In perfect void can we define time? Does time make any sense in absence of events? Is time related to event?
For instance we use Cesium atom's frequencies as measure for one second but if there is nothing would time exist?If it does exist would it be measureable?
The concept of time - and correspondingly the concept of space - has changed in time.
1.) According to Newton, time and space exist independently from all physical objects in the universe. There is a global time, a universal tick-tock, which cannot be influenced by physical objects. It goes on also in empty space.
2.) In the 20th century it was the theory of special relativity which united space and time to the concept of spacetime. One could no longer separate spacetime in two independent quantities space and time, like one cannot separate the two faces of a single coin. There is no universal splitting of spacetime in a universal time and a universal space, independent from the frame of the observer.
In general relativity spacetime becomes a physical object like other physical objects and is influenced - more precisely curved - by masses in the neighbourhood. Of course spacetime exists also in the absence of masses and also when no events happen.
It is quite a different question how to measure time in this case - possibly by introducing a small test clock, which is imagined to change spacetime in an arbitrary low way.
3.) Currently, in a certain version of quantum gravity named quantum loop gravity, the basic object is the event. Space and time are quantized and develop in a probabilistic way like other concepts in quantum theory. It is only during the event of interaction of two systems, when time gets a definite value. But the value is relative to the two systems. On the Planck scale it is not possible in general to fit the many local times from interactions into a global time order. Here time is related to events, there is no universal time.
E.g. see „Carlo Rovelli: The Order of Time“ and https://www.youtube.com/watch?v=-6rWqJhDv7M
4.) Summing up: Physics has no universally acccepted concept of time. The respective concept depends on the current theory. It may change according to the progress of physics. At this state of affairs, I do not expect that a fundamental concept of time will be invented by other disciplines, in particular not just by philosophical reasoning.
Our current best physics does not actually have a void. All space is filled with a sea of dark energy, which supports the continual creation and destruction of virtual particles. https://medium.com/nakshatra/the-nature-of-nothingness-understanding-the-vacuum-catastrophe-c04033e752f4#:~:text=The%20particles%20arising%20out%20of,particle%20and%20anti%2Dparticle%20pairs.
The nature of time is something that is still not settled. You used the logic state approach to time -- it is the sequence of state changes. Most physics is based on a semi-dimensional approach to time - that it can be treated effectively as a dimension, and there is a "space-time continuum". All historical studies treat past time as given, and future time as uncertain. This is the "growing time" approach.
Only the logic state approach to time has trouble with your "void" presumption. The dimensional and growing time approaches would work OK with it. Although there would not be any point to doing any of those time operations in your thought problem. But once one accepts the "void" is active with virtual particles -- there ARE events happening, continually, and all three models work just fine with our actual "voids".
Clearly not. In a perfect void there is nothing by which to define time, or anything else… yet even if that prevents definition, it says nothing about existence.
Whether time makes "sense" in the absence of events is a purely human Question; nothing to do with physics.
With no Cesium, you may not think of an atom's frequency as a measure for anything, but that's again about human perception, not the existence of time.
In a perfect void, time would not be measurable but that says nothing about whether it might exist; merely about how you or I or we might perceive it.
Is that difference not obvious?
Personally, I suspect time is the only thing that does or could exist independently but that's not a fact; merely my opinion.
In physics we (or I specifically) say that something exists if and only if it has at least one measurable property. In a perfect void there’s nothing to measure time with. Similarly in a universe containing just one particle there would be no way to measure the size of the particle and so that concept would be meaningless.
"In perfect void can we define time?"
First define time generally, define space (and hence voidness) generally, then you can attempt to answer :)
The variety of articulations of both time and space (sometimes intertwined as spacetime), is too large to encompass in a simple Phil.SE answer. @Jo gave the popularly scientifically accepted theories in history. But since you so clearly referenced "events" in your question, I'd like to add another theory, one inherently event-based.
I'll begin by providing Whitehead's criticism of Newtonian conception of space, and hence void:
Newton, basing himself upon current physical notions, conceived 'sensible objects' to be the material bodies to which the science of dynamics applies. He was then left with the antithesis between 'sensible objects' and empty space. Newton, indeed, as a private opinion, conjectured that there is a material medium pervading space. But he also held that there might not be such a medium. For him the notion 'empty space'—that is, mere spatiality—had sense, conceived as an independent actual existence 'from infinity to infinity'. ...Newton in his description of space and time has confused what is 'real' potentiality with what is actual fact.
(Process and Reality, p.72-73)
Whitehead claims that because Newton inherently connects the actual world with the empirical actual facts, he had to conceive of a concept for 'empty space'. This, according to Whitehead, is what made the history of philosophy of nature to struggle so much with articulating non-occupied space.
Now to sort out Whitehead's attempt to provide an answer, I'll begin with some definitions.
Alfred N. Whitehead defines event as following[*]:
An event is a nexus of actual occasions inter-related in some determinate fashion in some extensive quantum: it is either a nexus in its formal completeness, or it is an objectified nexus.
(P&R, p.80)
... Where 'actual occasions' mean:
'Actual entities'-also termed 'actual occasions'—are the final real things of which the world is made up. There is no going behind actual entities to find anything more real... The final facts are, all alike, actual entities; and these actual entities are drops of experience, complex and interdependent.
(P&R, p.18)
It should be noted that for Whitehead there is a difference between "the world" and the "extensive continuum", which is what we usually call the universe.
But we need one more definition:
Actual entities involve each other by reason of their prehensions of each other. There are thus real individual facts of the togetherness of actual entities, which are real, individual, and particular, in the same sense in which actual entities and the prehensions are real, individual, and particular. Any such particular fact of togetherness among actual entities is called a nexus (plural form is written nexūs).
(P&R, p.20)
I'll regard nexus as the primary type here, to avoid confusion with ordinary language. As defined, a nexus is actual occasions connected by facts or togetherness. If those connections are inherently of the kind of continuance, i.e. inheritance, then this nexus is an ordered nexus - i.e. a society. There are multiple kinds of societies, the one we refer to the most are the 'corpuscular societies'.
Yet another definition:
A 'society' in the sense in which that term is here used, is a nexus with social order; and an 'enduring object' or 'enduring creature' is a society whose social order has taken the special form of 'personal order.' ... A nexus enjoys 'personal order' when (a) it is a 'society' and (b) when the genetic relatedness of its members orders these members 'serially'.
(P&R, p.34)
Now after all those definitions, to come to the point in hand. A "perfect void" (in Whitehead terms, 'empty space'), is still a nexus - according to Whitehead, there still are actual occasions in an empty space. What it is not, is an enduring society (society with personal order). For Whitehead, an empty space is a spatio-temporal extensiveness with no relation of continuance in it (no "historic routes"). This means effectively that we can't measure an empty space, but it doesn't mean there aren't actual occasions inside of it - for Whitehead events pervade the extensive space itself.
In other words, time and space doesn't occupy empty space (more accurately, it is nonsensical to speak in those terms about it). But that doesn't mean there isn't anything "happening" inside it.
We may imaginatively conjecture that the first grade [i.e. empty space] is to be identified with actual occasions for which 'presented durations' are negligible elements among their data, negligible by reason of negligible presentational immediacy [meaning observability]. Thus no intelligible definition of rest and motion is possible for historic routes including them, because they correspond to no inherent spatialization of the actual world.
... [I]t is nonsense to ask of an occasion in empty space whether it be 'at rest' in reference to some locus... the relationship of 'rest' does not apply to them.
In fact, for Whitehead there is a pervading electromagnetic occasions in empty space:
Thus our cosmic epoch is to be conceived primarily as a society of electromagnetic occasions [i.e. empty space], including electronic and protonic occasions, and only occasionally—for the sake of brevity in statement—as a society of electrons and protons.
(P&R, p.92)
To conclude, Whitehead provides a systematic conception of nature that enables a different view of so-called 'empty space'. Furthermore, to answer your questions directly, according to Whitehead time is inherently related to events; but the absence of occupation in space does not mean absence of events.
[*] it should be noted that Whitehead's terms are a bit different in his other books; that's why I chose to consistently provide definitions from Process and Reality; square blocks in quotes are mine.
Perfect void is just an imagination. If there is something so called, there is nothing to experience time there. So no question of time will arise.
In perfect void can we define time?
No. Nobody will be there to define time.
Does time make any sense in absence of events?
If your mind works even if nothing else happens, there is time.
Is time related to event?
In many cases it is so. Imagine a boyfriend waiting for his / her boyfriend / girlfriend. But that is not the case when the event is associated with a watch, clock, etc.
We use Cesium atom's frequencies as measure for one second. But if there is nothing, would time exist? If it does exist would it be measurable?
If any comparison happens in any way, there is time. Otherwise, no.
