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As a supplement to this question as to whether particles can be observers, supposing that the answer is yes. One could suppose a setup where particle A is observing particle B, but what to stop us switching viewpoints around here and supposing particle B is observing particle A?
(I find this is an intriguing possibility considering the importance of symmetry in modern physics - all global conservation principles for example are derived from considerations of symmetry via Noethers theorem)
In quantum mechanics, if particle A affects particle B, then particle B also affects particle A. One way of saying this is that every action has a back action.
So if you assume that particles can be "observers", then if particle A observes particle B, it must also be the case that particle B observes particle A.
If I interpret this correctly you seem to be asking whether some kind of rudimentary form of awareness may be a property of all matter?
One person who I think would answer in the affirmative is Graham Harman in his metaphysics of 'polyspychism'. The most clear and complete exposition of his system is called The Quadruple Object, a great introduction can be found here in an article published in the journal Parrhesia by French philosopher Tristan Garcia.
In a different but related vein in 1000 Plateaus Deleuze & Guattari run the curious line of that "metals are the consciousness of the planet." .. This view coming from their observation that metallic catalysts are like probing heads which function to accelerate certain reactions and decelerate certain others, allowing exploration of the space of possibilities surrounding a mixtures relation to other mixtures. They do not however explore the minds of experimenters. Another interesting piece by Deleuze but involving humans is his article Desert Islands, where he says that the presence of the shipwreck victim does not mean the island is no longer deserted, it rather raises the island to a kind of perfection, with the stranded person becoming the "consciousness of the island". Larval selves in Deleuze's Difference and Repetition have this this strange property of fulfilling a self image through contemplation of something else .. Alan Watts is another who comes to mind, with his view that “you are an aperture through which the universe is looking at and exploring itself.” .. However that would be observed phenomena observing itself, not the observer, which is different from your question ..
The bean counters will say that the main obstacle is explaining why awareness or this capacity to observe is not itself an emergent property, as it has been demonstrated to be by modern psychology, and that this runs into the same difficulties which are associated with philosophical zombies.
I am reminded of Sartre's famous key-hole observer suddenly discovering himself being observed, suffusing the subject with shame and a kind of objectifying "mortification."
I know this is not what you had in mind, but I raise it in order the reintroduce the missing aspect of awareness and psychology in these inanimate "particle" observers, these Disney "atoms" with cartoon eyes.
While I too am fascinated by questions of symmetry and measurement and value metaphor, I simply fail to understand the definition of "observe" here. It is either metaphorical or collapses a meaningful distinction to little avail.
Why is "observe" an accurate description of this relation between particles? Certainly, we can might say that a "measurement" takes place in the purely physical sense that information is transferred between particles. Such a transfer is not necessarily reversible. I believe it is, in fact, physically irreversible. So these perspicacious "particles" do not necessarily observe one another, at least not with equal "accuracy."
But again, I can only take this as useful metaphor.The physical, particulate information has syntax, but no semantics. I see no gain in a massive, gratuitous reduction of what we normally call "observation" of an object by a "conscious subject" to a physical, mechanical relation between two objects under the same term.
And I tend to agree with the unpronounceable commenter that the subject cannot be an object to itself, just as we can never actually see our own face, only its reverse. While we can approach the imaginative ideal of subject-object identity, the distinction can never be meaningfully collapsed. They remain, as it were, inside-out or chiral to one another.
An observation is an interaction between a subject and an object. The observer must interact in some way with the object in order to get information about it. That's why in QM, measuring the object means modifying its behavior. That's not perceptible in the macroscopic world, but it happens anyway, and not only at an atomic level, but at a macroscopic level.
For example, in forensic science, Locard's exchange principle states that the investigator will always remove traces and leave new traces on the crime scene when he studies it. When one asks something to another person, the other person evidently changes due to the interaction, etc.
Now, when the subject observes itself, there's a dualisation of the observer: the subject becomes also the object. Observing himself means interacting with himself, taking both subject and object roles at the same time.
So, yes, in simple terms it can be said that the observer can observe himself. But in strict terms, the subject is not anymore a subject when an observer observes himself. So, the subject cannot be observed as such. In any case, perhaps such observation is just part of what Kant calls the unity of the self.
