FRIDAY, AUGUST 6, 2021
Apparently, nobody noticed: Way back in 1916, Albert Einstein did, in fact, describe "a very long train" moving with a "constant velocity" along a railroad track.
As part of the same thought experiment, he also described two lightning strikes. He can be said to have mentioned a person standing halfway between them.
In Einstein's scenario, the lightning strikes hit the embankment alongside the railroad tracks at two distant points, A and B. Also this:
According to Einstein's imagined example, the very long train was moving away from Point A. It was moving toward Point B.
Einstein sketched this thought experiment in Chapter IX of his 1916 book for general readers, Relativity: The Special and the General Theory. To review his short presentation, you can just click here.
As he sketched this scenario, Einstein mentioned a male "observer" (a passenger) seated on the long train. He didn't mention any specific person on the railway embankment, though in our view it's perfectly reasonable to act as if he did.
Einstein sketched this "thought experiment" in Chapter IX of his book. As we noted in our last report, Walter Isaacson discusses this matter at some length in his sweeping biography, Einstein: His Life and Universe, which appeared in 2007.
What point was Einstein trying to make through this illustration? As we've noted, this is the way Isaacson describes the "key insight" which allegedly lies at the heart of this matter:
[T]he key insight was that two events that appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly. And there is no way to declare that one of the observers is really correct. In other words, there is no way to declare that the two events are truly simultaneous.
Plainly, Isaacson treats that "key insight" as a major element in Einstein's special theory of relativity, which he formulated in 1905. After describing the thought experiment involving the train and the lightning strikes, Isaacson quotes Einstein from Chapter IX, then offers his own assessment:
“We thus arrive at the important result: Events that are simultaneous with reference to the embankment are not simultaneous with respect to the train,” said Einstein. The principle of relativity says that there is no way to decree that the embankment is “at rest” and the train “in motion.” We can say only that they are in motion relative to each other. So there is no “real” or “right” answer. There is no way to say that any two events are “absolutely” or “really” simultaneous.
This is a simple insight, but also a radical one. It means that there is no absolute time. Instead, all moving reference frames have their own relative time. Although Einstein refrained from saying that this leap was as truly “revolutionary” as the one he made about light quanta, it did in fact transform science. "This was a change in the very foundation of physics, an unexpected and very radical change that required all the courage of a young and revolutionary genius," noted Werner Heisenberg, who later contributed to a similar feat with his principle of quantum uncertainty.
In Isaacson's treatment, the thought experiment involving the train and the lightning strikes was based on a simple but radical insight. This radical insight produced a transformative change, "a change in the very foundation of physics."
In Isaacson's treatment, Einstein's thought experiment showed that "there is no way to say that any two events are 'absolutely' or 'really' simultaneous"—and the whole thing stemmed from that initial key insight. Here it is once again:
Two events which appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly.
According to Isaacson, that "key insight" produced a radical change in the world of physics. It came to Einstein in a "eureka moment"—a moment which led him to take "one of the most elegant imaginative leaps in the history of physics."
To Isaacson and almost everyone else, this "relativity of simultaneity" is a major component of Einstein's universe That said, there's a major problem with Isaacson's assessment of this important matter:
Isaacson's description of Einstein's "key insight" just doesn't seem to make sense.
Two events which appear to be simultaneous to one observer will not appear to be simultaneous to another observer who's moving rapidly? In some situations, that will be true—but in other situations, it won't be! And that's just the start of the problem with the formulation we've quoted.
On it's face, Isaacson's account of Einstein's "key insight" just doesn't make any sense. In order to see why that's true, let's consider an hour-long PBS broadcast which aired in November 2015.
That PBS program, Inside Einstein's Mind, was a production of Nova. Because Nova dumbed this matter down a bit, its broadcast makes it easier to see why this whole high-level shebang has never made any sense.
THE NOVA BROADCAST AIRED in November 2015. It was designed as a hundred-year commemoration of Einstein's general theory of relativity, which Einstein formulated in November 1915.
That said, the Nova broadcast started at the beginning. Roughly eight minutes into the program, Nova reviewed that thought experiment from the earlier part of Einstein's career—the one which featured the very long train and the two lightning strikes.
In certain ways which seem perfectly reasonable, Nova made the scenario a bit easier to describe and to follow. Nova's narrator said that Einstein had specifically pictured a man standing on a railway platform as a train went by. The narrator further said that Einstein had pictured a woman passenger on the train—and the narrator said that the train was moving "at close to the speed of light."
(To watch this part of Nova's broadcast, you can just click here.)
These were minor editorial changes to Einstein's original text. At least on their face, they strike us as reasonable—and they make the imagined situation easier to discuss and describe.
What was the source for Nova's treatment of this "thought experiment?" We'll take a guess—Nova may have been working directly from Isaacson's book, since Isaacson was one of the several major figures who appeared periodically as "talking heads" on the PBS program.
At any rate, as Nova proceeded, it simplified the matter—arguably, dumbed it down— in a way which turned out to be instructive.
Indeed, if Nova was working from Isaacson's somewhat jumbled text, they simplified it considerably. Below, you see the transcript of Nova's presentation:
ISAACSON: [Einstein] realized that any statement about time is simply a question about what is simultaneous. For example, if you say the train arrives at seven, that simply means that it gets to the platform simultaneous with the clock going to seven.
NARRATOR: In a brilliant thought experiment, [Einstein] questions what "simultaneous" actually means, and sees that the flow of time is different for an observer that is moving versus one that's standing still.
He imagines a man standing on a railway platform. Two bolts of lightning strike on either side of him. The man is standing exactly halfway between them, and the light from each strike reaches his eyes at exactly the same moment. For him, the two strikes are simultaneous.
Then Einstein imagines a woman on a fast moving train. Travelling at close to the speed of light, what would she see?
As the light travels out from the strikes, the train is moving towards one and away from the other. Light from the front strike reaches her eyes first. For the woman on the train, time elapses between the two strikes; for the man on the platform, there is no time between the strikes.
This simple thought has mind-blowing significance. Simultaneity, and the flow of time itself, depends on how you're moving.
(For Nova's full transcript, click here.)
Some parts of that short presentation are bafflegab. For starters, we'll advise you to ignore the narrator's remarks about "the flow of time." Stick to what the narrator says about "simultaneity."
Stating the obvious, this account of Einstein's thought experiment parallel's Isaacson's account:
Nova says that simultaneity "depends on how you're moving." Isaacson said that events which appear to be simultaneous to one observer will not appear to be simultaneous to someone who's moving rapidly.
Nova says that this simple thought "has mind-blowing significance." Isaacson said that Einstein's simple but radical insight produced a transformation of physics. The two accounts are virtually identical, but Nova's account is extremely concise.
Nova's account in quite concise. According to Nova, this is what was going on in that "brilliant thought experiment:"
For the man who's standing on the railway platform, "the two strikes are simultaneous," the Nova narrator says. For the woman on the fast-moving train, "time elapses between the two lightning strikes."
Rather plainly, that seems to mean that the two strikes "are not simultaneous" for the woman on the train. According to Nova's summation, this means that "simultaneity depends on how you're moving."
Except for one rather basic word change—Nova dropped the word "appears"—this concise presentation mirrors Isaacson's more convoluted account. According to Nova's concise presentation, here's what's going on:
In Nova's treatment, the man is standing on a railway platform. The woman is moving past at a high rate of speed.
For the man, the two lightning strikes are simultaneous. For the woman, they aren't.
Isaacson used the word "appeared." Nova spoke more simply.
That said, Isaacson's presentation didn't make sense. Eight years later, neither did Nova's.
AT LONG LAST, IT'S TIME TO EXPLAIN why Isaacson's account doesn't make sense. In his account, the story of the two lightning strikes illustrates this "key insight:"
Two events which appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly.
The lightning strikes appear to be simultaneous to the man on the railway platform. They don't appear to be simultaneous to the woman who's moving rapidly past him. According to Isaacson (and later according to Nova), this is supposed to illustrates a "mind-blowing" point about the way a pair of events will seem, depending on an observer's state of motion.
In reality, no such thing has been illustrated. It's time to explain why we say that.
FOR STARTERS, IT'S TRUE! In the specific situation which has been described, the lightning strikes will appear to be simultaneous to the man on the platform. Also, they won't appear to be simultaneous to the woman on the train.
Having said that, so what? To some other people on that fast-moving train, the lightning strikes will appear to be simultaneous. And to many other people standing on the railway platform, the strikes won't appear to be simultaneous, as they do to that one well-positioned man.
As a general matter, the state of motion of these observers has nothing to do with the appearance of simultaneity! Let's go into more detail:
As noted in the original story, the woman on the train is directly adjacent to the man on the platform when the two lightning strikes hit. But uh-oh! By the time the light from the lightning strikes arrives at the railway platform, she has moved far down the track.
The man is exactly halfway between the strikes. For that reason, light from the two strikes reaches him at the same time, and they appear to be simultaneous. By now, though, the woman on the fast-moving train is closer to the lightning strike which hit at Point B.
For that bone-simple reason, the light from lightning strike B will reach her before the light from lightning strike A. For that reason, the two strikes won't seem to be simultaneous to her.
In this particular case, the man is standing on the platform and the woman on the train is moving rapidly past him. But now consider another case. Consider the case of a second woman—a woman who's seated a hundred cars back inside this very long train.
The case of the second woman:
A second woman, Woman 2, is riding on this train. She's seated a hundred cars back from the original woman, Woman 1. As a matter of fact, she may be seated all the way back at the rear end of the train!
When the lightning strikes hit, this second woman is closer to lightning strike A; she's farther away from lightning strike B. But uh-oh! By the time the light arrives, she has drawn directly adjacent to the man on the railway platform!
As with that man, so too with this woman. Because of where she now finds herself, the light from the two lightning strikes will reach her at the same time!
For this woman, Woman 2, the lightning strikes will appear to be simultaneous! She's moving at the same high speed as Woman 1, but the lightning strikes will seem to be simultaneous to her.
This has now become a tale of two women. Each is moving at the same rate of speed. But for Woman 2, "the lightning strike are simultaneous." For Woman 1, "time elapses between the two strikes."
Einstein's key insight, as described by Isaacson, has already broken down. To make matters worse, let's consider the case of the additional men.
The case of the additional men:
The original man—we'll call him Ishmael—was standing on the railway platform. By Einstein's stipulation, he was exactly halfway between the two distant lightning strikes.
That said, the train is a very long train—and it's hurtling past a very long railway platform. With that in mind, consider two additional men—men who are standing at the far ends of this very long platform.
One of these men—we'll call him Man 2—is at the end of the platform which is closer to lightning strike A. Another man—we'll call him Man 3—is standing at the end of the platform which is closer to lightning strike B.
Man 3 is closer to lightning strike B; he's farther away from lightning strike A. For that reason, light from the two lightning strikes won't reach him at the same time!
For him, the lightning strikes won't appear to be simultaneous, even though he's standing stock still on the railway platform, exactly as Ishmael is.
Light from the two lightning strikes will reach our original man at exactly the same time. But that won't be true for Man 2, and it won't be true for Man 3. For them, time will elapse between the two strikes—and for that reason, the lightning strikes will not appear to be simultaneous.
All three men are standing on the railway platform. None of the three is in motion. But for one, the lightning strikes appear to be simultaneous. For the other two men, they do not.
Back to that key insight:
At this point, we return to Isaacson's account of Einstein's "key insight." By now, we should be able to see why it doesn't make sense.
Allegedly, the key insight was this: two events which appear to be simultaneous to one observer will not appear to be simultaneous to another observer who is moving rapidly.
Within the context of this thought experiment, that presentation has now broken down.
In some specific circumstances, that sweeping claim will turn out to be accurate. In some circumstances, two events will appear to be simultaneous to someone who is standing motionless, but will not appear to be simultaneous to someone else who's moving rapidly.
That will be true in some cases—but in other cases, it won't be! Indeed, given the scenario with which we're working, it won't be true is most cases.
Given the scenario with which we're working, the lightning strikes will appear to be simultaneous only to someone who is positioned exactly halfway between them (or is equidistant from them). But for everyone else—for people all through the surrounding area—the lightning strikes won't appear to be simultaneous.
That will be true for people who are in rapid motion; it will be true for other people who aren't. It isn't a question of their state of motion. It's a question of their position with respect to the two lightning strikes.
Nova and Isaacson convey a false impression. Without explicitly saying so, they seem to say that questions of simultaneity will always seem different to two people who are in relative motion.
It's hard to see why that would be true. On its face, their shared presentation just doesn't seem to make sense.
Something else is hard to see. At least as this matter has been described, it's hard to see how a revolution in physics could have emerged from this twaddle. And yet, the twaddle has come from a major, well-received book whose contents were fly-specked by a dozen major physicists, and from a journalistic organization thought of us one of our best.
DID EINSTEIN MAKE SOME SORT of mistake in Chapter IX of his historic 1916 book?
We don't know how to answer that question, though it's certainly possible that he could have. (Einstein was a genius as a theoretical physicist, not as a popular writer. He also wasn't an all-star shortstop or a master chef.)
In his presentation, Einstein used more technical language that Isaacson or Nova later did. Speaking as a general reader, we'd have to say that Isaacson's treatment seems to follow reasonably from what Einstein seems to have written. It's just that Isaacson didn't realize that his presentation of Einstein's "key insight" doesn't seem to make any sense.
On its face, Isaacson's presentation didn't make sense; eight years later, neither did Nova's. This is a point of special interest because Isaacson's scientific work was reviewed by all those major physicists, starting with Brain Greene himself, and because Nova is generally believed to work from the brainiac end of our vaunted PBS.
Did none of those physicists notice the fact that Isaacson's presentation of this seminal principle didn't seem to make sense? Eighty-nine years after Einstein's book first appeared, how could that be possible?
Also, please note:
Isaacson and Nova both quote major physicists saying that Einstein's treatment of this matter illustrates a transformative, mind-blowing point.
In the case of Nova, Sean Carroll instantly vouches for the claim that Einstein's insight was "mind-blowing." Unfortunately, as presented in the Nova program itself, the whole thing simply doesn't make sense.
Nova's treatment of this matter doesn't make a lick of sense. It may be the worst explanations we've ever seen of any matter, scientific or otherwise.
That said, so it goes! Borrowing from the old Soviet joke, so it goes as they pretend to explain Einstein's universe, and we pretend to get it!
Again and again, attempts to explain Einstein's universe have come to us from the higher ends of the journalistic, academic and publishing worlds. They come to us in Brian Greene's books, and in endless PBS programs.
These attempts to make Einstein easy pretty much always fail. Two recent attempts to make Gödel easy have also plainly failed, including one which was favorably blurbed by everyone from Steven Pinker on down.
They pretend to explain Einstein's universe. We pretend that they've done it! They jangle the chains of academic authority and we quickly defer. Ironically, Isaacson makes a key point in his excellent treatment of Einstein's life:
Einstein's genius was closely tied to his lifelong refusal to do that.
In part, this is an artifact of anthropology, of our basic human imperfections. More specifically, it's a reflection of the flight of the logicians, of their long-standing failure to serve.
As deeply imperfect creatures, we humans have a crying need for the skills of clarity and cogency. But our logicians walked off their posts long ago, and there's no sign that they plan to return.
The logicians have walked away from their posts! As the weeks and months roll by, we'll eventually get to that point. This will take us to Wittgenstein's muddled but valuable work, and also to Horwich's claim.
Next week: "Appearance" and its discontents