy photons). Correct?

Pengwuino
Gold Member
Ratzinger said:
But what's energy here? The energy of gamma rays (high energy photons). Correct?
hehehe Gamma rays.. x-rays.. visible light... all sortsa fun stuff.

Ratzinger said:
But what's energy here? The energy of gamma rays (high energy photons). Correct?
My understanding is that there's only one type of energy (AFAK). This energy can come in many different forms, including gamma rays. m=mc^2 obviously uses the SI unit of joules.

whats whe speed of light have to do with the deveration of energy from mass nanyway :yuck:

energy comes in form of photons when E=mc^2 is involved

learningphysics
Homework Helper
Ratzinger said:
energy comes in form of photons when E=mc^2 is involved
No. This doesn't have to be.

For example... if you heat up a pot of water... its mass will increase, and the increase in mass = $$E/c^2$$ where E is the amount of heat added.

Last edited:
Pengwuino
Gold Member
learningphysics said:
For example... if you heat up a pot of water... its mass will increase, and the increased mass = $$E/c^2$$ where E is the amount of heat added.
.... no. The mass will not increase at all.

learningphysics
Homework Helper
Pengwuino said:
.... no. The mass will not increase at all.
Yes it does. It may not be measurable. But it's a consequence of special relativity that the mass increases.

Pengwuino
Gold Member
learningphysics said:
Yes it does. It may not be measurable. But it's a consequence of special relativity that the mass increases.
Well if it does, news to me. Someone else should be along soon enough to tell me off.

Ich
The rest mass of a system of particles is generally bigger than the sum of the rest masses. The reason is that you can´t find a frame where all particles are at rest - the residual movement wrt the center of mass increases the mass of the system.
The most common form of residual movement is called temperature.

Matthias765 said:
What in the world does E =mc2 mean? (Einstein's equation.)
By definition the mass, m, of an object is associated with the momentum, p, of the same object. The sum of the kinetic energy, K, and the rest energy, E0, equals the inertial energy of the object. Therefore E = K + E0. If the object is free of all external influences, or the object is a particle, then it can be shown that E = mc2.

Phobos said:
mass and energy are two sides of the same coin. etc
[/quote]Not quite right. That expression is limited in form. In general it is incorrect. When you have an object of finite extent and there are forces being exerted on it then that equation is incorrect.

If you have Shutz's new text Gravity from the Ground up then you can read about an example he gives about how the inertia of a body increases with an increase in the body's pressure.

Pete

Pengwuino said:
Well if it does, news to me. Someone else should be along soon enough to tell me off.
This depends on what you mean by the term "mass." learningphysics is thinking of p = mv as the expression defining m. Others define mass as follows; p = M(v)v, m = M(0).

Pete

Pengwuino
Gold Member
Yah but if you heat up bunch of copper molecules or whatever, theres still the same # of molecules if its at 100K or 200K.

learningphysics
Homework Helper
pmb_phy said:
This depends on what you mean by the term "mass." learningphysics is thinking of p = mv as the expression defining m. Others define mass as follows; p = M(v)v, m = M(0).

Pete
Pete, but in this example (heating the water up... assuming the center of mass of the water is motionless in the frame of interest)... the inertial mass = invariant mass. So regardless of either definition, mass increases right? You clarified this for me in a thread a few months back.

Last edited:
learningphysics said:
Pete, but in this example (heating the water up... assuming the center of mass of the water is motionless)... the inertial mass = invariant mass. So regardless of either definition, mass increases right?
Yes.

Pete

Pengwuino said:
Yah but if you heat up bunch of copper molecules or whatever, theres still the same # of molecules if its at 100K or 200K.
But the molecules move faster if they're heated up, so their relativistic mass increases.

εllipse said:
But the molecules move faster if they're heated up, so their relativistic mass increases.
Yes. That's quite true. Its also part of the mechanism of why the mass of the object increases with the addition of heat. Take the simple case of a box of particles whose velocity has only an xy-component and no z component. Let the mass of the containment walls be insignificant when compared to the mass of the gas. Then as the gas is heated the particles move faster. The faster they move the greater the weight. Let the total momentum of the gas be zero. With all this in mind its rather easy to see why the mass of the gas increases when its heated up.

See details at http://www.geocities.com/physics_world/gr/weight_move.htm

Pete

pervect
Staff Emeritus
pmb_phy said:
Interesting, but a bit questionable. For instance, in your second derivation, if you take the result dead seriously, the weight would depend on the height 'z'.

In GR, mass is founded on asymptotic flatness, which is nowhere mentioned in your webpage. A standard method would be to use the energy pseudotensors in an asymptotically Minkowskian coordinate system.

pmb_phy said:
Then as the gas is heated the particles move faster. The faster they move the greater the weight. Let the total momentum of the gas be zero. With all this in mind its rather easy to see why the mass of the gas increases when its heated up.

See details at http://www.geocities.com/physics_world/gr/weight_move.htm
How can masses of the particles depend on their velocity ? Mass is a Lorentz-invariant quantity. All that changes is kinetic energy of the particles. Their masses remain the same. If this would not be the case, you would surely have different decays at different temperatures.