1. Using Neutrino Oscillations to Test the Foundations of Quantum Mechanics David Kaiser

2. Using Neutrino Oscillations to Test the Foundations of Quantum Mechanics David Kaiser J. Formaggio M. Murskyj T. Weiss

3. Bell and Leggett-Garg Inequalities Neutrino Oscillations Results and Future Tests

4. Superposition Does the object occupy a single, definite state at any given time (“either-or”), or can it genuinely occupy a “both-and” state?

5. Entanglement The state does not factorize: there is no way to describe the behavior of particle 1 ( u ) without referring to the behavior of particle 2 ( v ).

6. Bell’s Inequality John S. Bell detector settings: a, b measurement outcomes: A, B

7. Bell’s Inequality John S. Bell detector settings: a, b measurement outcomes: A, B Test “local realism” of EPR: particles carry definite values for their properties independent of measurement; distant events cannot influence local ones instantaneously.

8. Bell’s Inequality John S. Bell detector settings: a, b measurement outcomes: A, B Test “local realism” of EPR: particles carry definite values for their properties independent of measurement; distant events cannot influence local ones instantaneously. The alternative: “spooky actions at a distance” (Einstein)

9. Correlations at a Distance Dichotomic observables Correlation functions

10. Correlations at a Distance Dichotomic observables Correlation functions

11. Correlations at a Distance QM prediction: S max = 2√2 S  Dichotomic observables Correlation functions Any local-realist theory must obey

12. Correlations at a Distance John Clauser, LBNL, 1970s Alain Aspect, Orsay, 1980s QM prediction: S max = 2√2 Dozens of experiments: S max > 2 S  Dichotomic observables Correlation functions Any local-realist theory must obey

13. Closing Loopholes

14. First experiment to close both the locality and fair-sampling loopholes.

15. Closing Loopholes

16. Latest Experiments

17. “Cosmic Bell” Experiments Set a, b using real-time observations of astronomical objects. JG, AF, DK, Phys. Rev. Lett. (2014), arXiv:1310.3288 Select distant objects, such as quasars, whose light we observe today was emitted as early in cosmic history as possible.

18. “Cosmic Bell” Experiments JG, AF, DK, Phys. Rev. Lett. (2014), arXiv:1310.3288 Select distant objects, such as quasars, whose light we observe today was emitted as early in cosmic history as possible. Set a, b using real-time observations of astronomical objects.

19. Leggett-Garg Inequality A. Leggett A. Garg Correlations between the outcomes of measurements on a single system at different times. Two assumptions: “Macroscopic realism”: an object has a well-defined state independent of measurement. “Non-invasive measurability”: the state of an object may be measured without disturbing it.

20. Dichotomic observable Correlation function Leggett-Garg Inequality

21. Dichotomic observable Correlation function Leggett-Garg Inequality E.g.,

22. Two assumptions: “Macroscopic realism” “Non-invasive measurability” Dichotomic observable Correlation function Leggett-Garg Inequality E.g.,

23. Two assumptions: “Macroscopic realism” “Non-invasive measurability” Dichotomic observable Correlation function Leggett-Garg Inequality Experimental tests using superconducting qubits; NMR; photons; even macroscopic crystals. Nice review: Emary, Lambert, and Nori, Rep. Prog. Phys. 77 (2014), arXiv:1304.5133.

24. Neutrino Oscillations W. Pauli E. Fermi Neutrinos first postulated in the early 1930s, to address anomalies in  -decay spectra. F. Reines C. Cowan First direct detection of (anti- )neutrinos from a nuclear reactor, 1956.

25. Neutrino Oscillations B. Pontecorvo If neutrinos have tiny, distinct masses, then there could exist a mismatch between the mass eigenbasis and the flavor eigenbasis.

26. Neutrino Oscillations B. Pontecorvo If neutrinos have tiny, distinct masses, then there could exist a mismatch between the mass eigenbasis and the flavor eigenbasis. Neutrinos would propagate in a mass eigenstate, but be measured in a flavor eigenstate. The superposition would yield oscillations in the flavor-state detection probabilities.

27. Neutrino Oscillations Sudbury Neutrino Observatory (SNO) Super-Kamiokande

28. Neutrino Oscillations Sudbury Neutrino Observatory (SNO) Super-Kamiokande The quantum-mechanical description of neutrino oscillations works beautifully. Can we turn things around, and use the strength of recent experiments to test QM or constrain alternatives?

29. Neutrino Oscillations

30. The operators’ evolution depends on their accumulated phase,  a;ij.

31. Neutrino Oscillations The operators’ evolution depends on their accumulated phase,  a;ij. We may relate the correlation functions to the observed survival probabilities.

32. Comparing with Experiment Perform measurements on members of an identically prepared ensemble. “Stationarity”: assume that the correlations between measurements depend only on the duration between them (  = t j – t i ), rather than on t i or t j. The Leggett-Garg Inequality concerns repeated measurements on a single system. Neutrinos are difficult to detect once! So we rely on two assumptions: These assumptions restrict the class of “realist” alternatives to QM that we can test, but they do allow us to use existing data—and, unlike the original assumption of “non-invasive measurability,” the assumption of “stationarity” may be tested independently of the LGI.

33. MINOS Experiment

34. Coherence B. J. P. Jones, PRD 91 (2015), arXiv:1412.2264 In order to test for a violation of the LGI, we must ensure that the two-state system behaves coherently. Fortunately, due to their very small masses, neutrinos have extremely long coherence lengths (~10 2 – 10 9 km).

35. Data Extraction The LGI is formulated for measurements at different times. Yet the MINOS data are collected for a fixed distance between the Near and Far detectors. MINOS Collaboration, June 2014

36. Data Extraction The QM effect depends only on the accumulated phase,  a;ij : The LGI is formulated for measurements at different times. Yet the MINOS data are collected for a fixed distance between the Near and Far detectors. MINOS Collaboration, June 2014

37. Data Extraction MINOS Collaboration, June 2014 The QM effect depends only on the accumulated phase,  a;ij : The LGI is formulated for measurements at different times. Yet the MINOS data are collected for a fixed distance between the Near and Far detectors. For different times,  a;12 +  a;23 =  a;13 (sum rule). For fixed  = ( t j – t i ),  a;ij varies with energy, E a :

38. Data Extraction The QM effect depends only on the accumulated phase,  a;ij : Point a Point b Point c Energy Phase Select triples of points such that  a +  b =  c ± 0.5% The LGI is formulated for measurements at different times. Yet the MINOS data are collected for a fixed distance between the Near and Far detectors. For different times,  a;12 +  a;23 =  a;13 (sum rule). For fixed  = ( t j – t i ),  a;ij varies with energy, E a :

39. Results For K 3 : 82 triples satisfied  a sum rule. Of those, 64 yielded K 3 > 1. For K 4 : 715 quadruples satisfied  a sum rule. Of those, 577 yielded K 4 > 2. Point a Point b Point c

40. Results However, statistical fluctuations could cause violations of the LGI, even if the world really were governed by a “realistic” theory. Point a Point b Point c For K 3 : 82 triples satisfied  a sum rule. Of those, 64 yielded K 3 > 1. For K 4 : 715 quadruples satisfied  a sum rule. Of those, 577 yielded K 4 > 2.

41. Results However, statistical fluctuations could cause violations of the LGI, even if the world really were governed by a “realistic” theory. We create pseudo-data, distributing points randomly according to the same mean and width as measured. Point a Point b Point c This creates fake “experiments” with exactly the same correlations as the experimental data. Then we can use Markov Chain Monte Carlo simulations. For K 3 : 82 triples satisfied  a sum rule. Of those, 64 yielded K 3 > 1. For K 4 : 715 quadruples satisfied  a sum rule. Of those, 577 yielded K 4 > 2.

42. Results We can create distributions for both QM and “realist” theories.

43. Results We can create distributions for both QM and “realist” theories. K3K3 K4K4 ClassicalQuantum Observed We may then compare these expected distributions to the experimental data. K 3 : 6.2  violation of LGI K 4 : 7.0  violation of LGI Classical Quantum Observed

44. Results We can create distributions for both QM and “realist” theories. We may then compare these expected distributions to the experimental data. K 3 : 6.2  violation of LGI K 4 : 7.0  violation of LGI K3K3 K4K4 K n can attain multiple values for a given relative phase, because there are many n-tuples of phase points that add up to a given relative phase.

45. Results We can create distributions for both QM and “realist” theories. We may then compare these expected distributions to the experimental data. K 3 : 6.2  violation of LGI K 4 : 7.0  violation of LGI K3K3 K4K4 K n can attain multiple values for a given relative phase, because there are many n-tuples of phase points that add up to a given relative phase. The upshot: The MINOS data are most readily compatible with the idea that neutrinos traverse the 735 km between the Near and Far detectors as neither  nor e, but in a superposition of the two flavor states.

46. Robustness Systematic (correlated) uncertainties? Is the identical- ensemble assumption reasonable? Is the stationarity assumpition valid? Is the measurement subject to the “clumsiness loophole”?

47. Robustness Systematic (correlated) uncertainties? Is the identical- ensemble assumption reasonable? Is the stationarity assumpition valid? Is the measurement subject to the “clumsiness loophole”? Extracted from MINOS measurements of mixing and mass parameters; small effect. MINOS has 98% beam purity. Using a separate test of MINOS’s oscillation data, testing for Lorentz violation, the data appear consistently independent of times t i, t j. We do not perform weak measurements.

48. Next Steps By using data on neutrino oscillations, we have performed the longest-distance test of quantum mechanics to date. (Record for Bell tests: 144km.) The LGI was originally formulated to test “macroscopic realism,” though it has usually been applied to microscopic systems. We have tested (microscopic) realism across macroscopic distances.

49. Next Steps By using data on neutrino oscillations, we have performed the longest-distance test of quantum mechanics to date. (Record for Bell tests: 144km.) Neutrinos are everywhere! We are presently exploring LGI tests using solar neutrinos (L ~ 10 8 km rather than ~10 3 km). The LGI was originally formulated to test “macroscopic realism,” though it has usually been applied to microscopic systems. We have tested (microscopic) realism across macroscopic distances. Can we relate CP violation directly to LGI violation?

50. Next Steps By using data on neutrino oscillations, we have performed the longest-distance test of quantum mechanics to date. (Record for Bell tests: 144km.) Neutrinos are everywhere! We are presently exploring LGI tests using solar neutrinos (L ~ 10 8 km rather than ~10 3 km). The LGI was originally formulated to test “macroscopic realism,” though it has usually been applied to microscopic systems. We have tested (microscopic) realism across macroscopic distances. Can we relate CP violation directly to LGI violation? In relatively short order, neutrinos have gone from exotic phenomena at the edge of detection to a tool for testing our most basic understanding of nature.