A Fun Way of Understanding E=mc2

Monday, September 29, 2014

A Fun Way of Understanding E=mc2

Einstein’s famous equation. Image via Pixabay.

Many people fail to realize just how much energy there is locked up in matter. The nucleus of any atom is an oven of intense radiation, and when you open the oven door, that energy spills out; oftentimes violently. However, there is something even more intrinsic to this aspect of matter that escaped scientists for years.

It wasn’t until the brilliance of Albert Einstein that we were able to fully grasp this correlation between mass and energy. Enter E=mc². This seemingly simple algebraic formula represents the correlation of energy to matter (energy equivalence of any given amount of mass). Many have heard of it, but not very many understand what it implies. Many people are unaware of just how much energy is contained within matter. So, for the next few minutes, I will attempt to convey to you the magnitude of your own personal potential energy equivalence.

First, we must break down this equation. What do each of the letters mean? What are their values? Let’s break it down from left to right:

Albert Einstein. Image credit: Library of Congress

E represents the energy, which we measure in Joules. Joules is an SI measurement for energy and is measured as kilograms x meters squared per seconds squared [kg x m²/s²]. All this essentially means is that a Joule of energy is equal to the force used to move a specific object 1 meter in the same direction as the force.

m represents the mass of the specified object. For this equation, we measure mass in Kilograms (or 1000 grams).

c represents the speed of light. In a vacuum, light moves at 186,282 miles per second. However in science we utilize the SI (International System of Units), therefore we use measurements of meters and kilometers as opposed to feet and miles. So whenever we do our calculations for light, we use 3.00 × 10⁸m/s, or rather 300,000,000 meters per second.

So essentially what the equation is saying is that for a specific amount of mass (in kilograms), if you multiply it by the speed of light squared (3.00×10⁸)², you get its energy equivalence (Joules). So, what does this mean? How can I relate to this, and how much energy is in matter? Well, here comes the fun part. We are about to conduct an experiment.

This isn’t one that we need fancy equipment for, nor is it one that we need a large laboratory for. All we need is simple math and our imagination. Now before I go on, I would like to point out that I am utilizing this equation in its most basic form. There are many more complex derivatives of this equation that are used for many different applications. It is also worth mentioning that when two atoms fuse (such as Hydrogen fusing into Helium in the core of our star) only about 0.7% of the mass is converted into total energy. For our purposes we needn’t worry about this, as I am simply illustrating the incredible amounts of energy that constitutes your equivalence in mass, not illustrating the fusion of all of your mass turning into energy.

Let’s begin by collecting the data so that we can input it into our equation. I weigh roughly 190 pounds. Again, as we use SI units in science, we need to convert this over from pounds to grams. Here is how we do this:

1 Josh = 190lbs
1 lbs = 453.6g
So 190lbs × 453.6g/1 lbs = 86,184g
So 1 Josh = 86,184g

Since our measurement for E is in Joules, and Joule units of measurement are kilograms x meters squared per seconds squared, I need to convert my mass in grams to my mass in kilograms. We do that this way:

86,184g × 1kg/1000g = 86.18kg.

So 1 Josh = 86.18kg.
Now that I’m in the right unit of measure for mass, we can plug the values into the equation and see just what we get:
E=mc²
E= (86.18kg)(3.00 × 10⁸m/s)²
E= 7.76 × 10¹⁸ J

That looks like this: 7,760,000,000,000,000,000 or roughly 7.8 septillion Joules of energy.

Artistic rendition of energy released in an explosion. Via Pixabay.

This is an incredibly large amount of energy. However, it still seems very vague. What does that number mean? How much energy is that really? Well, let’s continue this experiment and find something that we can measure this against, to help put this amount of energy into perspective for us.

First, let’s convert our energy into an equivalent measurement. Something we can relate to. How does TNT sound? First, we must identify a common unit of measurement for TNT. The kiloton. Now we find out just how many kilotons of TNT are in 1 Joule. After doing a little searching I found a conversion ratio that will let us do just this:

1 Joule = 2.39 × 10^-13 kilotons of explosives. Meaning that 1 Joule of energy is equal to .000000000000239 kilotons of TNT. That is a very small number. At better way to understand this relationship is to flip that ratio around to see how many Joules of energy is in 1 kiloton of TNT. 1 kiloton of TNT = 4.18×10¹² Joules or rather 4,184,000,000,000 Joules.

Now that we have our conversion ratio, let’s do the math.

1 Josh (E) = 7.76 x 10¹⁸ J
7.76 x 10¹⁸ J x 1 kT TNT/ 4.18 x 10¹² J = 1,856,459 kilotons of TNT.

Thus, concluding our little mind experiment we find that just one human being is roughly the equivalence of 1.86 MILLION kilotons of TNT worth of energy. Let’s now put that into perspective, just to illuminate the massive amount of power that this equivalence really is.

The bomb that destroyed Nagasaki in Japan during World War II was devastating. It leveled a city in seconds and brought the War in the Pacific to a close. That bomb was approximately 21 kilotons of explosives. So that means that I, 1 human being, have 88,403 times more explosive energy in me than a bomb that destroyed an entire city… and that goes for every human being.

So when you hear someone tell you that you’ve got real potential, just reply that they have no idea….

Hydrogen Bomb Blast. Image via Pixabay.

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The National Aeronautics and Space Administration (NASA) is the United States government agency responsible for the civilian space program as well as aeronautics and aerospace research. President Dwight D. Eisenhower established the National Aeronautics and Space Administration (NASA) in 1958 with a distinctly civilian (rather than military) orientation encouraging peaceful applications in space science. The National Aeronautics and Space Act was passed on July 29, 1958, disestablishing NASA's predecessor, the National Advisory Committee for Aeronautics (NACA). The new agency became operational on October 1, 1958.

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The Oxford English Dictionary defines a UFO as "An unidentified flying object; a 'flying saucer'." The first published book to use the word was authored by Donald E. Keyhoe. The acronym "UFO" was coined by Captain Edward J. Ruppelt, who headed Project Blue Book, then the USAF's official investigation of UFOs. He wrote, "Obviously the term 'flying saucer' is misleading when applied to objects of every conceivable shape and performance. For this reason the military prefers the more general, if less colorful, name: unidentified flying objects. UFO (pronounced Yoo-foe) for short." Other phrases that were used officially and that predate the UFO acronym include "flying flapjack", "flying disc", "unexplained flying discs", "unidentifiable object", and "flying saucer". The phrase "flying saucer" had gained widespread attention after the summer of 1947. On June 24, a civilian pilot named Kenneth Arnold reported seeing nine objects flying in formation near Mount Rainier. Arnold timed the sighting and estimated the speed of discs to be over 1,200 mph (1,931 km/h). At the time, he described the objects' shape as being somewhat disc-like or saucer-like, leading to newspaper accounts of "flying saucers" and "flying discs". In popular usage the term UFO came to be used to refer to claims of alien spacecraft. and because of the public and media ridicule associated with the topic, some investigators prefer to use such terms as unidentified aerial phenomenon (or UAP) or anomalous phenomena, as in the title of the National Aviation Reporting Center on Anomalous Phenomena (NARCAP).

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UFO - Unidentified Flying Object An unidentified flying object, or UFO, in its most general definition, is any apparent anomaly in the sky that is not identifiable as a known object or phenomenon. Culturally, UFOs are associated with claims of visitation by extraterrestrial life or government-related conspiracy theories, and have become popular subjects in fiction. While UFOs are often later identified, sometimes identification may not be possible owing to the usually low quality of evidence related to UFO sightings (generally anecdotal evidence and eyewitness accounts). Stories of fantastical celestial apparitions have been told since antiquity, but the term "UFO" (or "UFOB") was officially created in 1953 by the United States Air Force (USAF) to serve as a catch-all for all such reports. In its initial definition, the USAF stated that a "UFOB" was "any airborne object which by performance, aerodynamic characteristics, or unusual features, does not conform to any presently known aircraft or missile type, or which cannot be positively identified as a familiar object." Accordingly, the term was initially restricted to that fraction of cases which remained unidentified after investigation, as the USAF was interested in potential national security reasons and/or "technical aspects" (see Air Force Regulation 200-2). During the late 1940s and through the 1950s, UFOs were often referred to popularly as "flying saucers" or "flying discs". The term UFO became more widespread during the 1950s, at first in technical literature, but later in popular use. UFOs garnered considerable interest during the Cold War, an era associated with a heightened concern for national security. Various studies have concluded that the phenomenon does not represent a threat to national security nor does it contain anything worthy of scientific pursuit (e.g., 1951 Flying Saucer Working Party, 1953 CIA Robertson Panel, USAF Project Blue Book, Condon Committee).

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Monday, September 29, 2014