My dear friend asked me a simple but very important question. His question was:

"Has Albert Einstein's famous formula E=mc² changed?!"

I decided to share the answer to this question with you in very simple language.

Albert Einstein's famous formula, E=mc², has not changed at all; rather, it remains one of the most accurate, proven, and important equations in physics, especially modern physics, or more specifically, the theory of special relativity. However, the reason you might have heard that this formula "has changed" or "is incomplete" relates to how it is used for objects in motion.

In fact, the formula E=mc² is merely a summarized version and a special case of a much larger and more comprehensive equation.

Let's first see what the full equation is. In reality, the formula E=mc² only works for objects that are at rest, meaning without motion. If an object is moving, in addition to mass, it also has kinetic energy or "momentum". Einstein's complete and original equation for energy is as follows:

E² = (pc)²+ (mc²)²

In this equation:

Now the question is, why do we usually only see E=mc²?

If an object is standing still in one place, its velocity is zero; consequently, its momentum (p) will also be zero. If we plug p=0 into the above formula, the (pc)² part is completely eliminated, and we arrive at this:

E² = (mc²)²

Taking the square root of both sides to simplify yields the familiar equation E=mc². Therefore, this formula is not wrong at all, but only shows the "energy of objects at rest".

Now we need to know why the complete equation is necessary. For example, particles of light.

If we only rely on E=mc², we run into problems regarding photons, or particles of light. Photons have no mass at all, meaning m=0. If we consider the mass to be zero in the simplified formula, the energy of light should be zero, which we know is not the case, and light does indeed have energy.

But if we use the complete equation, the secret of light's energy is solved. Since photons have no mass, the (mc²)² part becomes zero, and the equation becomes:

E² = (pc)² => E = (pc)

This means that particles of light, despite having no mass, have energy because they are moving at the speed of light and possess momentum (p).

In the past (mid-20th century), some physicists invented a concept called "relativistic mass" so they could use the same simple formula E=mc² for moving objects. They said that when an object moves faster, its mass increases.

But today, in modern physics, this concept has been discarded. Physicists realized that considering a variable mass causes confusion. Today, "mass" is considered an intrinsic constant value (rest mass), and to calculate the energy of moving objects, instead of assuming the object gets heavier, they use the same complete equation containing momentum. This change in "physics literature and education" might have created the misconception in public media that physicists have changed Einstein's formula.

Einstein's discovery has not been invalidated. For the sake of greater accuracy, instead of relying on the summarized state of rest (E=mc²), the science of physics simply emphasizes the complete original equation, namely E² = (pc)²+ (mc²)², so that it can explain the behavior of all particles in the universe, whether stationary, moving, or massless.