WEDNESDAY, JULY 28, 2021
What Galileo said: As we noted last week, several parts of Einstein's universe are easy to describe. In that sense, and to that extent, those parts of Einstein's universe are easy to understand.
As we noted last week, Walter Isaacson describes one such part of Einstein's universe at the end of Chapter Six in his 2007 biography, Einstein: His Life and Universe. Below, we show you that passage again:
The result 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.
It's easy to understand what's being said in that passage. Tiny amounts of matter can be converted into enormous amounts of energy.
The raisin which could fuel New York makes this presentation memorable. It may be hard to understand how any such thing could actually happen. But it's easy to understand what is being said.
That easy-to-understand presentation comes at the very end of Isaacson's Chapter Six. Once again, this is his full chapter title:
CHAPTER SIX Special Relativity, 1905
According to Isaacson, the raisin which could fuel New York emerges from Einstein's special theory of relativity. Chapter Six is devoted to that theory. It ends with a presentation which is easy to understand.
As we noted yesterday, the chapter doesn't start that way; in our view, it starts in a highly murky fashion. Today, we'll see the lack of clarity grow—or at least, so it says here—as Isaacson's presentation continues.
Yesterday, we looked at the first six paragraphs in Isaacson's Chapter Six. The chapter opens with a counterintuitive claim—"Relativity is a simple concept"—then wanders forward from there.
The first six paragraphs of the chapter form a fairly obvious unit. We've struggled to make clear sense of that unit ever since we first encountered Isaacson's book thirteen years ago.
As noted yesterday, Isaacson starts Chapter Six by saying what relativity "asserts." (At this point, he's speaking about the general concept of relativity, not about Einstein's "special theory.")
"Relativity asserts that the fundamental laws of physics are the same whatever your state of motion," Isaacson says in his opening paragraph. But he fails to explain why anyone should be surprised, or should feel informed in some way, by any such assertion.
From there, he meanders through a set of somewhat fuzzy claims concerning a rapidly-changing set of topics whose interconnections are poorly explained. Thirteen years into our search, we still can't master this wandering presentation.
At the end of this opening unit, Isaacson signals that he is moving ahead to a new point of focus. As we noted yesterday, the transition from paragraphs 5 and 6 to paragraph 7 reads like this:
The special theory of relativity that Einstein developed in 1905 applies only to this special case (hence the name): a situation in which the observers are moving at a constant velocity relative to one another—uniformly in a straight line at a steady speed—referred to as an “inertial reference system.”
It’s harder to make the more general case that a person who is accelerating or turning or rotating or slamming on the brakes or moving in an arbitrary manner is not in some form of absolute motion, because coffee sloshes and balls roll away in a different manner than for people on a smoothly gliding train, plane, or planet. It would take Einstein a decade more, as we shall see, to come up with what he called a general theory of relativity, which incorporated accelerated motion into a theory of gravity and attempted to apply the concept of relativity to it.
The story of relativity best begins in 1632, when Galileo articulated the principle that the laws of motion and mechanics (the laws of electromagnetism had not yet been discovered) were the same in all constant-velocity reference frames. ...
There you see paragraphs 5 and 6, plus the first sentence in paragraph 7. At this point, we'll be moving back to the year 1632, when "the story of relativity" can best be said to have gotten its start.
We're moving back to something Galileo said in 1632. In our view, the initial murkiness of this chapter only continues as Isaacson explores this early part of "the story of relativity."
AT THIS POINT IN HIS PRESENTATION, Isaacson transitions to a question Galileo addressed in 1632. Copernicus had advanced a revolutionary idea—the idea that the earth doesn't rest motionless at the center of the universe, with everything else revolving around it.
Traditionalists made the following claim: if the earth was moving, as Copernicus said, we would be able to feel it. In his Dialogue Concerning the Two Chief World Systems, Galileo offered an argument in support of Copernicus’s view.
By modern reckoning, of course, Galileo was right and the traditionalists were wrong. By modern reckoning, the earth is moving at a very high speed around the sun, as are the other planets in the solar system.
As he discusses this historical episode, Isaacson gives a perfectly coherent account of Galileo's response to the traditionalists in support of Copernicus. And sure enough:
As Isaacson proceeds, it's fairly easy to understand what Galileo is said to have said.
This new discussion makes fairly clear sense—but does it help the general reader understand what has gone before it in Chapter Six? We would be inclined to say no, but this is the way Isaacson starts this new discussion:
The story of relativity best begins in 1632, when Galileo articulated the principle that the laws of motion and mechanics (the laws of electromagnetism had not yet been discovered) were the same in all constant-velocity reference frames. In his Dialogue Concerning the Two Chief World Systems, Galileo wanted to defend Copernicus’s idea that the earth does not rest motionless at the center of the universe with everything else revolving around it. Skeptics contended that if the earth was moving, as Copernicus said, we’d feel it. Galileo refuted this with a brilliantly clear thought experiment about being inside the cabin of a smoothly sailing ship:
If the earth was really moving, we would be able to feel it! According to Isaacson, Galileo refuted this claim with a thought experiment about a smoothly sailing ship.
At this point, we offer a warning. The first part of that paragraph may be challenging for general readers. The notion that the laws of motion and mechanics "are the same in all constant-velocity reference frames" may be about as clear as Venetian mud for such non-specialist readers.
(Possibly adding to the problem: As we noted yesterday, the use of such technical language shifts about in various ways in this chapter's opening pages.)
That said, Isaacson's treatment of Galileo's thought experiment seems fairly easy to follow. Below, you see the way Chapter Six proceeds through paragraphs 8 and 9, with Galileo quoted at length:
"Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully, have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still."
There is no better description of relativity, or at least of how that principle applies to systems that are moving at a constant velocity relative to each other.
That's the full text of paragraphs 7-9. Question:
Back in 1632, would that presentation by Galileo have convinced the skeptics that their argument was flawed? Maybe yes and maybe no. But we'll guess that today's general reader would find it reasonably easy to follow the presentation, in which Galileo was apparently saying this:
You can be inside a moving ship without having any idea that the ship is moving. Similarly, you can be riding on a fast-moving planet without experiencing any effects of that motion.
So far, so understandable! But while this may help us understand what Galileo said to the skeptics, does it help us understand what "relativity" holds, asserts or maintains? Does it help us understand the "simple concept" described by Isaacson at the start of this chapter?
At this point, Isaacson proceeds to offer a set of full-length paragraphs fleshing out the physics behind Galileo's presentation. To give you a sense of where this goes, the next four grafs say this:
Inside Galileo’s ship, it is easy to have a conversation, because the air that carries the sound waves is moving smoothly along with the people in the chamber. Likewise, if one of Galileo’s passengers dropped a pebble into a bowl of water, the ripples would emanate the same way they would if the bowl were resting on shore; that’s because the water propagating the ripples is moving smoothly along with the bowl and everything else in the chamber.
Sound waves and water waves are easily explained by classical mechanics. They are simply a traveling disturbance in some medium. That is why sound cannot travel through a vacuum. But it can travel through such things as air or water or metal. For example, sound waves move through room temperature air, as a vibrating disturbance that compresses and rarefies the air, at about 770 miles per hour.
Deep inside Galileo’s ship, sound and water waves behave as they do on land, because the air in the chamber and the water in the bowls are moving at the same velocity as the passengers. But now imagine that you go up on deck and look at the waves out in the ocean, or that you measure the speed of the sound waves from the horn of another boat. The speed at which these waves come toward you depends on your motion relative to the medium (the water or air) propagating them.
In other words, the speed at which an ocean wave reaches you will depend on how fast you are moving through the water toward or away from the source of the wave. The speed of a sound wave relative to you will likewise depend on your motion relative to the air that’s propagating the sound wave.
The first three paragraphs help us understand the physics which prevails inside a smoothly moving ship. Presumably, the same principle obtains on our fast-moving planet, which carries its atmosphere along with it as it travels through space.
This is all well and good for those who want to understand this historical dispute. By now, though, we're on the fourth page of Chapter Six, and we still may lack a clear idea of the way this succession of ruminations is meant to illuminate the "simple concept" which appeared at the start of the chapter.
Does this presentation about Galileo help the general reader explain the puzzling description of relativity which appears at the start of the chapter? We can't really see why it would.
Meanwhile, how about this statement by Isaacson: "There is no better description of relativity" than the quoted passage from Galileo.
Will the general reader be able to explain that ringing endorsement? You'd have to question the general reader, but we'll guess that he or she would have a hard time expounding on that statement.
In what way does Galileo's presentation qualify as a "description of relativity" which can't be surpassed? Indeed, in what way can it be described as a "description of relativity" at all? We'll guess that many general readers will have a hard time with such basic questions.
Alas, this Chapter Six! The chapter starts with a somewhat peculiar statement concerning what relativity asserts. At this point, four pages in, to what extent would the general reader be able to speak to that basic topic in an intelligent way?
Has relativity emerged as "a simple concept" in the mind of the general reader? Again, consider the contrast with the presentation with which we began today:
The general reader will have no problem understanding the claim that a small amount of matter can be transformed into a huge amount of energy. Similarly, the general reader will probably have little trouble understanding Galileo's defense of Copernicus' revolutionary claim.
The statement about the production of energy is easy to understand. But at this point, can we expect the general reader to be able to explain what relativity has been said to assert?
The general reader may be able to repeat or recite the words in that opening paragraph. ("Relativity asserts that the fundamental laws of physics are the same whatever your state of motion.")
The general reader may be able to repeat those words. But how well will the general reader do if he or she is questioned about that somewhat puzzling statement? Even after the passage from Galileo, we'll guess that he or she wouldn't do especially well.
By the point we've reached today, the general reader is on the fourth page of Isaacson's Chapter Six. Isaacson is making a transition to yet another basic topic, to a discussion of the nature of light.
That next discussion may or may not seem to make sense to the general reader. But how well do these brief discussions of various topics form a coherent larger discussion? How well do these short, successive discussions illuminate some major point?
On a periodic basis, we've been reading Isaacson's book for the past thirteen years. We still can't make clear sense of these opening pages of Chapter Six. We still can't answer those questions.
Unlike the brief presentation about the raisin which fueled New York, this part of Isaacson's book has always seemed remarkably murky to us. After thirteen years of parsing his text, that impression hasn't changed.
Next week, we'll be moving to a part of Chapter Six which is taken straight out of Einstein's own book for general readers. At issue is an important part of Einstein's special theory of relativity, the subject of Chapter Six.
In Isaacson's words, the passage concerns the "eureka moment" in which Einstein "took one of the most elegant imaginative leaps in the history of physics." Isaacson's presentation concerning that leap comes right out of Einstein's 1916 text—the book whose lucidity was vouched for by Einstein's awestruck teen-aged niece.
On its face, the presentation in question has never seemed to make sense. Indeed, the passage doesn't seem to make sense in a remarkably straightforward way. More than a hundred years later, it seems that no one has noticed.
Next week, we'll look at that fascinating, straightforward part of Isaacson's Chapter Six. For now, we're still struggling with the meandering way the chapter begins as Isaacson attempts to explain what relativity asserts.
Is the general reader likely to understand the opening pages of Chapter Six? Despite the blurbs by major experts on the jacket of Isaacson's book, it seems to us that the answer is no.
Tomorrow, we'll offer more thoughts on that possible state of affairs. The science was going to be hard, Isaacson says he was told.
Tomorrow (or Friday): What Brian Greene (and Charles Krauthammer) said