Gfyuki

You already seem to know the scientific perspective on this, but perhaps it's still worth elaborating a bit on it.

You can define a second as the amount of time that passes between two ticks of the second hand of a clock. Our modern definition of the second is essentially a more precise version of the same idea, where the oscillations of the radiation emitted by a suitable atom play the role of the hand of the clock:

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

So if nothing happens during your "second" in the whole universe—if no clock moves its hand and no electromagnetic wave oscillates—then no time has passed.

From a theoretical point of view, this hand of the clock or radiation does not necessarily itself need to be "real". It's enough to consider what would happen if such a clock or such radiation was present. An empty universe which contains no matter at all but in which times passes is perfectly conceivable by the laws of physics. Plain Minkowski spacetime is like that.

The OP asks the following questions:

Does the minimum unit of time coincide with the smallest change? Does time dissolve without differences between things?

Bradley Dowden surveys two perspectives, substantivalism and relationalism, with regards to the question whether time requires change:

Substantivalism is the thesis that space and time exist independently of physical material and its events.

Relationism is the thesis that space is only a set of relationships among existing physical material, and time is a set of relationships among the events of that physical material.

Dowden notes that "Relationism is inconsistent with substantivalism; they both cannot be true, although they both could be false." Both sides agree that time cannot be measured without change. The disagreement is whether time exists without change. The substantivalist can have an "empty time". The relationist cannot.

The difference between these two views goes back to Plato, a substantivalist, and Aristotle, a relationist. More recently Newton was a substantivalist and Leibniz a relationist.

Leibniz claimed that Newton's substantivalism violated the Law of the Identity of Indiscernibles and the Law of Sufficient Reason. Leibniz argued that if God transformed the world in space or time but changed nothing else this would be a different world for Newton, but not for Leibniz, and there would be no reason for God to do something like that.

Kant sided with Newton and Ernst Mach sided with Leibniz. Einstein took both positions: initially a relationist and later a substantivalist.

Dowden offers a modern defense of substantivalism using fields:

Another defense of substantivalism says that what physicists call empty space is an energetic and active field. There is no region of the field where there could be empty time in the relationist sense of Leibniz.

The answer to the OP's question is a current controversy between substantivalism and relationism with a reminder from Dowden that both sides could be wrong.

Bradley Dowden, "Time" Internet Encyclopedia of Philosophy https://www.iep.utm.edu/time/

You seem to be asking "what is time?".

If you are asking in the sense of our science of physics, then time is defined by its measurement: time is what a clock reads. Quite literally that. And since Einstein, that is a rather flexible definition. Anyways, it does not tell you anything about what time actually is. But by that definition, in your example, since the clock itself would freeze for a minute or million years as well, your "pause" would indeed not be relevant, and time (sic) would not progress until the clock continued moving.

If you are asking in the sense of "reality", then the answer is "nobody knows". We don't know enough about the universe to decide what things actually, really, really are, and physics does not change that in the least. This is not only true for time, but for anything at all. We only have mathematic/physical theories, which happen to not having been proven wrong yet, but all they do is make predictions about how certain measurements could turn out in certain experiments (our eyes are only measuring instruments as well). We arguably can never leave Plato's Cave, or at least we are quite far away from it.

If you asking in a philosophical sense, then the answer is up to you, really, to go by taste and opinion. People have come up with plenty of different interpretations.

I once read a thought experiment (I wish I could remember where see below) which attempted to establish that there is a subtle difference between the passage of time and change. It basically went like this:

Imagine a hypothetical universe which is composed four islands separated by force fields that no matter could pass through, but which was permeable by light and radio waves. Travel and trade was not possible between islands, but they can freely communicate with one another.

Every so often, a pink cloud would appear over one of the islands, and would sit there for 1 week. After 1 week, from the perspective of the other islands, the island which had observed the cloud, would cease all radio communications and their section of the universe would effectively go 'dark' for a period of 1 week. However, from the perspective of the people living on that island, the cloud would simply disappear without any other perceivable change, and the other three islands' clocks will have been advanced by 1 week. Scientists studying this phenomena have been unable to detect the 'missing time' by any physical means other than by comparing their clocks with those on other islands. The universe has always been this way, and its residence just accept it.

One day, a pink cloud appears over all four islands simultaneously. After one week, the clouds simply disappear and all the clocks in every island remain in sync. No one will have been able to detect the 'missing time', even though it's perfectly reasonable for the residents of this universe to infer that it existed.

Of course, this thought experiment takes place in a very different universe than our own, it doesn't address the question about whether or not such a scenario is physically possible in our universe. The point of the thought experiment is to show that from a purely philosophical perspective it can be meaningful to say:

For some period of time, nothing happened.

Update: Francesco D'Isa pointed me in the right direction. The original thought experiment was proposed by philosopher Sydney Shoemaker in 1969 in "Time without Change".

Since one might say that one of the important properties of time is to allow for change; to then suppose time exists, but that there is no change, rather goes against this.

It's a logical possibility, but then so is a universe with nothing in it; or indeed, no universe at all.

Time is conceived by mind. There is no absolute time only brownian movement everywhere. We are scanning the world through our eyes at a rate of around 16 Hz. For a honey bee it is higher. So in Honey bee's perception we are slow. We have chosen some band width to scan this world and relatively we are calculating. Time also relative. one second can be dilated to even millions of years if we are that much faster.

Further expanding upon the computer simulation idea brought up in MattClarke's answer: One interesting idea is the idea of mind uploading. If human consciousness happens to be Turing-compatible, then it
would be theoretically possible to convert a human mind into a piece of software.

Then, just like normal software, the host computer would be able to arbitrarily suspend and resume the simulation program. Modern operating systems can run hundreds of processes simultaneously because it has a scheduler that is constantly suspending and resuming processes, giving each process a fair share of computing time, i.e. timeslicing.

The running process has no awareness of whether it has been sliced or not; it just continues normally. So in that sense, no time has passed for it, yet time has passed in the outside world. However, the process might realize that it is being sliced by observing skips in the system clock, for example. So there was a change. But if you completely sandbox the process, it would not be able to perceive time passing any differently than normal, no matter how often and how long you suspend it.

There's a science fiction novel called Permutation City that explores lots of interesting implications of simulated minds:

Within the story, "Copies" – digital renderings of human brains with complete subjective consciousness, live within VR environments after a process of "scanning". Copies are the only objects within VR environments that are simulated in full detail, everything else being produced with varying levels of generalisation, lossy compression, and hashing at all times.

Much of the plot deals directly with the "lived" experience of Copies, most of whom are copies of wealthy billionaires suffering terminal illnesses or fatal accidents, who spend their existences in VR worlds of their creating, usually maintained by trust funds, which independently own and operate large computing resources for their sakes, separated physically and economically from most of the rest of the world's computing power, which is privatized as a fungible commodity. Although the wealthiest copies face no financial difficulties, they can still be threatened because copies lack political and legal rights (they are considered software), especially where the global economy is in recession. Hence they cannot afford to retreat into solipsism and ignore what is happening in the real world.

The story also explores the ideas of time slowdowns and suspension in the context of simulation vs. outside world:

At the opposite end from the wealthy Copies are those who can only afford to live in the virtual equivalent of "Slums", being bounced around the globe to the cheapest physical computing available at any given time in order to save money, while running at much slower speeds compared to the wealthy Copies. Their slowdown rate depends on how much computer power their meager assets can afford, as computer power is traded on a global exchange and goes to the highest bidder at any point in time. When they cannot afford to be "run" at all, they can be frozen as a "snapshot" until computer power is relatively affordable again. A Copy whose financial assets can only generate sufficient interest to run at a very slow rate is stuck in a rut because he/she/it becomes unemployable and is unable to generate new income, which may lead to a downward spiral.

The concept of solipsism is also examined prominently, with many less-wealthy Copies attending social functions called Slow Clubs, where socialising Copies agree to synchronise with the slowest person present. Many of these less-wealthy Copies become completely deracinated from their former lives and from world events, or else become Witnesses, who spend their time observing (at considerable time lapse) world events unfold, at the cost of any meaningful relationships with their fellow Copies. A subculture of lower/middle-class Copies, calling themselves Solipsist Nation after a philosophical work by their nominal founder, choose to completely repudiate the "real" world and any Copies still attached to it, reprogramming their models-of-brains and their VR environments in order to design themselves into their own personal vision of paradise, of whatever size and detail, disregarding slowdown in the process.

Intuitively speaking, I find it hard for there to be time on the lapse you get at with the description, because the being that is that lapse lacks of numerous properties of time. For example, it lacks temporal asymmetry between events (any event occur at all), etc.

I am deducing this from Aristotle's interpretation of time in his Physics IV 10-14, where basically his strong claim is that time is composed of points that we mark in changes (as if we could represent changes in a line of real numbers, with a present (or now as he calls it) being a point in the line):

"when... the soul says the nows are two, the one before and the other after, then it is and this it is that we say is time" Physics (219a27-9).

For Aristotle, we know that time passes when we perceive two parts of a change, where an asymmetrical relation holds between them (one before the other), which we (our soul) mark as two nows with the correspondent temporal asymmetry (one before the other).

Therefore, if no change is contained in the lapse, no possible change part is in the lapse. This means there is no asymmetrical relation between parts that could possibly mark a correspondent relation between nows, that would mark the passing of time.

Another way to pose the same question might be to imagine that this universe we experience is in fact a computer simulation. Some rich kid outside this universe has been playing SimUniverse on the home computer. When the rich kid's mum calls him/her/it for dinner s/h/it presses the pause button. Nothing happens in our universe until s/h/it un-pauses. Has any time actually passed? Would any of us notice?

I think the answer depends on whether you are inside the simulation or outside it. From our perspective inside the simulation there is no change and no time passes.

My view is similar in that I think time is a function of change in the universe. I think the universe is composed of identical existent entities and that nothing happens without changes in shape or relative position of these entities. These entities are the smallest possible unit whole entity. So, time would be a function of the changes in shape and/or position of the entities. If these are the smallest possible units, then changes in their shape (e.g., passage of time) can only occur and seen on the level of the whole entity. I think that the entity can change shape, but it's the whole entity changing shape and not any parts of it because it has no parts. So, this leads me to think that the smallest possible change in the flow of time can only be measured in terms of whole units and to the observer's eyes is quantized.

This kind of model also means that if different entities are changing shape and/or moving in different ways in different locations, then the flow of time can be different in different locations and observers in one area may observe time flowing at a different rate than an observer in another area.

It also makes me wonder if a photon, which is moving at the speed of light and for which time isn't flowing, is a moving entity(ies) that is undergoing no shape changes or internal motions.

Anyways, even if it's totally wrong, that's my thinking for now.

It seems to me that you are asking about the nature of a thing (what you call stasis) that is constructed such that it has no bearing on anything at all.

You could construct an arbitrary number of such hypothetical phenomena, or argue that there can be at most one such phenomenon, since there is no observable or measurable difference between them, not even in theory.

What I would like to ask you, then, is this: If the presence of your phenomenon causes absolutely no difference, compared to the total absence of your phenomenon, then what good is it discussing the phenomenon, instead of discarding the idea as fruitless?

If you feel there are two (duality), there must be a second thing (i.e., 'YOU' and the 'second thing'). And so there must be a second thought. So, even though the Truth is, 'Time is an illusion', I would say (since we are already familiar with Time and it has made a deep impression in our mind) if there are two, Time can exist. There is no need to think of units of time or changing definitions of Time. Even the 'duality experience' implies that there is a change from YOU and the second thing. And this is the smallest 'thing/change' that almost all of us ignore (or one can doubt).

In deep sleep, even while so many changes happen in your body, you are not aware of Time. I mean, 'making other things still' is not the problem.