Special Theory of Relativity Part 4 - E=mc²

We have discussed in the last 3 blogs the important building blocks of the Special Theory of Relativity, a key cornerstone for modern physics. In this concluding blog we will discuss mass energy unification, better known as E=mc² . Let's start off with a summary of some of the key concepts of the Special Theory of Relativity.

Frames of Reference:
Reference frames are - in simple terms - the place from where one makes observations. It could be the sofa you are sitting on. The important point on frames of reference is that there is no absolute frame of reference, in other words, no frame of reference is ever absolutely stationary, i.e., motion is relative and everything is in motion with respect to something else.

We also spoke about how the laws of motion were not applicable to light. The speed of light according to Einstein is a constant.

The Postulates:

There are two postulates or consequences of relativity. They are:

1. The laws of physics hold true for observers in all uniformly moving frames of reference. 
• The laws of physics hold true for all frames of reference regardless of whether you are stationary or in motion.
2. The speed of light is measured as constant in all frames of reference (i.e. the speed of light is independent of the motion of the observer).
• Regardless of whether you are flying in an airplane or sitting on the couch, the speed of light would measure the same to you in both situations. In other words, the speeding airplane doesn't increase the speed of light unlike with other physical objects.

Time dilation and Length Contraction:

a) Time dilation is the phenomenon due to which time itself slows down with increase in velocity.

b) Length contraction is the phenomenon due to which, the length of an object contracts or reduces with increase in speeds.

Note: These concepts are grossly simplified. For detailed understanding of these concepts, check out their corresponding blogs.

Today we will talk about what is without doubt, the most prominent and famous equation in the history of physics, mass energy equivalence, or what is more universally known and recognized as - E=mc² .

Mass Energy Equivalence (E=mc²)

This equation says that energy is equal to the rest mass (mass of the object at rest) of the object times the speed of light squared (c is the speed of light).

In nuclear fission, an atom splits to form two more atoms and a neutron is released. What is interesting is that when you sum up new atoms' mass and the neutron's mass, it is actually  less than the mass of the initial atom. What happened to the missing mass?

Did you know that an atom of hydrogen weighs less than the sum of the proton and neutron that make it. That's right, less. But how can an object weigh less than the sum of its parts?

These bizarre phenomena is all a result of the equation E=mc² . The E symbolizes energy, the m is matter and c stands for the speed of light.

You might hear statements such as matter can be converted to energy or matter is frozen energy or matter is a form of energy. Unfortunately, all of these are quite incorrect, so understanding these equation can be quite frustrating. To understand this equation's true meaning, we should talk about some bizarre implication of it that seem odd with our day to day experience.

Even if two objects are made of the exactly same constituents, their mass isn't the same. The mass of an object is not the sum of its parts, it's total mass actually depends on two other things. One, how the constituents of the object are arranged as well as how the parts in the object move within the object. 

In the first case of nuclear fission, the missing mass is released in the form of heat energy. This energy is exactly what Einstein's E=mc² predicts. I'll explain the case of the hydrogen atom in detail below.

Let's assume that there are two wind-up clocks that are similar from atom to atom. One of them is wound up and fully running while one has stopped working. Here is the weird part, according to Einstein, the one that is running is very slightly heavier than the one that has stopped. Why? Well the hands and gears in the clock are moving, so they have some kinetic energy. The spring in the clock have some potential energy as it's compressed, and the gears of the clock rub together and the atoms get heated up ever so slightly, i.e., thermal energy.

                                           

Now according to Einstein, the difference in mass between the two watches, which is the additional mass in the watch that is running, is equal to the sum of all the additional energies divided by the speed of light squared. This in other words is m = e / c ^ 2. The energies in the clock manifests itself as extra mass in the running clock. Since the speed of light squared is a massive quantity, the additional mass is extremely tiny and is negligible.

We have always had a misconception that mass = the amount of matter in an object alone and neglect the extra mass due to energy. In real life we just don't feel this extra mass as it's negligibly small. Let's concretise this with few more examples.

When you turn on a flashlight, it's mass drops instantly. This is because the light carries energy which was previously stored as electrochemical energy in the battery. As the light leaves that flashlight, the mass contributed by the energy is lost and the mass drops.

All this while we spoke about cases in which the object has greater mass than that of its sub parts. The example stated in the beginning was quite the contrary to these examples as we said the mass of an hydrogen atom is lesser than the total mass of the proton and electron that make it up. This is because an electron's potential energy is negative. Imagine a proton and electron are infinitely far apart. In this case their potential energies will be zero. Now as they become closer to each other, they attract each other and their potential energies drop to become negative. Negative potential energy means that the objects are bound together and require additional energy to separate them, in this case the objects being the electron and proton. 

                                         

Now in the hydrogen atom, the electron obviously has a kinetic energy that is always positive because it is rotating at high speed around the nucleus. However, the potential energy of the electron is negative enough so that the sum of the positive kinetic energy and the negative potential energy will still be negative. Therefore, m = e / c ^2 is also negative and hence, the mass of the hydrogen atom is less that its parts. This is true for all the atoms in the periodic table. Also a molecule of hydrogen will weigh less than two atoms of hydrogen.

There it is, one of the greatest scientific advancements of modern physics. I hope you have understood this great theory of Special Relativity, and I hope that I've helped you understand this scientific marvel. We'll discuss about many marvelous phenomena of space in the upcoming blogs.