WEDNESDAY, JULY 21, 2021
Very, very hard to explain, but easy to "envision:" Many parts of Einstein's universe are hard to understand.
Indeed, that's true of modern physics in general, including the parts of modern physics which emerged in the decades after Einstein's breakthroughs. Just consider what Brian Greene said.
Brian Greene knows a boatload of math and physics. He's a professor of physics and mathematics at Columbia University. In his spare time, he's the director of Columbia’s Center for Theoretical Physics.
As such, Greene is a high-ranking academic. That said, he's best known in the wider world for his books about modern physics intended for general readers.
The first of these books was The Elegant Universe: Superstrings, Hidden Dimensions and the Quest for the Ultimate Theory (1999). Next came The Fabric of the Cosmos: Space, Time, and the Texture of Reality (2004). Other such volumes have followed.
Did those books, and those PBS programs, make Einstein (and the rest of modern physics) accessible to the general public, possibly even easy? We'll sign up as hard skeptics on that point. We may attempt to address that question as the weeks roll along.
That said, the task is very hard. Here's part of "A Conversation with Brian Greene," an interview published by Nova in connection with the 2003 series on PBS:
NOVA: Do you think there are limits to how much we can know about the universe?
GREENE: I don't know. I'd like to think that there aren't, but I suspect that's a little optimistic. An analogy that's used in the NOVA program that I'm quite fond of is: We are certainly aware of intelligent beings on this planet whose capacity to understand the deep laws of the universe is limited. No matter how hard you try to teach your cat general relativity, you're going to fail. There we have an example of an intelligent living being that will never know this kind of truth about the way the world is put together. Why in the world should we be any different? We can certainly go further than cats, but why should it be that our brains are somehow so suited to the universe that our brains will be able to understand the deepest workings?
We humans may not be built to understand this stuff, Greene has frequently said. We're inclined to think that these cautionary statements by Greene are extremely wise.
Let's return to Einstein's work—to his universe alone. As Greene has noted in both of the books we've cited, certain parts of Einstein's universe are very hard to internalize, visualize, fully grasp, intuitively understand.
As his interview with Nova continued, he went into more detail on this general point of concern. In this, the very next exchange, he's discussing a realm of physics which came after Einstein, but the point he's making would apply to Einstein's universe too:
NOVA: Well, for example, most people have trouble envisioning a fourth spatial dimension. Can you?
GREENE: No. I cannot envision anything beyond three dimensions. What I can do is I can make use of mathematics that describe those extra dimensions, and then I can try to translate what the mathematics tells me into lower dimensional analogies that help me gain a picture of what the math has told me. But the picture is certainly inadequate to the task of fully describing what's going on, because it's in lower dimensions, and in higher dimensions, things are definitely different.
To tell you the truth, I've never met anybody who can envision more than three dimensions. There are some who claim they can, and maybe they can; it's hard to say. But it's very hard, when your brain is involved in a world that appears to have three dimensions and is well suited to envisioning that world, to go beyond that and imagine more dimensions.
Greene can't "envision" basic parts of this puzzling new cosmos. He can only "make use of mathematics," then attempt to "translate what the mathematics tells him" into helpful analogies.
In the end, those analogies may or may not be helpful for the general reader. In the end, it all depends on the particular writer's skill. But as Greene himself has frequently said, understanding modern physics is just intrinsically hard—or at least, it's very hard in a wide range of basic respects.
Understanding modern physics is often intrinsically hard. The same is true for that part of modern physics which constitutes "Einstein's universe." But as we noted yesterday, certain parts of Einstein's universe are actually easy to understand. The example we gave involed the conversion of matter into energy.
We may not understand the process by which this happens, but it's easy to see that (what we think of as) an enormous amount of energy can be produced from (what we think of as) a fairly small amount of matter. As we noted yesterday, that elementary fact is easy to report and describe.
For that reason, it's easy to "envision." And in that sense, it's easy to understand.
Early in The Elegant Universe, Greene offers two other examples. He does so as he describes a finding which emerged from Einstein's special theory of relativity (1905).
Special relativity "makes the strange claim that observers in relative motion [to each other] will have different perceptions of distance and of time," Greene says in Chapter 2 of The Elegant Universe. He then provides a pair of examples to help readers picture what this means:
The first example: In the first example, Slim and his brother Jim are each measuring the speed of Slim's very fast new Trans Am. Using identical stopwatches, the brothers measure the time it will take for Slim to drive the length of a race track in this fast new car.
Slim is timing himself, using a stopwatch inside his car. Using an identical stopwatch, Jim is timing Slim as he stands alongside the track.
Slim is doing 120; Jim is standing still. According to special relativity, Greene says their (identical) stopwatches will not agree on the amount of time which elapses as Slim roars down the track.
The difference in measurement will be very small, Greene says. But the difference will happen every time, and it won't be an artefact of the brothers' stopwatches. If everything about this process goes right, the two stopwatches will not agree on how much time has elapsed.
The second example: In the second example, Jim is trying to measure the length of Slim's car as it speeds down the track. Slim has already measured the length of the car as it sat in the showroom.
According to special relativity, these two measurements will not be the same, Greene says. Again, the difference here will be quite small, but there will be a difference every time if the measurements are conducted correctly.
These examples may seem underwhelming, but they're easy to describe and they're easy to understand. Using identical stopwatches and identical measuring sticks, the two brothers will not agree on the length of time which has passed, or on the length of the car.
We may not understand why these differences would occur, but it's easy to see what's being described in these two examples. In that sense, this limited part of Einstein's universe is easy to "envision" and, in that sense, to understand.
In his subsequent book, The Fabric of the Cosmos, Greene provides a much more dramatic example of the peculiar way Einstein's work changed our comprehension of the universe. You may find it hard to believe what Greene is saying in this example, but what he's saying is easy to "envision" and to understand.
The heading in Greene's book is this: "The Puzzles of Time Travel." Brian Greene starts with this:
When Einstein discovered the nature of special relativistic spacetime, he laid out a blueprint for fast-forwarding to the future. If you want to see what's happening on planet earth 1,000, or 10,000, or 10 million years in the future, the laws of Einsteinian physics tell you how to go about it. You build a vehicle whose speed can reach, say, 99.999999996 percent of light speed [the speed of light]. At full throttle, you head off into deep space for a day, or ten days, or a little over twenty-seven years according to your ship's clock, then abruptly turn around and head back to earth, again at full throttle.
At this point, even Jeff Bezos can't construct such a speedy space ship. But it's easy to picture what Greene is saying here—and here's what would happen if you took that high speed trip into space, according to Greene's account of Albert Einstein's universe:
On your return, 1,000, or 10,000, or ten million years of earth time will have elapsed. This is an undisputed and experimentally verified prediction of special relativity; it is an example of the slowing of time with the increasing of time described in Chapter 3 [of Greene's book].
It may be hard to believe that any such thing would actually happen. It may be hard to explain why any such thing would or could occur.
That said, it's easy to understand what Greene is saying here. This part of Einstein's universe is easy to report or describe, and it's easy to "envision." In that sense, and to that extent alone, this particular part of Einstein's universe is easy to understand.
Indeed, how easy is it to envision this part of Einstein's universe? So easy that moviegoers saw it envisioned in the 1968 film, Planet of the Apes!
In the film, Charlton Heston travels at high speed into space, then accidentally ends up back on a vastly-changed Earth. This produces a famous surprise ending, but here's the way the famous film is said to begin:
Astronauts Taylor, Landon, and Dodge awaken from deep hibernation after a near-light-speed space voyage...Their spacecraft crashes into a lake on an unknown planet and the men abandon the sinking vessel. Before bailing out, Taylor reads the ship's chronometer as November 25, 3978, two thousand and six years after their departure in 1972.
At the end of the film, that "unknown planet" will turn out to be the Earth. Two thousand years have passed on Earth, but the handsome trio of astronauts have barely aged at all.
Planet of the Apes wasn't intended to present perfectly accurate science. That said, it did offer a picture of the type of "time travel" Greene describes in The Fabric of the Cosmos.
It may be hard to understand how or why an event like that could happen, even in theory. But it isn't hard to describe what special relativity predicts. In that sense, and to that extent, it isn't hard to envision or understand this part of Einstein's universe.
In this sense, some parts of Einstein's universe are actually quite easy. Most parts are extremely hard.
Much as Charles Krauthammer said in his 1988 column, Greene can proceed ahead through his knowledge of the mathematics. General readers are forced to rely on the analogies he constructs, and on the skill displayed by such writers when they form these allegedly helpful pathways to comprehension.
Brian Greene know tons of physics and math. But things can go badly wrong even when brilliant theorists like Greene start constructing analogies.
In his 1916 book for general readers, Einstein himself had trouble making Einstein easy. Borrowing on Greene's example, a house cat could never make Einstein easy—but it isn't clear that we humans are extremely well equipped for this task ourselves.
This is where the pitfalls of human reasoning begin to make their appearance. The later Wittgenstein lurks and cringes as misshapen language appears.
Tomorrow, we'll visit a very strange passage from Chapter 2 of The Elegant Universe. We'll also look in on a puzzling first attempt to make Kurt Gödel easy.
How well are we humans built for such tasks? We think Greene has been very wise as he's offered his words of warning.
Tomorrow or Friday: An extremely peculiar passage
Next week: "Relativity is a simple concept." One writer's famous last words?