EINSTEIN'S OWN WORDS: How to assess two (or more) lightning strikes!

THURSDAY, APRIL 28, 2016

Part 3—In search of simultaneity: How did Albert Einstein explain "special relativity" in his own brief book, the one aimed at general readers?

You're asking a very good question! The book was published one hundred years ago, in the year 1916. Last November, the PBS program Nova worked directly from its pages as it explained the "mind-blowing" significance of special relativity during an hour-long broadcast.

Nova described a "brilliant thought experiment," a chain of reasoning Einstein described in Chapters 8 and 9 of his brief book. In 2007, Walter Isaacson had worked from the same material when he explained "the great conceptual step" Einstein took when he formulated the special theory of relativity.

Question: Based upon that Nova program or that best-selling book, can you explain special relativity? Assuming that Einstein did produce a great conceptual step, can you explain what that giant step was? Can you explain why it's mind-blowing?

We'll go first. We can't explain that conceptual step. We'll bet a railway platform and two lightning strikes that you can't explain it either!

Bantamweights of the world, unite! This is where Einstein's own words theoretically ought to come in!

Nova and Isaacson were both working from two brief chapters in Einstein's book for general readers. If their presentations don't seem to make sense, what did Einstein say? How did Einstein explain the rumination involving that very fast train and those lightning strikes?

What did Einstein say, in his own words? For today, we'll review his very brief Chapter 8. Tomorrow, we'll move ahead to his brief Chapter 9. To peruse his whole book, click here.

Yesterday, we showed you how Einstein's Chapter 8 started. Again, the chapter is very brief. Chapter title included, this is the first of only three chunks we'll have to look at today:

VIII On the Idea of Time in Physics

Lightning has struck the rails on our railway embankment at two places A and B far distant from each other. I make the additional assertion that these two lightning flashes occurred simultaneously. If now I ask you whether there is sense in this statement, you will answer my question with a decided “Yes.” But if I now approach you with the request to explain to me the sense of the statement more precisely, you find after some consideration that the answer to this question is not so easy as it appears at first sight.

Einstein is asking a slightly puzzling question, and making a slightly puzzling statement, as his brief chapter starts.

He tells an interlocutor that two lightning flashes have "occurred simultaneously." He then asks his friend to "explain the sense of the statement more precisely." He suggests that "the answer to this question is not so easy as it appears."

Einstein has some explaining to do! In fact, the meaning of his statement seems to be perfectly clear. If we say that two lightning flashes (or two lightning strikes) have occurred simultaneously, we typically mean that the two events happened at the same time.

That's the simple-minded, everyday meaning of Einstein's simple-seeming statement. Where could a possible problem arise? Continuing directly, Einstein starts to explain:

After some time perhaps the following answer would occur to you: “The significance of the statement is clear in itself and needs no further explanation; of course it would require some consideration if I were to be commissioned to determine by observations whether in the actual case the two events took place simultaneously or not.” I cannot be satisfied with this answer for the following reason. Supposing that as a result of ingenious considerations an able meteorologist were to discover that the lightning must always strike the places A and B simultaneously, then we should be faced with the task of testing whether or not this theoretical result is in accordance with the reality. We encounter the same difficulty with all physical statements in which the conception “simultaneous” plays a part. The concept does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case. We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment whether or not both the lightning strokes occurred simultaneously.

Please note: Einstein is now describing a slightly odd situation.

In this slightly odd situation, we're trying to determine if two lightning strikes are actually simultaneous. The slight oddness comes from this:

A meteorologist has somewhat implausibly claimed that "lightning must always strike the places A and B simultaneously." To test this unusual-sounding claim, Einstein seems to say that we need to come up with a method to demonstrate that two such strikes really did occur simultaneously.

Please note: Einstein seems to be using some slightly unusual language. It seems that he is saying that we need to devise a method to test this unusual-sounding claim. As a matter of fact, he uses that very word.

But instead of simply saying that we need to devise a method, Einstein tells his interlocutor that we need a definition—"a definition of simultaneity such that this definition supplies us with the method by means of which" we can decide whether the two lightning strikes did occur simultaneously.

That seems like clumsy language. We don't know why Einstein states his point that way.

At any rate, Einstein proceeds to describe a method which would let us settle the question at hand. When he continues, he describes the way we would have to proceed.

In an act of generosity, he lets his interlocutor come up with the method which would settle the case:

After thinking the matter over for some time you then offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line AB should be measured up and an observer placed at the mid-point M of the distance AB. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90°) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.

Eureka! We'll place an observer exactly halfway between points A and B.

Einstein's description is still a bit fuzzy, but this seems to be what occurs:

Apparently, we imagine that this observer sees lightning strikes occur at points A and B. If he perceives the two flashes at the same time, this means that "they" (the lightning flashes? the lightning strikes?) are simultaneous.

Einstein's formulations are a bit fuzzy, but the physics here is quite simple. We seem to know where the two lightning strikes have occurred. We also know that our observer is located halfway between them.

In that circumstance, we would naturally judge that the strikes were simultaneous if the light from the strikes reached us at the same time. (If we were closer to place A and farther from place B, we wouldn't make that same judgment.)

The situation being described is a bit artificial. That said, nothing seems to be difficult or complex about what Einstein has said.

In Chapter 9, he goes on to refer to this formulation as "the most natural definition of simultaneity." If you're halfway between two events, and you see the events at the same time, it would be natural to declare that the events were simultaneous.

A few additional points are made in this very brief Chapter 8. Einstein answers a few half-hearted objections from his interlocutor. He notes that this method for judging simultaneity can be used in the case of two or more events.

That said, we've now covered Einstein's basic work in this very brief chapter. Chapter 9 lies ahead.

Why does Einstein keep describing a method of assessing simultaneity as a "definition?" In his biography of Einstein, Isaacson refers to this "definition" as an "operational definition." He seems to relate Einstein's formulation to some of the philosophers to whom Einstein had been exposed at this time.

At any rate, Einstein mainly crafts this "most natural definition of simultaneity" in his very brief Chapter 8. In Chapter 9, his fast-moving train will appear.

So will a degree of confusion, possibly even incoherence. One hundred years later, our elite professors, journalists and publishers haven't yet puzzled it out.

Tomorrow: The arrival of the fast train