Is the usage of ‘that’ in “I miss the day that I was trouble-free” ok, or must it use ‘when’?

Question

In this sentence:

I miss the days that I was trouble-free.

I know it would be correct if that were replaced by when, but would that also be correct here?

Also, I have this faint feeling that there are two types of clauses that denote the time of occurrences:

1. one type in which neither that nor when is needed
   (e.g., the day she left), and
2. the other type in which when is necessary
   (e.g., the days when I had to walk home alone after school).

I think in the first type, the action described is often transient, whereas in the second type, the action usually spans a period of time.

I’m confused and didn’t find the answer after several searches.

Any help would be appreciated.

Answer 1

John Lawler wrote:

That, as a relative pronoun (We know the man that she saw), or as a complementizer (We know that she saw him), occurs only in tensed clauses, which are otherwise independent, except for the machinery involving that.

...

The question of which wh-words can be swapped with that is difficult and varies a lot from person to person. Most English speakers wouldn't notice if that were used instead of when, since it can be used for where, why, and how. But some folks prefer when and disprefer that in this situation.

Answer 2

I miss the days that I was trouble-free.

I know it would be correct if "that" is replaced by "when," but can "that" also be correct?

The short answer is "Yes." The that subordinate clauses in question fall into three main categories:

The relative clause, which is basically adjectival: He saw the man that robbed the bank. In which the whole of the clause is an object and "that robbed the bank" specifies/defines/qualifies "the man".

The content clause, which is basically a noun clause: "John told me that the man robbed the bank." in which "that the man robbed the bank" gives the contents of John's speech.

The adverbial clause "He died that others might live" in which "that others might live" defines the purpose of "He died".

The adjectival clause I miss the days {when I was trouble-free} is simply adjectival = upon which I was trouble-free. = "I miss {my trouble-free days}

I miss {the days that I was trouble-free.} does not differ significantly from *I miss {the days when I was trouble-free.} as they both equate to *"I miss {my trouble-free days}