E=MC2 Explained

· Science

One of my friends on Facebook found a photo which I think perfectly illustrates how some people completely misunderstand Einstein’s energy equation.  Aside from the *facepalm* amusing and completely ignorant comments made by the author (which I’ve mostly deleted), it represents a fundamental misunderstanding of how to translate E=MC² into common language (in my case English).

Just because you can use big words doesn't mean you're smart

In physics, many words and symbols which appear common to native languages often times have different meanings to scientists.  Unfortunately the similarities to native language lead an unsuspecting public to believe these words to be interchangeable.

  • What we mean by =

In math, we learned that = means “equal to”.   2+2=4 or “the answer of figures calculated together“.   Or simple algebra where we solve for an unknown variable.   A(B+C)=AB+AC.   So it’s natural to assume E=MC² is an algebra type of equation.

However, in physics, = means “is the equivalent of” which if you think about it, doesn’t mean the same thing as “equals“.

Have you ever told someone a story that sounds like this?  “The other day, my manager was changed to someone I really like.  I didn’t get a raise, but it was equivalent to the feelings of liberation you experienced when you were released from detention”.

So in this example two things which would normally seem unrelated are compared.  Therefore, = means “is like” or “compares to” or… drum roll please is the equivalent to, or the equivalent of

“Reading this blog post is the equivalent of being strapped in a chair while repeatedly being whacked with a nerf bat” 🙂   You see…in this example = is being used as more of a comparison than as an actual mathematical value to describe something identical like 2+2 “is identical in value to” 4.

  • What ‘E’ Really Means:

What do you think of when hear the word Energy? Is it that stuff your kids have too much of, and you seem to run out of everyday at about 2PM? Is it that mysterious stuff everyone tells you to “save” and “conserve” but you can’t figure out what it is, or where to put it?

As it turns out, “Energy” like the word “Love” depends on how the word is being used. You “Love” your spouse and you “Love” your kids, but it’s not the same kind of “Love” when you “Love” your food or you “Love” your pets.  Isn’t English fun? Well, “Energy” is the same kind of thing.

Einstein was a Physicist, so I will explain the physics definition of the word “Energy” which is called “E” in the equation. But wait…before we can talk about Energy, we have to define what “Work” is.  The physics definition of Energy is the ability to do work.  And what is Work? In Calculus, work is defined as the “integral of the force over a distance of displacement”.  But we’re not doing calculus.  In physics, work is simply the amount of Energy that was transferred to an object.

Transferring energy to an object…work…force…you’re probably already in need of a drink…or an aspirin…or both…so let me make it really easy to understand.  Stand up, find a thick wall and push on it as hard as you can.  Did it move?  Of course not.  You don’t have enough “Energy” to do the “Work” required to move the wall.  When you pushed on the wall, no energy was transferred to the wall.  It was transferred to other places which I won’t go over now, but almost none of it was transferred to the wall, so it didn’t move.

Let’s review.  The “Energy” used by you pushing on a wall is “equivalent” to you trying to deposit money into your bank account using someone else’s ATM card with your PIN number.

With me so far?  We’ve covered “E” and “=“.  Stay Tuned because we’re about to cover Mass “M“.

  • The “M” is for Mass…and not the Catholic kind.

I’ll just get it out of way, because I know so many will ask.  Where did the catholic word for Mass come from? “Mass” is an English rendering of the Latin term “missa.”  In Latin the Mass ends with “Ite missa est,” which translated into English means “Go, it is sent,” the “it” being the Church.  From the Latin word “missa” comes the English word “dismiss.”  So “Mass” means “dismissal.”  The celebration takes its name from the sending forth that occurs at the end of every Mass.

And just how did the physics nerds get a hold of this word, and what does it mean to them?  Once again we’ve got to “Get Him to the Greek” 🙂 It seems lawyers and biologists like Latin while the physics nerds and college fraternities love Greek. In Greek, the word Mass meant “barley cake, lump (of dough)”.

But in Physics, we’re not really talking about food. If I may be permitted to over-simplify for a moment, mass is the sum total of all the stuff in something.  Mass is independent from size and weight because both size and weight dynamic and can change.  But the Mass of an object remains the same unless of course you add more mass.

Let’s do a small experiment.  Take a piece of paper (or a sheet of aluminum foil) and crumple it into a loose ball.  Take notice of the size and shape of the ball you’ve created.   Also notice the original size and shape of the original material you just crumpled into a ball.   By crumpling it into a ball, the size and shape of the material just changed, but it still has the same Mass (it didn’t get anymore stuff).  For the moment, it also has the same weight (because I’m assuming we’re on Earth), but I’m getting to that.  Weight and Mass are not the same thing.

Now crumple that ball of paper or aluminum foil into as tight a ball as your hands can stand.  Crumple it so tight until it won’t crumple any more.  Notice how the ball is now much smaller, but it still has the same Mass.

Ok, I said I’d get back to the issue of weight.  Let’s take an imaginary journey to the space station with your crumpled ball of Mass.  Everything on the space station floats around in a weightless environment because objects in orbit, traveling at the same rate of speed are in a constant state of falling.  They are effectively weightless.  No matter how you change the shape or where you go to change the weight, it always has the same amount of stuff, and that’s Mass.

By the way, and just because it’s a good place to bring this up, there is another kind of big ball of mass you can crumple down til you can’t crumple it anymore…except that it keeps on crumpling which doesn’t make any sense.   It’s called a collapsed star or a black hole.   I know, I know that doesn’t make any sense.  You know when your kids press you for information about something, such as the reason that can’t stay up past their bedtime, and you say “because I said so, that’s why”.   As it turns out, a lot of physics is the same way.   But black holes have nothing to do with explaining E=MC².  I just thought it was an interesting little side trip.

Anyway, we can’t stop there.  What fun would that be? There’s another kind of mass called “inertial mass”.  When you see the word “inertia” think “resistance”.  Therefore, inertial mass is the resistance of stuff to move.  On a Saturday morning, I have a lot of inertial mass.  This body ain’t movin’!  And I will fight anyone who tries to make me move on a Saturday morning.

Do you remember our really big building when we described Energy and the futility of trying to move that building by pushing it?  Well, the reason the building won’t move is because it has a lot of inertial mass.  It takes a tremendous amount of energy or force to move something that big that doesn’t want to be moved.  It’s not because the building is heavy.  If you and the building were in space and you tried to push the building, it wouldn’t move (well…it would but it’d be hard to measure), and you would be pushed back.  All the energy you tried to transfer to the building would transferred back to you and would be used to push you away from the building.

Another example is when you are driving in your car, and that idiot in front of you cuts you off and forces you to slam on your breaks.  What happens to your head?  It continues to move forward.  The mass of your head wants to keep moving, and the inertial mass of your head doesn’t want to stop just because the car you’re in does.

So you see, mass, and inertial mass aren’t really that complicated.  It’s everyday stuff you deal with all the time, just never using those words.

Let’s review.  Energy (E) is the equivalent of (=) Mass (M) times the speed of light squared (C²).  We now know about the E, the = and the M.

  • Relativistic Mass:

In this blog post, I’m trying to explain something that can only best be explained in the language of mathematics without using any mathematics at all.   Math is just a language like Spanish, German or Arabic.  Have you ever heard someone say to you, “It loses meaning in the translation”?  Well, I’m afraid the C² part of this equation falls into that category. Because, before I can begin to explain C² I first have to explain Relativistic Mass.  But wait, didn’t I already cover mass?  Well..yes, I did, but not quite…not really.

Relativistic Mass isn’t really the same kind of Mass that I talked about earlier.  This will take some explanation and I know you’re probably ready to gouge your eyes out with a number 2 pencil after reading my really long posts 🙂  So before getting into C² I have to explain both relativistic mass, and set a few ground rules about the nature of light itself.

If you recall, earlier we defined Mass as “the total amount of stuff in an object”.  That’s pretty final, isn’t it?  If I take a piece of paper and crumple it into a ball, it still has the same mass as the original sheet of paper.  If I crumple it up really really tightly, until I can’t crumple it anymore, it still has the same mass.  If we want to increase the mass of the ball of paper, what do we have to do?  Add another sheet of paper and crumple it up into the same ball.  So if you want to increase the mass, you have to add more mass.

Get ready because here is where our heads will start to hurt.  Just remember, it’s like telling your kids “because I said so, that’s why!”  As stuff approaches the speed of light, relativistic mass increases.  What?!  What does speed have to do with how much stuff there is?  When I drive in my car, ride a train, fly on an airplane, or even in a rocket ship, my mass doesn’t increase, does it?  I still have the same amount of stuff as I did when I was sitting on the couch watching TV.  If you were traveling in a spaceship with no windows out in space, you couldn’t tell how fast you were going.  Because as far as you are concerned, you’re sitting in a chair.  You are at rest and you’re not moving at all.   From your perspective, your mass does not change.   “Relative” to you, you are at rest and your relative mass is equal to whatever it was when you left.

But “relativistic mass” is not the same kind of mass you measure when you calculate your density or stand on a scale. Your regular mass doesn’t change.  People often mix these things up and get them confused.   And I can understand why.  It’s confusing, I’m not going to lie, and it makes no sense.   But it just is and we just have to accept it.   So how can I best define relativistic mass to you?  The easiest way I can explain relatavistic mass is that it’s how you see me as I approach the speed of light. Sitting in my little rocket ship, I don’t experience anything different. But as you’re looking at me, the closer I approach the speed of light, the more my mass increases. So who is right? It’s relative!. And that’s why it’s called relativistic mass.

The total relative mass of an object is relative to what percent the speed of light the stuff is moving and relative to who is watching the movement and from where. What?! You’re losing me here, Dave…this makes no sense! Just go with it and take my word for it. It will all make sense later on when I’ll explain, “why do I care? – E=MC² in everday life”.  But…yes…when you drive the kids to school, everyone’s relativistic mass increases in proportion the the percentage of the speed of light you’re traveling. Fortunately, that number is so tiny and has so many digits behind the decimal point, it’s not even worth mentioning.

Allow me to run off into a tiny bit of a tangent and further explain the word “relative”. When you say “relative,” you probably think of the people you try to avoid at weddings and family reunions. In those terms, the word relative means who those people are in relationship to you…or relative to you. You know, it gets complicated with the “second cousin twice removed” and all of that. But the point is that a person who may only be a second cousin relative to you, may be a brother, daughter, or parent “relative” to someone else. So when we say “relative” we mean from the perspective of who wants to know or who it is that’s asking the question. In physics we call this a “Frame of Reference”.

So this idea of “relativistic mass” which means the measure of the total amount of stuff, relative to the percentage of the speed of light that stuff is traveling, depending upon where you are when you were looking. Huh?! As of this posting, my total mass is 90KG. (I’m currently working on making that number smaller…lol). If I were to travel at 99% the speed of light, then from your perspective (frame of reference) my mass would be more than the mass of the whole Earth and the Sun combined. At this moment, humans don’t have any technology that can accelerate something the mass of the earth the way we accelerate a car or a rocket ship. It just takes too much energy. And that is the problem with the speed of light, and why we can’t go as fast, or faster. Because according the Einstein’s theory of Special Relativity, at the speed of light (which I’m going to start referring to a “C” to set you up for the C² part), your relativistic mass would increase to infinity…which is impossible…and also means you would need an infinite amount of energy to maintain that speed…another impossibility.

For this reason, “C” is a universal constant. Nothing can travel faster than “C”. Nothing can travel precisely at “C” either. “C” has limitations too. “C” can’t travel slower than “C” or faster than “C” “C” travels at “C” and that’s that. But what about “C” in water and refraction? Not to get too far off in a tangent, but light is not slowed down in the sense you were taught. It was simply delayed. I’ll explain that another time.

But getting back to “C”… The reason C can travel at C is because it has no mass.  Now wait a minute…what about the photon? And what about laser cutting torches, and laser eye surgery? Only something that has something can do something to something else, right? Yes, that’s right…light can do that.  It makes no sense.   Because I said so, that’s why! LOL.   Oh, and here’s another confusing but true statement about light.  It travels at the speed of light no matter how fast your are going, or where you are.  We say, light travels the same in all frames of reference.  You can never catch up to a beam of light the way a cat can catch up to a mouse.   I’m kind of getting into Newton’s and Einstein’s theories of Relativity here…but that’s a post for another time.   For now, just know that light is the same in all frames of reference. “Because I said so, that’s why!” LOL

  • Why C²

This part of the equation has taken me the longest to write.  Not because I don’t understand the material, but because the question is meaningless.  I had a physics professor call one of my questions “meaningless” once.  I have to admit I was kind of offended.  But he didn’t intend the comment to be hurtful.  What he meant was that the way I was asking my question involved a concept which only existed in theory, could never be actually measured, and therefore my question was meaningless.

There is a phrase in Viet Namese that describes the school of life.  The phrase is “truong doi“.  If you run that through the google translator it means “captain”.  The literal translation has absolutely nothing to do with the phrase.  It’s the same thing with C².  Earlier in the graphic, we see the author confusing the meaning of C² by saying the equation relates all matter to light.  This is wrong.  It has nothing to do with light, really.  It’s just that the speed of light is a universal constant.  It doesn’t change.  Nothing can go faster than the speed of light.  But it’s also not a literal value.  Einstein wasn’t referring to the literal translation of light.  The speed of light is 186, 000 miles per second, or 670, 000, 000 miles per hour.  Remember earlier when I explained “equivalency”?  When he said C² he did not mean 34, 596, 000, 000 miles per second or 448, 900, 000, 000, 000, 000 miles per hour.  “Equals” is not the same thing as “Equivalent to”.

But still, why use C²?  Why not use the number of crumbs in a piece of toast, or the number of farts in an elevator?  It’s because C² is the number used when a really big number that doesn’t change, and is the same everywhere in the universe is required.  There is another constant for small numbers called the “Planck Constant” but explaining that is beyond the scope of this blog.  Asking why the speed of light squared is used in this equation is like asking why R is squared in finding the surface area of a sphere.  It may have been a really long time since you’ve taken any math at all, but many people remember 4as the formula for finding the surface area for a sphere.  Pi is just a number that is made by dividing a circle’s circumference by its diameter.

If this part of the blog leaves you feeling unsatisfied and more confused than when we started, that’s because by itself, C² is meaningless.

Here is a YouTube that explains how C² was derived.

Warning:  Major Math Alert!!

  • E=MC² – Bringing it all together:

Out of respect, let’s take a moment to listen to Albert Einstein explain his own formula in his own words:

Even though Einstein clearly used the word “equals” in his own explanation, what he really means is “equivalency”.  When you look at this formula, think of a foreign currency exchange rate.  At the time this blog was written, 1 US dollar is equivalent to  79.5400 Japanese yen.  You only need a very small amount of US Dollars to get a whole bunch of Japanese Yen.  If you switch that around, you have to invest quite a lot of yen to get a little bit of US dollars.

What Einstein is saying is that you only need a very small amount of matter, to get a really large amount of energy.  But you need a tremendous amount of energy to make a small amount of matter.  Unfortunately, our first practical use of this formula was to blow the hell out of Japan, which is why I chose the Yen in my example.  It only took 64 grams of Uranium to make the bomb that blew up an entire city!  But to make a little bit of uranium you need over 2500 kilowatt hours of electricity.  There are some power plants that can do this with only 60 kilowatt hours, but that’s still a lot of work to get a little bit of stuff.

I’ve tried really hard to explain this in easy to understand terms.  For my Ph.D friends, if I’ve made any mistakes in my facts, or if I have misstated something, please correct me.  For my non-science friends, if there is any part of this that is confusing, please take the time to be specific about what you don’t understand.  My goal is to be able to explain this to anyone and have them fully understand it.

Einstein said that if you can’t explain something simply, then you don’t understand it well enough.  I hope I’ve made Einstein proud.


Comments RSS
  1. Bob Gilbreth

    I awoke at 1:30 AM because I could not remember what “c” stood for in Einstein’s formula. I tell you this because only a wonderfully written blog could have kept me awake for the last 45 minutes reading about it. At 71 years of age, I have trouble staying awake long enough to….uh, to…oh well, I forget, but thanks.

  2. Carlos Casados

    That was a fun read, David! Thanks! I’m going to ice my brain now 😉

  3. billy bob joe

    thanks this was a wonderful piece of writing and helped me with a school project

  4. seriousscience

    Edit Made: A physicist friend of mine pointed out that I had incorrectly asserted the force of gravity to be zero in space. This was not correct. I was trying to explain micro-gravity without getting sidetracked into a whole other side explanation. The error has been corrected (I hope) 🙂

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