APR can lead to another "endless debate" worse than QM interpretations. Fortunately we don't need to define it exactly. APR analysis works with any reasonable APR specification.
Remember APR is
a priori reality. People tend to include
a posteriori aspects of reality, that depend on experience.
I need to develop the theory a bit more in the light of your comments, then apply it to Bell and QM interpretations (the original goal). The best way to clarify the APR idea is to use it. BTW it's more about the
observer, whose intuitive concept of reality is APR.
ddd123 said:
I don't agree with all of the above, ...
Neither do I. That's just a first cut. Furthermore, the way you interpreted it is bound to be somewhat different than what I intended. This is an iterative and inter-subjective (inter-PF-poster) process.
Mentz114 said:
How does mathematics fit into this. Is mathematics always true (uniquely) in APR ?
Yes, it is. Let's ignore finite math (arithmetic, number theory, combinatorics, group theory). Calculus, diff eq's, continuous fields, lie algebras etc are the foundation of dynamical physics. They are extremely APR-analyzable. These concepts wouldn't exist without our APR physical intuition.
In this context probably the most important aspect of APR is: it's
local. Experience, observation, happens at one instant in one place to one observer. The derivative describes ("tames") a continuous curve by analyzing what happens to it locally, at a single point. Thus the curve can be dealt with quantitatively, rigorously. That's typical "applied APR theory". Tangent plane is particularly useful because as you approach a single point - the only place an observer can be - every derivative except the first becomes negligible.
A lot of math is not manifestly APR-compliant like Lagrangians, or an integral over a Cauchy surface. But (I claim) the calculations are always based on an APR-compliant process.
ddd123 said:
for example we use tangent planes because it's mathematically easier than to mess with nonlinear behavior.
It's easier precisely because it's APR-legal, i.e., intuitive.
ddd123 said:
In special relativity we use Lorentz transforms directly. But the APR there fits in as the receiver of the past light cone information and not a whole simultaneity plane.
Right.
ddd123 said:
Also the flat Earth illusion is broken if you've been on the ISS or one of those stratosphere capable jets.
Such knowledge is not APR, but a posteriori. Also, APR governs how you experience your current environment, in this case, your seat inside the jet. Sitting there, (looking down at the Earth, which is
not your current environment) you don't feel you're flying at mach two. The space around you feels like stationary 3-d Euclidean, like sitting on Earth. When you land you'll again intuitively "know" the Earth is stationary. And, you "know" the land around you is flat - APR is completely unaffected by your recent experience. Intellectually (even before you flew in the stratosphere) you knew Earth is actually round and spinning, but APR intuition doesn't know that. Admittedly the point is debatable.
Mentz114 said:
My internal model changes as I learn more physics. In fact I think that is the point of doing it, for me anyway.
That internal model is precisely your current version of PR, NOT APR. APR includes only the basics. Your knowledge that time passes. That objects can move when pushed on, but retain their identity even so. Etc. You didn't learn that in physics class!
Mentz114 said:
Einstein's clocks and rulers seems to cover classical physics because we can use those concepts as common existential currency.
"Common existential currency" is similar to APR. The clocks and rulers reduce, or represent, concept of space and time to the way we actually measure them. They are part of an "extended" APR model used in this particular analysis.
ddd123 said:
What can't change are the a priori forms and thinking categories: space&time, quantities&logic.
Those categories are, indeed, core APR.
ddd123 said:
APP: a priori perception, ... for lack of a better term ("perception" can and does involve thinking ...)
Perception is part of essential brain equipment, and in APR. But how the brain works in detail is irrelevant to our current purpose. Remember the Subjective Reality Principle can be stated "All our information consists of quantitative measurements". For physics that's the right approach: just assume we learn the value of the measurement, don't worry about how. Admittedly we must see the experiment and read the results, requiring perception, visual processing, qualia, whatever. But we should ignore such in physics almost entirely. They muddy the waters for no benefit. All we care about is the result: a quantitative measurement. The measurement or observation is localized in space and time, associated with the property of an object, and has other
abstract properties. Forget qualia.
ddd123 said:
One of the most obvious sensations is the pressure of your chair upwards on your bottom. One thing that you do not feel is a gravitational force (what we call “weight”) acting downwards on you, though the Newtonian theory tells us that there is such a force: there is a lack of correlation here between experience and Newtonian gravitational theory. In General Relativity, on the other hand, there is perfect correlation between experience and theory because in GR there is no gravitational force acting downwards on you: we are always, wherever we are, weightless. Perhaps one reason GR is so immensely satisfying to learn is that it accords with our experience in this way.
That's the APR attitude, alright!
zonde said:
As I understand you believe that we could discover some interesting models by discarding some unnecessary basic assumptions. I believe that we could discard some not very interesting models by establishing which basic assumptions we can't discard.
Our two "agendas" are compatible. BTW, perhaps your concept of "necessary" assumptions is what I've called the "core" APR. The part that any version of APR should include. Unnecessary assumptions might be applicable for special purposes but generally should be pruned.
zonde said:
I think that humans had very different model of reality than cats and monkeys even before there was physics around because of much more advanced communication between individuals.
I'm reluctant to include anything that had to be "figured out" in APR. But it's really not important at this stage. We need to understand the overall concept, then go ahead and apply it to specific areas to see how it works.