1. Heisenberg and the Incomplete-ability of Quantum Mechanics
1: SPRINGS from joint work with Guido Bacciagaluppi, now at Universitat Utrecht.
2: Granddaughter of Shimony twice-over through Guido and Don; thanks to Alisa for occasion to be apart of honoring Shimony, etc.
Elise M. Crull
The City College of New York, CUNY
Abner Shimony Boston University
9 October 2015

2. Synopsis 1. Contemporary Modal Interpretations (MIs)
2. Heisenberg’s usual role in the history of MIs
3. Expanding & Improving Heisenberg’s role
Thesis: A richer, more nuanced history of Heisenberg’s thought reveals to greater degree & in a more plausible manner the sense in which he anticipates MIs.
Contemporary Modal Interpretations (MIs)
Dieks
Heisenberg’s usual role in the history of MIs
Camilleri & Suárez
A new (and better?) role for Heisenberg
1927 Paper, Correspondence & Report
1935 Unpublished response to EPR
Introducing Grete Hermann
Her role in this history
The 1933 Essay

3. Modal Interpretations
Dieks’ SEP entry on MIs (2009)
van Fraassen’s original (1972 ff.) proposal for Q State:
Dynamical state – usual vector state describing possibilia
Value state – actual(ized) state assigning sharp values to observables
Privileging function – necessitated by Kocken-Specker Thrm
Dieks: “One should not consider this modality as arising from an incompleteness of the description” (my emphasis)
Kocken-Specker Theorem (1967): proves that it is not possible to ascribe precise values to ALL observables of a quantum
System simultaneously without violating functional relations between commuting observables

4. Modal Interpretations
Dieks’ SEP on MIs (2009)
Event space on which prob measure is defined is space of possible events; only one from this space is actualized
Implies objective probabilities. Two responses to this:
Bite the Bullet: claim possible reduces (ontologically) to actual (n.b. no need for observer, though)
Invoke Propensities: propensities are ontologically primal; reduction of possible to actual reflects ignorance of these

5. Modal Interpretations
Dieks’ SEP on MIs (2009)
Shared characteristics of MIs:
No projection postulate (no collapse of Psi)
Realist, i.e., assume Q systems possess [some?] definite properties at all times
QM is fundamental (explains QMCM)
Dynamical state (pure or mixed) gives possible properties & corresponding probabilities

6. Heisenberg’s Role Suárez (2007) ‘Quantum Propensities’, SHPMP.
Aristotelian notion of potentialities in Heis’s 1958:
“The probability function combines objective and subjective elements. It contains statements about possibilities … and these statement are completely objective…; and it contains statements about our knowledge of the system, which of course are subjective…” (p. 53; as quoted in Suárez pp )
“We may say that the transition from the ‘possible’ to the ‘actual’ takes place as soon as the interaction of the object with the measuring device, and thereby with the rest of the world, has come into play.” (p.54; loc. cit.)
“In experiments about atomic events we have to do with things and facts, with phenomena that are just as real as any phenomena in daily life. But the atoms or the elementary particles themselves are not as real; they form a world of potentialities or possibilities rather than one of things or facts.” (p. 160; loc. cit.)
Heisenberg’ 1958: Physics and Philosophy

7. Heisenberg’s Role
Camilleri (2009) Heisenberg and the Interpretation of Quantum Mechanics, CUP Heisenberg’s philosophy in post-war era:
“Heisenberg argues that fundamental theories in physics allow us to know something about the mathematical form or structural of the physical world, though they do not give us direct knowledge of the nature or essence of the entities of physics.” (p. 57)
“If we attempt to penetrate behind this reality into the details of atomic events, the contours of this ‘objectively real’ world dissolve – not in the mist of a new and yet unclear idea of reality, but into the transparent clarity of a mathematics whose laws govern the possible and not the actual.” (Heis p. 28; as quoted in Camilleri p. 160)
Heisenberg’s 1971: Physics and Beyond

8. Expanding Heisenberg’s Role: Pre-war contributions
Already in 1927 hints at incomplete-ability due to objective probability
Correspondence with Einstein (June)
Indeterminism is ``necessary, not just consistently possible”
Discussions at Como (Sept)
“For a new observation, the wave packet gives the probability of finding the electron at a determined position. The new observation itself however reduces the packet to its original magnitude ∆q, which makes a selection from a totality of possibilities and thereby reduces the possibilities for the future. This continual change of the wave picture at an observation appears to me a fundamental feature of quantum mechanics. One must just put into practice the conception of `probability waves’. (Bohr 1985, p. 140)
Solvay Report with Born (Oct) & discussion of transition probabilities:
“What Born and Heisenberg mean by ‘usual’ transition probabilities bears some resemblance to the notion of potentialities or propensities familiar from the philosophy of probability starting in the 1950s (e.g. Popper, 1959). Indeed, Born and Heisenberg’s transition probabilities are well defined even when there is no value that could make a transition.” (Bacciagaluppi & Crull 2009)
Letter to Einstein: The essence of the argument (electron hitting grating; considered locally, don’t get interference pattern explained. Considered globally, can no longer justify ‘particle’ description.) As we see it is that the existence of hidden variables (here in the sense of deterministic trajectories) will suppress interference effects, and is thus incompatible with the predictions of quantum mechanics.

9. Heisenberg’s Unpublished Response to EPR (1935)
“Ist eine deterministische Ergänzung der Quantenmechanik möglich?” No.
(Analyzed in our 2009)
2 parts of Cut Arg: movable & responsible for probabilities
“[W]e shall examine the assumption that the physical systems about which quantum mechanics makes statistical assertions are carriers of heretofore unknown physical characteristics that univocally determine the behavior heretofore known only statistically. For example, let us assume that the nucleus of the radium atom somehow possesses, in addition to the properties established through knowledge of its stationary state, still other previously unknown characteristics whose knowledge makes possible an exact prediction of when the atomic nucleus will emit an alpha-particle. And we assume specifically: this assertion should hold independently of the means of observation that are applied for the confirmation of the emission of the alpha particle.
“One can at first try letting this last particular assumption drop, and allow that the radioactive emission be also conditioned by the characteristic of the means of observation.”
In order to provide deterministic completion to QM, one can only add HVs at the place of the cut.
Since position of cut is arbitrary, one can remove it entirely
But then further predictions made on basis of these HVs contradicts predictions of QM
Thus, no such completion of the theory is possible
QUOTE: first separation between contextual and non-contextual – in a way, understanding dynamically the importance of context DEPENDENCE of values as being obviously absurd – consider moveability of cut: if it is placed in nominally Classical regime, trouble. Yes, generally – but Bohm succeeds here by tying privileged value (HVs) to position observable.

10. Heisenberg’s Unpublished Response to EPR (1935)
Argument for impossibility of context-indep’t HVs:
When the cut is between A and B,  freedom (possibility) at B to measure either a variable qA of A or conjugate variable pA
Assume  HVs and remove the cut beyond B
QM predictions for pA here require indeterminacy in value of qA
But this contradicts the existence of HVs
Considered from MI perspective:
Heis. takes probabilities to be (simultaneously) well defined –- recall Solvay. This argument crucially depends on inability of all values to be well defined simultaneously
Query: might he understand already the need for privileged observables?

11. Heisenberg’s Unpublished Response to EPR (1935)
I say yes, based on final section of his response to EPR:
Observational Contexts
“[T]he same anschaulich process can belong to different observational contexts – as opposed to classical physics, in which there is only a single observational context. The experimental results accumulated in quantum mechanics have further shown that the observation of a system in general leads discontinuously from one observational context to another. The causal flow can be followed only within a given observational context; in the discontinuous transition from one observational context to another (in fact a ‘complementary’ one in the Bohrian sense), only statistical predictions are possible. The possibility of different complementary observational contexts, unknown to the classical theory, is thus responsible for the occurrence of statistical laws.

12. How Heisenberg “pre-dated” himself regarding MIs
Dieks’ 4 “shared traits of MIs” fail in post-war Heisenberg:
No projection postulate (no collapse of Psi)
Heis speaks often of collapse after the war
Realist, i.e., assume Q systems possess [some?] definite properties at all times
Unclear, given talk about “world of potentialities”
QM is fundamental (explains QMCM)
“Linguistic turn” (Camilleri) seems to drive Heis from unified picture of actual world (appeal to semantics instead)
Aristotelian potentia at times sound like measures of rational degrees of belief (Suárez)
Dynamical state (pure or mixed) gives possible properties & corresponding probabilities
Suárez argues Heis fails to distinguish carefully between probabilities and property values

13. How Heisenberg “pre-dated” himself regarding MIs
Dieks’ 4 shared traits succeed in pre-war Heisenberg:
No projection postulate (no collapse of Psi)
Heis uses term reduktion in 1927; no collapse or reduction mentioned in 1935
Realist, i.e., assume Q systems possess [some?] definite properties at all times
Heis is clear that not all properties can have definite values (response to non-contextual HVs/context of observation)
Good arguments emerge from scrutiny of writings as to Heis’s nuanced philo, in particular unfair label of “positivist/operationalist”
QM is fundamental (explains QMCM)
Args in 1935 (esp. Cut) make clear his QM fundamentalism
Dynamical state (pure or mixed) gives possible properties & corresponding probabilities
Seeds of comprehending mixed states in discussion of observational context
Non-contextual HV considerations  anticipating Kocken-Specker at least in recognizing need for privileging function
QM fundamentality – expressed rather clearly in his correspondence with Bohr in autumn 1935

14. A better, earlier MI?
Recall 2 possible MI responses to objective probability:
Bite the Bullet: claim possible reduces (ontologically) to actual (n.b. no need for observer, though)
Invoke Propensities: propensities are ontologically primal; reduction of possible to actual reflects ignorance of these
Conclusion
In as much as serious doubt has been cast on propensity talk,* and in light of claim that pre-war Heis “bites the bullet” in response to objective probability, I suggest that we consider Heisenberg’s proto-MI to be better, earlier.
*cf. Eagle’s 2004 Erkenntnis paper: “Twenty-one arguments against propensity”