G\"odel Incompleteness and the Black Hole Information Paradox

Semiclassical reasoning suggests that the process by which an object collapses into a black hole and then evaporates by emitting Hawking radiation may destroy information, a problem often referred to as the black hole information paradox. Further, there seems to be no unique prediction of where the information about the collapsing body is localized. We propose that the latter aspect of the paradox may be a manifestation of an inconsistent self-reference in the semiclassical theory of black hole evolution. This suggests the inadequacy of the semiclassical approach or, at worst, that standard quantum mechanics and general relavity are fundamentally incompatible. One option for the resolution for the paradox in the localization is to identify the G\"odel-like incompleteness that corresponds to an imposition of consistency, and introduce possibly new physics that supplies this incompleteness. Another option is to modify the theory in such a way as to prohibit self-reference. We discuss various possible scenarios to implement these options, including eternally collapsing objects, black hole remnants, black hole final states, and simple variants of semiclassical quantum gravity.Comment: 14 pages, 2 figures; revised according to journal requirement

Effect of low-intensity physical activity and moderate- to high-intensity physical exercise during adjuvant chemotherapy on physical fitness, fatigue and chemotherapy completion rates: Results of the PACES randomized clinical trial

Purpose: We evaluated the effectiveness of a low-intensity, home-based physical activity program (Onco-Move) and a moderate- to high-intensity, combined supervised resistance and aerobic exercise program (OnTrack) versus usual care (UC) in maintaining or enhancing physical fitness, minimizing fatigue, enhancing health-related quality of life, and optimizing chemotherapy completion rates in patients undergoing adjuvant chemotherapy for breast cancer. Patients and Methods: We randomly assigned patients who were scheduled to undergo adjuvant chemotherapy (N = 230) to Onco-Move, OnTrack, or UC. Performance-based and self-reported outcomes were assessed before random assignment, at the end of chemotherapy, and at the 6-month follow-up. We used generalized estimating equations to compare the groups over time. Results: Onco-Move and OnTrack resulted in less decline in cardiorespiratory fitness (P < .001), better physical functioning (P ≤ .001), less nausea and vomiting (P = .029 and .031, respectively) and less pain (P = .003 and .011, respectively) compared with UC. OnTrack also resulted in better outcomes for muscle strength (P = .002) and physical fatigue (P < .001). At the 6-month follow-up, most outcomes returned to baseline levels for all three groups. A smaller percentage of participants in OnTrack required chemotherapy dose adjustments than those in the UC or Onco-Move groups (P = .002). Both intervention groups returned earlier (P = .012), as well as for more hours per week (P = .014), to work than the control group. Conclusion: A supervised, moderate- to high-intensity, combined resistance and aerobic exercise program is most effective for patients with breast cancer undergoing adjuvant chemotherapy. A home-based, low-intensity physical activity program represents a viable alternative for women who are unable or unwilling to follow the higher intensity program