E=MC²

Through discussion with friends I have found that the most famous equation in the world is known but not fully understood. So I think taking some time to explain this very important formula will benefit us all.

The Beginning:

Albert Einstein was perhaps one of the greatest minds in physics. His General Theory of Relativity has withstood the test of time and remains a good explanation as to why things behave the way they do.

In 1905 Einstein published a paper entitled “Does the Inertia of A Body Depend Upon It’s Energy Content?” which changed the way we look at mass and matter. This paper held our beloved equation e=mc² but in a different form.

The Meaning:

It was originally written as m=e/c² because deep down it is really a way to think about mass.

Let us take a fully charged battery. Nothing is different about what makes it up. It is simply a battery you would get at a convenience store. Now lets find that ever so common dead or depleted battery lying behind the couch or desk and compare them. Again nothing visibly different except the fully charged battery will have a greater mass than the depleted battery. You can’t feel this difference but it is there.

Alright, lets grab a couple batteries and put them in a flashlight. All of them are fully charged and ready to be used. The flashlight is off and nothing happens. However the moment we turn this flashlight on, it will immediately begin to lose mass.

I am sure at this point you get the idea. Energy is not equivalent to mass. But the statement mass is a property of energy fits a bit more snugly. Einstein clearly states exactly what is happening to the flashlight in this quote;

“If a body gives off the energy L in the form of radiation, its mass diminishes by L/c².”

Now ‘L’ was the original notation for the more modern notation of ‘E’. A much more striking quotation that can be drawn from the paper is as follows; “The mass of a body is a measure of its energy-content.”

So generally speaking every time we have weighed something we are weighing the accumulative energy in that given body. It is some pretty mind blowing stuff.

Where we can see it

We are able to see this concept in effect. Stars are giant balls of hot gas which undergo fusion. When fusion occurs there is a release of energy in the form of heat and light.

The fusion reaction taking place in the sun creating helium. This process is called a proton-proton reaction. There are other reactions.

The sun is losing mass at about 4 billion kg each second because it is releasing energy. Same goes for all stars. Black holes can evaporate because their mass is decreasing as they release energy and thus mass.

As a fun little fact all elements of the periodic table weighs less than the mass of their constituent parts due to this equation.

Why people thought he was wrong about the speed of light

In the year 2012 scientists at CERN were experimenting with neutrinos. Their research included aiming some of these wicked particles at a facility through the earth at another research facility. When they did the test the data came back saying the particles reached the target milliseconds before light would. Everyone went bananas. A bit later the researchers came back and explained that it was a wiring fault which caused the early reading.

Many people even today say that he was wrong when he couldn’t be more correct. Everything that he has said in his paper has been shown and explains why suns eventually die or why black holes eventually evaporate. Or even why atoms weigh less then the sum of their parts.

A more complete equation

The equation e=mc² is fine and dandy for objects which are motionless or at rest. However saying rest mass is redundant and is often times assumed because it is something that can be agreed upon by observers. One could argue that E=MC² is wrong in the sense that it is not relativistic. It doesn’t account for movement and velocity. It is good for velocities below the speed of light.

However there is an equation which accounts for motion as well and this equation is;

e²= (mc²)² + (pc²)²

Where ‘P’ is momentum and is calculated using the formula  p = mv . Velocity has an effect on a body’s relativistic mass.

Knowledge is good

There we have it. The most famous equation ever devised. It will live on for years and years to come. Hopefully more and more people will become familiar with its true meaning and share the knowledge with others. If you would like to see the paper yourself here it is.

Click to access e_mc2.pdf

 

 

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