FIRST REACTIONS: Isaacson calls spacetime a "fabric!"

THURSDAY, FEBRUARY 25, 2016

Part 4—The Beatles called it Arthur:
For the last time, we're going to show you what Walter Isaacson said.

In almost all settings, Isaacson is an extremely clear writer. In his best-selling book, Einstein: His Life and Universe, the passages about Einstein's life are lucid, clear, interesting, intriguing.

Then we come to the passages—and the chapters—concerning "Einstein's universe," by which we mean his science. Below, we once again see an early attempt at explaining a famous part of that science.

Granted, we're still in Chapter One of Isaacson's best-selling book. That said, how many readers had any idea what this passage meant?
ISAACSON (pages 3-4): [I]n 1915, [Einstein] wrested from nature his crowning glory, one of the most beautiful theories in all of science, the general theory of relativity. As with the special theory, his thinking had evolved through thought experiments. Imagine being in an enclosed elevator accelerating up through space, he conjectured in one of them. The effects you'd feel would be indistinguishable from the experience of gravity.

Gravity, he figured, was a warping of space and time, and he came up with the equations that describe how the dynamics of this curvature result from the interplay between matter, motion, and energy. It can be described by using another thought experiment. Picture what it would be like to roll a bowling ball onto the two-dimensional surface of a trampoline. Then roll some billiard balls. They move toward the bowling ball not because it exerts some mysterious attraction but because of the way it curves the trampoline fabric. Now imagine this happening in the four-dimensional fabric of space and time. Okay, it's not easy, but that's why we're no Einstein and he was.
How many readers had any idea what Isaacson was talking about in that passage? Just for starters, we'll offer this guess:

Roughly essentially none.

By that, we mean this: We'll guess that very few readers could answer even the simplest questions about the various statements made in the passage. To consider the various sources of confusion in those two paragraphs, click here to peruse Tuesday's post.

In the good-natured jest at the end of that passage, Isaacson himself seems to say that this passage is perhaps quite unclear. A fair-minded person would want to see if Isaacson unpacks this confusion in the later chapters he devotes to the science.

(Examples: Chapter Six, Special Relativity. Also, Chapter Nine, General Relativity.)

Is the work in those chapters clear? We'll set that aside for another day. For today, let's look at Kevin Drum's first reaction to the puzzles offered here.

We do so because Drum is smart. Also, because a few of his commenters were so dittoheaded that they reacted as such figures will typically do—by saying the whole thing is perfectly clear, and that you'd have to be an ass to challenge our exalted professors, who have been nice enough to hand us the metaphors we should recite for the rest of recorded time.

The dittoheads are always with us—and yes, they even exist over here, in our own self-impressed tribe. That said, Drum is not a dittohead, and he undertook, in last Saturday's post, to address a question we had raised about the presentation of this material in best-selling books, even on the front page of the New York Times.

Last Thursday, we commented on the sources of confusion found in Isaacson's passage. In the process, we apparently offered this deathless remark, spoken on behalf of the shlubs of the world:

No one has the slightest idea what Isaacson means when he refers to "the four-dimensional fabric of space and time." We all can picture that trampoline—but none of us knows how to imagine that "four-dimensional fabric!" Nor does Isaacson give us the tools to do so, or notice that he has failed.

In a perfectly sensible way, Drum undertook to explain what "the four-dimensional fabric of space and time" actually is. He offered this presentation, whose accuracy and completeness we aren't equipped to assess:
DRUM (2/20/16): As it turns out, explaining the "fabric" of spacetime isn't hard. Yes, it's four-dimensional. But all this means is that you define it using four numbers. If you described me via my age, weight, height, and IQ, that would be a "four-dimensional" representation of Kevin Drum. It's not a big deal.

Now suppose you want to describe an event. You need to specify where it happened and when it happened. Take, for example, the airplane crashing into World Trade Center 1. It happened at 40.71º latitude, -74.01º longitude, and 6,371 kilometers (relative to the center of the earth) at 13:46:30 GMT on 11 September 2001 (relative to the common era calendar). As an event in spacetime it's represented by an ordered 4-tuple:

(40.71, -74.01, 6371, 2001.09.11.13.46:30)

There are other events that happened at the same time in other places (me saying "oh shit" in California); at the same place in other times (breaking ground on WTC 1 in 1966); and entirely different times and places (the Battle of Gettysburg). If you collect every possible location of an event ever—that is, every combination of four numbers specifying times and places in the universe—that's all of spacetime. Physicists are likely to call it a manifold or a Minkowski space.
"This is all pretty simple," Drum goes on to say. As presented, we'll agree with that statement.

In fairness, it isn't clear why someone would want to "collect every possible location of an event ever—that is, every combination of four numbers specifying times and places in the universe."

It isn't clear what you'd do with this collection once you were done, if you ever could be.

But if that's all Isaacson meant by "the four-dimensional fabric of space and time," it seems that he was working with some fairly simple concepts. Only one question remains:

Why did he use the word "fabric?"

Sadly, our question is important. When Isaacson refers to "space and time" as a "fabric," it lets him employ the picture of that infernal trampoline, a picture which will be familiar to readers of Einstein-made-easy books.

The problem continues from there. When Isaacson refers to "space and time" as a "fabric," this lets him tell us to picture a bowling ball rolling onto a trampoline, then to imagine something dropping onto "the four-dimensional fabric of space and time" in some similar way. Somehow or other, this is supposed to help us understand gravity, which he has already said is "a warping of space and time."

Alas! It's easy to "picture what it would be like to roll a bowling ball onto the two-dimensional surface of a trampoline." That doesn't tell us why Isaacson then decided to compare "space and time" to that trampoline. It doesn't tell us what he means when he says that space and time constitute a "four-dimensional fabric."

Sadly enough, it doesn't tell us why he referred to space and time as a "fabric" at all! We the readers of simplified books are left on our own with that!

"Okay, it's not easy," Isaacson says, "but that's why we're no Einstein and he was." For ourselves, we'd offer a different explanation. We'd say it isn't easy because Isaacson has made no attempt to explain the peculiar things he has said!

In last Saturday's post, Drum explained what "spacetime" is. This is a step Issacson skipped in the passage we posted.

Let's assume that Drum's account of "spacetime" is accurate and complete. Having done that, let us also ask this:

Even now, do you have any idea why you, or anyone else, should regard spacetime as a "fabric?"

In Drum's account, which is perfectly lucid, "spacetime" sounds like a giant collection of data. So why on earth would someone want to call it a fabric? Why wouldn't you call it "a page full of numbers," or maybe "a vat of ball bearings?"

If we might borrow from the Beatles, why shouldn't we just call it Arthur?

(Reporter: "What would you call that hairstyle you're wearing?" George Harrison: "Arthur." Click here, move to 0:54.)

Why did Isaacson say that "space and time" are some sort of "fabric?" Uh-oh! As readers of Einstein-made-easy books know, this is a common notion.

Indeed, Professor Greene's second best-selling book was called The Fabric of the Cosmos: Space, Time and the Texture of Reality. In Isaacson's "Acknowledgments" chapter, he thanks Greene first among the seventeen different physics professors who helped him craft the science in the book. (Greene "honed the wording of the science passages," Isaacson says.)

That said, here's our question: Does Isaacson ever explain the way in which space and time can be considered a "fabric?" How about Professor Greene? How clearly does he explain this metaphor, concept, description in his own best-selling book?

Following Frost, we'll set that aside for another day. In closing, though, we'll show you one more thing Drum said as he explained spacetime. We'll continue a bit beyond what we posted before. This time around, we'll highlight just one remark by Drum:
DRUM (2/20/16): As it turns out, explaining the "fabric" of spacetime isn't hard. Yes, it's four-dimensional. But all this means is that you define it using four numbers. If you described me via my age, weight, height, and IQ, that would be a "four-dimensional" representation of Kevin Drum. It's not a big deal.

Now suppose you want to describe an event. You need to specify where it happened and when it happened. Take, for example, the airplane crashing into World Trade Center 1. It happened at 40.71º latitude, -74.01º longitude, and 6,371 kilometers (relative to the center of the earth) at 13:46:30 GMT on 11 September 2001 (relative to the common era calendar). As an event in spacetime it's represented by an ordered 4-tuple:

(40.71, -74.01, 6371, 2001.09.11.13.46:30)

There are other events that happened at the same time in other places (me saying "oh shit" in California); at the same place in other times (breaking ground on WTC 1 in 1966); and entirely different times and places (the Battle of Gettysburg). If you collect every possible location of an event ever—that is, every combination of four numbers specifying times and places in the universe—that's all of spacetime. Physicists are likely to call it a manifold or a Minkowski space. For laymen, fabric is fine.

This is all pretty simple. You might not know the mathematics for dealing with arrays of four numbers at a time, but it's well developed. And if you combine that with a few other concepts—like the idea that the speed of light is always constant—you'll eventually end up with the theory of gravitational attraction that's called general relativity.
"For laymen, fabric is fine?" He seems to be saying it's close enough for Einstein-made-easy work!

Our passage from Isaacson turns on the concept that "space and time" can be regarded as some sort of "fabric." Once we've agreed to regard "space and time" that way, we can imagine some counterpart to those bowling balls creating curving and warping.

That said, in what way can "space and time" be regarded as a fabric? Why would anyone say such a thing? Under the circumstances, this seems like an obvious question.

Alas! After explaining nothing, Isaacson simply says the whole thing is hard. After explaining what "spacetime" is, Drum simply says that the "fabric" metaphor, comparison or description is "fine for laymen!"

Copy and recite!

To his credit, Drum accepted the Einstein-made-easy challenge in a pair of posts. Routinely, Drum does excellent work. In this case, though, in the end, even he left us shlubs on our own.

Einstein-made-easy is very hard work! In our view, it's part of a fascinating culture—an upper-end culture of incomprehension. This culture suffuses the failing work of our unhelpful academic and journalistic elites.

Coming next: Nova tackles the plight of the lady on the fast-moving train

20 comments:

  1. Dave the Guitar PlayerFebruary 25, 2016 at 12:12 PM

    Although Bob fails to see it, Kevin's "page full of numbers" is not random (like a vat of ball bearings). Each number is connected to all the other numbers in a specific manner. This interconnection is why it is commonly referred to as a "fabric", where each thread is woven together with other threads and they are affected by each other. Isaacson apparently felt he did not need to explain his analogy, but apparently he did.

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    1. You think those numbers are connected? In what way? Simply because they are not random?

      No, he uses the analogy of fabric because the trampoline is a fabric. And 3-dimensional space is supposed to be as bendable as the trampoline.

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    2. Dave the Guitar PlayerFebruary 26, 2016 at 12:33 PM

      Dr. T - I'm guessing from your response that you don't believe that space-time-matter is all interconnected. This would certainly make it difficult to explain what Einstein was trying to say without first using the hard math to prove it to you. Do you believe that time is relative?

      Delete
  2. Why does everyone refer to the trampoline as two dimensional? Once the bowling ball drops onto it and it sags down, isn't it three dimensional?

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    1. We are supposed to imagine it as two dimensional creatures who cannot see that their two dimensional reality is bent in a third dimension.

      In the same way, we are supposedly three dimensional creatures, who, unless they have studied higher math, cannot see that our three dimensional reality is bent in a fourth dimension.

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  3. To expand on Dave's comment: the fabric is a "metric" and from this metric we may construct the Riemann and Ricci curvature tensors and then we can state the Einstein field equations. I'm sorry that can't be popularized. You have to devote a few years to physics and mathematics.

    Maybe Bob's complaint, that the books for laymen don't really explain it, is valid.

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    Replies
    1. What's a "metric"?

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    2. Sadly, your question is important.

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    3. Aha, but it HAS been popularized.

      And once popularized, people who have studied very little physics and math will (or have) rush(ed) to compliment the emperor on his new clothes.

      Or shall I say - the FABRIC of his new clothes.

      But Riemann, Ricci, tensors? That's some serious esoterica there.

      Delete
  4. What, no bafflegab?

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  5. Just be glad you don't have to explain Minkowski!

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  6. You asked:"in what way can "space and time" be regarded as a fabric? Why would anyone say such a thing? Under the circumstances, this seems like an obvious question." The notion is that they are not independent, and that they affect one another, time and space being aspects of something called "spacetime." Unfortunately, "fabric" is about as good a metaphor as various authors have been able to come up with, a thorough understanding of relativity requiring understanding physics after Newton and high level math. So us schlubs are stuck with only somewhat adequate metaphors.

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  7. Drum leaves out quite a few things though. Mainly, he seems to feel that the earth is stationary. As I sit motionless in my easy chair putzing around on the internets for an hour, I am actually also hurtling through space.

    First, the earth is rotating, spinning around the center of gravity of the earth-moon system at about 1,000 mph. Second the earth is revolving, spinning around the center of the sun-earth system at about 66,000 mph. Third, the galaxy is spinning, so the solar system is moving around the center of the Milky Way-Sun system at who know how fast (the google machine digs up a speed of 515,000 mph). Fourth, they say the universe is expanding (language, but it is really not) So the milky way is hurtling at some unknown speed away from the center of the universe.

    So giving coordinates on the surface of the earth as if those represent fixed coordinates in space is not accurate, but in order to make any sense, a person must have a starting point, chosen here as the center of the earth.

    Modern physics, instead of describing three dimensions of space with objects changing their positions in it over time - chooses to describe reality as if there were actually four dimensions - x,y,z, and t. Stuck inside a three dimensional reality, we cannot even visualize 4 dimensions except in mathematical equations. After all the y axis is 90 degrees from the x axis. The z axis is 90 degrees from both x and y. Now insert the t axis, 90 degrees from x,y, and z.

    Good luck, and may the force be with you.

    Go back to that bowling ball on the trampoline. Instead of rolling some mindless marbles at it, let's put Antman in a working hot wheels car. Send him on the same path as a marble (or a light beam). Well, instead of blindly being pulled towards the bowling ball, Antman has the option, does he not, of turning the wheel and hitting the gas, so that he continues to drive in a relatively straight line?

    How is that possible, modern physicist, if space is really being bent? A simple car is somehow un-bending it?

    Fun questions for a college sophomore who wants to believe he can understand the universe, and somewhere people are getting paid decent money to engage in this kind of mental masturbation, but now that the mail has been delivered, I will take another beer.

    yours,
    Cliffy

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    1. Dave the Guitar PlayerFebruary 26, 2016 at 12:41 PM

      Yes, space is being bent. In a classic experiment they measured the light from a star as it passed our sun (a large local mass). The path of the light was not straight, but bent, as predicted by Einstein. This is not just a theory, but a measurement.

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    2. If space wasn't bent, why does Antman need to turn the wheel to go straight?

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    3. space is bent or light is bent? how can nothing be bent. space is nothing, yes? if space is being bent, what is being bent?

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  8. The definition of "fabric" includes "form" and "construction" and "framework." The textile meaning of the term we use most often came from that definition and not the other way around. To use trampoline fabric is just plain ridiculous since the first use of "fabric" for spacetime referred to the fundamental definition, not a textile metaphor.

    Sadly when physics is popularized it's in the form of someone minimally impressive like Neil Degrasse Tyson gathering a following of worshipping lefties who confuse credibility with zealous but banal political views.

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    ReplyDelete
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    ReplyDelete