What is the difference between もう...ました and もう...ています?


For example, もう開いています and もう開きます or もうしゅくだいをしました and もうしゅくだいをしていました。What is
the difference in interpretation and understanding between the sentences?

I know that ました when paired with もう means _already have done_ , but how is
that different from ています and もう?




開いています is most likely understood as describing a state where something is
open, although it is not impossible for it to mean something is in the process
of opening. もう simply adds that it is already in that state.

> もう開いています。  
>  It is **already** open.  
>  It is **already** opening. (much less likely)

開きます alone could refer to either something that opens habitually (like a store
opening at a regular time every day) or something that will open in the
future. もう rules out the first option as it obviously refers to a one-time
event. It means something like “soon” or “in no time” in this case.

> もう開きます。  
>  It will open **in no time**.

[宿題]{しゅくだい}をしました alone would refer to what someone did at some point in the
past. When used with もう, however, its focus shifts to the current state where
that person has already passed that point.

> もう[宿題]{しゅくだい}をしました。  
>  I have **already** done my homework.

[宿題]{しゅくだい}をしていました could mean either someone was doing their homework or
someone had done their homework by some reference time in the past. もう doesn’t
completely remove this ambiguity.

> もう[宿題]{しゅくだい}をしていました。  
>  They were **already** doing their homework.  
>  They had **already** done their homework.

