Dear Sir,
You are absolutely correct that "each general domain relates a physical object differently to the background against which it exists". We have extended this concept to the Universe in our essay "INFORMATION HIDES IN THE GLARE OF REALITY by basudeba mishra http://fqxi.org/community/forum/topic/1776" published on May 31.
The central idea of QM that "a physical system does not have a definite state because it must be described in terms of what is called a quantum superposition of states, until one attempts to make an observation or measurement of the system", only expresses the limitations of our observation. The result of measurement is always related to a time t, and is frozen for use at later times t1, t2, etc, when the object has evolved further. All other unobserved states are combined together and are called superposition of states. Hence there is an uncertainty inherent in it, which Shannon calls entropy. In perception, the concept about the object of information remains in a superposition of states in the memory because the mind is not attached to it - hence not observing it. In response to some stimuli that draws our attention, it collapses to a yes/no state to conform or deny its resemblance with the predefined concept. It has nothing to do with the state of the object, which evolves temporally in accordance with deterministic laws of physics. The Moon will continue to exist and the proton-neutron or up-down quark conversion will continue even when we are not looking at it. There is nothing like a 'undead' cat. It evolves independent of observation. The so-called collapse is fantasy, as observation does not kill or make the cat alive. It only reports the state of its temporal evolution in relation to the condition it exists.
Practical application of QM is related to technology that is developed by trial and error methods taking hints from the observations and not theory. The theories in QM are postulates guided by technological factors and not the opposite. The original postulates like extra dimensions, graviton, strings, quantum foams, branes and braids, etc have not been found - some after more than a century.
Your "pattern of distinctions" is at the root of number system. Number is a property of all substances by which we differentiate between similars. If there are no other similars, then it is one. If there are similars, then it is many. Depending the times of perception of similars, many can be 2. 3. ....n. Zero is the spatio-temporal absence of something that exists elsewhere. Infinity is like one - without similars - with one difference. While the dimensions (the perception of difference between the "inner structural space" from "outer relational space" of an object) of 'one' are fully perceptible, the dimensions of 'infinity' are not perceptible. Since there are no similars like space or time and since the dimensions of space and time cannot be perceived fully, both are infinite. Like different objects with numbers can co-exist, different similarities can co-exist. Mathematics, which is linear and non-linear accumulation and reduction of similars or partly similars, is possible only between numbers, whose dimensions are fully perceived. Hence mathematics using infinities is not possible. Complex numbers are hypothetical and not physical. It is like adding horn and rabbit to describe the horns of a rabbit, which is physically not permissible. Hence, they cannot be used in computer programming.
Information is specific data reporting the state of something based on observation (measurements, i.e., comparison between similars), organized and summarized for a purpose within a context that gives it meaning and relevance and can lead to either an increase in understanding or decrease in uncertainty. Information is not tied to one's specific knowledge of how particles are created and their early interactions, just like the concepts signifying objects are not known to all. But it should be tied to universal and widely accessible properties. Fresh impulse (readings, symbols), when cognized by a conscious agent (compared with memory as those known concepts or otherwise - yes/no), is information. Otherwise, it is data.
Both space and time are related to the order of arrangement in the field, i.e., sequence of objects and changes in them (events) as they evolve. The interval between objects is space and that between events is time. Both space and time co-exist like the fundamental forces of Nature. To that extent, space can be a background structure also. This makes motion possible. Similarly, the sequential arrangements of letters form words with different concepts conveying fixed meanings. This makes communication possible.
The statement that "general relativity is considered a background-independent theory" is not correct because velocity of light is medium based, as it is related to the refractive index of the medium. Maxwell's equations are background invariant. Transverse waves are always characterized by particle motion being perpendicular to the wave motion. This implies the existence of a medium through which the reference wave travels and with respect to which the transverse wave travels in a perpendicular direction. In the absence of the reference wave, which is a longitudinal wave, the transverse wave can not be characterized as such. Transverse waves are background invariant by its very definition. Since light is a transverse wave, it is background invariant. Einstein's ether-less relativity is not supported by Maxwell's Equations nor the Lorentz Transformations, both of which are medium (aether) based. Thus, the non-observance of aether drag (as observed in Michelson-Morley experiments) cannot serve to ultimately disprove the background structure. The so-called non-interacting dark energy may be the background structure. We have discussed it in our essay.
In the thread of Dr. Reed and many others, we have proved that the equivalence principle is wrong description of facts. Relativity is an operational concept, but not an existential concept. The equations apply to data and not to particles. He assumed space as empty and mass-less, which it certainly is not. Since space is full of energy; hence mass according to the mass energy equivalence principle, then the mathematics of General Relativity is highly misleading. Further, it should be based on a constant differential that is not zero and seek the motion of some given mass or volume. This mass or volume may be as small as we like, but it cannot be zero (hence no infinities). This causes several fundamental and far-reaching changes to the mathematics of GR, but the first of these changes is of course the elimination of singularity from all solutions. Therefore the central "fact" of the black hole must be given up. Whatever may be at the center of a black hole, it cannot be a "singularity".
Our purpose is not to criticize your essay, but express our views so that you can take these into consideration. Learning is a never ending process and we learn from each other. We liked many of your discussions. You are welcome to read our essay or write to mbasudeba@gmail.com.
Regards,
basudeba