FRIDAY, APRIL 29, 2016
Interlude—Truthfully, clear as mud: One hundred years ago, Albert Einstein wrote a brief book aimed at general readers.
To peruse the entire book, click here. In the preface to the book, Einstein stated his general intention:
"The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics," Einstein wrote.
"The book presumes a standard of education corresponding to that of a university matriculation examination," he further said. "Despite the shortness of the book," he said its presentations would require "a fair amount of patience and force of will on the part of the reader."
Albert Einstein wasn't claiming that he could make Einstein easy. In truth, much of his historic book is about as clear as mud, at least for the general reader for whom the book was intended.
That wasn't Einstein's "fault." By all accounts, he had spent the previous twenty years exploring, examining and challenging the established state of physics as it had developed since Newton. He hadn't spent time developing skills as a writer of popular science.
He didn't hold an advanced degree in magazine writing, the way some of "these kids today" do. Judging from appearances, he hadn't spent a lot of time wondering how to explain his revolutionary work to us bantamweights and rubes.
What made him think that his brief book would make sense to general readers? According to Walter Isaacson, he read the text of the book to his niece, who was 16 years old.
His niece was baffled by the book, Isaacson says, but she didn't want to say so to her famous uncle. In this wonderfully comical way, history's greatest physicist got the idea that his book would make sense to us, the unwashed and clueless.
One hundred years later, that judgment is still mistaken. The humor enters the story when our leading professors, publishers and journalists can't discern or refuse to acknowledge this unmistakable fact.
In yesterday's award-winning post, we reviewed the text of Einstein's very brief Chapter 8. In that chapter, he imagines a pair of lightning strikes and develops "a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, [we] can decide by experiment whether or not both the lightning strokes occurred simultaneously."
In that brief chapter, Einstein's writing is somewhat fuzzy, but his basic rumination is simple. In his next chapter, which is even shorter, he introduces a fast-moving train—and his work becomes clear as mud.
We'll go first! One hundred years later, we have no idea what point Einstein was making in that three-page chapter, which runs perhaps one thousand words.
We don't know what point he was making and, dear reader, neither do you! In our view, neither did Isaacson when he tried to explain that material in his 2007 best-seller, Einstein: His Life and Universe.
Neither did the PBS program Nova, when it tried to explain the same material in last November's hour-long broadcast, Inside Einstein's Mind.
At roughly the ten-minute make of its broadcast, Nova tried to explain what Einstein was saying in chapters 8 and 9 of his historic book. Ninety-nine years later, Nova's presentation was less clear than your typical puddle of mud. Truthfully, though, so was Einstein's own work, back in 1916!
It shouldn't be shocking to think that Einstein may not have been a skilled popular writer. The humor enters our tale when professors and journalists, one hundred years later, are still unable to notice this fact, or perhaps refuse to acknowledge it.
We had planned to move on today to the text of Einstein's Chapter 9, in which he discusses the fast-moving train which Nova explained so poorly. Reading back through Einstein's chapter this morning, we noticed again that its text is very unclear.
It can be extremely hard to unpack such balls of confusion. One hundred years later, we're therefore going to postpone our reading until Monday.
It's easy to create incoherence; it's hard to untangle such webs. In the Philosophical Investigations, Wittgenstein described the matter thusly:
"We feel as if we had to repair a torn spider's web with our fingers."
Wittgenstein wasn't trying to untangle confusing accounts of modern physics, but he was discussing a near relation. He was discussing so-called philosophical problems, the kinds of confusions which "only occur in doing philosophy."
It's hard to untangle certain kinds of confusion and incoherence. One hundred years later, no general reader will be able to explain what Einstein meant in his brief chapter 9.
That said, Nova and Isaacson can't explain what he meant either! For ourselves, we're going to take a few more days before we walk you through its text. One hundred years later, we want to address that particular "web" in the clearest possible way.
You won't understand Einstein's Chapter 9! If you read it and think you do understand, we'll suggest that you haven't read with sufficient care.
One hundred years later, the professors and publishers still seem inclined to defer to Einstein's greatness. They still haven't noticed the ways in which his discussion of that fast-moving train just doesn't seem to make sense.
One hundred years later, has anyone ever explained that chapter? In fairness, high-profile programs like Nova will always go out and pretend.
Coming Monday: That very brief chapter 9
So what?
ReplyDeleteI love Bob, but this series is beyond ridiculous. With exciting Presidential races going on in both parties, and with media playing a very big role, you'd think Bob would find other things to write about.
ReplyDeleteIt's Bob's blog and he can post whatever he wants.
DeleteGo away.
DeleteBob has never failed to be Johnny-on-the-Spot when something in this Presidential campaign coverage reminds him of 2000 and bears repeating for us readers.
Ok, as most would agree Nova's little presentation doesn't explain the thought experiment. Isaacson also doesn't, but I think Einstein actually does explain it (although you need to think about it and understand the chapters leading up to this).
ReplyDeleteHere is the relevant text from Einstein's chapter 9:
====================================================
Now in reality
(considered with reference to the railway embankment)
he is hastening towards the beam of light
coming from B, whilst he is riding on ahead of the
beam of light coming from A. Hence the observer
will see the beam of light emitted from B earlier
than he will see that emitted from A. Observers
who take the railway train as their reference-body
must therefore come to the conclusion that the
lightning flash B took place earlier than the lightning
flash A. We thus arrive at the important
result:
Events which are simultaneous with reference
to the embankment are not simultaneous with
respect to the train, and vice versa (relativity of
simultaneity)
====================================================
So, he first says that as viewed from the embankment, the train moves towards the light from the lightning flash at B and away from that at A. So the observer on the train will see light from B first. This is just commonsense.
Then Einstein considers the observer on the train using the train as their reference body.
For this observer, the train is not moving, but the embankment is moving past the train in the opposite direction with velocity v.
The lightning flashes occur at A and B at equal distances on either side of the observer on the train (at the same time as measured by the observer on the embankment). Einstein is postulating that the speed of light is constant in any reference frame, so the observer on the train would expect flashes to arrive at the same time since they are traveling the same distance to him (in his reference frame of the train).
The light from B arrives first, so he has to conclude that it occurred earlier (since the speed of light is fixed, and the distance traveled is the same, the timing has to be different). So flash B occurs before flash A. The tricky point is that for the observer using the train as his reference body, he is not moving and the lightning strikes occur at equal distances on either side and travel at the speed of light.
The pre-Einstein classical viewpoint would be that the light from strike B arrives first because that light is moving faster relative to the train than the light from strike A. Einstein postulates that the speed of light is constant, so how does he account for the light from B arriving first? The lightning strike at B occurred first.
Meanwhile, the person on the platform would say the flashes both occurred at the same time.
Hence, Einstein's conclusion of the relativity of simultaneity.
"The lightning flashes occur at A and B at equal distances on either side of the observer on the train (at the same time as measured by the observer on the embankment)."
DeleteAren't you using simultaneity to disprove simultaneity?
Also, why are we concerned with the passenger that is equidistant from the lightning strikes when they hit the ground, rather than the passenger that is equidistant when the light from both arrives?
Aren't you using simultaneity to disprove simultaneity?
DeleteNo, he isn't. What makes you think that? There are two observers. When the one on the platform takes measurements, he finds that the strikes were simultaneous. When the passenger takes measurements, she finds that the strikes happened at different times. It's not that one is correct and the other isn't: both of their measurements are valid.
why are we concerned with the passenger that is equidistant from the lightning strikes Both the woman on the train and the man on the platform are equidistant from the lightning strikes. By the design of the thought experiment, the man is standing equidistant from the ends of the platform where the lightning strikes. The woman is standing at the midpoint of her train car, the car is the length of the platform, and when the lightning hits the platform, she is adjacent to the man. Thus the ends of the train car are adjacent to the ends of the platform. For both observers, the light has to travel the same distance.
Your excellency Lord Rat, you were doing so well, until the end, when you said, "For both observers, the light has to travel the same distance." No. The two strokes are equidistant from her, that is true, but the flash from the forward stroke travels farther, so that it meets the flash from the rear stroke behind her, and that's how she knows that the two strokes weren't simultaneous, that the forward stroke had in fact occurred before the rear stroke.
DeleteIt looks like the slowest boy on the world's slowing moving narrative train has a traveling companion! Hey, impCaesarAvg, wake up TDH when the train finally pulls into the station. I wouldn't want him to miss a chance to tell us we're all clueless because he is.
DeleteLet's make this thought experiment even simpler and assume that the train car and the platform are both 30 feet long. Same scenario: the train pulls into the station, and at the moment the woman in the middle of the train car is adjacent to the man in the middle of the platform, lightning strikes both ends of the platform. The man see the strikes at the same time. He concludes, of course, that the lightning at one end of the platform struck at the same time as the lightning at the other end. How does he know this? Well, the photons from the strike 15 feet to his left and photons from the strike 15 feet to his right had to travel the same distance. The speed of light is constant, so the photons from each strike must have taken the same amount of time to reach the man, about 18ns. So if the man sees both flashes at noon exactly, he knows that both strikes took place 18ns to noon.
What about the woman? The photons traveling through the back window of the car and the photons traveiing through the front window of the car both have the same distance to go -- 15 feet -- before they reach her. Remember that she's standing in the middle of the car, which is the same length as the platform. But the woman is moving toward the photons from the lightning strike near the front of her car, so she's going to encounter those photons first. And conclude that the lightning strike must have hit first. She'll make the same calculations as the man with the same distances, the same speed of light, and thus the same time for the light to travel. But she'll see the strikes at different times, so she'll calculate different times for them to have struck.
Deadrat says:
Delete[QUOTE]The woman is standing at the midpoint of her train car, the car is the length of the platform, and when the lightning hits the platform, she is adjacent to the man. Thus the ends of the train car are adjacent to the ends of the platform.
...What about the woman? The photons traveling through the back window of the car and the photons [traveling] through the front window of the car both have the same distance to go -- 15 feet -- before they reach her. Remember that she's standing in the middle of the car, which is the same length as the platform. [END QUOTE]
Hard to keep the hypothetical directions clear and the imagined visuals realistic if we're down to one train car but here goes. As it turns out this train car is of a type that's somewhat familiar to the Man but it looks a little odd, it is shorter in length but just as tall as the stationary cars to be found on other tracks around the train station.
The stationary cars are each longer than the entire station platform but the man adjudges the train car which is moving to be exactly the length of the station platform from its western edge to its eastern edge.
It all happened so fast but later, when he had performed his calculations, the Man concluded on the train car that was barreling westward the Woman at the center of the car had been exactly due north, nearly adjacent to him at the exact moment the two lightning bolts simultaneously went to ground at the western and eastern edges of the station platform.
Given that the train car was the same length as the station platform, obviously this was also the same moment that the train car's east and west ends were next to the platform's eastern and western edges.
The train station with its platform is of a type with which the Woman is familiar though this particular one appeared odd to her. Whereas she expected her train car to be longer than a station platform this platform seemed especially narrow. The station building seemed of ordinary height but its width likewise in its east-west dimension seemed unusually narrow.
This oddity of narrowness prevailed from the time the entire train station complex rushed into her view from the west until it disappeared heading east.
It all happened so fast but later, when she had performed her calculations, the Woman concluded the Man was southwest of her near the middle of the platform when the first bolt struck the western edge/the trailing edge of the platform. At that moment, also, the western edge/the trailing edge of the station platform had drawn exactly abreast of the western end of her train car.
When the second bolt struck the eastern edge/the leading edge of the moving platform, it had just drawn abreast of the east end of her train car. The Man at that moment was to her southeast and still near the middle of the moving platform.
The Woman could then assert that it was at some moment in between when the first the second lightning bolts struck that the Man had been directly south, almost adjacent to her.
Esteemed Rat, in the woman's own frame of reference, she is NOT MOVING. The platform and the man are moving past her, but that doesn't affect her observation of the lightning strokes. The there's a stroke some distance ahead of her, then there's a second stroke at that same distance behind her. Because the forward stroke occurred first, she sees it first. Its photons meet the rear stroke's photons right next to the man, who is behind her and moving further behind.
DeleteI think CMike's description may be correct, but he'll have to edit it. (For example, in the last sentence he says, "the first the second". )Then, for bonus points, he might want to estimate the kinetic energy of the train as observed by the man. This is an express train -- do not step in front of it!
impCaesarAvg, we may be in violent agreement, but I can't tell because like TDH you keep changing the description of the experiment. LIght from one stroke starts from the front of her car; light from the other starts from the back. They have the same distance to go at the same speed, so they'll take the same time to reach her because she's standing in the exact middle of the car. Depending on the frame of reference, the light from the front stroke reaches her first either because she's moving toward it or its being carried toward her. There's no sense to a statement that starts Because the forward stroke occurred first because there's no way to determine that except by picking a frame of reference. Which is the whole point.
DeleteI can't quite follow CMike either, but I'm guessing his point is that just as there are no absolute clocks whereby every observer may obtain the universally correct time, there are no absolute rulers by which every observer may measure universally correct distances. From the point of view of the man, the train car is foreshortened from what he sees as its direction of travel. The woman finds the car's length unchanged.
In her frame of reference, the the front stroke happens first. In his, the strokes are simultaneous. It's the relativity of simultaneity! Duh.
DeleteYou, Mike, and I get it. I think even David gets it. But alas, poor Bob. I knew him, Rat. A fellow of infinite jest, of most excellent fancy. He hath bored me a thousand times, and now how abhorrent in my imagination he is! My gorge rises at it. Where are his jokes now? His flashes of merriment that used to make an audience roar?
CMike wrote:
Deletethe first the second lightning bolts struck
when he should have written:
The Woman could then assert that it was at some moment in between when the first *and* the second lightning bolts struck that the Man had been directly south, almost adjacent to her.
Deadrat, what do you think the Woman sees? How is it she sees one bolt strike at the western edge of the platform which is next to the west end of her train car and she sees the other bolt strike at the eastern edge of the platform next to the east end of her train car? The respective platform edges and car ends are only momentarily next to each other and the Woman sees the light from the equidistant strikes at separate times.
It can not appear to the Woman that the moving platform is the same length as her train car and that the western and eastern platform edges are next to the east and west ends of her train car at the same time if she sees one bolt strike at one end of her car next to the western platform edge at a different time than she sees the other bolt striking at the other end of the train car next to the eastern edge of the platform.
The two platform edges are next to the two ends of her train car at different times because the platform is in motion and not as long as the train car- according to the Woman.
Right?
If the train car and the platform were ever at rest next to each other the train car would measure as longer than the platform.
The man sees the fast moving train car as reduced to the same length as the platform, the Woman sees the fast moving platform as reduced to a shorter length than she remembers another one like it being when it was stopped next to her train car.
Left at the station again, as the slowest boy on the slowest narrative train tells everybody else that his ignorance is also theirs.
ReplyDelete"Interlude"? Oh dear God, is there still more coming?
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