The user John Rennie suggested I ask the following as a new question:
If time is continuous why would the perception of time being continuous or flowing be an illusion?
Whether or not time is continuous or has some sort of discrete time step, consider the following. Imagine you had a very powerful computer at your disposal, or that the laws of physics happened to be simple enough that we could simulate something as complex as a sentient, self-aware organism using it. Now, we hit "start" on our simulation, and wait a few zillion cycles until the humans pop up. Now, we hit "pause", commit our results to storage, and turn off the computer and go have lunch. Later, we come back, and because we want to show our colleagues what we've found, we run the simulation backwards a few million years and hit "start" again. The humans are non the wiser. Can you see why it might be argued that the flow of time might be illusory?
I looked at the previous discussion that you had about this here in the comments and I think I may have an idea about what is going on here, but I expect someone else will post a better reply here.
First I want to quote three of John Rennie's comments.
See this article on the block universe. Note that most us regard this as philosophy not physics
The interval between two timelike separated points certainly isn't an illusion. The illusion is the human perception that time flows
No, there's no suggestion that time isn't continuous. The illusion is that it flows. We wouldn't say that distance flows; it just is. The same argument applies to time. Do some Googling for block universe for more on this idea.
The way I see it is the following.
1) we can measure distance and we can measure time.
2) distance and time are not always what we expect them to be, which can be understood (or at least modelled) with relativity, particularly general relativity.
3) For example, people in different frames can measure the time to pass at different rates.
It may, therefore, be an illusion that time flows steadily the same everywhere.
In addition to this John Rennie made an interesting link, which I don't understand to the idea of the block universe.
He or someone else may provide a better answer.
I think we're getting into the philosophical and metaphysical.
Perhaps the flow of time is an illusion in the sense we believe it to be. If we take the points on a graph, we can see a proportionate of them simultaneously, whereas we don't perceive "all time" instantly.
Not only can we record a point in the past, time appears to flow from the past, into the present and on into the future.
Do different organisms perceive this flow at the same rate? A 400 year old tree growing imperceptibly slowly, to us?
the key is the word "perception" no person can get another person's perception of anything. the question could be re-worded to be more amenable to physics by asking something about the physical world of matter and energy not one's internal perceptions, just a suggestion.
If I do not misunderstand your question, what you are asking refers to what is called block universe. In the block universe, time does not unfold, but is equivalent to the the spatial coordinates in the sense that all the time past present and future already exists, in the same way that the negative axis, the origin, and the positive axis direction in space at any given time exists, and space does not flow. In this universe the flow of time is an illusion, a causal estructure is no much different than a spatial structure, and, the present time is a illusion. There is a infinite numbers of you's each experiencing the different presents. The more philosophical part is what is consciousness and why it exists, why a temporal structure actually has a subjective experience. Philosopher Daniel Dennet goes beyong, and states not only that time is an illusion, but that consciousness itself is an illusion too.