The short story in the link does not speak about the time, but the direction of time.It is quite clear that even in the story the time exists. You see a clock moving, you feel hungry after a while, you see the paint fall from the wall. In All these cases, there are physical processes In which you can distinguish earlier and later. You can even do an (inaccurate) time measurement using the number of heartbeats you count, or the number of paint chunks that fall from the wall. Time is a fundamental trait in any physical description: classical mechanics, Relativity and quantum mechanics.
The direction of time is another story.Any theory of nature does not give a preferred direction towards the time. If a physical law says that by doing A B follows, then the reverse must also be possible. Yet when we look around us, even in the grey room, we see the time walking in one direction. The clock never runs backwards, the paint chunks will never jump out of the floor and stick back to the wall, the fallen hairs will never jump back to their position on your head. This was discovered at the end of the 19th century by Boltzmann, which applied the properties of natural laws to very large systems. It turns out that all natural laws at micriscopic level are insensitive to the reversal of time, yet at macroscopic level only time will go ahead. This is due to the statistical properties of systems on a large scale. A single oxygen molecule can fly from the floor to the upper right corner of the room and back again. But the likelihood that all oxygen molecules do that in the room is unlikely to be small (but in absolute terms not 100% impossible). A radioactive atom can disintegrate into electron, neutrino and smaller atom, but also an electron and neutrino can be captured and again make a radioactive atom. The probability that this last happens is just very small (but not 100% impossible). The bigger the systems the smaller the chance to see natural processes running in reverse order. And that chance is very small, unlikely to be small even on atomic scale.
The direction of time is an illusion, which exists only because the universe is so large, and relatively young (compared to the eternity that our universe can exist), and can grow endlessly.The time itself is real.
Time exists and space too.The three spatial dimensions and the time dimension form our four-dimensional space time, the universe.
Time has to do with entropy.With rising of the time the Entropy (disorder) rises. The past is a state of greater ordination than it is now, the future is a state of greater disorder. That is why we can remember the past. Indeed, a state of greater organisation is known. A state of greater disorder is inherently unpredictable and unclear. The past is therefore fixed and the future is completely open.
Time is indeed tricky in some areas of physics.
In quantum mechanics, many formulas have no time component.This means that comments can go on each side, there is no preferred direction.
For example, the annihilation of matter and antimatter in two photons can happen just as well reversed.
On a larger scale, however, this is no longer true: dropping a cup in shards can easily but reversed shards into each other as a cup is practically impossible.
An idea of Sean Carroll is that time is related to entropy, because entropy (the degree of disorder) only increases.
In The theory of relativity, time and distance are linked and relative.At very high speeds, the clock will slowly tap, if you compare it to a clock on earth, for example. At light speed, the clock stops ticking. So for a photon there is no time (or distance).
Time is relative.It may even dwell, as for a photon. Also time in itself does not exist IDD. It’s always space time. You cannot actually split this. If you have a date you also do not agree to only 20h off, right?
No, as a non-physicist I say: No, time does not exist.
You can long search for 芒 鈧?虄time 芒 鈧劉, in your home, garden, City, on Earth, in the universe -but you will not find anything anywhere you say 芒 鈧?艙h脙 漏, I have 芒 鈧?虄m: The time. 芒 鈧?The same goes for length, weight, temperature…All untraceable.
Physical models do not exist either.What we do is try to divide an incomprehensible world into bite-sized chunks and we do so with models and concepts. And that’s a great way. We are increasingly understanding something that is large and elusive.
Incidentally, there are thinkers who believe that past and future do not exist either.The only thing that exists is the 芒 鈧?虄nu芒 鈧劉, an endlessly elongated now. That has an advantage: I have taught my children that if you do it right now, few problems will come.