PITFALLS: Some parts of Einstein really are easy!

TUESDAY, JULY 20, 2021

Most parts pretty much aren't:  Kurt Gödel has often been called "the greatest logician since Aristotle."

This assessment is often attributed to Albert Einstein, the lone friend of Gödel's adult years and the greatest physicist since Newton.

Einstein and Gödel developed their friendship in the 1930s, during the period when each was working at Princeton, New Jersey's Institute for Advanced Study.

By that time, the greatest physicist was already quite well-known. For better or worse, the man described as the greatest logician never achieved that status.

Have academics, writers and journalists ever been able to make Einstein or Gödel easy? An array of books have tried to do so, but to what extent have writers been able to explain / describe / elucidate the work of these two men?

In the case of Einstein, we'll guess that people who know the name—many people still do—would associate him with "the theory of relativity," and more specifically with the most famous equation in the history of physics:

E = mc2.

When it comes to explaining Einstein's universe, that famous formula has turned out to be relatively easy. Almost everything else has turned out to be quite hard.

In the next few weeks, we'll examine some of the ways Walter Isaacson tried to make Einstein easy—tried to explain Einstein's universe—in his well-regarded 2007 biography,  Einstein: His Life and Universe. 

Like others before him, not excluding Einstein himself, Isaacson struggled with the task of explaining most parts of relativity—in explaining most parts of Einstein's universe. By way of contrast, shedding light on that one famous formula was relatively easy. 

Isaacson turns to that task at the end of his Chapter Six: Special Relativity. He does so in a short, concise manner. 

Below, you see the bulk of what he writes at that point in his book. For certain fairly obvious reasons, the general reader will be able to grasp large parts of this presentation:

The result [of certain of Einstein's explorations] was an elegant conclusion: mass and energy are different manifestations of the same thing. There is a fundamental interchangeability between the two. As he put it in his paper, "The mass of a body is a measure of its energy content."

The formula he used to describe this relationship was also strikingly simple...

E = mc2.

Energy equals mass times the square of light. The speed of light, of course, is huge. Squared it is almost inconceivably bigger. That is why a tiny amount of matter, if converted into energy, has an enormous punch. A kilogram of mass would convert into approximately 25 billion kilowatt hours of electricity. More vividly: the energy in the mass of one raisin could supply most of New York City's energy needs for a day.

"Mass and energy are different manifestations of the same thing?" Unexpected and ultimately puzzling though it may be, this formulation is one of the most approachable parts of Einstein's work for the non-specialist / general reader.

In the presentation shown above, Isaacson offers examples from everyday experience which are easy to visualize, however surprising or puzzling they may be. 

In Isaacson's treatment, "a tiny amount of matter" can be converted into an amount of energy we would regard as enormous. Indeed, "the energy in the mass of one raisin could supply most of New York City's energy needs for a day."

This may be a deeply surprising claim, but it comes from the realm of the everyday and it's easy to understand. Meanwhile, the plausibility of this claim comes from a place Isaacson doesn't mention at this part of his book:

Starting in the 1940s, the rise of nuclear weapons demonstrated, in the most dramatic and tragic ways possible, the fact that relatively small amounts of matter can somehow be converted into (what we would regard as) enormous amounts of energy.

We'll note that Isaacson uses the terms "mass" and "matter" almost interchangeably in that particular passage. That said, how can it be that mass and energy (whatever they are) turn out to be "different manifestations of the same thing?"

Attempting to answer that question wouldn't turn out to be easy. But to the extent that Einstein found that "a tiny amount of matter" can be converted into an enormous amount of energy, Einstein's universe is remarkably easy to describe or explain to the general reader. 

Basic questions are left unexplored. But other basics are easy to report and are easy to understand.

Amounts of matter which strike us as small can be converted into amounts of energy which strike us as enormous! In his 2001 book, E = mc2: A Biography of the World's Most Famous Equation, David Bodanis presents this basic part of Einstein's universe in the way shown below.

(To read this part of Bodanis' book, you can just click here.)

Bodanis starts by discussing Marie Curie's exploration of the "mysterious energy" emerging from "several metal-streaked ores that had been brought back from the Congo and Czechoslovakia and other places" in the 1890s.

Curie won the Nobel Prize twice for her work on such topics. She also died from her extended exposure to this mysterious energy, which she called "radioactivity."

Can small amounts of matter be converted somehow into large amounts of energy? "At first," Bodanis writes, "even she 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."

In this process, "immeasurably tiny portions of mass" were passing out of existence as they were converted into energy. Bodanis goes on to describe the part if Einstein's universe which really is relatively easy:

Einstein's equation showed how large the result could be. To work it out for any chunk of mass, take the great speed of light and square that to get an even more immense number. Then, multiply that by the amount of mass you're looking at, and that's how much energy, exactly, the mass will be able to pour out.

It's easy to miss how powerful that idea is. For E=mc2 says nothing about what sort of mass can fit into the equation! Under the proper circumstances, any substance can have its mass exploded outward as energy. This is the power that's around us, encased within the most ordinary rocks and plants and streams. A single page of this book, weighing only a few grams, seems to be just an innocuous, stable mix of cellulose fibers and ink. But if that ink and cellulose could ever be shifted into the form of pure energy, there would be a roaring eruption, greater than that of a large power station exploding. It's easier to access that power in uranium than in ordinary paper as we'll see later but that's simply a limitation of our current technology.

The greater the mass being transformed, the more fearsome the power released. Put a single pound of mass into the "m" slot, and after multiplying by the vast 448,900,000,000,000,000 value of c2, the equation promises that, in principle, you could get over 10 billion kilowatt hours of energy. This is comparable to a huge power station. That's how a small atomic bomb with a core small enough to fit in your cupped hands could heave out enough energy to rip open streets and buried fuel lines; to shatter street after street of brick buildings; to tear open the bodies of tens of thousands of soldiers and children and teachers and bus drivers.

A uranium bomb works when less than 1 percent of the mass inside it gets turned into energy. 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.

And so it goes. 

We can't vouch for the perfect accuracy of every statement made in that presentation. That said, surprising though this conversion of matter into energy may be, the basics are easy to describe or report. The basics are easy to understand, even for the non-specialist / general reader.

As such, some parts of Einstein's universe actually are fairly easy! We offer this as a preemptive contrast to the many other parts of that universe which have proven to be extremely hard.

We'll turn to some of those difficult areas in the next few weeks. Tomorrow, we'll let theoretical physicist Brian Greene offer some other formulations which may be jaw-dropping in their strangeness, but are easy to understand.

On Friday, the worm will start to turn. We'll look on as Greene struggles badly at one point. 

We may visit a similar breakdown as Rebecca Goldstein, a biographer of Gödel, discusses the basic outlines of the findings of that "greatest logician." At such times, we start to encounter the pitfalls of human intellect which may obtain, even today, at the highest academic and journalistic levels.

Some parts of Einstein's universe actually are fairly easy. Others parts have been extremely hard, though we rarely seem willing, or possibly able, to come to terms with that fact.

Tomorrow: As seen in Planet of the Apes! Profoundly counterintuitive, but easy to understand


20 comments:

  1. "By that time, the greatest physicist was already quite well-known. For better or worse, the man described as the greatest logician never achieved that status."

    This is not quite true. This book popularized Godel's work and was widely read, making Godel much more familiar to those outside fields to which his work has been central:

    https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567

    Somerby assumes that if Godel wasn't familiar to him, then he wasn't familiar to anyone. That is always a dangerous assumption to make.

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  2. Somerby says that E=MC*2 is the most famous equation in physics.

    I think this one is:

    f = ma

    "Newton's second law, which states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration a of its centre of mass, F = ma, is the basic equation of motion in classical mechanics."

    ReplyDelete
  3. "At such times, we start to encounter the pitfalls of human intellect which may obtain, even today, at the highest academic and journalistic levels."

    This is a ridiculous statement. If Goldstein were failing as a biographer, Somerby might have a point. But Somerby instead pretends that her expertise is in the same field as Godel's, when it is not. She does fine as a biographer and she is not an example of the failure of expertise among those in other fields.

    Somerby doesn't dare attack Hawking in the way he attacks Goldstein. This is an example of the kind of assholery men display when they go out of their way to diminish women.

    ReplyDelete
    Replies
    1. It is depressing. It almost makes one want to retire from a career in psychiatry and spend their days trolling a blogger.

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    2. Like Bandy Lee?

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    3. Exactly, Anonymouse 1:13am.

      Except for the difference between a internet blogger and POTUS.

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  5. "Kurt Gödel has often been called "the greatest logician since Aristotle."

    Who cares. We feel that you, dear Bob, turned to obscure topics to avoid lively discussions you wouldn't shy away from in years past.

    What about the greatest abstract painter since ... ever. The greatest abstract painter, period, whose astonishingly beautiful paintings are flying off the easel for 500 large a piece?

    Or, what about the manifestly degenerate mental abilities of the one holding the nuclear codes?

    Or about one infamous crazy anti-vaxxer who lambasted the greatest-safest vaccine of all times as "if Donald Trump tells us to take it, I'm not taking it"?

    Why are these topics ignored, dear Bob? Conspicuously ignored! We've grown to expect so much from you, and we now feel betrayed, we're sorry to say...

    ReplyDelete
  6. As Bob points out, it's not difficult to visualize a small amount of mass turning into a large amount of energy. However, for me at least, it IS difficult to visualize a large amount of energy turning into a small amount of mass. Yet, since mass and energy are manifestations of the same thing, the energy-to-mass conversion ought to be possible, least theoretically.

    ReplyDelete
    Replies
    1. Dave, it's just the second law of thermodynamics. Even with an ordinary explosive, we expect a solid lump to become a big cloud of hot gas, but we don't expect hot gas to become a solid lump. If we convert matter completely to radiation, the increase in entropy is even greater than in a chemical reaction.

      Delete
  7. I did the multiplication on this myself, so I'm not really sure, but I think a kilowatt-year is about thirty-five grams. Anyone want to correct me?

    ReplyDelete
  8. Well, Bob, are you taking into account that your aptitudes and proficiencies led you to become a writer and not a scientist? (q.v. Gardiner's Theory of Multiple Intelligences. None of that theory is hard.)

    ReplyDelete
  9. Somerby himself never addresses the targeting of Hillary Clinton, but here is an interesting article about it and Q-Anon's role:

    https://www.nytimes.com/2021/02/05/opinion/qanon-hillary-clinton.html?action=click&module=RelatedLinks&pgtype=Article

    ReplyDelete
    Replies
    1. anon 10:26, TDH did address the unfair targeting of Clinton (including by the so-called liberal pundit nabobs) more penetratingly and more often than probably anyone else.

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  10. That must have been before Bob downloaded the Right-wing Grievance of the Day app he starts every morning with now.

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