E = m c square

There are 3 mass definitions:


inertial mass, which respond with acceleration when force applied.
gravitational mass, which produced the among of force by gravity.
relativistic mass, which is a fictional mass created by Einstein.

Many people say, when something get heated, than energy increased, thus the mass increased and it becomes heavier. According to Einstein's equation E = m c^2. Completely incorrect. They totally mix all three definitions of mass all together, and has a mis-understanding of heavy and "hard to be moved".

This equation tells us that mass and energy are equal, mass can change to energy and vice versa.

therefore, as long as the kinetic energy still "functioning", as shown that the heated thing still hot. thus the energy did not covered to mass yet.

In nuclear reaction:

He-4 + N-14 -> O-17 + H-1

the mass of He-4 + N-14 = 18.00567 unit
the mass of O-17 + H-1 = 18.00696 unit


The gain of mass from energy. the energy is needed because, the 2 nuclei has great electromagnetic force between 2 cluster of protons. After the combination, the kinetic energy will be converted to mass, as a blinding energy.


To fully understand this equal, we have to distinguish 2 similar but different concepts - equivalent and exchange. Both concepts are simple. They mean the same or equal value. Like 1 US dollar can exchange/equivalent for 7.8 HK dollars. However they are little bit different.


First of all, may be we should return to a more fundamental equation:

E = K + mc^2

Where K is the kinetic energy, m is the rest mass of the object.

This equation means the total energy contains 2 parts. 1st is the kinetic part (you can say, the energy because of motion), 2nd is the mass part (you can say, the still one). Now, you may argue why "Total" energy only has these 2 things, how about sound energy? light energy? chemical energy? The answer is, if you are smart enough, the kinetic part contained all this kind of energy and the truly amazing thing is, mass can be energy as well!!

Let me explain a little bit about the kinetic energy as well. As we known, sound energy is same as vibrating energy of air molecules. For light, it is a non-stop particle (in particle sense), and according to special relativity, it only has kinetic energy but no mass. And for chemical energy, which is in fact electromagnetic energy, which is light energy. How about Potential energy?? Good question! as you can see, for gravitational potential energy, this energy is stored in the field, not on the object.

Thus, E = m c^2 is just a simplified form when there is no kinetic energy.

According to special relativity, it is more harder to accelerate a body for a higher speed. however, it does not implies the body was heavier! More technically, it is because the momentum changes lesser due to non-linear space-time.

remember, there is no relativistic mass. this is a great misleading simplification of Einstein. he likes to simplify equation a lot and he made this:

K + m c ^2 = M c^2

where m is the mass (or rest mass), and M is the so called "relativistic mass".

He introduced this misleading concept because it is much more easy to tell the public why it is harder and harder to reach the light speed.

Correct interpolation for E = m c^2 is exchange, or replace, but not equal. This means, energy or mass can either exist, but not both. Just like you pay 2 dollars for an apple, you will not get back the 2 dollars. another example is light, photon. Photon has energy in electromagnetic form. Does it mean photon has mass? NO, photon has no mass according to special relativity, otherwise, it cannot move in speed of light. Therefore, we can see, the kinetic energy has no contribution to mass.