AlNg:
If a tree falls in a far away forest and nobody is there to hear anything, does it make a sound?
Not really. It still sends vibrations and such on the air but it isn’t sound as we know it until the vibrations reach the ear and is translated.
This isn’t a logical proof that no phenomenon of sound somehow “accompanies” the vibrations. The way science has constructed the scenario makes it seem like the explanation rules out the possibility that the perceived “sound” can exist outside the mind that constructs it from the stimulus, but that assumes the world is nothing but the theoretical atomic and subatomic constructs that are themselves imagined by physicists. It also assumes the world is a meaningless and purposeless place with only sub-molecular interactions occurring there. The problem with this perceived view is that it reduces reality to a meaning-poor narration about reality and relocates all meaning into the human psyche.
Perhaps this reductionist view is fundamentally confused in its assumptions. The entire perspective would be like assessing what a novel is simply by analyzing the composition of the ink and paper and claiming that the content is entirely composed within the minds that read the novel because the story is nowhere to be found in the molecular components of the physical book.
Perhaps your analysis that there “isn’t a sound” in the objective world unnecessarily constrains you to the view that there isn’t a story in a novel, either. Well, okay, but where is the reality which contains the story? Perhaps this is an indicator that the naturalistic and reductionist view isn’t comprehensive because it doesn’t account for large sectors of reality and constrains those who accept it to distorted perspectives of the real world.
To answer @AINg’s question…
If the objective world is something like a 3D story or novel with its own time signature, time could exist within physical reality independently of what is outside of the objective universe. I.e., the universe could have its own time signature much like a novel or story could have its own, completely independent of the reality within which the author of the story resides. The author could live in some other time-constrained place or could be eternal and unconstrained by time since the feature of time within the universe need not be a feature outside of it.
This, I assume, you would accept even on the basis of the description of sound that you gave. If the phenomenon of sound need not exist in the objective world, then time need not. However, merely because we perceive sound does not imply there is no sound in the objective, physical reality around us. Ditto with time.