If we hypothetically lost all watches and all devices that keep track of time, how would we say what is the current time? Or we actually don't and time is just a convention?
For any system, whether classical or quantum, the time evolution is given by the Hamiltonian (well, the derivative of the Hamiltonian for classical systems). A clock is simply a system where the time evolution has a convenient form e.g. a regular tick, water level in a clepsydra, sand in an hourglass, etc. Any physical system can be used as a clock by measuring its initial state and then comparing its later state with the calculation from the Hamiltonian.
So when you talk about all devices that keep track of time if you really mean this you would have to completely empty the universe.
We can see the positions of heavenly bodies to determine the time, relative to an earlier time when we knew their positions. Although the year 2014 is definitely man-made, the age of the universe is a discovery, which can be rediscovered.
So, seeing as we probably won't lose the heavens (which also tell us what season it is), we can't really lose track of time. But if hypothetically we couldn't reference our current system of months and years, we could just devise a new one based on the planets.
Put a stick in the ground and observe the shadow cast by the sun. When the shadow is at its shortest that's local noon. Mark that point on the ground or your sun-dial.
Each day mark the azimuth at which the sun rises. Also mark its height at noon (by measuring the length of the shadow it casts if you aren't on the equator). The day at which the sun is at its highest at noon and its shadow therefore shortest is the summer solstice.
Then invent clockwork.
If we hypothetically lost all watches and all devices that keep track of time, how would we say what is the current time?
Standardized time via time zones are a relatively recent invention. Before that, you could use a sundial; when the shadows stopped getting shorter and started getting longer, that was noon. If you needed a more accurate measurement then you could use a sextant, which is simply a device with mirrors and lenses and whatnot to more accurately determine when the sun stops going up and starts going down.
Since local noon differs by 1/360th of a day for every degree of lattitude you travel, this system quickly becomes inconvenient if you can travel faster than a horse. When railway travel became widespread we had to invent time zones, where all clocks in a particular geographic region are made to agree regardless of when it is locally noon. If this interests you, "Time Lord" by Clark Blaise is an enjoyable read on the subject.
If we were to lose all watches or other helpful devices which tell time, we would lose our common reference point to time as well as our mechanically enhanced ability to precisely perceive and communicate time.
Virtually no one would be able to accurately refer to the correct minute of the day and only few people could refer to the hour. I'm sure that a few organizations would quickly develop some means of tracking and communicating time, but for the rest of us, we would probably default to the sun and refer to time using a description of the day like:
- In the late afternoon
In general, most of us would lose the ability to collectively understand or communicate time with a level of precision greater that 2 or 3 hours, over the distance of a few thousand miles. Keep in mind that 'noon' is not the same for people in different time zones.
"If we hypothetically lost all watches and all devices that keep track of time, how would we say what is the current time? Or we actually don't and time is just a convention?"
OK, say a band of intergalactic thieves appeared and stole every timepiece on Earth, from hourglasses and sundials to atomic clocks. Is your question, "How would we reestablish 12-noon in, say, New York?" Assuming we didn't forget how to build clocks, or what the time zones were or what that brass strip running through the Royal Observatory is for, we could get pretty close, knowing the position (elevation) of the Sun (and knowing the longitude of the site and the Equation of Time and the date). Beyond that, super-precise time is arbitrary, and we'd have to come to an agreement on setting our rebuilt atomic clocks. Basically, whoever gets one up and running first gets to declare the exact time.
Yes, we have those super-precise atomic clocks, but the time they show is adapted to the astronomical phenomena.
There are Leap seconds added because of irregularities in the Earth's rate of rotation. Our astronomical knowledge and instruments are precise enough to determine our conventional time more precise than atomic clocks.
So even if all clocks have stopped to function, we would still could very precise say what time it is. Because we do it anyway.