If there were no physical laws of causality (law of gravitation, etc.) would there be "events", what would happen in the world when we act in our day to day life's? Trying to imagine a world without causality is extremelyhard. Apples in a tree, for example, would move upward, then side-ways...or whichever way; we could throw a ball at a window yet the window would not shatter, etc. etc.
Conceivably, there is another way for a universe to be ordered rather being random and chaotic with invoking casuality: teleology.
In a teleological universe things would do the things they do because that is the purpose they serve, or because that is what they want to do. Apples would still fall but because they want to be on the ground not in the tree rather than because of gravity, and so on. I suppose you could even recreate our universe if the reasons were boring enough, but you could also easily have heavy objects that float, etc.
I think this question cuts much deeper than most are giving it credit for. It is quite similar to free will versus determinism.
Consider a simple universe consisting of a single snake and a sequence of apples that it wants to eat. The locations of the apples are predetermined by a very complicated pseudorandom generator, and the snake is controlled by an AI programmed with deterministic foreknowledge knowledge of the generator.
Surely the arrival of a new apple causes the snake to turn and move toward it? No, everything is predetermined. If you could change the positions of the apples, the snake would not change its path. It looks like this world has cause and effect, but it doesn't.
Now consider why we have the maxim "Correlation does not imply causation." It is not easy to distinguish the two, is it? No, in fact, we need very careful and rigorous science, such as randomized controlled experiments, to tell the difference between correlation and causation. For example, we can drop various objects in various places to test if gravity exists and what laws it obeys.
The key assumption there is that we have access to randomness that is independent of the phenomenon. But in a universe with sufficiently advanced correlation, even the randomness we use in experiments -- coin flips, dice rolls, etc. -- might have been programmed by an all-powerful Creator to perfectly correlate so as to fool us. In your example, the laws of gravity might not exist, but certain objects are preprogrammed by other laws to move downward at certain times, and they happen to be the ones we drop, so we never learn the difference.
So as far as I can tell, a predetermined world could be made to look arbitrarily similar to one that has actual cause and effect. We could run experiments, but if we did not have free will, then they could be predetermined to look like causation exists, when it doesn't.
TL;DR it could be arbitrarily similar to our own, in theory.
In counterfactual scenarios, the more fundamental the counterfactual hypothesis, the more arbitrary the conclusion. If Kennedy had not be assassinated, presumably he would have run for a second term at the next presidential election of 1964. This is still arguable one way or the other, essentially because once you introduce a counterfactual hypothesis, everything else is up for grab, but reasonable people limit themselves to what would reasonably follow from the counterfactual hypothesis.
If the counterfactual hypothesis is something fundamental to the way the world seems to be, then we are a bit lost. Essentially, while we may very reasonably claim that Oswald could very easily have missed Kennedy, there is nothing reasonable in musing about what would happen if something we don't even know that it exists was not there.
So, very plausibly, there would be no change because causality does not exist to begin with. Causality may not exist somewhat in the same sense as we say that free will doesn't exist or that time doesn't exist. That is, causality is likely the wrong explanation for what we believe there is.
So, you might just as well ask what reality would be like if it was different.
If there is no causal relation then you'd have no fixed chain in which events do occur and so things just happen randomly. Now the question is whether there is local or short ranged causality or whether you interdict any and all forms of causality.
Browse the fantasy section of a library and pretend that they all happen in one universe and you'll find that this universe does not adhere to the rules of physics and might not follow causal relations perfectly, yet within a specific story they might adhere to some internal, localized form of causality.
Whereas if you forbid all forms of causality then things must not be continuous so that would be really just random and pretty impossible to describe as any structured explanation would need to make use of patterns that must not exist otherwise you'd be able to construct rules from those patterns which hint at causal relationships.
According to Hume and Kant, causality is a subjective intuition, and not a physical necessity; that is, causality needs to be understood as an epistemologic phenomenon, and not as a physical fact. Hume associates causality with custom and habit.
So, a world without causality cannot be rationally understood. Pavlov's Dog associates the ringing of a bell (cause) with food (consequence): even animals have a sense of causality. In consequence, in order to understand a reality without causality, a null rational capability is required, which is evidently an oxymoron.
But you can get a taste of what a reality without causality would be, if you observe a process for which you don't know or understand the causal rules:
A) observe the development of a game for which you don't understand the rules. As soon as you start to understand the rules, you are experiencing causality. For example, Truco (tutorial signals here) is a very complex Argentinian game which depends a lot on signals and selected words, cards being almost accessory.
B) observe a cpu emulator running an assembly program: you will see a lot of switching zeros and ones. There are precise and strict causal rules behind, but if you don't understand them, you can't perceive the causes and effects, so, you are perceiving a reality without causality: https://youtu.be/7H-PHc1CNSU
"Apples in a tree, for example, would move upward, then side-ways...or whichever way" This seems like a rather limited view of the effects of causality (or lack of it). If laws like gravity no longer apply consistently, then the laws that hold atoms together should also no longer apply. Any apple would instantly dissolve into a cloud of random particles. Humans would similarly cease to exist, or never have existed in the first place, or by some improbable fluke flicker into existence for one moment (too brief to even form a full thought) and then never be seen again.
We can actually get a few clues from reality itself. There are plenty of situations where events are causally disconnected from one another, allowing some weirdness to occur.
Causality is intertwined with spacetime. Indeed, we generally talk about spacetime giving rise to the causal structure of reality in the context of special and general relativity.
The speed of light is, in reality, the speed of causality, or speed of interaction. And within this causal structure, certain things are relative. For example, 3 events that occur at the same time but separated by a certain amount of distance can occur not simultaneously but at different times (with the event appearing to occur last to one observer instead occurring first to another) depending on the relative motion of an observer to these events (and these events are all stationary relative to each other),
This is fine because the distance between the events makes them causally disconnected - it takes time for one to have an impact or interact with another. So in these situations, simultaneity is relative and depends on who is observing the events and their relative motion to them.
But to further answer your question, some theoretical physicists actually believe that before the big bang, spacetime was exactly as you are imagining - completely lacking any causal structure.
Space and time are tightly intertwined with causality, so losing causality not only makes time as we know it vanish, but space as well.
It is theorized that prior to the big bang, if there is a quantized 'unit' of spacetime, a smallest possible part, that these individual quanta were analogous to a fluid or perhaps a gas - all points in space in time moved around randomly, connecting and disconnecting to other points in spacetime at random. All interactions would occur simultaneously to any thing in this mess, there would be no past or future, just the infinite present where all things occur at once. Here we can see that ideas like 'before' and 'after', which in our reality only exist thanks to causality, lose all meaning. One event can only be definitively said to occur after another for all observers only if that second event was influenced, or caused, by the interaction with the first event. This is what makes that first event definitively occur 'before' or 'earlier' for all observers. Otherwise, it can be observed to have occurred before or after the other events depending on the observer and their motion (inertial reference frame).
Anyway, those same physicists theorize that there was some kind of phase transition in spacetime coinciding with (or perhaps causing) the big bang. We believe big bang happened everywhere there was a 'where' at the same time due to the decay of a quantum field called the inflaton field. This then resulted in exponential inflation of the very early universe and pumped it full of energy that would ultimately form the matter we are made of now.
Spacetime may have turned from something analogous to a liquid to something analogous to a solid. Yes, that sort of phase transition. Spacetime froze, or turned solid, crystalizing into an ordered structure with constant and ordered connections between each point within it. This ordered structure gave us things like space itself, time as we know it, and causality. Indeed, distance is really just the separation of two events in space as well as time, since there is always both an interval of distance and time which must be crossed, thanks to the speed of light making changing location require taking a minimum distance in time that must be traveled as well.
That is one way to think about it.
Another is something we suspect of the universe right now, as it is. A universe without causality would be a universe without a speed limit. All interactions would happen instantly and regardless of separation in space and time.
Which is how quantum entanglement seems to behave. It is inherently non-local, meaning measurement of something entangled with something else instantly determines the properties one will measure for both regardless of distance in time or space. In a famous experiment, it was shown that entanglement can determine what is measured for something that has already happened, some call this retrocausality. This experiment is called the delayed-choice quantum eraser. One can delay the choice to 'erase' the measurement of an entangled pair, resulting in either the interference pattern or random distribution of the double slit experiment after one half of the entangled pair has already passed through the slit.
Going further with this, some physicists believe that the real first principle of reality is quantum entanglement, and things like causality and time itself are emergent properties that result from entanglement. They only exist to things that are entangled with other things, a universal wave function so to speak. And the past is merely the common entanglement, the consistent history, we share.
But if there was an observer who could exist completely outside the universe and have never interacted with it (not entangled with it), the universe would appear static, just a single wave function, oscillating but without ever evolving or changing - one in a super position of all possible states it could possess simultaneously. The only way to collapse it down to a single possibility would be to interact - and thus become entangled with it. We see this behavior all the time when we create entangled particles in a superposition of states. Entanglement simply means several things are described by a single wave function (probability wave). This is something that does not occur in time, but rather the frequency domain.
It would be the same for something outside the entire universe, and time would not exist for the universe from that observer's perspective for the same reason it doesn't exist for a wave function in super position. If something is a super position of all possible states, it cannot change state, something required for cause, effect, and the progression of time.