The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.htm

Tree Rings Reveal Unmatched 2nd Century Drought in the Colorado River Basin

The ongoing 22-year drought in the Upper Colorado River Basin (UCRB) has been extremely severe, even in the context of the longest available tree-ring reconstruction of annual flow at Lees Ferry, Arizona, dating back to 762 CE. While many southwestern drought assessments have been limited to the past 1,200 years, longer paleorecords of moisture variability do exist for the UCRB. Here, gridded drought-atlas data in the UCRB domain along with naturalized streamflow data from the instrumental period (1906–2021) are used in a K-nearest neighbor nonparametric algorithm to develop a streamflow reconstruction for the Lees Ferry gage starting in 1 CE. The reconstruction reveals a second-century drought unmatched in severity by the current drought or by well-documented medieval period droughts in the UCRB. Although data are sparse, analysis of individual long tree-ring records and other paleoclimatic data also support the occurrence of an exceptional second-century drought. © 2022. American Geophysical Union. All Rights Reserved.6 month embargo; first published: 09 June 2022This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Upper Colorado River Basin 20th century droughts under 21st century warming: Plausible scenarios for the future

This study builds on a collaboration with a water resource management community of practice in the Upper Colorado River Basin to develop scenarios of future drought and assess impacts on water supply reliability. Water managers are concerned with the impacts of warming on water year streamflow, but uncertainties in projections of climate make the application of these projections to planning a challenge. Instead, water managers considered a plausible scenario for future drought to be historical droughts to which warming is added. We used a simple statistical model of water year streamflow with temperatures increased by 1 °C to 4 °C, and then examined reductions in flow and runoff efficiency (RE) with each degree of warming for the six droughts defined in the observed streamflow record. In order to place these results into a management context, we employed an existing framework for system reliability, and in particular, a vulnerability assessment for water delivery metrics. Using modeled streamflow resulting from 1 °C to 4 °C warming, we found vulnerable condition thresholds for the two water delivery metrics assessed, Upper Basin Shortage and Lees Ferry Deficit, were crossed relatively infrequently at +1 °C, but with a substantially increased frequency under additional warming. Results are more relevant to resource management because the impacts of warming on Upper Colorado River streamflow were assessed in the context of management metrics and vulnerability thresholds, in collaboration with members of the water management community of practice. © 2020 The Author(s)Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Saturated x-ray lasers at 196 and 73 Å pumped by a picosecond traveling-wave excitation

Traveling-wave irradiation with a laser pulse of duration ∼1 picosecond has been shown to achieve saturated operation of Ne- and Ni-like x-ray lasers. Gain at 196 Å was confirmed by observation of both forward and backward x-ray laser beams from a germanium plasma under ideal and nonideal traveling-wave conditions at a small signal gain of >40 cm-1. Saturation was observed for targets >4 mm long consistent with a model of laser amplification along the plasma medium and with the output of a detailed ray-tracing post-processor coupled to a hydrodynamic and atomic physics code. Ni-like samarium targets, pumped under ideal traveling-wave conditions exhibited a small signal gain of ∼19 cm-1 at 73 Å with saturation observed for targets 8 mm long