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How would one translate “daher” in the following, please?

“Im oberen Bild liegen A und B außerhalb des Kondensators, die Gesamtladung im Quadervolumen verschwindet, es existiert daher auch kein Feld.”

— Gerthsen Physik, Auflage 25, p318.

If I translate it as “therefore”, then the statement is questionable.

If, however, I translate it as “from there (von dem Quadervolumen?) then the reasoning appears to be incomplete (i.e., the assertion is true but has not been proven to be true).

Thank you.

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    I consider Keine Ladung, daher kein Feld as striking, so which part is unproven?
    – guidot
    Nov 21, 2018 at 11:25
  • @guidot The final assertion (“es existiert ...”) is not a direct consequence of the antecedents, although it happens to be true at certain points in space (the author hasn’t really specified where there is no field and it is not true to say that the field is everywhere zero).
    – Invertible
    Nov 21, 2018 at 12:06
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    @Invertible: I still don't see your claimed gap in the implication: all formulas concerning an electric field which I found, have the amount of charge as a multiplicative factor. My guess is, that Quadervolumen refers to the space within the condensator and it is just this space for which absence of field is claimed.
    – guidot
    Nov 21, 2018 at 13:30
  • I probably haven’t explained it very well and I’m not very satisfied with my wording above. The problem is that the conclusion is consistent with the earlier reasoning, but does not necessarily follow from it. It’s akin to saying that A + B = 0, therefore A = 0 and B = 0.
    – Invertible
    Nov 22, 2018 at 11:49

2 Answers 2

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It must be translated as therefore or hence, daher does not have the meaning from there here

The translation of the full sentence reads:

In the image above, A and B are positioned outside of the condensator, the overall electric charge over the cuboid is zero, hence there is no field as well.

(I am not quite sure whether my term overall electric charge over the cuboid is actually correct english. Since you seem to deal with physics and speak english yourself, you might know that better than I do. What is meant definitely, is the integral of the electric charge over the volume of the cuboid.)

The meaning von dort (from there) which daher could have on a lexical basis, is not ruled out by the position of the conjunction, but by the fact that this meaning is referring to a direction and there is no motion-verb in the sentence. existieren semantically just does not come with von dort, because it does not make sense. This is the same in english - the sentence The charge exists from there is insemantic.

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  • Does position rule out “von dort” (Duden Universalwörterbuch)? Thank you.
    – Invertible
    Nov 22, 2018 at 11:21
  • @Invertible I added the answer to your comment to my post. Nov 22, 2018 at 11:27
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    Thank you. That makes sense. I suppose the problem is coming up with a translation that is acceptable whilst simultaneously making the author’s argument work. I was very reluctant to accept that the argument could be flawed and so I’ve been trying to force some other translation (but even that may not rescue it). For what it’s worth, this is my translation: “In the picture above A and B lie outside the capacitor and the net charge in the volume is zero, hence there is no field [through A and B].”
    – Invertible
    Nov 22, 2018 at 12:03
  • I do not have expertise in physics to judge whether the assertion is factually wrong or not. But I can understand that it is a special problem when both the sentence or your understanding of it could possibly be wrong. Nov 22, 2018 at 13:37
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    Yes indeed. It’s an interesting situation. Another difficult situation is where the author makes mistakes with the language itself. Being competent in a language means also being able to make (and recognize) the right mistakes ;)
    – Invertible
    Nov 22, 2018 at 13:52
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So, since I am sitting in a physics library I looked this up (thank you for providing the page and edition!) and I think the solution to your logical problem is in the context.

This is an example for the application of Gauss's law. It says the field on the outside of a closed surface is given by the charge it encloses. Of course there is a field inside the condensator, but the example deals with the field on the outside of the closed surface indicated in the image.

If you include this into the argument you can conclude that there is no field (on the outside), so that "daher" as therefore or hence can be used.

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  • I would put it slightly differently: the total flux through a closed surface is proportional to the charge contained therein. In the Gerthsen example the net charge within the given volume is zero. The total flux through the entire surface that defines the volume is, therefore, also zero. Due to symmetry, it can be argued that the total flux through A and B considered together is zero. Unfortunately, the author goes a step further and concludes that the flux through B alone is zero. (“und weil wir schon wissen, dass durch B kein elektrisches Feld hindurch tritt”). This claim is not supported.
    – Invertible
    Nov 22, 2018 at 13:42
  • @lizzie Your answer is turning this into a discussion about physics, not about german language any more. Nov 22, 2018 at 14:29

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