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Der Wissenschaftler erläuterte genau, wie er bei dem Experiment vorgegangen ist.

Should not ist in this sentence be sei (the Konjunktiv I)?
The basic question is: in the indirect speech, when to use Konjunktiv I and when not?

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The subclause in question is not indirect speech; it’s a relative clause or modal clause (depending on your choice of categories). You can test this easily by trying to express this with direct speech, i.e., with quotation marks – which is impossible here. This works in both, German and English. For example, the following does not make sense, because the scientist did not say what is put in quotation marks:

* Der Wissenschaftler erläuterte: “Wie ich bei dem Experiment vorgegangen bin.”
* The scientist explained: “How I performed this experiment.”

As this is not indirect speech you cannot use sei (Konjunktiv I) here no matter what you want to express.

A similar sentence that would contain indirect speech would be:

Ich fragte den Wissenschaftler, wie er bei dem Experiment vorgegangen sei.
I asked the scientist how he performed the experiment.

Here wie is an interrogative pronoun (of the indirect speech), not a relative adverb. Therefore in old grammar or very formal grammar, we have to use sei (Konjunktiv I) because it’s indirect speech. Nowadays, this is not consistently used anymore though, and I thus wouldn’t consider using ist (Indikativ) wrong.

Note that the above test now works and we can replace the indirect speech by direct speech:

Ich fragte den Wissenschaftler: »Wie bist du bei dem Experiment vorgegangen?«
I asked the scientist: “How did you perform the experiment?”

Sidenote: Using wäre (Konjunktiv II) is possible in both cases. It signifies that the scientist did not perform the experiment. There is some implicit, irreal condition (that should be clear from the surrounding context). For example, the scientist is talking/asked about an experiment that somebody else performed and he would have performed differently:

Der Wissenschaftler erläuterte, wie er bei dem Experiment vorgegangen wäre [wenn er es durchgeführt hätte].
The scientist explained how he would have performed the experiment [if he had done it].

Ich fragte den Wissenschaftler, wie er bei dem Experiment vorgegangen wäre [wenn er es durchgeführt hätte].
I asked the scientist how he would have performed the experiment [if he had done it].

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Der Wissenschaftler erläuterte genau, wie er bei dem Experiment vorgegangen ist/sei/wäre.

All variants are correct, but they mean a different thing.

  • If you use ist, the scientist tells what he himself did. Not about what he heard of. It's a fact. No place for the Konjunktiv.

  • If you use sei, people will automatically assume er is a different person than the scientist. Because then, it's hearsay. May be true. May be not. The Konjunktiv I conveys that.

  • If you use wäre, the scientist tells the experiment he would have set up would be different from one he described before. But his experiment did not happen. It's a counterfact. That's what Konjunktiv II tells.

In short: Konjunktiv I is about uncertain facts. Konjunktiv II is about counterfacts. That's why they are used for indirect speech, thoughts and conditionals.

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    I think, your explanation of the semantics of Konjunktiv I in that case are not fully correct. I would agree, that Konjunktiv I expresses a distance from what has been said, but I think it would not express that the scientist is talking about someone else, but rather it would express doubt of the narrator in the assertion of the scientist. The meaning is more like: The scientist said, which approach they took during the experiment (But I doubt this represenation is true.) – jonathan.scholbach Nov 20 '18 at 21:25
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    I thought that when "sei" is used, the whole sentence in an indirect speech. I thought there is no 3rd different person assumed about a scientist speaking about his experiment. like this example: Ärzte sagen, Stress sei der Auslöser für viele Krankheiten. – Millen Nov 21 '18 at 6:02
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    You can use the indicative here. It implies that you have no doubts about the reported fact being true. If you use Konjunktiv I you make clear that you stay absolutely neutral about whether the fact is true or not and that it might be not true. – RHa Nov 21 '18 at 10:21
  • The use of Konjunktiv I is a matter of being neutral about what has been said or about if another one has said that or not? In this example: if I am sure about the information then the sentence would be: Ärzte sagen, Stress ist der Auslöser für viele Krankheiten. Did I understand correct? – Millen Nov 21 '18 at 11:29
  • Konjunktiv I is about uncertain facts. – Nope, it is used for some purposes (such as indirect speech) who often come along uncertainty. It cannot express uncertainty on its own. There is no case where you can use a Konjunktiv I in this subclause (and this subclause only). – Wrzlprmft Nov 21 '18 at 11:54

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