This note is a continuation of Why Algebra? Rudolf Haag
Haag’s Assertions
Concerning the interpretation of quantum mechanics Haag noted that
“to this day, there remains some uneasiness about its status, some disagreement concerning its interpretation. This is not restricted to crackpots. Different camps of eminent scientists advance widely different opinions.”
It is good, at this point, to remember the advice of the philosopher, Bertrand Russell, namely that when experts do not agree on a given subject, then “no opinion can be regarded as certain by a non-expert”. Then Haag defines his position, and I will concentrate on just two points here:
The subject of physics is ‘nature’ and, whatever this means precisely, it is something beyond and apart from human knowledge.
In other words, physics should be formulated in such a way that it concerns objective phenomena. All twists, so popular, trying to make physics subjective, invoking the necessity of an “observer”, and so on, do not belong to physics! They result from arbitrarily assumed metaphysical prejudices that affect rationality of thinking.
Then we have the second assertion:
B. Individual knowledge is gained by observation, typically by experiment. In describing the set up and the result of an experiment we are bound by limits emphasized by Bohr: ‘We must be able to tell our friends what we have done and what we have learned.’ Bohr concludes from this that in the description of both the arrangement and the result we are bound to use “the language of classical physics’’.
Thus Haag takes a rational point of view. The language of physics, one that physicists should use when talking about Nature, should be a classical language that deals with real, material objects and their placement in space time.
Popper’s “Propensity”
Further in his paper he notes that many issues in quantum theory are still open, in particular the issue of whether the correct description should be deterministic or not. Instead of using the term “probability”, that requires repeated experiments, Haag opts for the Popperian term “propensity”, that characterizes an objective property associated with a given situation. The fact that “propensity” per se cannot be observed should not worry us, because:
The use of concepts in the theory which are not directly amenable to observation is neither forbidden nor unusual. It seems unavoidable.”
Then he addresses the quantum mechanical superposition principle and superselection rules:
Strict superselection rules forbid (coherent) linear combinations of states which differ in some charge quantum number (electric, baryonic, leptonic,…).
This alone, at least for me, dismisses the “Schrödinger cat paradox”; the paradox exists only because it is based on arbitrary assumptions.
The fact that there IS a paradox tells us that these assumptions are wrong. But, for some reason, most physicists simply ignore this fact.
The Problem of the Observer
The concept of an “observer” was, for Haag, and also for me, causing a serious problem, as it meant that we forcefully limited the scope of physics, which was/is unnecessary. Instead of introducing an “observer” that is external to the physical system, it is better to introduce the concept of an event – as a fundamental concept. Things happen, with or without observers. Reality is Real on its own terms. Another fundamental concept that we should not be afraid of is irreversibility at a fundamental level. All these corrections should lead to:
…a self consistent theory in which all relevant objects are included as parts of the physical system.
Then Haag discusses different possible strategies that could lead to such a theory, and, in particular, notes:
In a series of papers Ph. Blanchard and A. Jadczyk have described a formalism which generates real events in the interaction of an atomic object with a macroscopic measuring device. The latter is idealized as a classical system in the sense that it is described by a commutative algebra which may include some discrete variables. The scheme, called “Event Enhanced Quantum Theory”, introduces irreversible decisions into the interaction process and yields a good phenomenological description of the quantum measurement process. (Italics mine)
As this concerns my own contribution, it is time for me to develop the comment of my teacher, one of the clearest and sharpest minds I ever knew in my life.
P.S.1 My wife likes it. SC looks a lot like FLA - Her childhood home. This is for Her.
P.S.2.12-06 13:00 I am trying to find out if the conformally compactified Minkowski space is orientable or not. Its double cover certainly is (it is S^1 x S^3), but its image by the covering map? I feel really shameful that I don't know it. Big holes in my working knowledge of differential geometry. Work, work, work and more work needed! So I work.
Diana Walsh Pasulka
P.S.5. The beginning of "Geometry of the conformally compactified Minkowski space"
"Thus, Protoconsciousness can be imagined as current awareness by a living cell of the gap, that being expressed as non-congruence, divergence, incompatibility, collision, conflict - between the ideal geometrical form and its physical realization. This means that such discrepancy between the Ideal Geometry and Robust Physics is "felt" by the cell. The ideal geometry is species-specific, initially pre-existing, and pre-determined, while the robust physics is actually occurring and constantly fluctuating to adapt, to adjust, to fit, to accommodate, to approximate to the ideal geometry. Accordingly, the living process can be expressed as continuous dynamic approximation of the "real" physical form to its geometrical "ideal". Since this approximation is felt until there is the non-congruence between physical and geometrical (which can diminish only asymptotically, i.e. the physical will never coincide with geometrical), then the geometrical feeling (protoconsciousness) is an inalienable part of any living entity. Hence, the Geometrical Feeling is suggested for the role of the Protophenomenal Fundamental alongside physical fundamentals (Mass, Charge, Time/Space). As to the deep ontological meaning of the concept of "Geometrical Feeling", it could be analogized with the "Universal Grammar" by N. Chomsky (1988), which may be considered as "intrinsic part of the structure of matter ever since the Big Bang, or a necessary part of the eternal Platonic world oflogic and mathematics" (Hamad, 2001). "
P.S.7. From Christopher Langan "The Theory of Theories":
"For example, modern physics is bedeviled by paradoxes involving the origin and directionality of time, the collapse of the quantum wave function, quantum nonlocality, and the containment problem of cosmology. Were someone to present a simple, elegant theory resolving these paradoxes without sacrificing the benefits of existing theories, the resolutions would carry more weight than any number of predictions. Similarly, any theory and model conservatively resolving the self-inclusion paradoxes besetting the mathematical theory of sets, which underlies almost every other kind of mathematics, could demand acceptance on that basis alone. Wherever there is an intractable scientific or mathematical paradox, there is dire need of a theory and model to resolve it.
If such a theory and model exist – and for the sake of human knowledge, they had better exist – they use a logical metalanguage with sufficient expressive power to characterize and analyze the limitations of science and mathematics, and are therefore philosophical and metamathematical in nature. This is because no lower level of discourse is capable of uniting two disciplines that exclude each other‘s content as thoroughly as do science and mathematics.
Now here‘s the bottom line: such a theory and model do indeed exist "
I don't think so. Attempts to create such a beast - they exist.
P.S.8. In the pdf note I have made a few changes comparing to the previous version.. I have multiplied the factor in front of the matrix by "i", and the matrix by "-i". The whole matrix U(Z) is unchanged. The proof (I will write it later today) will be somewhat more "elegant" after these "cosmetical" changes.
Where did I get the matrix U(Z) from? I am not sure. Reading, thinking, making errors, and correcting them. Until it works the way I envisaged it to work.
P.S.9. Uploaded a new version of the pdf note. The proof of the last lemma is not yet finished.
