Look up what an "operational" definition is. Your definition is not "operational" until you define "observer" which is really the crux of the matter.
Suppose, for example, that we are doing an experiment along the lines of the classic two-slit single electron diffraction experiment. When the electron emerges through the slits it has no definite position, only a "wave" function that gives the probability of "measuring" it at various locations. While this "wave" is indeed a mathematical abstraction, we find that this mathematical abstraction appears to interfere with itself in a well-recognized interference pattern in the real world. However, when a "measurement" of the position of the electron is made, there is no longer a "wave" probability function. At the instant of "measurement" the electron is in a single position with probability one.
The question then is, what constitutes a "measurement"? Or in your wording (begging the question), what constitutes an "observer"?
Could a single particle be an "observer"? In a practical sense this question would seem to be unknowable for us, since we must then observe the "observer" particle to read its "observation." I believe, however, that experiments have succeeded in demonstrating that a system consisting of more than one particle into superposed states. If I am correct on that, the experimental evidence would suggest that if a single particle attempted to "observe" an electron in a superposed position, then rather than the "observation" forcing the electron to be found in a single position, the "observation" would force the "observer" particle into a superposed state. And this is what current quantum theory would predict.
The problem is that quantum theory currently predicts this outcome for any number of particles--even the enormous number of particles in a human body. How is it that our "observations" force the electron to manifest a single position, instead of the superposition of the electron forcing our "observations" into a superposed state?
The only useful understanding from the mathematical statement-superposition of states- is, that the entity is not interacting with anything at the moment.
But the "entity" WILL be continually interacting with other particles--virtual particles a la Richard Feynman. Also, as stated above, if the "entity" interacts with one other particle, then quantum theory predicts that they will both end in superposed states.
They are not reality itself.
Judging from this statement, it seems that you do at least believe in an objective reality. So, when we set up a single electron diffraction experiment, what is "really" happening?
In otherwords, it can't be observed by anything any other entity that could observe it.
Here your grammar is such that I can't make out your intent. Did you mean "In other words, it can't be observed by any other entity that could observe it?" That would be a grammatically-correct self-contradicting sentence.
When considering the word observer in physics, consider that a window and a ball are observers.
Here your grammar is fine, but I still can't make out your intent. Sarcasm? Irony? Absurdity? Seriousness? A reference to a ball breaking a window?
Yes. It is in fact a perfect observer of all things it has the capacity to observe. For instance, an election will never see an comprhend a dog pee, but it can see the electrostatic field created by the dog's stream.
"In a practical sense this question would seem to be unknowable for us, since we must then observe the "observer" particle to read its "observation."
You are just introducing a second observer here. In reality that particular second observer is composed of a multitude of varied observers all working together.
"When the electron emerges through the slits it has no definite position, only a "wave" function that gives the probability of "measuring" it at various locations. While this "wave" is indeed a mathematical abstraction, we find that this mathematical abstraction appears to interfere with itself in a well-recognized interference pattern in the real world."
The wave function you are refering to is complex. By itself there is nothing observable given by it. If the wave function is multiplied by it's complex conjugate a probability amplitude is obtained that gives the probability of finding an electron as a function of coordinate behind the slited screen. Any single electron will be found and if you keep firing them at the slit, a pattern will be found that is the same as the probability amplitude vs distance behind the screen.
What I was saying before is that these particles are neither particles, nor waves. They are something else. Particles and waves are mathematical concepts that allow modeling of reality. In the case of massive particles like the electron, the wave function is complex. That means nothing can be observed directly about the particle. Only the product of wave function with it's complex conjugate has meaning. That product will given the probability of observing a particle like entity having certain properties.
A massive particle can never interfere with itself. It will never cancel itself, nor will it multiply itself into something bigger. Considering the features of the experiment that way leads to error. Consider the toss of a die. On any particular role the die ends up rolling a particular way that it can and ends up with a particular face pointing perpendicular to the table. The observers are the die of a particular mass and geometry, the gravitational field, the randomness of the tosser's toss and the table top and it's physical characteristics. On any particular role the die has a definite and particular motion through space and there's a particular outcome. The same with the electron. Notice no information is given about the die itself in this experiment only the outcome of one, or many rolls is given. If the number of rolls approaches infinity, the envelope of the probability distribution of outcomes is given. The same with the slit experiment. On any particular role, or shot at the slit, the projectile has a definite path and ends up in a particular way. In niether experiment is the path and the projectiles nature discerned.
"superposed states"
Consider in the die experiment that the face taken as perpendicular to the table top s obtained while the die is still in motion. THat is done with a camera as the die crosses a line on the table. It is in a superposition of states before(their are six of them) and it is in a superposition of states after. In reality the superposition of states in QM is the same. Before and after the camera shot, the particulars are not known. In physical experiments the particles never settle down, they keep going. In the slit experiment they keep going after they are detected somewhere on the other side of the slit.
"A reference to a ball breaking a window?"
In physics the idea of observer is simple. The observer is just an entity that will act according to physical laws and w/o error. Balls and windows are perfect observers, humans are not. Both the ball and window will see each other at the moment they interact and act accordingly. Before they interact, they will not know each other though.
You are thinking of single particle QM. In that conception the action of single particles is quantized. In field theory the action of fields is quantized. There if the fields are small, the number of particles arising out of that field is indeterminate. The field has more of a reality than the idea of single particle does. For the electromagnetic field the wave function is real. The fields can be observed directly. The square of the field gives the energy flux. If the field is small though the number of photons is indeterminate.