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

Measurement of the ratio of the ppˉ→Wp\bar{p}\to W+cc-jet cross section to the inclusive ppˉ→Wp\bar{p}\to W+jets cross section

We present a measurement of the fraction of inclusive $W$+jets events produced with net charm quantum number $\pm1$, denoted $W$+$c$-jet, in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using approximately 1~fb$^{-1}$ of data collected by the D0 detector at the Fermilab Tevatron Collider. We identify the $W$+jets events via the leptonic $W$ boson decays. Candidate $W$+$c$-jet events are selected by requiring a jet containing a muon in association with a reconstructed $W$ boson and exploiting the charge correlation between this muon and $W$ boson decay lepton to perform a nearly model-independent background subtraction. We measure the fraction of $W$+$c$-jet events in the inclusive $W$+jets sample for jet $p_{T}>20$ GeV and pseudorapidity $|\eta|<2.5$ to be 0.074$\pm0.019$(stat.)$\pm^{0.012}_{0.014}$(syst.), in agreement with theoretical predictions. The probability that background fluctuations could produce the observed fraction of $W$+$c$-jet events is estimated to be $2.5\times 10^{-4}$, which corresponds to a 3.5 $\sigma$ statistical significance.Comment: submitted to Physics Letters

Multiwavelength observations of a TeV-Flare from W comae

We report results from an intensive multiwavelength campaign on the intermediate-frequency-peaked BL Lacertae object W Com (z = 0.102) during a strong outburst of very high energy gamma-ray emission in 2008 June. The very high energy gamma-ray signal was detected by VERITAS on 2008 June 7-8 with a flux F(>200 GeV) =(5.7 0.6) × 10-11 cm-2 s -1, about three times brighter than during the discovery of gamma-ray emission from W Com by VERITAS in 2008 March. The initial detection of this flare by VERITAS at energies above 200 GeV was followed by observations in high-energy gamma rays (AGILE; E γ≥ 100 MeV), X-rays (Swift and XMM-Newton), and at UV, and ground-based optical and radio monitoring through the GASP-WEBT consortium and other observatories. Here we describe the multiwavelength data and derive the spectral energy distribution of the source from contemporaneous data taken throughout the flare. © 2009. The American Astronomical Society. All rights reserved

The Great Markarian 421 Flare of 2010 February: Multiwavelength Variability and Correlation Studies

We report on variability and correlation studies using multiwavelength observations of the blazar Mrk 421 during the month of 2010 February, when an extraordinary flare reaching a level of ∼27 Crab Units above 1 TeV was measured in very high energy (VHE) γ-rays with the Very Energetic Radiation Imaging Telescope Array System (VERITAS) observatory. This is the highest flux state for Mrk 421 ever observed in VHE γ-rays. Data are analyzed from a coordinated campaign across multiple instruments, including VHE γ-ray (VERITAS, Major Atmospheric Gamma-ray Imaging Cherenkov), high-energy γ-ray (Fermi-LAT), X-ray (Swift, Rossi X-ray Timing Experiment, MAXI), optical (including the GASP-WEBT collaboration and polarization data), and radio (Metsahovi, Owens Valley Radio Observatory, University of Michigan Radio Astronomy Observatory). Light curves are produced spanning multiple days before and after the peak of the VHE flare, including over several flare "decline" epochs. The main flare statistics allow 2 minute time bins to be constructed in both the VHE and optical bands enabling a cross-correlation analysis that shows evidence for an optical lag of ∼25-55 minutes, the first time-lagged correlation between these bands reported on such short timescales. Limits on the Doppler factor (δ ⪆ 33) and the size of the emission region (δ-1RB≲ 3.8 × 1013cm) are obtained from the fast variability observed by VERITAS during the main flare. Analysis of 10 minute binned VHE and X-ray data over the decline epochs shows an extraordinary range of behavior in the flux-flux relationship, from linear to quadratic to lack of correlation to anticorrelation. Taken together, these detailed observations of an unprecedented flare seen in Mrk 421 are difficult to explain with the classic single-zone synchrotron self-Compton model.</p

Insights into the high-energy γ-ray emission of Markarian 501 from extensive multifrequency observations in the Fermi era

We report on the γ-ray activity of the blazar Mrk 501 during the first 480 days of Fermi operation. We find that the average Large Area Telescope (LAT) γ-ray spectrum of Mrk 501 can be well described by a single power-law function with a photon index of 1.78 ± 0.03. While we observe relatively mild flux variations with the Fermi-LAT (within less than a factor of two), we detect remarkable spectral variability where the hardest observed spectral index within the LAT energy range is 1.52 ± 0.14, and the softest one is 2.51 ± 0.20. These unexpected spectral changes do not correlate with the measured flux variations above 0.3 GeV. In this paper, we also present the first results from the 4.5 month long multifrequency campaign (2009 March 15-August 1) on Mrk 501, which included the Very Long Baseline Array (VLBA), Swift, RXTE, MAGIC, and VERITAS, the F-GAMMA, GASP-WEBT, and other collaborations and instruments which provided excellent temporal and energy coverage of the source throughout the entire campaign. The extensive radio to TeV data set from this campaign provides us with the most detailed spectral energy distribution yet collected for this source during its relatively low activity. The average spectral energy distribution of Mrk 501 is well described by the standard one-zone synchrotron self-Compton (SSC) model. In the framework of this model, we find that the dominant emission region is characterized by a size ≲0.1 pc (comparable within a factor of few to the size of the partially resolved VLBA core at 15-43 GHz), and that the total jet power (≃1044 erg s-1) constitutes only a small fraction (∼10-3) of the Eddington luminosity. The energy distribution of the freshly accelerated radiating electrons required to fit the time-averaged data has a broken power-law form in the energy range 0.3 GeV-10 TeV, with spectral indices 2.2 and 2.7 below and above the break energy of 20 GeV. We argue that such a form is consistent with a scenario in which the bulk of the energy dissipation within the dominant emission zone of Mrk 501 is due to relativistic, proton-mediated shocks. We find that the ultrarelativistic electrons and mildly relativistic protons within the blazar zone, if comparable in number, are in approximate energy equipartition, with their energy dominating the jet magnetic field energy by about two orders of magnitude. © 2011. The American Astronomical Society