Origin of probabilities and their application to the multiverse Andreas Albrecht UC Davis

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# Origin of probabilities and their application to the multiverse Andreas Albrecht UC Davis

## Origin of probabilities and their application to the multiverse Andreas Albrecht UC Davis

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1. Origin of probabilities and their application to the multiverse Andreas Albrecht UC Davis Phy 262 lectures Adapted from a U. Penn Seminar April, 2014 A. Albrecht Prob. Lectures for Phy 262

2. My history with this topic AA: All randomness/ probabilities are quantum (coin flip, card choice etc) A. Albrecht Prob. Lectures for Phy 262

3. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) A. Albrecht Prob. Lectures for Phy 262

4. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) A. Albrecht Prob. Lectures for Phy 262

5. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) A. Albrecht Prob. Lectures for Phy 262

6. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) Hartle, Srednicki, Aguirre, Tegmark, … A. Albrecht Prob. Lectures for Phy 262

7. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) AA: A deeper problem than the measure problems for the multiverse A. Albrecht Prob. Lectures for Phy 262

8. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) AA: A deeper problem than the measure problems for the multiverse A potential issue even for finite models A. Albrecht Prob. Lectures for Phy 262

9. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) AA: A deeper problem than the measure problems for the multiverse AA: Write paper explaining this with Phillips A. Albrecht Prob. Lectures for Phy 262

10. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) AA: A deeper problem than the measure problems for the multiverse AA: This is fundamentally about giving permission to dismiss certain probability questions (the non quantum ones) as “ill posed”. AA: Write paper explaining this with Phillips A. Albrecht Prob. Lectures for Phy 262

11. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) AA: A deeper problem than the measure problems for the multiverse AA: This is fundamentally about giving permission to dismiss certain probability questions (the non quantum ones) as “ill posed”. Perhaps this type of discipline can help resolve the measure problems of the multiverse/eternal inflation AA: Write paper explaining this with Phillips A. Albrecht Prob. Lectures for Phy 262

12. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) X ? AA: A deeper problem than the measure problems for the multiverse AA: This is fundamentally about giving permission to dismiss certain probability questions (the non quantum ones) as “ill posed”. Perhaps this type of discipline can help resolve the measure problems of the multiverse/eternal inflation AA: Write paper explaining this with Phillips A. Albrecht Prob. Lectures for Phy 262

13. My history with this topic All randomness/probabilities are quantum (coin flip, card choice etc) AA: All randomness/ probabilities are quantum (coin flip, card choice etc) Page: Quantum probabilities cannot address key multiverse questions. (OK, just use classical ones) X ? AA: A deeper problem than the measure problems for the multiverse AA: This is fundamentally about giving permission to dismiss certain probability questions (the non quantum ones) as “ill posed”. Apparently this type of discipline can help resolve the measure problems of the multiverse/eternal inflation AA: Write paper explaining this with Phillips A. Albrecht Prob. Lectures for Phy 262

14. Outline Quantum vs non-quantum probabilities (toy model/multiverse) Everyday probabilities Be careful about counting! Implications for multiverse/eternal inflation A. Albrecht Prob. Lectures for Phy 262

15. Outline Quantum vs non-quantum probabilities (toy model/multiverse) Everyday probabilities Be careful about counting! Implications for multiverse/eternal inflation NB: Very different subject from “make probabilities precise” in “Stanford sense”. A. Albrecht Prob. Lectures for Phy 262

16. Outline Quantum vs non-quantum probabilities (toy model/multiverse) Everyday probabilities Be careful about counting! Implications for multiverse/eternal inflation A. Albrecht Prob. Lectures for Phy 262

17. Planck Data --- Cosmic Inflation theory A. Albrecht Prob. Lectures for Phy 262

18. Slow rolling of inflaton Observable physics generated here A. Albrecht Prob. Lectures for Phy 262

19. Slow rolling of inflaton Observable physics generated here Extrapolating back A. Albrecht Prob. Lectures for Phy 262

20. Slow rolling of inflaton “Self-reproducing regime” (dominated by quantum fluctuations): Eternal inflation/Multiverse Q Observable physics generated here Extrapolating back Steinhardt 1982, Linde 1982, Vilenkin 1983, and (then) many others A. Albrecht Prob. Lectures for Phy 262

21. The multiverse of eternal inflation with multiple classical rolling directions Self-reproduction regime Classically Rolling B Classically Rolling A Classically Rolling C Where are we? (Young universe, old universe, curvature, physical properties A, B, C, D, etc) Classically Rolling D A. Albrecht Prob. Lectures for Phy 262

22. The multiverse of eternal inflation with multiple classical rolling directions Self-reproduction regime Classically Rolling B Classically Rolling A “Where are we?” Expect the theory to give you a probability distribution in this space… hopefully with some sharp predictions Classically Rolling C Where are we? (Young universe, old universe, curvature, physical properties A, B, C, D, etc) Classically Rolling D A. Albrecht Prob. Lectures for Phy 262

23. The multiverse of eternal inflation with multiple classical rolling directions String theory landscape even more complicated (e.g. many types of eternal inflation) Self-reproduction regime Classically Rolling B Classically Rolling A “Where are we?” Expect the theory to give you a probability distribution in this space… hopefully with some sharp predictions Classically Rolling C Where are we? (Young universe, old universe, curvature, physical properties A, B, C, D, etc) Classically Rolling D A. Albrecht Prob. Lectures for Phy 262

24. Quantum vs Non-Quantum probabilities Non-Quantum probabilities in a toy model: Page, 2009; These slides follow AA & Phillips 2012/14 A. Albrecht Prob. Lectures for Phy 262

25. Quantum vs Non-Quantum probabilities Non-Quantum probabilities in a toy model: Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

26. BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured. Quantum vs Non-Quantum probabilities Non-Quantum probabilities in a toy model: Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

27. BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured. Quantum vs Non-Quantum probabilities Non-Quantum probabilities in a toy model: Could Write Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

28. BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured. Quantum vs Non-Quantum probabilities Classical Probabilities to measure A, B Non-Quantum probabilities in a toy model: Could Write Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

29. BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured. Quantum vs Non-Quantum probabilities Classical Probabilities to measure A, B Non-Quantum probabilities in a toy model: Could Write Does not represent a quantum measurement Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

30. BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured. Quantum vs Non-Quantum probabilities Classical Probabilities to measure A, B Non-Quantum probabilities in a toy model: Could Write Does not represent a quantum measurement Page: The multiverse requires this (are you in pocket universe A or B?) Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

31. BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured. Quantum vs Non-Quantum probabilities Classical Probabilities to measure A, B Non-Quantum probabilities in a toy model: Could Write Does not represent a quantum measurement Page: The multiverse requires this (are you in pocket universe A or B?) Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

32. All everyday probabilities are quantum probabilities AA & D. Phillips 2012 A. Albrecht Prob. Lectures for Phy 262

33. All everyday probabilities are quantum probabilities Our *only* experiences with successful practical applications of probabilities are with quantum probabilities AA & D. Phillips 2012 A. Albrecht Prob. Lectures for Phy 262

34. All everyday probabilities are quantum probabilities • One should not use ideas from everyday probabilities to justify probabilities that have been proven to have no quantum origin AA & D. Phillips 2012 A. Albrecht Prob. Lectures for Phy 262

35. All everyday probabilities are quantum probabilities • One should not use ideas from everyday probabilities to justify probabilities that have been proven to have no quantum origin A problem for many multiverse theories AA & D. Phillips 2012 A. Albrecht Prob. Lectures for Phy 262

36. All everyday probabilities are quantum probabilities • One should not use ideas from everyday probabilities to justify probabilities that have been proven to have no quantum origin A problem for many multiverse theories (as practiced) AA & D. Phillips 2012 A. Albrecht Prob. Lectures for Phy 262

37. BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured. Quantum vs Non-Quantum probabilities Classical Probabilities to measure A, B Non-Quantum probabilities in a toy model: Could Write Does not represent a quantum measurement Page: The multiverse requires this (are you in pocket universe A or B?) Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

38. BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured. Quantum vs Non-Quantum probabilities Classical Probabilities to measure A, B Non-Quantum probabilities in a toy model: Could Write Where do these come from anyway? Does not represent a quantum measurement Page: The multiverse requires this (are you in pocket universe A or B?) Possible Measurements  Projection operators: Measure A only: Measure B only: Measure entire U: A. Albrecht Prob. Lectures for Phy 262

39. Outline Quantum vs non-quantum probabilities (toy model/multiverse) Everyday probabilities Be careful about counting! Implications for multiverse/eternal inflation A. Albrecht Prob. Lectures for Phy 262

40. Outline Quantum vs non-quantum probabilities (toy model/multiverse) Everyday probabilities Be careful about counting! Implications for multiverse/eternal inflation A. Albrecht Prob. Lectures for Phy 262

41. Quantum effects in a billiard gas A. Albrecht Prob. Lectures for Phy 262

42. Quantum effects in a billiard gas Quantum Uncertainties A. Albrecht Prob. Lectures for Phy 262

43. Quantum effects in a billiard gas A. Albrecht Prob. Lectures for Phy 262

44. Quantum effects in a billiard gas A. Albrecht Prob. Lectures for Phy 262

45. Quantum effects in a billiard gas A. Albrecht Prob. Lectures for Phy 262

46. Quantum effects in a billiard gas Minimizing  conservative estimates for my purposes (also motivated by decoherence in some cases) A. Albrecht Prob. Lectures for Phy 262

47. Quantum effects in a billiard gas Subsequent collisions amplify the initial uncertainty (treat later collisions classically  additional conservatism) A. Albrecht Prob. Lectures for Phy 262

48. Quantum effects in a billiard gas After n collisions: A. Albrecht Prob. Lectures for Phy 262

49. Quantum effects in a billiard gas is the number of collisions so that (full quantum uncertainty as to which is the next collision) A. Albrecht Prob. Lectures for Phy 262

50. for a number of physical systems (all units MKS) A. Albrecht Prob. Lectures for Phy 262