Part 1—This week's dramatis personae: What did Albert Einstein say in 1916, in Chapter 9 of a short, famous book?
The famous book bears this title: Relativity: The Special and the General Theory. It was Einstein's attempt to explain relativity to non-specialist readers.
Einstein had propounded the special theory of relativity in 1905, when he was 26. In 1915, he presented the general theory of relativity.
One year later, he tried to explain this scientific revolution in his brief, famous book. To peruse that book, click here.
Last November, Nova presented an hour-long broadcast, Inside Einstein's Mind. The broadcast was timed to mark the hundredth anniversary of general relativity.
About ten minutes into the program, Nova presented an explanation of the "thought experiment" which led Einstein to the special theory of relativity in 1905. To watch that broadcast, click this.
To our eye and ear, Nova's presentation made and makes no apparent clear sense. Before the week is done, we're going to look at the part of Einstein's brief book from which the PBS program was working, almost one hundred years later.
One hundred years later, we ourselves are going to make a strange suggestion. Einstein's own explanation of his historic thought experiment is muddy, clouded, unclear.
One hundred years later, our professors and journalists don't seem to have noticed. But so it goes inside our society's ubiquitous "culture of incoherence."
Is it possible? Is it possible that Einstein's explanation of his own work didn't and doesn't exactly make sense? Is it possible that, one hundred years later, our most famous professors haven't yet noticed this fact?
It may seem hard to imagine such a state of affairs. That said, Einstein's own revolution started with his rejection of the professors of his own day.
Are our professors sharper than his? We'll explore that question this week.
For today, let's start by reviewing the problem which arose in Nova's broadcast. More specifically, let's produce a dramatic personae to which we'll refer all week.
To get started, let's list the characters of the "brilliant thought experiment" the PBS program tried to describe and explain. As described by Nova, there were two players in Einstein's thought experiment. The thought experiment involved two people along with two lightning strikes:
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 is standing still.In Nova's treatment, we have a man standing on a railway platform and a woman passing by on a fast-moving train. If we restrict ourselves to Nova's treatment, our cast of characters will therefore look like this:
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 traveling 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.
Dramatis personae, Einstein's thought experiment:If we restrict ourselves to Nova's account, that's our complete cast of characters. From the story as Nova tells it, Einstein deduced this "mind-blowing" conclusion:
The man on the railway platform: This man is standing at the midpoint of a very long railway platform.
The woman on the train: The woman is riding in the middle car of a very long fast-moving train. She's passing the man on the railway platform at a high rate of speed.
"Simultaneity...depends on how you're moving." At first glance, that conclusion may appear to be sound.
(Warning! In street cons, the "mark" is always sure he knows under which shell the marble is hiding.)
At first glance, Nova's conclusion may appear to be sound. As described by Nova, the lightning strikes will at least seem to be simultaneous to the man on the platform. But the lightning strikes won't seem to be simultaneous to the woman on the train. And she is moving very fast, while the man is standing still!
Case closed, Nova has said! Simultaneity depends on how you're moving. If we leave the matter there, we can exit the Nova program with the sense that we've mastered some "mind-blowing" physics.
Unfortunately, Nova's limited, two-person presentation doesn't quite seem to make sense. When we watched the program last fall, we thought that presentation was one of the worst non-explanation explanations we had ever seen.
A few weeks ago, we began explaining that claim by introducing two more characters. Let's recall who they were:
First, we introduced Man B. This man is standing all the way down at the end of the very long railway platform.
(In his 1916 book, Einstein specifies that we're talking about "a very long train." He further specifies that the two lightning strikes occur "at two places A and B far distant from each other.")
Uh-oh! Even though Man B is standing still, he will experience those lightning strikes much as the woman on the train does. She will be directly adjacent to Man B's position when light arrives from the nearer strike. She is in motion, he is not. But in terms of simultaneity, they will experience the two lightning in much the same way.
For Man B, "time elapses between the two strikes," in the language used by Nova. For Man B, "the two strikes are [not] simultaneous," again using Nova's construction.
Man B introduced confusion into Nova's story-line. To him, the two strikes won't seem simultaneous, even though he's standing still, like the original man on the platform.
Man B introduced confusion into this story. Woman B made things even worse.
We said that Woman B was in the caboose of that fast-moving train. She's moving at the same high rate of speed as the original "woman on the train." But because she's at the rear of their train, she's directly adjacent to the original "man on the platform" when the light arrives from the two lightning strikes.
In terms of simultaneity, we'll allege that Woman B will experience the lightning strikes exactly as the original "man of the platform" does. As with him, so with her—the light from the two lightning strikes will reach her at the exact same time.
For Woman B, as for the original man on the platform, "the two strikes are simultaneous...there is no time between the strikes." But she's moving at a high rate of speed, and he is standing still.
We now have a more complex thought experiment, with a longer list of characters. For better or worse, our cast of characters will now look like this:
Dramatis personae, Einstein's (expanded) thought experiment:For us, Nova's presentation broke down when we imagined Man B. Like the original woman on the train, he won't experience the two lightning strikes as simultaneous. But she is moving at a very high speed, and he is standing stock still.
The man on the railway platform: This man is standing at the midpoint of a very long railway platform.
The woman on the train: The woman is riding in the middle car of a very long, fast-moving train. She's passing the man on the railway platform at a high rate of speed.
Man B: This man is standing at the end of the railway platform. He is directly adjacent to the woman on the train when the first light arrives from one of the lightning strikes.
Woman B: This woman is in the caboose of the fast-moving train. She is directly adjacent to the man on the platform when the first light from the two strikes arrives.
Presumably, he won't experiences the two lightning strikes in exactly the same way as the original woman. Because she's moving away from the more distant strike, it will take longer for the light from that strike to reach her eyes.
On the other hand, it seems that Woman B will experience the two lightning strikes in exactly the same way as the original man on the platform. Because he's midway between the two strikes, the light from the two strikes will reach him at the same time. Why wouldn't she have the same experience?
Back in November, we instantly pictured Man B down at the end of the platform. For him, "time elapses between the two strikes," as is the case for the original woman on the train.
What then, exactly, was the point of Nova's formulation? What becomes of Nova's "mind-blowing" take-away:
"Simultaneity...depends on how you're moving."
What becomes of that nugget formulation when we introduce Man B and Woman B?
In our new cast of characters, both of our men are standing still. But in the language of Nova, the strikes "are simultaneous" for the original man on the platform, but not for Man B.
Beyond that, though, a second problem is swimming around in Nova's presentation. The program makes no attempt to separate seeming from being. To wit:
The original woman on the train may initially judge that the two strikes were sequential, not simultaneous. That may be her first impression, based on the way the light reaches her from the two strikes.
That said, she will likely change her assessment when she's told that one of the strikes occurred closer to her position. We humans adjust our judgments in such ways about a wide array of phenomena involving light, sound and other sensory experience. We my such adjustments of judgement all the time.
(You experience two earthquake shocks. One shock rattles your dishes more; you judge that it was stronger. But you later learn the other shock occurred much farther away. You accept the claim you hear on the news—the shock which rattled your dishes less was in fact much stronger.)
Citizens, can we talk? To this day, we can't explain the point the Nova broadcast was making in the passage under review. Almost surely, you can't explain it either.
Tomorrow, we'll review the way Walter Isaacson described this same thought experiment in his best-selling biography, Einstein: His Life and Universe. His book appeared in 2007, ninety-one years after Einstein published his brief book.
On Thursday, we'll go to the ultimate source. How did Einstein explain and describe this important thought experiment?
One hundred years later, is Einstein's explanation clear? If not, riddle us this:
They've had a hundred years to do it. One hundred years later, can our professors explain this part of his book?
Tomorrow: Einstein's "eureka moment"
OK, I just reread Chapter 9. It's lucid, and, even better, it's correct. If you don't understand it, read Chapters 1-8, then try again.
ReplyDeleteForget Nova and forget Isaacson.
Peak ahead to Chapter 10 first and the discussion of distance.
DeleteThe man in the center of the platform knows he's standing still and he knows where the bolts struck. (As for the man standing still, others might point out he's on the surface of the earth which is spinning on its axis and revolving around the sun, while the sun, itself, is revolving around the center of the Milky Way galaxy.)
The woman knows she's standing still and where the bolts struck. Sure, she can see the platform (or the embankment) where both of the bolts struck is moving past her but that doesn't matter as to whether she is standing still. Why she can pour herself a cup of tea without spilling a drop.)
For her, the platform is not as long as the train she is on (or, rather, the distance between the two strike points on the embankment were not at points as far apart as the length of the train). If she is facing south, and the man who is facing north thinks the train she is on is moving west, the woman will know it was when the western edge of the platform moving past her was next to the locomotive that that was when and where the first bolt struck. Later, when the eastern edge of the platform was next to the caboose, that was when and where the second bolt struck.
Both the man and the woman would agree, the light from the strikes reached the man at the same time and the light from the strikes reached the woman at different times. The man would conclude the light from the simultaneous strikes reached the woman at different times because she was moving towards one strike point and away from the other. The woman would conclude the light from the strikes which occurred at separate times reached the man at the same time because he was moving away from the first strike and towards the second strike.
Should the train and the platform ever be at rest next to each other the train would be longer than the platform but not by as great of a distance in length as the woman thought there was when the platform rushed past her.
And the Milky Way is moving toward the Andromeda Galaxy. And the Local Group of galaxies is moving toward the Virgo Cluster.
DeleteRight, right impCaesarAvg. And not to say your wry comments aren't appreciated, but I write up my comments and replies on this subject for my own benefit. I use these threads as a prompt to work out a run through of my own version of this thought experiment and whenever I get stuck with it I use the various cheat sheets that are available on the net for help. Go ahead and enjoy, take all the satisfaction you can derive from thinking you're stringing me along, but that's not what's going on here.
DeleteNo, I'm not stringing you along, CMike. I don't understand string theory at all.
DeleteNow how did I know you were going to pick up on my use of "stringing" just that way? Guess you can't always be creative.
Delete"The woman would conclude the light from the strikes which occurred at separate times reached the man at the same time because he was moving away from the first strike and towards the second strike."
DeleteI think if the woman would see the man move she is also going to see the strikes move since they are on the same plane as the man, so it would not seem like he was moving away from the first strike.
The strikes each occur in an instant at a specific place relative to the woman- some of the light from the first strike moves away from the strike point towards the man who is moving away from what the woman perceives as where he and the middle of the platform were when the first bolt struck. The woman perceives the western edge of the platform, also, as moving relative to her. In other words, the edge is moving away from where it was when it was when it was struck by the first lightning bolt. The western edge of the platform would maintain its own relative distance from the man at the middle of the platform. Some of the light from the strike would be moving eastward faster than the platform or the man is moving eastward relative to the woman. That is why she ends up seeing some of the light from the first strike reaching the man.
Delete(I think.)
The western edge of the platform would maintain its own relative distance from the man at the middle of the platform.
DeleteI think from the perspective of the woman this might not be true. I think as the platform comes into her view, as it seems to be moving towards her from the west, she sees it as elongated with the man looking like he's closer to the east end of the platform than the west end.
When he is exactly south of her she thinks there are equal lengths of the platform to his west and his east. And when the platform is getting farther away it looks to her like the platform was shorter than it was on its approach and that the man is back to being closer to the east end.
I think this is because as the woman approaches the platform from east she's seeing daylight (not the light from the lightning strike) which reflected off the east end of the platform more recently than the daylight she's seeing at the same time from the west end of the platform. Therefore she's seeing the west end of the platform when the platform was farther away than the platform was when she's seeing the east end of the platform.
When the platform is receding from view she is seeing light reflected off the east end of the platform from where the platform, itself, was at an earlier time (less far away, sort of) than when the light she's seeing from the west end gets to her at the same time. It's sort of like a doppler shift without the shift- she's always seeing the leading edge of the platform's direction of travel, relative to herself, look scrunched up relative to its trailing edge.
I could be completely wrong about all this so I'd appreciate any input from someone who is following what I'm saying.
I recommend reading Issacson's book about Einstein if you want to learn about the life of Albert..Its not the book to read to fully understand physics.Daily Howler isn't nor will he be the last person to get his mind all twisted in knots trying to understand relativity
DeleteAlso read Appendix 1, where Einstein derives the Lorentz transformation. With that, given the time and position of an event in the platform (or embankment) coordinates, you can calculate the time and position in the train coordinates.
DeleteAdding the 2nd set of observers is just another way of restating the issue. The first set has the stationary observer seeing the 2 lightning strikes as simultaneous, the moving observer sees them as sequential.
ReplyDeleteWith the 2nd set of observers, the moving observer sees the 2 strikes as simultaneous, the stationary observer sees them as sequential. The difference is from the time it takes light to travel the distance between the 2 sets of observers. It adds some clutter to the example by restating the basic hypothesis as an inverted example.
" It adds some clutter..."
DeleteAnd also makes transparent that Nova's simplistic summary ["Simultaneity...depends on how you're moving"] is utterly inadequate -- really, it's a misunderstanding dressed to parade as understanding.
Let's conduct another thought experiment. Suppose Man A is traveling along County Road 123, when he realizes that he's lost, although he'd thought he was thoroughly familiar with the area. He pulls up to the general store in Middleboro to ask for directions from Man B who is sitting on the porch there.
ReplyDelete"Hey, there friend," says Man A to Man B. I thought I knew my way around Route 123, but I'm lost. Can you tell me where Middleboro is?
"Sure, stranger," says Man B. "We're a few miles down 123 from Centralia. Does that help?"
"No," says Man A. "I've never heard of Centralia."
"Really?" says Man B somewhat skeptically. "Well, if you go a fair piece farther in one direction, you'll come to East Bumfuck. If you go in the other direction, you'll come to West Bumfuck.
"Oh, sure," says Man A. I know where East and West Bumfuck are."
"There ya go," says Man B. "Actually Middleboro is equidistant from East and West Bumfuck."
"Really?" says man A, whose turn it is to be skeptical. "How do you know?"
"It's easy," replies Man B. "If two drivers start out at the same time for Middleboro, one from East Bumfuck and one from West Bumfuck, and they drive at the same speed, they'll get here simultaneously."
Man A is about to say that the explanation is convincing, when a boy on the porch pipes up. "Not so easy," the boy says. "I don't think we can rely on the two drivers to tell us that Middelboro is the same distance between the Bumfucks."
"Why not?" Man A asks, not noticing that Man B is rolling his eyes.
"Well," says the boy. "If a driver starts out from East Bumfuck and another driver starts out from Centralia, they won't get here simultaneously."
Man A says to Man B, "Are all of you that stupid? Is it genetic inbreeding or something in the water around here?"
Man B replies, "None of us around here is an Einstein, but that's just Bob. He's kinda slow, but we like him."
"Really?" Man A asks again.
"Well," says Man B, "He's really slow.
To this day, we can't explain the point the Nova broadcast was making in the passage under review. Almost surely, you can't explain it either.
ReplyDeleteYou can't explain it because you insist on being an ignoramus. Don't tell me what I can and can't do.
Man B and Woman B are irrelevant distractions. Both Man B and Woman B, along with other people who can think straight, understand that if two events are simultaneous in your frame of reference, you will see the closer one first. You can work out the time each occurred using the formula c=d/t, where c is the speed of light, d is the distance to the event, and t is the time it took the light to report the event to you.
Stop changing the thought experiment. Stick with the Man and the Woman. The lightning strikes when the two are adjacent, he on the platform, she on the train. The light from each strike reaches the man at the same time, because each is the same distance from the man (one half the train car length) and light always travels at the same speed.
The Woman on the train measures the same distance for the light to travel (one half the car length because she's in the middle of the car), and she measures the same speed of light. But she'll see the light from the strike at the front of the car first because she's moving toward it. If the speed of the light from each strike is the same, and the distance the light from each strike has to travel is the same, then what is she to conclude from the fact that she sees the light from the first strike first? It must be that for her, the front strike happened first.
deadrat, why would she not conclude that she sees the one strike first because she is moving towards it and that therefore the strikes happened at the same time?
ReplyDeletealso how is it an eureka moment?