The different usage of「知っている」and「知っていた」

Question

I am curious about the tense of ”知る” because both present and past tenses are often used.

1. 来月、このビルが壊されます。知っていましたか。(present, past)

2. 彼女がどこへ行ったか知っていますか。(past, present)

3. 〇〇ってどこにあるか知っていますか。(present, present)

And, another observation is the tense of "知る" doesn't correlate with the tense of the object.

My intuition/interpretation is:

1. The dismantle of the building is in the future, but the news was released before now. Both past tense and present are fine.

2. Not sure / No intuition

3. The existence of an object is regarded as an "present action" and therefore present tense only.

Is there any rule to tell when we can use "知っている" only, and when "知っていた" only, and when both are interchangeable?

Answer 1

知っていましたか is used to provide information the listener might not know. In English it's "Did you know <fact I already know>?" 知っていますか is sometimes used in the same situation, but it is mainly used to get information the listener is expected to have. "Do you know <fact I want to know>?" or "Can you tell me ～?"

The tense of the information itself (target of 知る) has nothing to do with the choice between 知っていましたか and 知っていますか.

• 彼が明日何をするか知っていますか。
  Do you know what he will do tomorrow?
• 彼が今何をしているか知っていますか。
  Do you know what he is doing now?
• 彼が昨日何をしたか知っていますか。
  Do you know what he did yesterday?
• 彼が明日結婚すると知っていましたか。
  Did you know he will marry tomorrow?
• 彼が昨日結婚したと知っていましたか。
  Did you know he married yesterday?

Answer 2

I'd interpret those sentences as

来月、このビルが壊されます。知っていましたか。(present, past)

Did you (already) know (so past tense) that that building will (future) be destroyed? In Japanese future is expressed with a present tense.

彼女がどこへ行ったか知っていますか。

Do you (in this moment, present tense) know where she has gone? (she's already gone somewhere, so a past verb is required)

〇〇ってどこにあるか知っていますか

As the previous question, the speaker is asking if in this moment we know that piece of information.

Is there any rule to tell when we can use "知っている" only, and when "知っていた" only, and when both are interchangeable?

The former is used for present situations (it's like a present continuous, since it's a て form) while the latter is the same form, but in a past tense. There are some rules which require a specific tense, for example 方がいいです form (that translates to "you'd better do ...") always want a past tense in a plane form like 知っていた。