The US measures distance in feet. However, even if humans had not grown feet, the general concept of distance would still exist.
Similarly, if there are no solar days on this planet, they wouldn't be using a unit of time based on a solar day; but that doesn't mean that the locals are oblivious to the general concept of time progression.
How are people able to keep track of which day of the week it is, since a week is an artifical construct that does not occurr naturally?
The answer is that it is inherent to tracking time. When you track time, you are inherently aware of what time it is at a given point.
if a planet is tidally locked to its sun, how would the people on the surface, assuming its habitable, be able to tell time?
Even though our planet experiences sunrises and sunsets (and your tidally locked planet does not), our method of keeping time is no longer connected to the sun rising and setting.
We've created completely independent time tracking systems (atomic clock, quartz crystal, expressing time as a function of lightspeed, ...), and we've simply decided to retain the traditional time units that used to be relevant when we tracked time based on the position of the sun.
There is nothing that stops humans from changing the time units to something completely artificial and unrelated to our planet's movement relative to the sun. We could e.g. decide that a year is now 400 days long for the sake of mathematical simplicity (i.e. the length of a day is unchanged, but there are now more days in a year). Although a year (400 solar days) would then no longer accurately reflect Earth's orbit around the sun, there is no problem with this change from a time tracking perspective.
What devices would they be able to use? Obviously a sun dial is out of the question.
Sundials are passive clocks that do not need to be set (other than physically placing them). Which is nice, but much too inaccurate for our modern day standards anyway.
Your civilization can use any other clock that we use. Since they have no natural frame of reference (e.g. sunrise/sunset), they are free to choose whatever method they want. The only thing that's important is that the used time tracking method must independently yield consistent results. If you and me synchronize our watches, split up and meet again in the future, our watches should still be in sync (I'm omitting relativistic time dilation for the sake of simplicity).
So, assuming they evolved on this planet, what would a device look like to measure time on this planet, and how would this device have come about to begin with?
As I said, most human clocks nowadays do not observe the movement of the sun. They simply happen to be using a unit of time that coicides with the duration of a solar day.
Therefore, you can use any timekeeping system which does not rely on solar positioning:
- Quartz crystals (the crystal's resonance defines the passage of time)
- Atomic clocks (the atoms' resonance defines the passage of time)
- Pendulum clocks (as long as gravity is constant everywhere on the planet at a given altitude, a pendulum can define the passage of time)
- Hourglasses (as long as the material consistently takes the same amount of time to go through the hour glass)
I am also curious as to how they would develop a concept of time because they wouldn't be able to not the passage of time nearly as easily.
I don't quite agree with you. Even if our sun would not have moved, or would have moved erratically, animals would still have needed to rest from time to time.
Because we have a consistent sunrise/sunset, animals have historically adapted to setting their biological clocks to this rhythm, for the sake of simplicity (so that e.g. our eyes only really need to work in daylight, and less so in darker conditions). If we had evolved a sleeping pattern that was unrelated to the sun's position in the sky (e.g. awake for 30 hours, sleeping for 10 hours), then our bodies would simply have evolved to deal with life both at night and during the day.
Time is not inherently tied to planetary movement. Time is nothing more than a linear progression of events. It just so happens that we decided to use our planetary movement as a unit of time.
Analogously, the US measures distance in feet. However, even if humans had not grown feet, the general concept of distance would still exist! We would simply have used a different unit of distance, possibly either related to a different body part ("This wall is ten heads long and fifty heads wide") or using an artificially decided unit of distance.
Interestingly, the meter is such an artifically constructed unit of distance:
In 1799, [the meter] was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889).
People literally just made a metal bar, and then said "the length of this bar is now called a meter."
A definition for a meter was then drafted, which may have tweaked the actual distance of a meter, since they used a rounded definition: one ten-millionth of the distance between the equator and the pole. However, before they decided to define a meter as such, they were already aware of roughly the unit of measurement they were looking for. If the outcome of this definition would have been 1mm or 1km, then they would have used a different definition for a meter, rather than define the meter as whatever the outcome of the definition is. Therefore, the decision came before the definition.
Why was this bar exactly that length? No reason. They just had to pick anything, really, so they picked this particular distance.
The only real consideration that was made is that the chosen distance was sensical to humans, e.g. it's impractical to define a unit of distance based on something a human cannot perceive, whether it's the width of an electron or the diameter of the sun. These are not intuitive because we have no way to easily see this distance or use it for comparative purposes.
As it is defines, the meter makes sense. It's roughly as long as a human leg, which means that we have a somewhat accurate representation of the meter on our body (just like the US foot).