I Problems with Einstein's 1920 "Relativity"

vanhees71

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minkowski diagram is beautiful once i understand how it slides. And I have become accustomed to picturing time as a sort of 'spatial' dimension that moves through the 3rd dimension even before I picked up this book, and yet this book still confused me
The only difficulty with the Minkowski diagram is that you have to forget Euclidean geometry entirely when interpreting it. The "length" is given by the Minkowski fundamental form rather than the Euclidean one, i.e., by the metric of space-time increments defined as
$$\mathrm{d}s^2 = c^2 \mathrm{d} t^2 - \mathrm{d} \vec{x}^2.$$
The ##-## signs make all the difference!

Usually you depict only one-dimensional motions within a planar Minkowski diagram, but you must interpret it not as the Euclidean plane you are used to from elementary-geometry school geometry. All the measures of lengths are to be inferred from the Minkowski product rather than the usual scalar product of Euclidean (affine) space. The Minkowski plane thus is rather a kind of hyperbolic plane than a Euclidean one, i.e., the temporal and spatial unit lengths are defined by hyperbolas,
$$(ct)^2-x^2=\pm 1,$$
rather than circles as in the Euclidean plane.

Then, very importantly, there are also "null lines", given by light-like curves. In Minkowski space these define the light cone. In the plane it's given by
$$(c t)^2-x^2=0.$$
For details, see my SRT FAQ article,

 

FactChecker

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Going back to the original OP, when one understands what is going on, the explanation in Einstein's book is, IMHO, about a good as it can be. The objections in the OP can be answered with an understanding of simultaneity.

One contributor here (sorry, I can't remember who) has this saying that I love in his posts:
"You did not take relativity of simultaneity into account." - The answer to 99% of all paradox threads in the relativity forum
 
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Nugatory

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One contributor here (sorry, I can't remember who) has this saying that I love in his posts:
"You did not take relativity of simultaneity into account." - The answer to 99% of all paradox threads in the relativity forum
That would be @Orodruin
 
Going back to the original OP, when one understands what is going on, the explanation in Einstein's book is, IMHO, about a good as it can be. The objections in the OP can be answered with an understanding of simultaneity.

One contributor here (sorry, I can't remember who) has this saying that I love in his posts:
"You did not take relativity of simultaneity into account." - The answer to 99% of all paradox threads in the relativity forum
there's a "trainload" of problems with it. For one, it starts off with the focus and question on whether the light flashes would be simultaneous with each other alone, not whether they would be simultaneous with the simultaneous positions of the observers.
It then goes on to specifically state that the light flashes occur when M coincides with M'. You can see where this becomes confusing fast.

Then it describes how the train observer moves forward, to run into the light, this from the perspective of the embankment, simple enough at first, yet the whole passage sort of flip flops into the train perspective. My focus isn't even on whether the two were at point M and M' when the flashes occurred, this is stated quite clearly. They were. Or so it says. I'm just trying to determine what happens from that point forward. There is no direction of attention to questioning that at all, all my focus has been guided by the chapter to the two lightning strikes.

It's not like I can't accept non-simultaneity, obviously I was expecting to analyze the trains perspective and see that he had a different idea of what happened moving forward then what the embankment observer says of where he was when it happened. If I am expected to have a very exact understanding of precisely how simultaneity operates in order to understand the passage, than how can it be a good learning tool to understand exactly that thing?

What was my fatal error? When he describes how the embankment observer (which is so unclear I mostly wrote it off as meaning from the trains perspective, even after rereading multiple times - the bit in parenthesis could be interpretted as a moving reference frame relative to the train, as the rest of the paragraph describes it as the trains perspective) sees the train man run forward into the first ray, I didn't just stop thinking there and assume that the train observer saw the same thing, and that that just must be the infallible universal truth. I took it upon myself to determine what his own perspective would be, assuming he could have a different experience, that would lead to insight into whether the two light beams were simultaneous with each other, as was the primary question posed at the beginning of the chapter.

Other people here have explained more or less the same experiment without headache.
 

PeroK

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Other people here have explained more or less the same experiment without headache.
You'd be far better off with a modern text that is built on 100 years experience teaching SR.

Also, in my view, the train and lightning experiment is fraught with the potential for misconceptions.

You can study simultaneity more simply with a single light source in the middle of a train carriage.
 

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there's a "trainload" of problems with it. For one, it starts off with the focus and question on whether the light flashes would be simultaneous with each other alone, not whether they would be simultaneous with the simultaneous positions of the observers.
The diagram shows the events A and B occurring at the instant when M and M' coincide.

EDIT: I stand corrected here. I used the word "instant" when that is relative. I am looking it as an observer on the embankment, not on the train. So I see that there can be multiple interpretations. Much of his description must be interpreted as an observer on the embankment.
It then goes on to specifically state that the light flashes occur when M coincides with M'. You can see where this becomes confusing fast.
That is exactly what the diagram shows and it confirms that aspect of the diagram. There is no conflict, ambiguity, or confusion. I won't continue farther since this point is essential in order to understand the rest.
 
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