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I met both constructions in quite respectable texts. Is it a matter of taste, or of a shade of meaning?

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There is a shade of meaning.

Minkowski space is a mathematical entity that can be studied and applied to several different cases, but there is one specific case which stands out, as this entity describes the space-time in which "the laws of nature" are elegantly described (as part of Einstein's special relatively theory).

So when you talk about "the Minkowski space" it can be understood that you are talking about the well-known space-time of the physical universe. But you could also discuss other Minkowski spaces, perhaps alternate universes, spaces within computer simulations, or as pure abstract math models. In these cases you would use "(a) Minkowski space".

This is somewhat similar to "a President" vs. "The President" - in most cases it is obvious which President is discussed, but in a wider perspective there could be more than one.

(See https://en.m.wikipedia.org/wiki/Minkowski_space and links within)

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    Dear @eijen and laugh. Does the following quotation from Hawking well fit in your explanations: "One can obtain other spaces which are locally equivalent to the de Sitter space, by identifying points in de Sitter space"?
    – Serguei
    Commented Jul 1, 2016 at 14:46
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    In this case I think Hawking says the de Sitter space to mean "the de Sitter space locally equivalent to these other spaces", and de Sitter space to mean "de Sitter space in general".
    – eijen
    Commented Jul 1, 2016 at 14:54
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I think this is a question of whether we consider (the) Minkowski space to be a strong proper name.

According to Language Log here, here, and here (referring to The Cambridge Grammar of the English Language, pp. 517ff), there's a distinction in English between weak proper names and strong proper names. Weak ones require an article, and strong ones do not.

However, this distinction is different across dialects and speakers. I would say that especially (the) Minkowski space, being a specialized term, is prone to having both strong and weak forms since there aren't as many speakers to formalize it.

As for the reason why there are weak and strong proper names, we can only guess. My intuition is that in the case of (the) Minkowski space that it's a question of how understand Minkowski. If Minkowski is understood syntactically to be modifying space, then we have to specify that there only exists one space that Minkowski is modifying. However, if we understand Minkowski to be a noun inside the compound noun Minkowski space, then we don't need to specify that there's only one Minkowski space because that compound noun is unique.

P.S. Laugh's comment is also pertinent, since it's true that you can talk about other Minkowski spaces.

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  • laugh's comment is also pertinent, since it's true that you can talk about other Minkowski spaces.
    – eijen
    Commented Jul 1, 2016 at 14:18
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When a scientific idea is first presented to the scientific community, which is only gradually becoming familiar with it, we tend to find the definite article. At this stage the dyad {definite article + proper noun} link the idea to its proponent or "owner". Once the idea has become mainstream, and even consensus opinion, so that its owner or originator is less relevant, the definite article tends to drop out and the proper noun becomes adjectival.

P.S. That last sentence should read "...and the proper noun becomes part of the name of the thing."

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