The curious connection of Isaac Newton and Harry Potter (and how to weigh a whole planet with an apple and two metal balls).

“Albert who was smarter, you or Isaac Newton?”

I think we both did pretty well at unravelling how the universe works.

“That’s not an answer.”

It’s an answer of sorts. So let me ask you a question, which of us would you rather be?

“Me? Well, I quite like being myself but I suppose I wouldn’t mind being you Albert. As for Newton, I can’t really imagine what that would be like.”

I think I’d rather be me too. I not sure being Isaac Newton would be that much fun. He was certainly brilliant but I’m not sure how happy he was. Certainly my childhood was simpler. True we had to move around a bit as my father’s various businesses struggled, but we were happy enough. Isaac Newton wasn’t quite so lucky. He was given away as a baby to his grandmother. His real father died just before Newton was born and his mother abandoned the young Isaac to marry a vicar from the next village, Rev. Barnabas Smith.

“That’s a tough start.”

Certainly was. His stepfather only lived another eight years before he died, which was just long enough for Isaac to learn to hate him and resent his mother for abandoning him.

“But he turned out good in the end?”

Oh he did very well, a professor of Mathematics at Cambridge University by the time he was only 27. His theory of gravity would have been enough for most people but he had the laws of motion and all his work on light too. All brilliant work, and most of done as a young man he didn’t publish most of it until he was much older. He was as grumpy as he was brilliant and a terrible man for getting into arguments with people.

“What kinds of people?”

Oh, almost everyone including his friends, but mostly people who disagreed with him.

“So he would have hated you?”

Oh I don’t know, I think meeting Newton would be fun. At least meeting him when he was still interested in physics. He left Cambridge University after 20 years or so and literally made money working for the Royal Mint in London. He’d been fascinated with the strange art of alchemy all his life and later in life he spent more of his time on that, than he did on physics.

"Alchemy?"

A strange mix of witch-craft and science that tried to convert metals into gold and discover the secret of eternal life. Newton became fascinated with the story of Nicholas Flamel.

"Nicholas Flamel? He was just a character in the first Harry Potter book, ‘Harry Potter and the Philospher’s Stone’ What’s he got to do with Newton?"

There really was a man called Nicholas Flamel that some people claimed did discover the secret of immortality. Legend has it that Flamel discovered the secrets of making gold out of ordinary metals and the secret of immortality from a book he saw in a dream. One day someone came into his bookshop in Paris and offered to sell him the very book he'd seen in his dreams. He immediately bought it and spent years trying to unravel its secrets. Some people claim he succeeded, but no-one knows for sure.

"Gold and other metals are elements or different types of atoms. How can you change one type of atom into another?"

They are indeed. We now know that you can't change one atom into another type of atom without changing the atomic nucleus in a nuclear reaction. So no amount of mixing of mercury and magic potion ingredients is going to create gold atoms. That's why there are no more alchemists, and alchemy changed from a mystical magic to the science of chemistry. Sadly Newton seemed to become quite crazy for a while from playing around with the metal mercury in his alchemy experiments. The tested some of his hair they had in a museum in Cambridge a few years ago. It was still full of mercury.

"Why was messing with mercury in the first place?”

Mercury is an amazing metal as it is actually a liquid and you can dissolve other metals in it which is why the idea of making gold seemed possible. The problem is mercury is poisonous and can send you mad. Remember the Mad Hatter in Alice in Wonderland?

“The Mad Hatter’s tea party?”

Exactly, well Hatter’s or people who made hats were often crazy because they used mercury in the making of hats.

"What did hatters do with mercury?"

They used it to harden hats to help them keep their shape until it was eventually banned. Anyway Newton eventually recovered from his mercury madness, but it is hard to tell if he was happy. He was only recorded to have laughed once in his entire life when someone asked him what he thought was a stupid question.

What might have made him smile was an experiment that showed that Newton was right in that a kilogram of anything has a gravitational pull.

“You said ‘might have’, he didn’t even smile when his ideas were shown to be right?”

No, because he had died 71 years before Henry Cavendish did his famous experiment with two large metal balls. Cavendish used a very sensitive machine built by a churchman, the Reverend John Michell who had died before finishing the experiment, to measure how much gravitational attraction there was between two heavy pound lead balls. Each weighed 350 pounds but there was a tiny but definite pull between the two balls. Cavendish measured the tiny gravitational force between these balls. From that he could calculate the mass of the Earth, though in fact he was trying to work out how much denser the earth was than water.

“You can stand on the Earth, do an experiment with two metal balls and an apple and measure how heavy the Earth is?”

Absolutely, but it is really the Earth’s mass you are measuring not its weight.

“Weight and mass are the same thing aren’t they?”

Not at all. Weight is just an effect of gravity on mass. Out in space an astronaut is weightless, but not mass-less, he still exists and has just as many atoms in his body. When people say they want to loose weight, what they really mean is they want to loose mass.

“OK, Albert we can talk about the Einstein mass-loss clinic later, first tell me how you work out the weight, sorry mass, of the Earth from a falling apple.”

Well, if you drop an apple it starts accelerating, going faster and faster.

“Yeah?”

So Newton’s second law of motion that I told you about last time can tell us how much force is required to accelerate an apple at a particular rate. We can measure how fast an apple accelerates easily enough. His experiment with the metal balls told him how much gravitational pull each kilogram of Earth could have, so all he needed to work out was how much mass was needed to create enough gravity to accelerate the apple in the way that it does according to Newton’s laws of motion and gravity.

“I couldn’t work out the mass of the Earth from that.”

Well if you tried hard you might, but luckily you don’t have to, that is why God invented physicists. The important thing is to appreciate how with a little thought and imagination you can do what sounds impossible like working out the mass of the Earth.

“Which is?”

Oh, almost six thousand billion billion or 6,000,000,000,000,000,000,000 tons. One last thing. Remember I said that gravity doesn’t make people fall in love?

“Yes, one of your stranger statements, Albert.”

Well, it doesn’t make people fall in love but it does make them attractive, especially if they are a bit fat.

“What!?”

Well every body floating in space has a gravitational pull and so does everybody on Earth. Every kilogram of bone, heart muscle or fat has exactly the same gravitational pull as a lump of rock. It doesn’t matter if you’re pretty or not and a few extra pounds just makes you a little bit more gravitationally attractive. So everyone is in reality attractive to everyone else. A little fact of physics that the crueller aspects of human nature have hidden from view for far too long.

The Story of Gravity: The weakling, the plague and the apple.

“Albert, is the gravity that makes stars the same as the gravity on Earth?”

It’s the very same force that keeps your feet on the ground and makes apples fall out of trees.

“Was that story true about the man who invented gravity being hit on the head with an apple really true?”

Well the man who was supposed to be under the tree was Isaac Newton and he certainly existed. Many people think he was the most brilliant scientist who ever existed.

“I thought you were the most brilliant scientist that ever existed Albert.”

Like Newton said, if I have seen farther it is by standing on the shoulders of giants. Newton was one my giants.

“So tell me about Isaac Newton then.”

Well he was born on Christmas Day in the year 1642 in the small village in Lincolnshire in England and he almost died the same day.

"What happened?"

He was tiny and feeble when he was born. He was so small his mother, Hannah Newton, said he'd fit in a two pint pot. Luckily for science young Isaac proved them wrong. He proved them so wrong he lived for 84 years which was almost a miracle back then. He also survived an outbreak of a deadly plague in 1665 that closed down Cambridge University. That was when he was sent back to deepest Lincolnshire for some uninterrupted thinking time. This was when he was supposed to sitting under the apple tree.

“Surely people had always known apples fell of trees?”

Of course they did. The difference was that Newton asked the question ‘Why?’
He was also smart enough to answer the question by developing his theory of gravity.

“So what was his theory?”

Newton said that everything big and small has a gravitational pull. The bigger the thing the stronger the gravity. He also worked out that the pull of gravity from an object gets less and less as you get further away.

“So even an apple creates gravity? I thought it was just the earth pulling the apple down.”

Exactly. The Earth pulls the apple and the apple pulls the Earth so they move together. It’s just that the Earth is so huge it has a much greater gravitational pull than the apple does. In mathematical terms gravity increases with the sum of the masses of two objects and reduces with the square of their distance apart.

“Whoa, hold on try that again in English.”

OK, for a start if you double in weight (or mass as we scientists call it) your gravity doubles.

“Got that.”

Right, the next thing is that if there are two objects then each pulls the other.

“Sounds weird, but OK.”

And lastly if you move away from a big object gravity reduces so that at twice the distance it is reduced by four times, two times two.

“I know what two times two is Albert.”

OK, so what happens to gravity at fives times the distance?

“Oh, er…”

It’s just five times five.

“Twenty five. I get it, so at three times the distance gravity is reduced by 9, three times three.”

Exactly, so now you know Newton’s theory of gravity.

“Can you really explain how a whole planet moves with this law of gravity?"

You certainly can, But there is one thing that gravity doesn’t do.

“What’s that?”

Gravity doesn’t make people fall in love.

“Thanks Albert, I’ll try and remember that.”

Now Newton didn’t stop there he worked out the rules for how things move in the universe, his laws of motion. How many rules or laws do you think that would take?

“Oh, millions I suppose. It’s a complicated place the universe.”

Newton only needed three extra laws but.these three laws explain how objects, from footballs to planets, move and what happens when you kick a football. Now pay attention.
“I’m listening.”

Newton's first law of motion is that objects keep doing whatever they are doing unless a force is applied to them. This works if the object is still or moving. Leave a football on the ground and its stays there. Kick it and it moves.

"But it doesn't keep moving for ever."

No because two other forces act on it. Gravity pulls it down to earth and friction between the ball and the air and ground stops it. In space there is no friction so a football could keep going forever as long as it didn't hit anything.

Newton's second law is a bit more mathematical but explains the link between how much an object accelerates, how big it is (it's mass or in simple terms weight) and the force applied. Simply put it says that for a given force, the smaller the object the faster it will accelerate. If you hit a golf ball and a football with a golf club, the golf ball goes much further because it is smaller and lighter.

“That makes sense.”

Newton's last law sounds a bit odd but is just as important as the others. It says that for every action there is an equal and opposite reaction. Most of the time you don't see this in action but it's still there. Step out of a small rowing boat at a jetty and it becomes a little more apparent. As your front foot moves forward, the equal and opposite reaction pushes the boat away from the jetty. Ignore Newton's third law and you'll get wet.

Together with his theory of gravity, these laws create what scientists call Newtonian mechanics. Four laws to explain most of the movement in the universe.

“So if Newton got it right, what was left for you to discover Albert?”

Well these four rules seemed to explain everything about how the universe worked and for most situations they still do. It's only when things are going spectacularly fast or gravity becomes very strong that Newton's law start to stop working but I'll explain all about that one day. Even though I ending up disagreeing with Newton on some things, when they sent a man to the moon they used Newton’s equations and not mine to make sure he got there.