Do Quanta Need a New Logic? John Stachel

1. Do Quanta Need a New Logic?John Stachel Frontiers of Fundamental Physics 14 Epistemology and Philosophy Marseille, 17 July 2014

2. Do Quanta Need a New Logic?

3. Three Aspects of a Logic Syntax: A formalism, or set of symbols and rules for well-formed formulas using these symbols Semantics: An interpretation of the formalism: Its meaning as a description of some aspect of the world Pragmatics: Its application to that aspect of the world

4. Logic-Language-World • Three steps: • Logic is about Language, • Language is about The World. Panlogism • The attempt to “short circuit” this process by identifying the real object and the “concrete-in- thought” leads to the assertion: Logic is about The World

5. AronGurwitsch

6. Leibniz: Philosophie des Panlogismus “Things are realizations of concepts of reason. It is not sufficient to maintain that the logical and the ontological viewpoints can never be fully distinguished from each other, or that no separation, no abyss exists between reason and reality. One seems most faithful to the situation, if one speaks of an identity, or better of an equivalence of the logical and the ontological”

7. Panlogism Reborn! “ By panlogismI mean the philosophical tendency to obliterate the distinction between logical and ontologicalprinciples” JS, “Do Quanta Need a New Logic?” (1986) I have been combating this viewpoint for over 35 years: ”The ‘Logic’ of Quantum Logic” in PSA 1974 (Dordrecht: Reidel 1976), pp. 515-526.

10. Logic(s) For Quantum Mechanics If we abandon panlogism, and the search for The Logic of Quantum Mechanics, we shall see that quantum logics (note the plural!) are just different waysof reformulating the same content of quantum theory.

11. The Danger: If we accept one formulation of The Logic of Quantum Mechanics as providing the answers, it prevents us from confronting the real questions about the nature of quantum mechanics.

12. Chris Isham

13. Is it True; or is it False; or Some-where In Between? The Logic of Quantum Theory "A key feature of classical physics is that, at any given time, the system has a definite state, and this state determines-- and is uniquely determined by-- the values of all the physical quantities associated with the system.“ Realism is "the philosophical view that each physical quantity has a value for any given state of the system.“

14. In a Letter to Chris, I Raised Two Problems: 1) Conditional Properties: “each physical quantity has a value” 2) The Primacy of Process: “for any given state of the system”

15. First Problem: 1) Conditional Properties: “each physical quantity has a value” 2) The Primacy of Process: “for any given state of the system.”

16. 1) Conditional Properties • This is just not true of conditional properties, as discussed in detail in Do Quanta Need a New Logic? The exampleI use concerns the properties "hardness h" and "viscosity v": Given a system defined by its chemical composition, the property "hardness" will only apply-- let alone have a numerical value on Moh's scale-- if the system is in its solid state; while "viscosity" will only apply if the system is in a fluid (liquid or gaseous) state.

17. Simple Classical Example Hardness and Viscosity can be applied to any substance, but not simultaneously. If it is in solid state, hardness applies; if it is in a fluid state viscosity applies.

18. 1) Conditional Properties • With the definition of the logical 'negation' operator, [logic] has already gotten as complicated as it gets. … [M]y article … discusses the difference between choice negation (-) and exclusion negation (∼) in general, and the inevitability of choice negation for a conditional predicate … if one wants to derive other predicates from it, and what follows from this choice even before getting to the special case of QM.

19. Non-Standard Logic Needed Semantics If we allow elementary propositions of the form: “System S has hardness h,” “System S has viscosity v” Then a non-standard logic is needed: negation (“not”), conjunction (“and”) and disjunction (“or”) cannotall follow the laws of classical logic

20. Which Negation? How shall we interpret the proposition: “System S does not have hardness h1” It could mean: “System S has some hardness h2≠ h1” or it could mean: “System S is not in the solid state, so the concept of hardness does not apply”

21. Which Negation? The law of the excluded middle: “p or not p is always true” (p∨∼p=I) If we choose “System S has some hardness h2≠ h1” Then the law of the excluded middle Is not valid for this variant of intuitionistic logic. To keep the law, we must choose the disjunction: “System S has some hardness h2≠ h1orit is not in the solid state so the concept of hardness does not apply” This choice also leads to a non-standard logic!

22. Simplest Example Only Two States, Solid and Liquid: Solid State, only two values h1, h2 of hardness Liquid State, only two values v1, v2 of viscosity Then there are only four elementary propositions, symbolized byh1, h2, v1, v2 We also need symbols for: Negation (∼) The identically false propositionϕ The denticallytrue proposition I

23. Simplest Example If we plot all possible combinations of propositions p, starting from the identically false propositionϕand ending with the identically true proposition I, and use dotted lines to represent logical implication, then we get the following diagram of a propositional lattice

24. Propositional Lattice I (∼ϕ) . . . . . . . . . . . h1(∼h2) v2(∼v1) v1(∼v2) h2(∼h1) . . . . . . . . . . . ϕ(∼I )

25. David Ritz Finkelstein

26. The Physics of Logic (1969) Finkelstein uses the same diagram to describe the polarization of photons, and states: “The system is the simplest quantum-like lattice and exhibits nondistributivity and coherence.”

27. Enter Pragmatics But such propositions cannot be tested without the additional specification of the conditions C under which system S is being observed (e.g., temperature T, pressure p). So if we add these conditions to the form of the proposition: “System S under conditions C has hardness h”

28. Classical Logic Returns! Then, either: The proposition is not well-formed, if system S is not in the solid state under conditions C, or: The proposition is well-formed, if system S is in the solid state under conditions C, and Classical logic holds for all well-formed propositions!

29. Objection Well and good for this example, but there is no analogue of the superposition principle in it. We cannot superpose two states S1 and S2 of different hardness or a state of hardness and and a state of viscosity to get a new state S Answer: Let’s look at another classical example:

31. What Are Colors? Colors are literally in the mind of the beholder: The human eye and brain combine to interpret all electromagnetic waves within a certain range of frequencies that impinge on the retina in terms of three dimensions, e.g.: Brightness, hue and saturation or Three primary colors So colors are conditional properties of an open system, forming a 3-dimensional vector space

33. Color Logic Three primary colors: Red Green Blue

34. Additive Color

36. They can be mixed (color superposition) to get:MagentaYellow Cyan

38. Complementation Two colors are complementary if, when superposed (mixed) they produce white. Red Cyan Green Magenta Blue Yellow

40. Enter Logic Define elementary propositions: “Object O has color c” Interpret negation (“not”) as color complementation Interpret conjunction (“and”)as color addition And you have a non-standard logic with superposition of colors!

41. What Is a Quantum System? So neither conditional properties nor superposition are unique to quantum systems. Then what makes a quantum system? As we shall see, it is the role of h, the quantum of action.

42. What is Quantization? Quantization is just a way of accounting for the effects of h, the quantum of action, on any process involving some system,– or rather on theoretical models of such a system-- “fundamental” or “composite”, in which the collective behavior of a set of more fundamental entities is quantized

43. “Atoms and Human Knowledge”--Niels Bohr 1957 “..an element of wholeness, so to speak, in the physical processes, a feature going far beyond the old doctrine of the restricted divisibility of matter. This element is called the universal quantum of action. It was discovered by Max Planck in the first year of this century and came to inaugurate a whole new epoch in physics and natural philosophy.

44. “Atoms and Human Knowledge”-- (cont’d) We came to understand that the ordinary laws of physics, i.e., classical mechanics and electrodynamics, are idealizations that can only be applied in the analysis of phenomena in which the action involved at every stage is so large compared to the quantum that the latter can be completely disregarded.

45. The Second Problem 1) Conditional Properties: “each physical quantity has a value” 2) The Primacy of Process: “for any given state of the system”

46. Lee Smolin

47. Three Roads to Quantum Gravity “[R]elativity theory and quantum theory each ... tell us-- no, better, they scream at us-- that our world is a history of processes. Motion and change are primary. Nothing is, except in a very approximate and temporary sense. How something is, or what its state is, is an illusion.

48. Three Roads to Quantum Gravity It may be a useful illusion for some purposes, but if we want to think fundamentally we must not lose sight of the essential fact that 'is' is an illusion. So to speak the language of the new physics we must learn a vocabulary in which process ismore important than, and prior to, stasis.”

49. 2) Primacy of Process Phrases such as "at any moment of time", "at any given time” may be applied in Newtonian-Galileian physics, which is based on a global absolute time. But from SR on to GR, this phrase involves a conventiondefining a global time., and nothing physical can depend on the choice of convention!

50. 2) Primacy of Process The only convention-invariant things areprocesses, each involving a space-time region. This suggests-- as do many other considerations-- that the fundamental entities in quantum theory are the transition amplitudes, and that states should be taken in the c.g.s. system (cum granosalis).