Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

This week, we’re going to look at one of the most well known equations from the world of physics, Einstein’s Mass–Energy Equivalence.

All the way back in Season 1, Episode 2 **Bart the Genius**, Maggie shows us that there is more than one genius in the Simpson family, when she is seen playing with blocks that spell out EMCSQU. Her blocks are clearly meant to represent the famous equation E = mc^{2}.

**Mass–Energy Equivalence¹**

E = mc^{2} is an equation in German-born physicist Albert Einstein’s (pictured below) theory of special relativity that expresses the fact that mass and energy are the same physical entity and can be changed into each other. In the equation, the increased relativistic mass (m) of a body times the speed of light squared (c^{2}) is equal to the kinetic energy (E) of that body.

E = energy (measured in joules, J)

The word “energy” is actually quite new. Its modern use dates from around the middle of the nineteenth century, when it was beginning to be realised that the power that drove many different processes could be explained by the concept of energy being transferred from one system and form to another. Energy comes in many forms, and it can be transferred from one system to another. The basic unit of measurement for energy is the joule (J).

m = mass (measured in kilograms, kg)

Mass is strictly defined as a measure of a body’s inertia, i.e. its resistance to acceleration. Another and simpler way of defining mass is to say that it’s the total amount of matter in an object. This latter definition isn’t strictly true, but is good enough for our purposes here. Mass is measured in kilograms (kg).

c = the speed of light (measured in metres per second, ms-1).

We use the letter c to represent the speed of light. The ‘c’ comes from the Latin word “celeritas”, meaning swift, and it’s a very apt definition – there is nothing faster than light. In a vacuum, such as space, it travels at close to 300,000 kilometres per second (186,300 miles per second). That’s about seven times around the Earth every second.

In physical theories prior to that of special relativity, mass and energy were viewed as distinct entities. Furthermore, the energy of a body at rest could be assigned an arbitrary value. In special relativity, however, the energy of a body at rest is determined to be mc^{2}.

Thus, each body of rest mass m possesses mc2 of “rest energy,” which potentially is available for conversion to other forms of energy. The mass-energy relation, moreover, implies that, if energy is released from the body as a result of such a conversion, then the rest mass of the body will decrease.

What Einstein showed via his now famous equation was that mass and energy are in fact the same thing. Converting one into the other doesn’t therefore violate either of the two conservation laws – the law of the conservation of mass or the law of the conservation of energy. Both quantities are conserved, although the state of the mass/energy may have changed.

Here is a rare recording from Einstein himself explaining his famous equation:

“*It followed from the Special Theory of Relativity that mass and energy are both but different manifestations of the same thing – a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to mc2, in which energy is put equal to mass, multiplied with the [by the] square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned before [E = mc2]. This was demonstrated by Cockcroft and Walton in 1932, experimentally.*”

The Mass–Energy Equivalence makes another appearance in The Simpsons. In **Bart’s Friend Falls in Love** (Season 3, episode 23), a picture of Albert Einstein is seen on Martin’s wall and his famous equation on Martin’s bed sheets, amidst other mathematical formulas.

Now we know more about one of the most famous formulas of all time. Were you familiar with the Mass–Energy Equivalence? Were you familiar with the formula? Did you notice that Maggie’s blocks spelled out E = MC2? Did you catch the formula on Martin’s bed sheets? Sound off in the comments below. You know we love hearing from you.

E = mc2 was my whole adult life until I retired at 55 in 2013. Out of high school, I served as a Reactor Operator on the USS Enterprise CVN-65. After getting an Electrical Engineering degree, I was a Control Room Supervisor at one of the civilian nuclear plants that surround Chicago. No, I don’t glow, but I have some great shots of the nuclear core glowing blue during a refueling outage!! I wish I knew how to post them. People that see them are amazed and say they though it was just a joke that a Reactor glows. I bet you could find pics on Google.

What the ???

Great explanation Safi!

I’d noticed Einstein’s picture on the wall but was so proud of noticing jt I never knew I’d missed the sheets! D’oh!

~MIB👤

Cool fun learning for a Monday morning. I feel like i understand this better than before. Thanks Safi.

https://gcaptain.com/u-s-navy-decommissions-uss-enterprise-the-worlds-first-nuclear-powered-aircraft-carrier/ (2nd photo!)

I was a Reactor Operator on the USS Enterprise CVN-65 for four years. She had eight reactors and I operated them all at one time or another.

A fun fact (if you are geeky like me) – In most of the ways to solve Einstein’s field equations, the equation that naturally results is actually E^2=m^2c^4. The formal solution is then E = ± mc^2. The ‘negative energy’ solution seems like something you would just ignore as a formality insisted up by your maths teacher, but is intrinsically related to what physicists call “anti-matter”. In particle theory, this is stated as every particle has its own “anti-particle” with common examples being the proton and anti-proton or the electron and position. Those pairs of particles have the exact same mass, but differing quantum structures such that they will instantly annihilate (and be converted to Energy) when in contact with their anti-particle. Seems esoteric, but physicists create these ‘anti-particles’ all the time in particle accelerators.

Second Fun fact – I learned this all in a ‘modern physics’ class many years ago at Matt Groening’s alma mater – The Evergreen State College in Olympia, WA.

Thanks Safi, for this and your other posts.

Thanks

Reminds me of “The Glass Space Ship” analogy.

Light always travels at 300,000 km per second (1c), relative to the position of the observer.

Forgetting sound doesn’t travel in a vacuum…..

You are in the middle of the glass spaceship traveling at 90% speed of light (0.9c). You have a light gun in each hand and a light sensitive panel at the front and back of the ship. You turn on the guns, the panels are activated and they sound a bell. You will hear both bells go off simultaneously.

You are passing me when you do this. I hear the rear bell go off and then the front bell.

Why?

Because you believe you are stationary. I see the back of the ship ‘racing’ toward the light at 0.9c and the front running away at 0.9c.

Soooo, to me,

The back panel and light from the gun are coming together at 1c + 0.9c = 1.9c

The front panel and light are coming together at 1c – 0.9c = 0.1c

Everything is relative to the position of the person observing the action.

Now if only I could understand Watts, Volts, Coloumbs,

Hi,

I’m enjoying these discussions, thanks.

One thing you didn’t mention is the difference between mass and weight. Mass is the resistance to acceleration, while weight is the pull due to local gravity. Thus your weight will change if you travel to the moon, but your mass remains the same. Another example is that you are (essentially) weightless in space, but don’t forget that your mass is unchanged and you can hurt yourself if you are moving fast and strike the wall of the capsule!

Interesting stuff. There’s a typo in the 7th paragraph of the 2nd part: you mention the law of conservation of mass twice in the same sentence. The second should probably read ‘energy’ instead of ‘mass’. I am familiar with all this stuff, but never noticed it on the show. I was a lot younger when I watched them and I knew a lot less…

Thanks, typo corrected.

Thanks Safi! I’d say this equation is… relatively known (eyyy)