As the time passes by = specific time = (imagine you and I were in the same room and I am referring to the current time we are both experiencing) "As the time passes by, I want you to focus on your breathing." As time passes by = general time = As time passes by, we become more selective as to how we live our lives.

Ray gave a good answer. Yes, you can use both 'passes' and 'passed'. You can use 'be' forms, e.g. 'as the time is passing by' or 'as the time was passing by', but again those would be less common. I would like to emphasise the fact that using 'the' with time is only used in very specific cases, so it is relatively uncommon to use that form. When you say 'more examples' it's not clear what you want examples of. Of 'passed by'? or what time can do? Slowly, the crowd passed by. <- here we use 'the' because it is a specific crowd. The train slowly passed by the station. The time ticked away'. <- again, some specific time, e.g. to an event.

"As time passes by I become more aware of how quickly my children grow older". "As time goes by" (more commonly used )

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