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I am trying to understand how to use the verb must in past tenses.

Found a rule in "English grammar in use: "You cannot use must to talk about the past".

But in real life I met a lot of phrases with "must have been".

As I understand - we use "must have been" when the meaning is close to may/might. Is it correct?

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    I think when a probability becomes high, you switch from may or might to must. "How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" Sherlock Holmes. Once we’ve found the truth, we can use "must have been" rather than probably. – Pam Apr 25 '18 at 20:34
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Must is not an ordinary English verb. It's a Modal Auxiliary Verb, which are very irregular.

One of the strange facts about modal auxiliaries is that they always have at least two kinds of meaning. One use of modals (like must, should, or may) is called the Deontic sense, and it always deals with social permissions and obligations. All of the following are deontic, and have to do with what you are obliged or allowed to do, in the present or future:

  • You must remove your shoes before entering.
  • You should study harder.
  • You may leave after finishing the exam.

The deontic sense of must is the meaning that the English grammar book was talking about; obviously you can only have an obligation to do something in the future, so deontic must can't be used in the past.

However, the Epistemic sense, the other meaning of modal auxiliaries, works just as well in the past as the present, since it doesn't refer to social necessity, but logical necessity.

Present epistemic (indicating a logical conclusion about the present time):

  • This must be the place he told us about.
  • He should be home by now.
  • That may be true, but there's no evidence.

Past epistemic (indicating a logical conclusion about a past time):

  • That must have been the place he turned East.
  • He should have been home by then.
  • That may have been true then, but it isn't now.
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From what I found in terms of Merriam-Webster's definitions (https://www.merriam-webster.com/dictionary/must) the word "must" is an obligatory word toward upcoming action; and not something which refers to a past event. However, in your example, "must have been", it's used to describe something which already occurred "have been", which, is basically turning "been" into a form of verb; therefore "must" isn't being used to convey a past event per se.

Also, a similar question was asked previously; and I found the SE response to be excellent. (How can I use “must have been”?)

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Found a rule in "English grammar in use: "You cannot use must to talk about the past"

No ...

The rule is this:

The only thing that can follow a modal verb (except adverbs) is the infinitive form of a second verb. Must X is one of these (same category as should X, would X, could X, may X, might X, etc.)

I must go to the park.

I must went to the park (fails).

Given this rule, the only way you can make must talk about anything having to with the past is use have. The rules don't change for have even if must is before it, so you can say have gone or have been going.

Technically, what's going on is that the X in modals does not refer to an actual action. Something cannot exist in the past if it hasn't actually happened. So this:

I must have gone to the park

is not past tense, or talking about something definite in the past. However it is talking about something possible in the past.

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