I've learned about the idea of "real time combat" in old school games a long while ago. It goes like this: since in Old School D&D combat turns take longer (usually one minute), the time it takes to resolve combat in real life is about the same time it takes inside the fictional world. If the players take 10 minutes to fight the dragon, 10 minutes have passed for their PCs too.
(This doesn't usually work for modern D&D, since combat turns are only six seconds and combat is more complex; a combat may take an hour to resolve in the table, but only one minute has passed in the fictional world).
Recently, I've been hearing about "real time downtime" or something similar (usually called "1:1 Timescale" or something; Jeffro Johnson has been talking about this recently, as have some YouTube channels). This means that if you spend one week (or one month, etc.) between sessions, one week has passed for the PCs, allowing them to heal, research, rotate characters, etc.
These are both interesting ideas that I have not tried extensively.
This post is about a similar idea, that I haven't heard elsewhere (AFAICT).
Old school D&D has strict rules governing how long exploration takes: one exploration "turn" takes 10 minutes and allow moving 120 feet (for an armored PC) or searching through a 10 x 10 square (or something; I do not remember the exact numbers).
This is a simplification. It should be obvious that finding a key on the ground of an otherwise empty, featureless room is faster than finding it in a chest full of objects.
Of course, creating (or dealing with) different rules for every situation would be cumbersome.
So why not try real time?
Take this example (a room with six statues, the only treasure is an emerald eye in one of them):
GM: "You enter a small room with six painted statues. They depict humans in various poses."
PC 1: "Do we recognize anyone"
GM: "No, they look like ordinary people. One statue has sculpted fruits around its feet, another has a couple of dogs, a third one has coins and ...".
PC 2 (interrupting): "I'll examine this one!"
GM: "The one with the coins?"
PC 2: "Yes! Can I take the coins?"
GM: "No, they are sculpted in the rocks."
PC 2: "Is there anything else in the statue?"
GM: "When you look closer, you see one of the eyes is completely green... looks like an emerald (or: "roll perception", etc.).
As you can see, the longer the players and GM converse, the longer the PCs take. If the PCs are uninterested in looking further, they only see the obvious, but it takes less time. Conversely, detailed exploration will take longer both in the real world and in the fictional world.
Our example takes less than 10 minutes, of course, but that's only because the PC chose the right statue right away.
There are lots of caveats and exceptions, of course.
Six PCs could search the six statues simultaneously; in that case, the DM should briefly describe there is nothing important about any of them except for one. Conversely, if a single PC wanted to examine every single statue, the DM could simply ask "how long will you take" and decide if the time chosen by the PC is enough to find the eye (one minute would not be enough IMO, but 10-20 minutes might).
Every time that the players or GM mention time units ("we will rest for 10 minutes", "it takes half an hour to climb the mountain", etc.) is an exception for the "real time" procedure.
As an aside: it is obvious that the "real time" rule applies to interactions, conversations, etc. Usually, we reproduce in the real world the conversations the PCs and NPCs are having. The same applies to conversations between the PCs - even if the players are talking about metagame issues ("Is anyone hurt? I can heal.", "Let's see, I lost 10 HP..."), we assume the PCs are having a similar discussion ("I have only a small wound....").
For outdoor exploration, applying "real time" is really hard; I wouldn't use it. For urban exploration, it would work when interacting socially, but transportation would require fictional time ("it takes twenty minutes to go to his house"...). Both of these are beside the point; this idea is for dungeon exploration, and you're not usually searching through 10x10 squares in the forest or city streets.
I it far from perfect, but I feel there is something to it...
What is the point?
My main goal here is the following experiment:
Get a timer. Mark 30 minutes (or one hour, etc.). When the bell rings, maybe you roll for random encounters, torches go out (if appropriate), and so on.
This happens no matter what the PCs are doing - exploring, resting, or even fighting. Torches might go out while you're looking at the statues; another encounter may happen in the middle of combat*! Maybe reinforcements? Or potential allies?
(*Combine this with real time combat for great results!)
It feels organic, and it is one less thing for the GM to worry about. You do not need to keep careful track of time... just use a timer!
(Make sure it is a timer you can readjust on the fly. If the PCs rest for 10 minutes and there is more than 10 minutes left, adjust the clock. If there is less than 10 minutes left, they might be interrupted during the rest).
This is not only for the GM - the players will hear the alarm too (being interrupted by surprise is the whole point), although it would probably be better if they don't try to "game" the system (to rest with no chance of encounters, for example).
I'm expecting that this will create a sense of urgency in dungeon exploration, increasing focus, and making conversation between players much more deliberate. Might even increase attention, etc. On the other hand, it might feel too intense for casual games.
Well, I think it is worth a try. Let me know if you ever tried something similar!