I'm currently reviewing a thesis by a student who's native language is German (like mine as well). They are often using "thereby" to express concurrency, as in
Fritz walked down the street; thereby he was whistling a song. (meaning: Fritz walked down the street while whistling a song)
To me this sounds like direct (and wrong) translation of the corresponding German sentence
Fritz ging die Straße entlang; dabei pfiff er ein Lied.
My intuition tells me that "thereby" should be used for things like causal relations, which would mean in the sentence above that Fritz's walk caused the whistling, but my intuition might be wrong as well. That said I have looked at some usage examples of "thereby" and none of them expressed the "concurrency" in the way the German "dabei" does.
Can "thereby" be used that way? If yes, is it appropriate for a scientific thesis? If no, what would be a nice replacement (in the best case one that preserves the sentence structure)?