Ken G said:
Actually, you left out the most important one:
3. Property is acquired at an unknowable point in time.
You must admit, it is that third case that we have here, must you not? And doesn't that seem like a problem to the "intrinsic property" idea? After all, we booted the aether as soon as we found it was unknowable what some "aether frame" must be, so here we have the same issue-- when nature herself does not adjudicate the question "when was the property acquired,", then we must seriously face that problem and admit that perhaps there is something bogus in the entire concept of "acquiring an intrinsic property." Put differently, your position rests on the ability to distinguish between "unknowable" and "arbitrary", and I cannot see how you can support any such distinction.
But even if you insist on that distinction, we can still agree that we have it down to two possibilities for anyone who wishes to think that u is an intrinsic property of the particle:
1) It is an intrinsic property that is acquired at an unknowable point in the proper time history of the particle. (In which case we have the problem similar to an unknowable aether frame.)
2) It is an intrinsic property that is acquired when the measurement is done on the particle itself. (In which case people need to significantly change the language they use about when entangled states undergo their changes!)
Alternatively, we have the perspective that suffers none of these problems:
3) It is not an intrinsic property, a property is a concept a scientist uses to achieve understanding and make predictions, and so there is no problem about when the scientist attributes the property as it is a free choice by the scientist that is not intrinsic to the particle anyway.
Entangled particles are animating the research and your discussion here is one supplementary proof for that. The fact that two entities may be “instantaneously” correlated over a distance, any distance, is highly contradicting one of the pillars of relativity. This explains the intensity of the debates. Discussing about this item forces us to reconsider basic concepts (chronology, instantaneity, etc.) which we believed were totally understood and mastered.
Let me bring my modest contribution. Let examine the situation. It is of course impossible for a given object to be in two different places at the same time (the time here being an instant in a chronology for an observer working outside that object. In extenso: I observe for example a plane or a wave staying on the ground, not in the plane or on the back of the wave). This impossibility is mainly based on the fact that the human brain realizes a short cut, often unconsciously, between observed object and point. Within a very classical vision, this is resulting into an abusive confusion between observed object and locality. Any given object is necessarily localized at a given and relatively restricted small place.
This interpretation of the reality doesn’t hold true for waves. Let fall a stone in the water of a quiet lake and observe the front of the wave. The same object (the front of the wave) is occupying a whole circle at the same time in my chronology. Now imagine the same or a similar scenario at a quite greater scale. For example, consider a tsunami starting somewhere in the ocean with a front wave arriving in Sumatra and in Los Angeles. Imagine that each observer (the one in Sumatra and the one in Los Aneles) only have a radio to communicate. Imagine they speak together about anything. Imagine that they suddenly see a wave front arriving at the same instant in their respective local chronology but have no knowledges about wave propagations. They probably will conclude that two waves are arriving at the same time on their respective coasts. Only a third observer owning a satellite and a deeper understanding of the physics acting there will be able to tell them: “In fact, it’s the same and unique object!”
Analyzing this fictive scenario is telling us that an object may have a spatial size and may not always be reduced to a local position. It also tells us that it is not always easy to understand that two spatially separate phenomenon may eventually be two manifestations of a unique one object. This effectively pushes us back to the beginning of that dissertation: “How can we concretely be certain that we are observing an entangled objet?”
Coming also back to the main topic of your conversation: “Is an observed property intrinsic to the (eventually entangled) object? Or is the property just the result of a local analysis which has been developed by the observer… Or is that property only a property of the place where the manifestation of the object has been observed?” This is really not an easy task, although a really interesting and deep question.
Let consider as a simple example: the mass of a proton or the charge of an electron which may be easier to measure. Why is this charge a universal value (1, 6. 10-19 Coulomb)? I mean: “What can explain that, you or me, where ever we are measuring it, will always find the same value?”
A analysis of that fact exhibits a first information: what is interpreted as a charge depends neither on our localization, nor on the one of the observed electron, nor on our relative motion to it. The value is frame and motion-independent. This is the reason why we believe that it is intrinsic to the electron.
But exactly here, I come back to my second paragraph above. In extenso, in believing that the charge is intrinsic, we intuitively have though that that electron was a local particle and we have automatically put a flag on its back: its charge.
This is probably not a totally correct way to think about the reality because of the duality particle-wave, because of the non-locality of any electron (around an atom for example).
So, my questioning: “From your perspective (the property is highly depending on the observer and on his/her technology): what do we measure when we try to measure the charge of an electron?”Thanks in advance for criticism concerning that short dissertation.