THE LATEST ATTEMPT TO EXPLAIN: Nugget statement fails to compute!

THURSDAY, MARCH 31, 2016

Part 3—Einstein just isn't that easy:
Was Nova's program, Inside Einstein's Mind, able to make Einstein easy?

Let's restate that question. Did last November's hour-long broadcast make the work of this intellectual giant understandable at all?

We're going to say that the answer is no. Let's return to the non-explanation explanation which occurs near the start of the program.

At roughly its nine-minute mark, the Nova program begins to discuss the "thought experiment" which led to "special relativity," the famous theory Einstein unveiled in 1905.

As described by Nova, Einstein's thought experiment involved a man on a railway platform; a woman on a fast-moving train; and a pair of lightning strikes. Below, you see the transcript of the part of the program which describes this thought experiment.

Nova's visuals will help you picture the scene. To watch the full program, click here:
WALTER 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 7, that simply means that it gets to the platform simultaneous with the clock going to 7.

NARRATOR: In a brilliant thought experiment, he 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.

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.

PROFESSOR CARROLL: If there's no such thing as simultaneity, then there's no such as absolute time everywhere throughout the universe, and Isaac Newton was wrong.

NARRATOR: This concept, that time and space as well are relative, became known as "special relativity." It led to remarkable results, such as the famous equation relating energy to mass.
For a slightly longer chunk of that transcript, see Tuesday afternoon's post.

The homely example described in that passage involves very basic physics. The man is standing exactly halfway between the two lightning strikes. For that reason, "the light from each strike reaches his eyes at exactly the same moment."

As you can see from Nova's simulation of the thought experiment, the woman is directly adjacent to the man when the two strikes occur. But because she's on a fast-moving train, she moves toward one of the lightning strikes and away from the other.

By way of contrast, the man on the platform just stands there.

Because of her very rapid movement, the woman is soon closer to the one strike, farther away from the other. For this reason, light from the strike which she is approaching reaches her eyes before the light from the strike she is moving away from.

This is a very simple example. Based on this homely example, Nova viewers were quickly deluged with a set of statements we'd almost call "metaphysical."

It's implied that these are "mind-blowing" statements. We can tease seven such statements from just that small chunk of text. Essentially, these are direct quotations from the Nova transcript:
Mind-blowing statements:
1) The flow of time is different for an observer that is moving versus one that is standing still.
2) Simultaneity depends on how you're moving.
3) The flow of time depends on how you're moving.
4) There's no such thing as simultaneity.
5) There's no such as absolute time everywhere throughout the universe.
6) Time is relative.
7) Space as well is relative.
We'll note that statements 2 and 4 don't go together real well. For what it's worth, we're also told this:

"The concept that time and space are relative is known as 'special relativity.' "

In effect, viewers are told that a revolutionary theory has now been explained to them in a way they can grasp and explain. That suggestion is utterly silly.

In fact, none of those seven statements follow in any obvious way from the homely example Nova has sketched. In the rest of today's post, let's start explaining why:

Let's start with a suggestion. Let's ignore the mind-blowing statements which deal with "the flow of time."

That particular phrase is extremely fuzzy. Later in our course of study, we'll return to that particular type of murky locution, drawing on Wittgenstein's work.

For today, let's focus on this apparent nugget: "Simultaneity depends on how you're moving."

Although that statement is also quite fuzzy, it seems to be the key take-away from Nova's homely example. Because of its fuzziness, it's hard to paraphrase that statement. But it sounds like Nova is saying this:

The man and the woman have different experiences because they're in relative motion.

It also sounds like Nova is saying something like this: Because the man and the woman are in relative motion, the events are simultaneous for the man but not for the woman. Or something like that! Truth to tell, Nova makes little attempt to explain what its key nuggets actually mean.

In truth, Nova's attempt at explanation moves almost as fast as that fast-moving train. Let's do the best we can with its presentation, which is very sketchy.

In conventional terms, the man on the platform is stationary. The woman on the very fast train is moving very fast.

Expressed in a more rigorous way, the man and the woman are in motion relative to each other. In this particular example, this leads to our mind-blowing outcome:

The light from the two lightning strikes reach the man at the exact same time. By way of contrast, the light from the strike the woman is approaching reaches her before the light from the other strike.

Even that doesn't explain Nova's nugget about simultaneity. As we'll note tomorrow, the woman on the train may yet judge and declare that the two lightning strikes were simultaneous.

In our own lives, we make such judgments quite routinely. That said, let's put that off till tomorrow.

For today, let's restrict ourselves to simpler observations. For starters, let's launch a second thought experiment!

In this case, let's imagine that a second man is standing on that (very long) railway platform. (In his 1916 book, Einstein specifically says that the train in this thought experiment is "a very long train.")

We'll call this new fellow Man B. We'll imagine that he is standing all the way down at the end of the very long platform. He's off at the end of the platform which lies in the direction the very fast train is going.

Our original man, who we'll call Man A, is right where he ever was. Let's picture this new scene:

Man A is standing where he always was, in the center of the very long railway platform. Man B is standing all the way down at the end.

Can you see where this second situation takes us? In conventional terms, neither of these men is in motion. Expressed more rigorously, they aren't in motion relative to each other.

Motion plays no role in this second thought experiment, but so what? Because he's way down at the end of the platform, the light from the nearer lightning strike reaches the eyes of Man B before the light from the other lightning strike.

For Man A, it's just as it always was. Quoting Nova, "The light from each strike reaches his eyes at exactly the same moment."

According to Nova's clumsy formulations, the lightning strikes are simultaneous for Man A. But it isn't like that for Man B! Continuing with Nova's formulations:

"For [the man at the end of the very long platform], time elapses between the two strikes." But this is precisely what will occur for the woman on the fast-moving train.

Motion played no role in this second thought experiment, the one involving Man A and Man B. There is no motion here at all! Each man is standing still on the same railway platform.

Motion plays no role in what happens here. For Man B, time elapses between the arrival of light from the two lightning strikes--but it does so because he's closer to the one lightning strike and farther away from the other. It's just as simple as that.

Of course, that's why the woman on the train will have the same experience! By the time the first light reaches her, she too is closer to one lightning strike and farther away from the other.

In her case, that wouldn't have happened if her train had suddenly stopped moving. But it's hard to see what point is being made when we're simply told, full stop, after just that one example:

"Simultaneity depends on how you're moving." Amazingly, that statement is fuzzy in two different ways, as we'll note tomorrow.

"Simultaneity depends on how you're moving?" What was Nova trying to say when it stressed that formulation? How would you paraphrase, elucidate or explain that portentous, mind-blowing statement?

In Nova's lone thought experiment, two people who were in relative motion had a different experience of two lightning strikes. But as we showed you today, two people who aren't in relative motion could differ about the two lightning strikes in the exact same way.

For ourselves, we have no idea what Nova was trying to say with that formulation. But neither did anyone else who was watching that show last November. It wouldn't be easy to explain what Nova meant by that formulation, or by the other "mind-blowing" statements in our list of seven.

For our money, it's hard to see what we're supposed to learn from the man on the platform and the woman on the train. Tomorrow, we'll ask you to imagine a second woman on that train, all the way back in the train's caboose.

Despite her very rapid motion, she'll experience the two lightning strikes in the same way Man A does. Meanwhile, as lightning strikes all around us, we find ourselves left with an obvious thought:

Einstein simply isn't as easy as Nova was willing to say.

Tomorrow: A woman in the caboose of that train! Also, lightning versus thunder

29 comments:

  1. My takeaway here is the lack of commuter train service in the US.

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    1. My takeaway is that the woman in the caboose was probably paid less than the men if she worked for the railroad, which was unlikely, or was paid by the men, in which case she might have made more and white lightening was involved.

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    2. Can't wait for Rachel to cover this:

      http://www.huffingtonpost.com/entry/uswnt-wage-discriminatory-suit-us-soccer_us_56fd33c3e4b0a06d5804ecac

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  2. How dumb is the vastness of the whale? Under the ideal gas law we have no idea for ourselves whether it is relatively more important that culture collapses before or after complete incoherence sets in.

    Our thumbs are roughly tied.

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  3. For my money, last Tuesday's slightly longer chunk of transcript made Einstein easier and more understandable. But nobody reading this is able to grasp that. Amazingly, when you try tomorrow you can avoid being fuzzy by selecting a more appropriate chunk of transcipt. Provided, of course you have the slightest clue what that chunk contains.

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  4. I'm reminded of the internet video of the baboon being blown away by a card-disappearing trick. The ape, unlike a cow, is smart enough to be impressed by the trick, but not smart enough to realize it's a trick.

    Maybe we're the apes and Einstein, or Nova, is the prestidigitator.

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    1. Maybe the video was fake. I've seen cows with picket signs.

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    2. Jeeves, to a chimpanzee, you're a closer relative than that baboon is. So, yes, we're apes.

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    3. Wait a minute. Who's the chimp supposed to be?

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  5. I'm really sick of hearing about this one program. What's the point?

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    1. Too bad. You must read this blog every day, and twice for all articles about the theory of relativity. I insist.

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  6. These theories might be more useful if they would lead to the development of trains, actually space ships, capable of traveling at the speed of light.

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  7. These theories might be more useful if they would lead to the development of trains, actually space ships, capable of traveling at the speed of light.

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    1. It might be useful if you learned how to post comments.

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    2. Might be even more useful if he forgets what he DOES know.

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    3. It's not what he knows that's troubling, even less what he doesn't know...

      No, it's what he only thinks he knows that causes all the trouble.

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    4. This theory shows that we can't develop a spaceship that goes as fast as light.

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  8. Why spend time trying to understand something with so little practical application when there are incomprehensible things with much greater relevance to misunderstand? Poverty, for example.

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  9. If the gal passes the guy just when he sees both strikes, she sees them both at the same time, too. To him, they happened equally long ago and were equally distant. But to her, the forward strike happened longer ago and further away than the rear strike.

    Also to her, the light from the forward strike is blue-shifted, and the light from the rear strike is red-shifted.

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    1. Superposition is a principle of quantum theory that describes a concept about the nature and behavior of matter and forces at the sub-atomic level. The principle of superposition claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously, as long as we don't look to check. It is the measurement itself that causes the object to be limited to a single possibility.

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  10. How much higher must our nation's outstanding young people score on their NAEP math tests before Einstein comes easy for them?

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  11. two people who aren't in relative motion could differ about the two lightning strikes in the exact same way.

    No, not in the same way. Suppose there are two men on the platform, one midway between the points A and B where the lightning strikes and one closer to A than to B. The first man will check his watch and note the time when the light from the flashes reaches him. The second man will have to check his watch twice, once when the flash from point A reaches him and a little while later when the flash from point B reaches him. Let's suppose the lightning left marks on the platform. Each can measure the distance the light flashes had to travel because they can measure the distances from points A and B to where each is standing. The first man will get two equal distances; the first man will get two different distances. They both agree on the speed of light c, since that's constant for everybody. Now velocity equals distance traveled divided by time elapsed (c = d/t) or with a little algebra, time elapsed equals distance traveled divided by velocity (t=d/c). So both men can work out how long it took for the light to reach them. The first man has only one calculation to do since he's equidistant from A and B. The second man has two calculations to do. Both men will take their elapsed time results and work backwards from the times they noted on their watches and calculate that the lightning struck A and B at the same time.

    The fact that the thought experiment places the man on the platform midway between A and B is simply an artifact so that he doesn't have to take measurements and make calculations to determine the simultaneity of the strikes. I hope we can now return to the original situation -- man on platform midway between the lightning strikes, woman on train midway between ends of the train car and adjacent to man when the lightning strikes.

    So what about the woman on the train? The speed of light for her is still c, the same as the value for the man on the platform. The distance the light travels is the same for her as for the man. But because she's traveling toward one lightning strike, she'll move to meet the former, and so she'll see that strike's light first. Since she's moving away from the second lightning strike, she'll see the light from the second strike later because it has to make up the distance that she's moved. There's no calculation that she can do that shows that the flashes occur at the same time.

    The conclusion is that simultaneity depends on one's frame of reference.

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    1. It's good to have a rat back in the basement.

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    2. "The distance the light travels is the same for her as for the man." ?? The light from the lightning strike she is moving towards will have traveled a shorter distance by the time it reaches her than it will have traveled by the time it reaches the man. The light from the other lightning strike will have traveled further by the time it reaches her than it will have traveled by the time it reaches the man. So in what sense is it true that, "The distance the light travels is the same for her as for the man"?

      "There's no calculation that she can do that shows that the flashes occur at the same time." ?? If we're assuming we know the exact time the light from each strike reached her, the distance each traveled, and of course the speed of light, why couldn't we calculate the time the strikes occurred?

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