Re: In quantum physics, what exactly constitutes and observer?

There are at least two kinds of observers in quantum physics.  At speeds 
much less than the speed of light, there are no relativistic effects to 
consider and so the definition of an observer can be concerned merely with 
the location of the observer relative the the particle or event to be 
observed.  In most instances, speeds less than one tenth the speed of 
light are considered to be non-relativistic.  At relativistic speeds, 
generally those greater than one tenth the speed of light, an inertial 
observer is needed.

In special relativity (applied at relativistic speeds), a mouse, 
bacterium, computer, or another particle could not be an inertial 
observer.  Instead, what is usually described as an inertial observer is 
more like a huge information gathering system, or a coordinate system for 
spacetime.  There are differences between special and general relativity, 
but those are not particularly relevant for this response.

To be inertial, the observer, or coordinate system must satisfy the 
following properties;

1)  The distance between any two points in the coordinate system must be 
time independent, the distance is not different for different times,

2)  The clocks, assumed distributed throughout the coordinate system, are 
synchronized (the time reported is not dependent on the location of the 
clock) and run at the same rate throughout the coordinate system (the 
observer), and

3)  The geometry of space at any constant t is Euclidean.  The simplest 
way to think of a Euclidean space is that it is a space (a coordinate 
system) in which the geometry most people are familiar with is 
applicable.  If you were a mathematician, you would probably take issue 
with that last sentence, claiming it to be an oversimplification, but it 
should work in this instance.

"An observation made by [an] inertial observer in the act of assigning to 
any event the coordinates x, y, z of the location of its occurrence and 
the time read by the clock at (x,y,z) when the event occurred.  It is not 
the time  t  on the wrist watch worn by a scientist located at the origin 
(0,0,0) of the coordinate system when the scientist first observed the 
event."  This quote is from pages 4 and 5 of Bernard F. Schutz's A First 
Course in General Relativity, Cambridge University Press, 1985 - the 
principal source I used in preparing this response.

Thanks for the question, I hope this response helps.