"At this time" vs "At that time"

Question

Is it acceptable to use "at this time" when referring to a specific point in time in the past? While in the process of telling a story, for example, that happens completely in the past?

To me it just does not sound right, and I used to correct a non-native speaker (even though I am one also, only more advanced). Since then, however, I have heard it a couple of times (I'm in the USA).

EDIT

After receiving couple of answers confirming my view, I would like to give a specific example I just found of that "incorrect" (I think) usage in this Wikipedia article on the Holy Roman Empire. (Please do a search in the text there for "at this time.")

Answer 1

"This" and "that", much like their counterparts in most other European languages, indicate relative proximity. "This" refers to a thing that is literally or figuratively "here", as in "within reach" of the person. "That" refers to a thing that is literally or figuratively further away, but "within view". "At this time" is thus normally used when referring to the present time, and "at that time" is used when referring to specific past or future times.

HOWEVER, "this" can also be used to refer to something being discussed in the present context, even if the subject of the discussion is far away in place or time. "At this point in time" or simply "at this time", then, could be used to refer to the particular point in time that is central to the discussion. Similarly, one could point at something they're holding in their hand and refer to it as "that". So, more generally, "this" is something central and implicit in the statement; "that" by contrast is something more separate or which must be identified by location or time.

Answer 2

When telling a story, I (a native American English speaker) would most likely say "at the time". For example, if I were telling someone else about my day I might say:

When I was little, I went to school 6 days a week. At the time I thought it was brutal, but it was actually beneficial to my education.

At this time to me refers more to a scenario in the present. It is used more in announcements or on signs, for example:

Commenting is not available at this time.

There is some discussion about this phrase in a blog here.

Finally, at that time is very similar to at the time. It refers to a very particular point in the past. A sample sentence where I might say it would be:

Four years ago, I broke my leg. At that time, I thought it was the end of the world.

Answer 3

I found Keith's answer excellent (+1) and agree completely with it. What is left is to apply it to the given question.

Now, I feel (as a non-native speaker) that it is possible to use "this" to refer to any time. However, the context should be such that the word feels as (quoting Keith):

"this" is something central and implicit in the statement

For example

The "move" is finished when the player releases the piece. At this time the button on the clock should be pressed.

Here the present simple is used to express a rule (as it is used to express habits and routines) - actual time is only grammatically in present, the rule applies to future and past. If we put it into past tense

The "move" was finished when the player released the piece. At this time the button on the clock was pressed, but the clock was broken and the match was stopped.

This does not sound to awkward to me, although that can substitute this with no loss in meaning.

Overall, if you can keep "this" central to the statement so that it can be easily and implicitly understood to which time it refers, I feel as if it can be used.

EDIT: In the example you are asking if in:

It is important to note, however, that jurisdiction at this time did not include legislation, which virtually did not exist until well into the 15th century.

the use is improper.

However, here, I would say that it is permissible; it is often the case that in history text the narrator transposes the point of view so that here, this, now and so on refer not to the readers present, but to the present of the events and vicinity of places that the text talks about. Keith's criterion still applies - such use of "this" is implicitly obvious. It works quite well if the events (or places) are presented chronologically.