If a physicist (who have never seen people) is constantly watching on shadows and hear voices behind, will he make a statement that shadows are talking? I'm talking about physical experiment in terms of Allegory of the Cave.
The physicist should want to demonstrate whether talk and shadows have a necessary relationship, or that they are independent.
If you can do experiments things are fairly easy. As RetroCausalElectron points out, holding up objects to (1) make a shadow or (2) hide a talking shadow demonstrates that (1) shadows on the wall do not necessarily talk and (2) just because a shadow looks like a non-talking shadow doesn't mean it isn't talking. So the physicist would at least conclude that shadows he could make have no effect on talking.
A sceptic in the cave would point out that maybe cave-people don't have the right shadow technology to make talking shadows. However, the physicist can also talk and generate shadows, producing a talking shadow that obviously was causally generated by the cave-person. A platonist might suggest that maybe the physicist is a shadow somehow projecting a 3D person into the world, but the physicist would note that he still exists when he is in the shade and has no shadow.
If the cave-people cannot cast shadows (they are chained below a ledge unable to access the light above) then the whole issue is observational physics and theory formation. Gathering data will show many cases of talking and non-talking shadows.
Careful gathering of data will also reveal differences in volume correlated with size and diffuseness, and a really astute physicist would notice that the delay between something happening to the shadow (a shadow horse kicking a shadow person) and the sound (a bang and a curse) exists, and is also correlated with the size and diffuseness. If the physicist can make sounds he might also recognise similar delay effects in echoes in different directions, giving a hint at what is going on. A possible hypothesis is that shadows generate delayed/weakened sounds with an effect size linked to the size/diffuseness property, another possible hypothesis is that some separate thing causes both shadows and sound and has a property that affect both observations. Which one is simplest and most testable?
A counterexample to the first hypothesis would be a sharp shadow with a long-delayed sound. More research will demonstrate that the delay and volume relation is imperfect, but for particular kinds of shadows like the philosopher-shadows or horse-shadows they hold relatively well. There are quiet shadows like the downcast slave-shadow that are low volume even when very sharp, and loud shadows like the demagogue-shadow that are loud even when diffuse. So the size/sharpness to volume relation appears to be a weaker explanation than assuming there are two parameters for individual shadow types, "distance" that determines a scaling of the basic shadow size and basic volume, and loudness that scales the volume but depends on type.
At this point the sophist complains that with that many parameters the physicist can fit anything to his data, and the physicist says he just has made a useful model. The philosopher next to them will complain about assuming unseen abstractions and the problem of induction. Meanwhile the engineer long ago picked the lock on his chains and escaped, none the wiser.
Assuming that you are talking about a scientist standing alone in a cave talking and trying to see if his shadow is the one talking or not:
He can just stand where the light will project the shadow far enough to see the discrepancy. However, to arrive at the conclusion, he might need some kind of echo to be present in that cave so that he can clearly notice that he is hearing a voice without the mouth of the shadow moving.
Assuming you are talking about the allegory of the cave: (it is an allegory after all, the people watching the shadows might as well just turn their heads around)
Here it is easy to see that the ears alone will do the work. There is no real physics experiment, the listener naturally can detect the origin of the sound. But assuming he was born in that cave and is not accustomed to any other sound then an experiment to determine the truth can take many forms:
- Hold up an object and obstruct the shadow which will show the voices are independent of the shadows. Or maybe shine a light on the wall that might make the shadows disappear.
- Talk at the same time and try to notice the discrepancies and similarities between the person's voice and the shadows
I am pretty sure there are some other ways but all are based on intuition since we are assuming that this person in a cave has always been in that cave and that he does not have any equipment or technological resources.