E= MC2

 or doesn't every story need a beautiful woman?

part 1 of a series...

Light from the Earth to the Moon takes about 1.333... seconds

Floating Away

The entire Saugeen area is dominated by a single industry --- Energy.  It's amazing that we don't know much about it.   When this area was just farming and tourism, we knew a lot about both.  The trouble is that Energy is complicated and hard to understand.  It may even involve that dreaded thing called an equation.

The famous cosmologist Stephen Hawking was about to write his first book for the masses.  The title was "A Brief History of Time".  That's a great title and the Saugeen Times popular science section has written a few articles about  the concept of time. 

Hawking was warned by his editor that equations were verboten.  "For every equation you have", he was told, "you will cut your readership in half."  That's a daunting task for a scientist like Hawking.  Poor Hawking lives in a world of equations, but forced himself to popularize his subject.

The book is wonderful and spent 237 weeks on the London Sunday Times best seller list.  He put one equation in the book and even with that he had sold 4 years later a total of 9 million copies.  By now he must have sold 20,000,000 copies, so that's half of what he could have sold.

The one equation he put in the book was Einstein's famous ...

E = MC2.

which is certainly the one equation every Saugeen resident recognizes and knows.

There have been hundreds of books written on this equation because it states in a few symbols a meaning of our times.  Bach and Mozart could not have done it better.  The C-Major Triad pales in comparison.

Like many such books about science, they are not often read to conclusion and A Brief History shares that fate.. 

So what is this  E = MC2.

What is an Equation?

An equation is a set of symbols in which there is exact balance on each side of the equal sign.  That is, you cannot add or subtract anything from either side without causing an imbalance.... same with division or any other operation that changes a value.  It's like a teeter totter with the board parallel to the ground.  Add an egg to one side and you have to add an egg of like weight to the other side.

What is Energy?

Broadly speaking Energy is the ability to do work  Once you try to define it further, you get tied in a web of more definitions, which is not fun. 

We know that energy is stored in our muscles, in lightning and thunder, the sun and in electricity and magnetism. Since Energy is so basic, it is difficult to define in terms of other things.  It is now measured in joules which is a metric term so it is defined in terms of metric units like the joule.  We know, we know... metric is supposed to make it easier.  These terms are no fun and you can see that it does not shed much 'light' on what's going on with energy, but here goes!.

One joule is the work done, or energy expended, by a force of one newton moving one meter along the direction of the force.  We have an idea of what a force is and a newton is equal to the amount of force required to give a mass of one kilogram an acceleration of one meter per second squared.  Big deal... it's still opaque.

Energy tied to all these other terms does not really enlighten us.  We can stay for the moment with the big idea that energy is the ability to do some sort of work.  So a car with a 200 HP engine can in a crazy way do the work of 200 horses. That's more like it! I can understand a horse. We can convert these to watts or joules or.... James Watt is responsible for horsepower and watts too.

Equal Sign 

The equal sign is something we can understand.  We have to be precise though with it.  Kids in school use it with abandon and so do capitalists.  You can't fudge it.  Apples are not equal to Oranges, after all.  Sometimes we play with it by saying X = Y + Constant.  This tells us that X is not really equal to Y.  You have to factor in some constant.  Sometimes we say X = Y + Epsilon, which means that X and Y differ by some tiny thing called an epsilon.  For E = MC2. we don't throw in Epsilons.  It says what it says and that's it. I've added two more equations... now please don't just quit here.

M Stands for MASS

Mass and weight are often confused.  Here is an example that will show you the difference.

Suppose we take a bowling ball up in the Space Shuttle that weighs 10 pounds on Earth and a small ball weighing one pound. Let's suppose they are made of exactly the same 'stuff'.  When we reach zero gravity, the two balls will hover inside the cabin just as an astronaut would, if not tethered.

 

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So both have nearly zero weight, but they have a mass that can be related.  If the astronaut bowler attempts to push the small ball with some constant force, it will move off nicely.  To get the same effect on the big ball, the spaceperson will have to exert 10 times the force, so somehow the weight now has no meaning, because that force is toward the earth and we have equalized that in orbit (not quite), but the mass has stayed the same.  We are ignoring the relativistic changes in mass due to gravity and motion.

Mass is such a fundamental thing in our universe.  It is hard to describe in terms of other more basic things.  It is tightly related to inertia.  That is, the objects ability to stay in motion or resist motion based upon a force is what mass is all about.  We know by intuition that starting a big ball in motion is harder than a small ball made of the same stuff.

C Stands for the Speed of Light and a Woman

Now we are getting more abstract.  C stands for the speed of light and Einstein considered this so fundamental that he said it was constant and was the upper limit of velocity for anything in the universe ..., but what the heck is it doing in the mix of things with energy and mass?

Every story needs a beautiful woman, don't you think?  The woman is the elegant and aristocratic Emilie du Chatelet. (We got the C in, didn't we?) She was at the court at Versailles and bored to death. 

She took up fencing and challenged one of the Kings Guards and master swordsman to an exhibition duel.  She was like a Geena Davis type being tall and lithe and MENSA smart, but more importantly, she had an intense curiosity pouring over the works of science.

She fell in love with Voltaire who shared many of her passions about politics and life.  She loved science more than he did.  So she started a scientific academy using an abandoned chateau that belonged to her husband's family.  It gave her the isolation she needed and the ability to 'import' key people to further her quest for knowledge.  She was far from a trivial hanger on at the court.

Her visitors included all the leading lights, even the famous Bernoulli of the great family of mathematicians.  They stayed for weeks at a time.

Emilie was not satisfied with the great Newton's arguments about energy.  In Newton's world, if you had two objects moving toward a collision at the same velocity the energy each had before the collision would disappear... go to zero, if they were of equal mass!  Just think of that.  If that happened or we had a sinkhole of energy going poooooooooooooooooof, pretty soon everything in the universe would stop because all energy would be leaking away atom by atom. It would seep away in all the collisions.

Picture a pin-ball machine that goes bong, bada bing, bong... as the ball hits objects and finally comes to rest. This did not sit well with Emilie.  She had read Liebniz and he had said that two carriages running at the same velocity and mass in opposite directions would not lose energy, but it would be transferred to all the bits and pieces of the wreck and would be somehow passed on in heat and other things that he could not explain.  The mysterious hand of God was at work.

Emilie went further than both Newton and Liebniz.  Newton had said that E = MV.  So Emilie started to try to duplicate some experiments that had been made by a Dutch researcher.  She found that if you took an object, let's say a heavy ball and dropped it with a certain velocity, it would punch a hole in soft clay to a certain depth.  If Newton was right, then if you increased the velocity by a factor of 2, you would get a depression twice as deep.  She found this not to be true.  The depth was not twice as deep, but 4 times as deep.  If you increased the velocity by a factor of 3, the depth was 9 times as deep.  Conclusion E = MV was wrong and E = MV2 was the right formula

Now the Speed of Light C in Einstein's Worldview

We know that the speed of light is a big number 186,282.397 miles per second or 299,792,458 meters per second.  If you square those you get huge numbers.  How did Einstein take the E = MV2 and put in C for V?

He extended his thought process to the ultimate velocity in the universe and used Emilie's, by that time (1905) well known equation.  What did that say to him?

The Real Meaing

The meaning of the equation   E = MC2. is that energy and mass are really one with a conversion factor of the speed of light squared.  What would it mean to us if Emilie had been wrong and Newton right? 

Well, the atom would not yield this tremendous energy that it does and we'd have to deal with the sun more wouldn't we?

But it is still a mystery why things are squared.  If you look at physical things of all types, this idea of squaring comes into play.  If the light is too dim and you move closer by half, the light goes up by 4 times.  If you increase your speed by two in your car, it takes you not twice as long to stop as it did at your original speed, but 4 times the distance.

The universe seems to like to square things.  Bruce Power likes it too!  Hope they don't square our bills.