Would time exist if there was nothing? I thought about this topic briefly, and this is what I came up with. It could be wrong. If you see any points that are not right, or don't make sense, please let me know. Thanks.
I was reading Hume on Time, and his idea of time is that it is the internal perception of mind, just like cause and effect, when objects exist in duration and succession. So without the external objects, and without changes in duration and succession, there would be no time. I agree with this view on time.
Indeed, time does not exist in the external world. It is in human perception when the mind perceives changes of the external objects, or movement of the objects in succession, the perception of time happens internally.
The time we are using now on the clocks is the universal cultural agreement by the movement of the Earth around the Sun (365 days per one rotation), and also rotation of the Earth (24 hours per one self rotation), and it is just measurement of the duration for general life conveniences. It has nothing to do with the actual time itself. They could easily declare today is year 0, and 1 day will be 100 hours on some other duration measurements, and the whole time contract will work differently.
The reason that time travel is not possible in the physical world is that actual time doesn't exist in the physical world.
Time is just a product of human perception, which is mental in nature. If one is put into a room with no windows, but just 4 walls, floor and ceiling, and he has been kept in the space for few days, he will never have a single clue on the amount of time passed while he was in captivity in the space, because there was no events, changes or movements at all around him for his perception to realise the time durations happened in that space.
We only feel time because every morning, we see the Sun rise, even if it is raining or cloudy, it still is brighter than the night, and the daylight changes to the evening, and nights again, hence knows a day has passed. Therefore with nothing existing, there is definitely no time. With everything existing, still there is no time, because time is in the human mind inaccessible to the outside world and other humans.