ONE HUNDRED YEARS LATER: Einstein's eureka moment!


Part 2—Isaacson sets the scene:
Just this once, just tell us the truth.

Do you understand—if necessary, could you explain—the "mind-blowing" nugget conclusion from Nova's presentation of Albert Einstein's "brilliant thought experiment?"

Tell the truth. We all know how to repeat script and cant, formulaics we may have received from academic authority figures.

We can all learn how to recite standard bumper stickers. But in the case of the Nova broadcast, could you really explain this conclusion:

"Simultaneity, and the flow of time itself, depends on how you're moving."

Let's simplify that a tad: "Simultaneity depend on how you're moving." Based on Nova's depiction of Einstein's thought experiment, could you really explain what that means?

Do you have a clear idea of what that statement actually means? Would you know how to explain it, especially if questions were allowed?

Bravely, we'll go first:

Based on Nova's presentation, we don't know how to explain that "mind-blowing" concept. Based on Nova's account of Einstein's thought experiment, we don't know how to invest that nostrum with something resembling clear meaning.

Quickly, let's review. Nova presented two characters—a man standing on a railway platform and a woman passing by on a fast-moving train.

In that sense, "how they're moving" is different. And Nova showed us something else—the light from a pair of lightning strikes would reach these two observers in a different sequence.

(For more detail, see yesterday's report.)

In Nova's example, the light from the two atrikes would reach the man at the same time. But for the woman, time would elapse between the arrival of the light from the two strikes.

"For him, the two strikes are simultaneous," Nova declared, using some shaky language. By implication, Nova also seemed to say that, for the woman, the lightning strikes weren't simultaneous.

The woman is moving, the man is not. "For him," the strikes "are simultaneous." For her, we're basically told that they aren't!

It seemed that things were moving along, until we imagined two more people. Man B was standing at the end of the railway platform. But uh-oh! Even though he's standing still, "for him, the strikes are not simultaneous."

Woman B is in the caboose of the train. But uh-oh! Even though she's moving as fast as the other woman, "for her, the two strikes are simultaneous."

"Simultaneity depends on how you're moving?" With the addition of these players, do you still feel sure you know what Nova means?

For ourselves, we don't know what Nova means. We don't know how to explain the "mind-blowing" conclusion offered by the PBS org.

If we might borrow from our Frost, something someone is withholding seems to have made us weak! And this is intriguing, because Nova really was describing the "thought experiment" which led Einstein to his special theory of relativity in 1905, when he was just 26.

Nova didn't invent its example. Einstein describes the same thought experiment in the book he published in 1916—a book intended to explain relativity to general readers.

That historic book bears the following title: Relativity: The Special and the General Theory. You can peruse the short book here. Nova was working from chapters 8 and 9 (pages 30-35).

Nova didn't imagine that thought experiment; it comes from Einstein's own account of his work. That thought experiment has long been considered to be quite central to Einstein's revolution.

How central to Einstein's work is that thought experiment? For today, let's review the way Walter Isaacson introduces that thought experiment in his best-selling biography, Einstein: His Life and Universe.

Isaacson's book appeared in 2007. As we noted a few weeks ago, it carried blurbs from an array of ranking professors, praising Isaacson for the way he'd managed to make Einstein easy.

Except when the science hits the fan, Isaacson is an extremely lucid writer. In Chapter Six, "Special Relativity," he starts us toward that thought experiment in the passage shown below.

In Isaacson's account, Einstein experiences a "eureka moment." Within five weeks, Einstein, then just 26, has written and submitted "his most famous [scientific] paper:"
ISAACSON (page 122): It was a beautiful day in Bern, Einstein later remembered, when he went to visit his best friend Michele Besso, the brilliant but unfocused engineer he had met while studying in Zurich and then recruited to join him at the Swiss Patent Office. Many days they would walk to work together, and on this occasion Einstein told Besso about the dilemma that was dogging him.

“I’m going to give it up,” Einstein said at one point. But as they discussed it, Einstein recalled, “I suddenly understood the key to the problem.” The next day, when he saw Besso, Einstein was in a state of great excitement. He skipped any greeting and immediately declared, “Thank you. I’ve completely solved the problem.”

Only five weeks elapsed between that eureka moment and the day that Einstein sent off his most famous paper, “On the Electrodynamics of Moving Bodies.” It contained no citations of other literature, no mention of anyone else’s work, and no acknowledgments except for the charming one in the last sentence: “Let me note that my friend and colleague M. Besso steadfastly stood by me in my work on the problem discussed here, and that I am indebted to him for several valuable suggestions.”

So what was the insight that struck him while talking to Besso? “An analysis of the concept of time was my solution,” Einstein said. “Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity.”
Quickly, note a small hint of a possible problem.

Isaacson is about to start describing the thought experiment involving that fast-moving train. As he does, he offers this quote from Einstein: “Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity."

Isaacson hasn't tried explaining those statements yet, but he's already introduced an element of confusion. How many readers will have any idea what "signal velocity" means?

Because he's writing for general readers, the answer is "very few." But as he continues, Isaacson doesn't try to define this technical term. As best we can tell, the term appears nowhere else in his 551-page book—a book which is extremely lucid until the science starts.

We offer this as a minor point. Einstein actually used the term. There's no hard and fast rule which says it mustn't be quoted.

But just like that, a possible bit of confusion has wormed its way into Isaacson's text. For the general reader, the lucidity of this passage has already perhaps been eroded.

At any rate, Isaacson proceeds as shown below. As you can see, we're on our way to a seat on that fast-moving train:
ISAACSON (continuing directly): More specifically, the 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.
Isaacson goes on to describe and discuss the same "thought experiment" Nova discussed in last November's program. Like Nova, Isaacson is working straight out of Einstein's book.

Tomorrow, we'll see if Isaacson was able to craft a clearer account of that material. In our view, Nova tried and failed. Isaacson, a very clear writer, had a chance to do better.

For today, let's only note this:

Essentially, Isaacson says that the fast-moving train is part of Einstein's "eureka moment." After a few short weeks, he says this eureka moment led to Einstein's most famous scientific paper.

In his next paragraph, Isaacson starts describing the two lightning strikes. It's now his turn to try to explain the experiment's "mind-blowing significance."

How well was Isaacson able to do that? We'll leave you today with a minor warning:

You'll note he says that two events may not appear to be simultaneous to each of two observers. Is that the language Einstein used? We ask that question because, truth to tell, that isn't the language from Nova.

Final point:

Einstein's work is hard to explain. Truth to tell, we don't know if anyone has ever done it.

That said, no one made Nova and Isaacson say that they could do it. It's up to them to accomplish the task they chose to undertake.

Can you explain what Nova and Isaacson are saying about that thought experiment? Remember—it's up to them to explain the science to you. It isn't your job to nod your head, like Einstein's niece, and cover for these journalistic authorities.

According to Isaacson, Einstein always refused to blindly affirm his professors, to recite what he saw as their cant. We think you'd be well advised to trundle along in his shoes.

Tomorrow: Isaacson's attempt


  1. Just from reading a simple account or Einstein's ground-breaking thought experiment, Bob can't fully understand it. He wrongly faults the writers for lack of clarity.

    Bob is asking too much IMHO. Has it occurred to Bob that no other physicist figured it out before Einstein? That this insight required an Einstein?

    1. He correctly credits Einstein with writing a slender book, though.

    2. I think the truly bad food images used by
      Bob's reCAPTCHA service ask too much of those of us with queasy stomachs.

      OT, I know, but some of that stuff makes me want to barf.

  2. Bob in his Nutshell:

    "Tomorrow, we'll see if Isaacson was....

    For today, let's only note this....

    Essentially, Isaacson says....

    In his next paragraph, Isaacson starts....

    "Final Point.....

    Einstein's work is....

    That said, no one made....

    Can you explain....

    According to Isaacson....

    Tomorrow: Isaacson's attempt"

  3. Eureka: Good News on Lead that Both Bob and Rachel Missed

  4. Will the other shoe EVER drop?

    I'm sure that at some unknown point, this endless series will resolve into a complaint about the naughty, naughty behavior of Our Tribe.

    1. You are welcome to leave the New Pavilion at any time.

  5. Sometime after midnight tonight a dead rat will crap in Bob's ThinkPad.

    1. Here I am before midnight. I wonder what that means?

    2. Zilch to most.

    3. If the man asks a rhetorical question on the platform as the train passes him, will the woman answer it?

  6. Remember—it's up to them to explain the science to you. And remember it's up to you to listen to explanations and not be an ignoramus.

    Bob sums up the results of the thought experiment thusly: Simultaneity depend on how you're moving. "Could you really explain what that means?" he asks plaintively. Well, history says no, that nobody can overcome the mental block erected in the mind of a willful ignoramus. But amid the gnashing of the teeth of the analysts around here, we'll give it another try.

    It certainly seems that simultaneity is simply a result in the universe, that there's a universal clock for everybody's reference. When we want to know whether two events happened at the same time, all we have to do is ask for the timestamp given to the two events by the clock. Of course, we may see closer events sooner than we see farther events because light reaches us first from the shorter distance. But if we can refer to the universal clock, we can find when events actually took place. Thus we'll kown the order of the events or whether they took place simultaneously.

    Let's enhance the thought experiment. Suppose we have the train parked in the station, and a man from the National Bureau of Standards shows up with two identical clocks that he's calibrated with the universal clock. For good measure (yeah, I know) he shows up with two clones of the universal yardstick (yeah, I said yardstick; this is in the US where we use the English system of measurement because it was good enough for Jesus.) The man marks the points of the platform adjacent to the front and end of the woman's train car, and he marks the midpoint of the train car and the point on the platform adjacent to that midpoint. The man and woman watch him measure the distances from the midpoint of the train car to the front and back of the car. They're the same. The NBS official then marks the the points on the platform adjacent to the middle and ends of the of the train car, and he measures the distance from the two marks on the platform adjacent to the ends of the train car to the mark adjacent to the middle of the train car. They are equal and also equal to the corresponding distances measured on the train car.

    The NBS official then sets up an apparatus to flash a light from the ends of the train car, and he uses one copy of the universal clock to find out how long each light flash takes to get to the middle of the car. He does the same thing using the other clock on the platform for the points adjacent to the ends of the train car and the point on the platform adjacent to the middle of the train car. All the measurements agree. (Which means, of course, that everyone agrees on the speed of light.)

    Next, the woman boards the train with her yardstick and her clock, and the train backs up some miles down the track and then starts toward the station. When the train comes up to speed, in an excess of caution, both the man and the woman take the measurements again. The results are the same -- the length of the train car is the same, the time it takes light beams to reach the midpoint of the train car from the ends are the same. The man gets the same results when he does his measurements using the points marked on the platform. The woman takes her place at the midpoint of her train car; the man stands on the midpoint marked on the platform.


  7. [<-con't]

    The train speeds through the station, and when the man and woman are adjacent, lightning strikes the ends of the train car. (How do they arrange for that to happen?) The two light beams race toward the woman at the midpoint of the train car, covering identical distances as confirmed by the woman's yardstick. The light beams take the same time to reach the woman, as confirmed by the woman's copy of the universal clock. The results are the same on the platform for the man using his copy of the universal yardstick and his copy of the universal clock.

    But because she's moving toward the light from the front of the train car, that light reaches her before the light from the back of the train car. That means that the supposedly universal clock doesn't deserve its name because even with that clock, the two people can't agree on whether the events are simultaneous. The man says yes (the light flashes reach him at the same time); the woman says no (the light from the front reaches her first).

    Is something wrong with the yardsticks? No, they get the same measurements whether the train is stationary or moving. Have the clocks been affected by the movement? No, they measure the same speed of light that they always have.

    But, no matter. The order of the events differs between the stationary party and the moving party, so that clock can't be universally valid for all observers no matter what the NBS official says.

    1. How do the light beams cover identical distances, yet simultaneously the front light beam reaches her first because she is moving towards it - it reaching her first because she has shortened the distance by moving towards it?

      "The light beams take the same time to reach the woman"

      How can you explain this when clearly the front beam reaches her first, thus taking less time to reach her than the rear beam?

    2. The woman is standing at the midpoint of her train car, so the light beams both cover the same distance, that is, one half of the car's length. Call that distance D. Since the speed of light is constant for everyone, the time it takes each beam to reach the woman is the same. It's easy to do the math with the definition of velocity, v=D/t. The actual velocity in question is c the speed of light, so a little algebra gives t=D/c for both beams. From the woman's point of view (aka, her frame of reference), she hasn't shortened anything since she's still standing halfway between the front and back of the train car. She'll see the light beam from the front of the train car first since she's moving toward it, but the only explanation she can make is that the lightning struck the front of the car first.

    3. The lightning did strike at the same time. Isn't the only reason she thinks the front strike happened first is because she is unaware that she has moved toward the front beam?

      Also, c is constant and no issue with your algebra, except that D is actually different for the two beams. The distance from her to the strikes is the same; however, the distance to the front beam is shortened because she moves towards it.

  8. Jesus Rode A DinosaurApril 14, 2016 at 1:33 AM

    Starlight deflected by any sun-like star with solar mass Msun and solar radius Rsun will come to a focus at 550 astronomical units(AU's). Arbitrary stars with stellar mass M and stellar radius R will have a plasma focal length of [(R/Rsun)(Msun/M)]x550 AU's. Hence, a more dens star with a solar radius Rsun will have a shorter plasma focul length < 550 AU's. A less dens star with a solar radius Rsun will have a longer plasma focul length > 550 AU's.
    Rays of starlight will come to a focus at 550 AU's from the sun. We shall refer to this distance as the Solar Plasma Focal Length.

    Light rays from any sun-like star of solar mass Msun and solar radius Rsun will come to a focus at a distance of 550 astronomical units, assuming a gravitational deflection at the angle of 1.75 arcsec.

    The image of a low impact parameter Einstein Ring would be visible to any observer located near, but not beyond the Plasma Focal Length of a sun-like star, as illustrated above. For this very reason the gravitational lensing of a stellar plasma-limb lensing system would not be visible to observers at astronomical distances from the stellar plasma lens. Plasma Limb Focusing can be observed only by placing a remote sensing system in deep space near the Plasma Focal Length of the Sun or a Star.
    The gravitational deflection of light apparently does not take place anywhere in plasma-free vacuum space. As supported observational evidence, Einstein Rings are not seen anywhere in the star-filled skies; a direct violation of the light bending rules of General Relativity.

  9. Hey, Bob! JRAD has posted material from one Edward Henry Dowdye, Jr. Check him out at Here's a taste:

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  11. If the forward lightening stroke isn't earlier as observed from the train, its light is moving faster than light emitted on the train, (again, as observed on the train). If the speed of light depended on the relative motion of the source and detector, Maxwell's equations would be wrong.

    Suppose a star is between the sun and a more distant star, a little off the direct line so we can ignore gravitational deflection of light. Suppose the farther star is moving toward us, the nearer star is moving away. Then the light from the farther star and the light from the nearer star, on the way to us, would be moving at two different speeds in the same place at the same time.

    Or think about the spinning, orbiting earth. The speed of light would vary daily, as the spin added to and subtracted from the orbital motion. It would also vary yearly, as the orbital motion added to and subtracted from the motion of the solar system through the galaxy.

    What an effed-up universe we'd have. Relativity is hard to understand, but the relativistic universe is simpler.

  12. One thing that is missing in Isaacson's and Nova's explanations is that it is the occurrence of the lightning strikes itself that is not simultaneous in the moving train and not just the time difference in the observation of the lightning strikes due to the finite speed of light. According to Einstein, even after accounting for the transit time of light, the lightning strikes that are simultaneous in one frame are not in the other frame. According to the observer on the train (already accounting for the time light takes to travel), the first strike occurs even before the positions of the observer on the platform and the observer on the train coincide.

    1. I haven't read Isaacson nor have I watched the Nova episode. But if what you say is true, Polaron, neither of them deserves any attention.

      Read Einstein. His book is permanently valuable, a classic. Having read it, move on to serious study of mathematics and physics. Relativity will then be understandable.