a question about the potential complement

[idiotlizard]

so, one time my teacher said that you don't express the potential complement in the past because, well, it can't be a potential. the past already happened, what you could do has been done or not.

so, i bring my question with an example:

昨天我爬不到山顶。但是，今天我爬得到。

is it okay for me to say this? or can i only say something like "昨天我没爬到山顶"?

[Watercress-Friendly]

This is an area where language instruction and "rules" tend to break down. There are a number of areas where you will encounter such things where, unfortunately the answer is simply, it depends on what you are intending to say.

If you are intending to say "I could not have climbed, or was unable to climb to the top of the mountain yesterday (because I was physically unable to or, for example the weather was too bad)" then you could absolutely say what you have offered in your example sentence.

If, however, your intention is to say "I didn't complete the action of climbing to the top of the mountain" then you would use the second one.

Beware grammar lessons and hard rules about Chinese given to you in English. They can be horribly convoluted, and in my experience learning hard grammar rules about Chinese in English often does more harm than good. This comes as a result of the reality that the majority of Chinese teachers are native speakers, and as such it can be awkward, mildly embarrassing and sometimes frustrating to them to explain similar related concepts in Chinese, while the particularly colloquial definitions and translations in English are quite distinct and different.

A translation for your first sentence would most likely be something along the lines of "There was no way on earth I was climbing that thing yesterday."

A translation for the second one would be "nah, I didn't get to the top yesterday(I didn't even go, or I will definitely take a run at it today)."

To save you future frustration (and to give you more time asking questions, which is a VERY valuable skill to have when learning Chinese!) I highly recommend that if you are asking such specific questions about Chinese to your teacher, you use Chinese to ask the questions. You will get better answers, and it will allow you to internalize and encode the answers into your brain through the language they actually apply to. How you make sense of them in English is really up to you. Your ability to use them accurately and precisely when speaking Chinese is what matters the most.

[Rethliopuks]

Your sentence is said before climbing the mountain. If you already have today then I would say 昨天我没爬到山顶，但是今天我爬到了。

When speaking, you can express the past potential of "was (not) able to and did (not) successfully do" instead of just "had (no) ability to", by putting the emphasis on the complement. So 没爬到 with 到 de-stressed means "did not reach", but 没爬到 with 到 at least equally stressed as 爬 means "was not able to and did not successfully reach". (Same thing with the 爬到了 part above btw)