Einstein's famous equation

ISBN: 0 330 39165 8

by David Bodanis

http://davidbodanis.com/

It got me thinking. Everyone knows that E=mc² is really important, but they usually don't know what it means and that's frustrating, because the equation is so short that you'd think it would be understandable.

There are plenty of books that try to explain it but who can honestly say they understand them? To most readers they contain just a mass of odd diagrams - those little trains or rocketships or flashlights that are utterly mysitfying.

Here's the intro at Dave's site itself

Because Faraday did not have that bias of thinking in straight lines, he could turn to the Bible for inspiration. The Sandemanian religious group that he belonged to believed in a different geometric pattern: the circle. Humans, they said, are holy and we owe an obligation to one another based on our holy nature. I will help you, and you will help the next person, and that person will help another, and so on until the circle is complete.

It's easy to miss how extraordinary a vision was the energy concept that Faraday's work helped create. It's as if, when God created the universe, He had said, I'm going to put X amount of energy in this universe of mine. I will let stars grow and explode, and planets move in their orbits' and I will have people create big cities, and there will be great battles which destroy those cities, and then I'll let the survivors create new civilisations, there will be fires and horses and oxen pulling carts; there will be coal and steam engines and factories and even mighty locomotives. Yet throughout the whole sequence, even though the types of energy that people see will change, even though sometimes the energy will appear as the heat of human or animal muscle, and sometimes it will appear as the gushing of waterfalls or the explosions of volcanoes: despite all those variations, the total amount will remain the same. The amount I created at the beginning will not change. There will not be one millionth part less than what was there at the start.

Expressed like this it sounds like the sheerest mumbo jumbo - Faraday's religious vision of a single universe, with just one single force spreading all throughout it. It's something like Obi-Wan Kenobi's description in Star Wars: "The Force is the energy field created by all living things; it binds the galaxy together."

By the mid-1800's, scientists accepted the vision of energy and mass as being like two separate domed cities. One was composed of fire and crackling battery wires and flashes of light - this was the realm of energy. The other was composed of trees and rocks and people and planets - the realm of mass.

Each one was a wondrous, magically balanced world; each was guaranteed in some unfathomable way to keep its total quantity unchanged, even though the forms in which it appeared could vary tremendously.

Everyone though that nothing connected the two realms. This is what Einstein was taught in the 1890's: that energy and mass were different topics; that they had nothing to do with each other.

Einstein later proved his teachers wrong, but not in the way one might expect. It is common to think of science as building up gradually on what has gone before. The telegraph is tinkered with and becomes the telephone; a propeller airplane is developed and studied, and then improved planes are built. But this incremental approach does not work with deep problems. Einstein did find that there is a link between the two domains, but he didn't do it by looking at experiments with weighing mass and seeing if somehow a little bit was not accounted for, and might have slipped over to become energy. Instead he took what seems to be an immensely round-about path. He seemed to abandon mass and energy entirely, and began to focus on what appeared to be an unrelated topic.

He began to look at the speed of light.

In the usual history of science accounts, it's not supposed to happen this way. Roemer had carried out an impeccable experiment, with a clear prediction, yet Europe's astronomers still did not accept that light travelled at a finite speed. Cassini's supporters had won: the official line remained that the speed of light was just a mystical, unmeasurable figure; that it should have no impact on astronomical measurements.

Emilie was different. As her father wrote: "My youngest flaunts her mind, and frightens away the suitors ... We don't know what to do with her."

... Emilie had long black hair and a look of perpetual startled innocence, and although most debutante types wanted nothing more that to use their looks to get a husband, Emilie was reading Descartes analytic geometry and wanted potential suitors to keep their distance.

... Here intellect left her isolated at Versailles, for there was no-one with whom she could share her excitement about the wondrous insights she was discovering through the work of Descartes and other researchers.

"According to [Newton's] doctrine, God Almighty wants to wind up his watch from time to time: otherwise it would cease to move. He had not, it seems, sufficient foresight to make it a perpetual motion." {Leibnitz}

In this view of Leibnitz's, nothing is lost. The world runs itself; there are no holes or sluicegates where causality and energy rushes away, so that only God would be able to pour them back in. We're alone. God may have been needed at the very beginning, but no longer.

But that's not what 'sGravesande found. If a small brass sphere is sent down twice as fast as before, it pushed four times as far into the clay. If it was flung down three times as fast, it sank nine times as far into the clay.

The c²2 is crucial in saying how this link operates. If our universe were created differently - if c² were a low value - then a small amount of mass would be transformed into an equally small puff of energy. But in our real universe, and viewed from the small, ponderously rotating planet to which we're consigned, c² is a huge number. In units of mph, c is 670 million, and so c² is 448,900,000,000,000,000. Visualise the equals sign in the equation as a tunnel or a bridge. A very little mass gets enormously magnified whenever it travels through the equation and emerges on the side of energy.

"We are in the position," Einstein explained later, "of a little child entering a huge library, whose walls are covered to the ceiling with books in many different languages. The child knows that someone must have written those books. It does not know who or how. It does not understand the languages in which they are written. The child notes a definite plan in the arrangement of the books, a mysterious order, which it does not comprehend, and only dimly suspects."

When the chance came to reach through the gloom, and pluck out The Old One's book that had the shimmering equation E=mc² written on its pages, Einstein had been willing to take it.

The reasoning Einstein followed to come up with his extraordinary observation - that mass and energy are one - had begun with the seemingly irrelevant observation that no one could ever catch up with light.

Marie Curie was one of their first investigators, and indeed in 1898 coined the word radioactivity for this active spurting out of radiation. Yet, even she, at first, had no understanding that these metals achieved their power by sucking immeasurably tiny portions of their mass out of existence, and switching that mass into the greatly magnified form of sprayed energy. The amounts seemed beyond credibility: a palm-sized chunk of these ores could spray out many trillions of high-speed alpha particles every second, and repeat this for hours and weeks and months, without any loss of weight that anyone could measure.

An even larger amount of matter, compressed into a floating star, can warm a planet for billions of years, just by seemingly squeezing part of itself out of existence, and turning those fragments of once-substantial matter into glowing energy.

In time, a few scientists did begin to hear of his work and then jealousy set in. Henri Poincare was one of the glories of Third Republic France, and, along with David Hilbert, in Germany, one of the greatest mathematicians in the world. As a young man, Poincare had written up the first ideas behind what later became chaos theory. As a student, the story goes, he'd once seen an elderly woman on a street corner knitting, and then, thinking about the geometry of her knitting needles as he walked along the street, he'd hurried back and told her there was another way she could have done it: he'd independently come up with purling.

By now, though, he was in his late fifties, and although he could still get some fresh ideas, he increasingly didn't have the energy to develop them. Or maybe it was more thatn that. Middle-aged scientists often say that the problem isn't a lack of memory, or the ability to think quickly. It's more a fearfulness of stepping into the unknown. For Poincare had once had the chance of coming close to what Einstein was doing.

In 1904 he'd been in the large group of disoriented Europena intellectuals invited to the world's fair being held in St Louis. (Max Weber, the German sociologist, was also there, and he was so startled by the raw energy he saw in America - he described Chicago as being like "a man whose skin has been peeled off" - that it helped jolt him out of a depression he'd been suffering for years.) At the fair, Poincare had actually given a lecture on what he'd labeled "a theory of relativity", but that name is misleading for it only skirted around the edges of what Einstein would soon achieve. Possibly if Poincare had been younger he could have pushed it through to come up with the full results Einstein reached the next year, including the striking equation. But after that lecture, and the exhausting schedule his St Louis hosts had for him, the elderly mathematician let it slide. The fact that so many French scientists had turned away from Lavoisier's hands-on approach and instead insisted on sterile overabstraction only made it harder for Poincare to be immersed in paractical physics.

By 1906, realising that this young man in Switzerland had opened up an immense field, Poincare reacted with the coldest of sulks ...

Note: Just found some extended excerpts of this section online ... click

Includes ref to an essay by Veblen

At this point there's a major shift in our story. The equation's first theoretical development is over; Einstein's personal contribution fades away. Europe's scientists accepted that E=mc² was true: that, in principle, matter could be transformed so that the frozen energy it was composed of could be let out. But no one knew how actually to get that to hapen.

University students in 1900 were taught that ordinary matter - bricks and steel and uranium and everything else - was made of smaller particles called atoms. But what atoms were made of no one knew. One common view was that they were like tough and shiny ball bearings ...

Their finding is so widely taught in schools today that it's hard to get back to the time when it was still surprising. What Rutherford realised was that these solid impregnable atoms were almost entirely empty. Imagine that a meteor plunges into the Atlantic Ocean,

To say that people have been charming, as Hahn had been all his life, is simply to say that they have developed a reflex to do what will put the individuals around them at ease. It sys nothing about their having a moral compass deeper than that.

You don't throw a simple pebble at a large boulder and expect the boulder to break in half.

No one had ever chipped off more than a fragment from a nucleus. They were confused.

Now, in the snow with her nephew, she stopped by a tree trunk, and they settled down to work it out.

In a small nucleus, such as that of carbon or lead, the gluing strong force is so great that it doesn't matter that there's a lot of electrical power hidden away inside, trying to push the protons apart. It won't win. But in a big nucleus, a really huge one such as that of uranium, could the extra neutrons tip the balance?

That would be as if the uranium nucleus were a water droplet that already was stretched apart as far as it could go without bursting. Into that overstuffed nucleus, one more plump neutron was then inserted.

One-fifth of a proton is a preposteroulsy tiny speck of matter. The dot over a letter i contains many more protons than there are stars in our galaxy.

In the long history of governments assigning the wrong man to a job - and there have been some choice ones - this is one of the choicest. {Lyman Briggs}

These were the quirks of fate that would influence who ended up using the equation first.

Then there was a chapter about Norway & heavy water ...

Click here for a few sites that delve into that aspect of history

More later ... maybe ... or just buy it ...