Why and why not e=mc²?
The world's most famous equation explained...
I am become death, the shatterer of worlds - Bhagavad Gita
Greetings, fellow Bohron
If there exists an equation that is loved by people all over the world, it must be simple enough to be understood even by a layman. The good news is, there is indeed one! The most famous equation of all time, Einstein’s mass-energy equivalence relation, E = mc², is a win of the power of fundamental physics.
In November 1905, Annalen der Physik published Einstein’s fourth paper that year, named Does the Inertia of a Body Depend Upon Its Energy Content, in which he derived what is now the most famous equation in the world.
But what is the physical significance of this equation? Is it even correct?
Mass-Energy Equivalence
The relation, E = mc², known as the Mass-Energy equivalence implies that although the total mass of a system changes, the total energy and momentum of the system always remains constant.
Consider the collision of an electron and a proton. The collision destroys the mass of both the particles but generates a large amount of energy in the form of photons. So, E = mc² tells us about the correlation of mass with every form of energy.
History
In the 18th century, there were theories on the correlation of mass and energy which also included that light particles and matter particles were interconvertible. In "Query 30" of the Opticks, devised by Isaac Newton in 1717, he asks:
Are not the gross bodies and light convertible into one another and may not bodies receive much of their activity from the particles of light which enter their composition?
During the 19th century, several attempts were made to show that mass and energy were proportional in various ether theories. In physics, ether theories propose the existence of a medium, a space-filling substance or field as a transmission medium for the propagation of electromagnetic or gravitational forces.
By assuming that every particle has a mass that is the sum of the masses of the ether particles, the authors concluded that all matter contains an amount of kinetic energy either given by E = mc² or 2E = mc² depending on the convention.
Explanation
Mass–energy equivalence affirms that all objects having mass, do have corresponding intrinsic energy, even when they are not in motion. In the rest frame of an object, the one in which is motionless and has no momentum, the mass and energy are equivalent and they differ only by a constant, the speed of light squared, c².
According to Newton, a motionless body has no kinetic energy, and it may or may not have other amounts of internally stored energy, like chemical energy or thermal energy, or it may possess some other energy because of its position in addition to any potential energy.
Due to this principle, the atom’s mass that comes out of a nuclear reaction is less than the mass of the atoms that go in, and the difference in mass can be observed as heat and light with the same equivalent energy as the difference. After analyzing all these explosions, Einstein's formula can be used with E as the energy released, and m as the change in mass.
This principle is used in modelling nuclear fission reactions and it states that a great amount of energy can be released by the nuclear fission chain reactions used in both nuclear weapons and nuclear power.
E = mc² is incomplete!!!
Yes, you read it right. E = mc² is incomplete and it doesn’t describe the whole story. This equation is only applicable to objects that are at rest. The full equation reads:
This equation is applicable to any situation. For the reference frames that are not moving, velocity and hence momentum are zero. This gives back the familiar version E = mc². For massless particles like light, we get E = pc which is of course the energy carried by light particles(photons).
Why the speed of light is unapproachable?
In a vacuum, light travels at a mind-bending speed of 3*10⁸ m|s. That's not just very fast, its as fast as it is physically possible for anything to move!
As energy is equal to mass times the speed of light squared, the speed of light serves as a conversion factor, explaining exactly how much energy is contained within matter. Since the speed of light is such a huge number, even a small amount of mass equates to a vast amount of energy. Einstein asserted that light moved through a vacuum and in such a manner that it moved at the same speed no matter what the speed of the observer.
So, according to the laws of physics, as we try to reach the speed of light, we have to provide more and more energy to make an object move. To reach the speed of light, we need an infinite amount of energy, and that's impossible!
Consequences: Manhattan Project
Although Einstein never worked on the atomic bomb directly, he is often mistakenly linked with the origin of nuclear weapons because of this famous equation E = mc², which explains the energy released in an atomic bomb but doesn't explain how to build one. He continuously reminded the public,
I do not consider myself the father of the release of atomic energy. My part in it was quite indirect.
Einstein's always said that his only act had been to write to President Roosevelt proposing that the United States research atomic weapons before the Germans harnessed this deadly technology. But these were not only the isolated actions of a scientist who was indulged in the world of politics indirectly.
People all over the world know about this equation, but only a few understand its true meaning. And thanks to me, now you even know that it isn’t complete! All because of a genius, perhaps the greatest to ever set foot on this planet, Albert Einstein.
