The grammatical term 'tense' is defined in Oxford as follows:
A set of forms taken by a verb to indicate the time (and sometimes also the continuance or completeness) of the action in relation to the time of the utterance.
And in CGEL*:
The general term tense applies to a system where the basic or characteristic meaning of the terms is to locate the situation, or part of it, at some point or period of time.
Apparently, therefore, the consensus in both traditional and non-traditional grammars is the term 'tense' can only be defined with the help of the term 'time', and that there is at least some relationship between the two.
But I think this relationship between the two terms is not at all guaranteed, partly because the present tense differs for a third-person singular subject and the other kinds of subjects.
She goes there.
I go there.
Now, most grammars, traditional or non-traditional, explain away the different verb forms that denote a present time, as in goes and go above, by simply saying that they are not inflections of tense but those of the grammatical person and number.
But what they can't really explain is why there exists such a difference in forms depending on the grammatical person/number, much less why past tense verbs don't have such a person/number inflectional difference, nor why the verb be retains such a person/number inflectional difference even in its past tense (was/were) as well as in its present tense (am/are/is).
Even if such a person/number inflection is somehow a valid way of explaining it all away, the time in which those so-called 'present' tense forms is not invariably the present:
I hope she goes there. [Future time]
I go there, but no one shows up. [Past time]
So, it's not even logical to argue that these so-called 'present tenses' have anything to do with the present time.
And this is not the only case where the relationship fails.
Modals often don't show any such relationship between tense and time, as shown here:
You can leave now, but you also can tomorrow.
You could leave now, but you also can tomorrow.
You can leave now, but you also could tomorrow.
You could leave now, but you also could tomorrow.
And for those of you who argue that the 'could' here somehow represents not a tense but a "subjunctive mood", I believe that except for some set phrases such as so be it, subjunctives are only possible in subordinate clauses in the Present-day English: See this Oxford article and this Wiki.
All things considered, is there any relationship between time and tense? Or should 'tense' be redefined without using the term 'time'?
*The Cambridge Grammar of the English Language by Huddleston and Pullum (Page 116)