A measurement-based measure of the size of macroscopic quantum superpositions

Recent experiments claiming formation of quantum superposition states in near macroscopic sys- tems raise the question of how the sizes of general quantum superposition states in an interacting system are to be quantified. We propose here a measure of size for such superposition states that is based on what measurements can be performed to probe and distinguish the different branches of the state. The measure allows comparison of the effective size for superposition states in very different physical systems. It can be applied to a very general class of superposition states and reproduces known results for near-ideal cases. Comparison with a prior measure based on analy- sis of coherence between branches indicates that significantly smaller effective superposition sizes result from our measurement-based measure. Application to a system of interacting bosons in a double-well trapping potential shows that the effective superposition size is strongly dependent on the relative magnitude of the barrier height and interparticle interaction.Comment: 21 pages, 20 figures. Accepted by Phys. Rev. A. Replaced old version with accepted version. Significant changes and improvements, particularly to section on 1-particle measurement

The Fulling-Unruh effect in general stationary accelerated frames

We study the generalized Unruh effect for accelerated reference frames that include rotation in addition to acceleration. We focus particularly on the case where the motion is planar, with presence of a static limit in addition to the event horizon. Possible definitions of an accelerated vacuum state are examined and the interpretation of the Minkowski vacuum state as a thermodynamic state is discussed. Such athermodynamic state is shown to depend on two parameters, the acceleration temperature and a drift velocity, which are determined by the acceleration and angular velocity of the accelerated frame. We relate the properties of Minkowski vacuum in the accelerated frame to the excitation spectrum of a detector that is stationary in this frame. The detector can be excited both by absorbing positive energy quanta in the "hot" vacuum state and by emitting negative energy quanta into the "ergosphere" between the horizon and the static limit. The effects are related to similar effects in the gravitational field of a rotating black hole.Comment: Latex, 39 pages, 5 figure

Drivers of declining CO2 emissions in 18 developed economies

Global emissions of carbon dioxide (CO 2 ) from fossil fuels and industry increased by 2.2% per year on average between 2005 and 2015 1 . Global emissions need to peak and decline rapidly to limit climate change to well below 2 °C of warming 2,3 , which is one of the goals of the Paris Agreement 4 . Untangling the reasons underlying recent changes in emissions trajectories is critical to guide efforts to attain those goals. Here we analyse the drivers of decreasing CO 2 emissions in a group of 18 developed economies that have decarbonized over the period 2005–2015. We show that within this group, the displacement of fossil fuels by renewable energy and decreases in energy use explain decreasing CO 2 emissions. However, the decrease in energy use can be explained at least in part by a lower growth in gross domestic product. Correlation analysis suggests that policies on renewable energy are supporting emissions reductions and displacing fossil fuels in these 18 countries, but not elsewhere, and that policies on energy efficiency are supporting lower energy use in these 18 countries, as well as more widely. Overall, the evidence shows that efforts to reduce emissions are underway in many countries, but these efforts need to be maintained and enhanced by more stringent policy actions to support a global peak in emissions followed by global emissions reductions in line with the goals of the Paris Agreement 3

Global Carbon Budget 2016

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere &ndash; the &ldquo;global carbon budget&rdquo; &ndash; is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and methodology to quantify all major components of the global carbon budget, including their uncertainties, based on the combination of a range of data, algorithms, statistics, and model estimates and their interpretation by a broad scientific community. We discuss changes compared to previous estimates and consistency within and among components, alongside methodology and data limitations. CO2&nbsp;emissions from fossil fuels and industry (EFF) are based on energy statistics and cement production data, respectively, while emissions from land-use change (ELUC), mainly deforestation, are based on combined evidence from land-cover change data, fire activity associated with deforestation, and models. The global atmospheric CO2concentration is measured directly and its rate of growth (GATM) is computed from the annual changes in concentration. The mean ocean CO2 sink (SOCEAN) is based on observations from the 1990s, while the annual anomalies and trends are estimated with ocean models. The variability in&nbsp;SOCEAN&nbsp;is evaluated with data products based on surveys of ocean CO2&nbsp;measurements. The global residual terrestrial CO2&nbsp;sink (SLAND) &nbsp;is estimated by the difference of the other terms of the global carbon budget and compared to results of independent dynamic global vegetation models. We compare the mean land and ocean fluxes and their variability to estimates from three atmospheric inverse methods for three broad latitude bands. All uncertainties are reported as &plusmn;1&sigma;, reflecting the current capacity to characterise the annual estimates of each component of the global carbon budget. For the last decade available (2006&ndash;2015),&nbsp;EFF was 9.3 &plusmn; 0.5 GtC yr-1,&nbsp;ELUC 1.0 &plusmn; 0.5 GtC yr-1,&nbsp;GATM 4.5 &plusmn; 0.1 GtC yr-1,&nbsp;SOCEAN&nbsp;2.6 &plusmn; 0.5 GtC yr-1, and&nbsp;SLAND 3.1 &plusmn; 0.9 GtC yr-1. For year 2015 alone, the growth in&nbsp;EFF was approximately zero and emissions remained at 9.9 &plusmn; 0.5 GtC yr-1, showing a slowdown in growth of these emissions compared to the average growth of 1.8 % yr-1 that took place during 2006&ndash;2015. Also, for 2015,&nbsp;ELUC was 1.3 &plusmn; 0.5 GtC yr-1,&nbsp;GATM&nbsp;was 6.3 &plusmn; 0.2 GtC yr-1,&nbsp;SOCEAN&nbsp;was 3.0 &plusmn; 0.5 GtC yr-1, and&nbsp;SLAND was 1.9 &plusmn; 0.9 GtC yr-1.&nbsp;GATM&nbsp;was higher in 2015 compared to the past decade (2006&ndash;2015), reflecting a smaller&nbsp;SLAND for that year. The global atmospheric CO2&nbsp;concentration reached 399.4 &plusmn; 0.1 ppm averaged over 2015. For 2016, preliminary data indicate the continuation of low growth in&nbsp;EFF with +0.2 % (range of &minus;1.0 to +1.8 %) based on national emissions projections for China and USA, and projections of gross domestic product corrected for recent changes in the carbon intensity of the economy for the rest of the world. In spite of the low growth of&nbsp;EFF in 2016, the growth rate in atmospheric CO2&nbsp;concentration is expected to be relatively high because of the persistence of the smaller residual terrestrial sink (SLAND) in response to El Ni&ntilde;o conditions of 2015&ndash;2016. From this projection of&nbsp;EFF and assumed constant&nbsp;ELUC for 2016, cumulative emissions of CO2&nbsp;will reach 565 &plusmn; 55 GtC (2075 &plusmn; 205 GtCO2) for 1870&ndash;2016, about 75 % from&nbsp;EFF and 25 % from&nbsp;ELUC . This living data update documents changes in the methods and data sets used in this new carbon budget compared with previous publications of this data set (Le Qu&eacute;r&eacute; et al., 2015b, a, 2014, 2013). All observations presented here can be downloaded from the Carbon Dioxide Information Analysis Center (doi:10.3334/CDIAC/GCP_2016).</p

Global carbon budget 2019

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere – the “global carbon budget” – is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFF) are based on energy statistics and cement production data, while emissions from land use change (ELUC), mainly deforestation, are based on land use and land use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) and terrestrial CO2 sink (SLAND) are estimated with global process models constrained by observations. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the last decade available (2009–2018), EFF was 9.5±0.5 GtC yr−1, ELUC 1.5±0.7 GtC yr−1, GATM 4.9±0.02 GtC yr−1 (2.3±0.01 ppm yr−1), SOCEAN 2.5±0.6 GtC yr−1, and SLAND 3.2±0.6 GtC yr−1, with a budget imbalance BIM of 0.4 GtC yr−1 indicating overestimated emissions and/or underestimated sinks. For the year 2018 alone, the growth in EFF was about 2.1 % and fossil emissions increased to 10.0±0.5 GtC yr−1, reaching 10 GtC yr−1 for the first time in history, ELUC was 1.5±0.7 GtC yr−1, for total anthropogenic CO2 emissions of 11.5±0.9 GtC yr−1 (42.5±3.3 GtCO2). Also for 2018, GATM was 5.1±0.2 GtC yr−1 (2.4±0.1 ppm yr−1), SOCEAN was 2.6±0.6 GtC yr−1, and SLAND was 3.5±0.7 GtC yr−1, with a BIM of 0.3 GtC. The global atmospheric CO2 concentration reached 407.38±0.1 ppm averaged over 2018. For 2019, preliminary data for the first 6–10 months indicate a reduced growth in EFF of +0.6 % (range of −0.2 % to 1.5 %) based on national emissions projections for China, the USA, the EU, and India and projections of gross domestic product corrected for recent changes in the carbon intensity of the economy for the rest of the world. Overall, the mean and trend in the five components of the global carbon budget are consistently estimated over the period 1959–2018, but discrepancies of up to 1 GtC yr−1 persist for the representation of semi-decadal variability in CO2 fluxes. A detailed comparison among individual estimates and the introduction of a broad range of observations shows (1) no consensus in the mean and trend in land use change emissions over the last decade, (2) a persistent low agreement between the different methods on the magnitude of the land CO2 flux in the northern extra-tropics, and (3) an apparent underestimation of the CO2 variability by ocean models outside the tropics. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set (Le Quéré et al., 2018a, b, 2016, 2015a, b, 2014, 2013). The data generated by this work are available at https://doi.org/10.18160/gcp-2019 (Friedlingstein et al., 2019)

Global Carbon Budget 2022

Accurate assessment of anthropogenic carbon dioxide (CO$_2$) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodologies to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO$_2$ emissions (E$_{FOS}$) are based on energy statistics and cement production data, while emissions from land-use change (E$_{LUC}$), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO$_2$ concentration is measured directly, and its growth rate (G$_{ATM}$) is computed from the annual changes in concentration. The ocean CO$_2$ sink (S$_{OCEAN}$) is estimated with global ocean biogeochemistry models and observation-based data products. The terrestrial CO$_2$ sink (S$_{LAND}$) is estimated with dynamic global vegetation models. The resulting carbon budget imbalance (B$_{IM}$), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the year 2021, E$_{FOS}$ increased by 5.1 % relative to 2020, with fossil emissions at 10.1 ± 0.5 GtC yr$^{−1}$ (9.9 ± 0.5 GtC yr$^{−1}$ when the cement carbonation sink is included), and E$_{LUC}$ was 1.1 ± 0.7 GtC yr$^{−1}$, for a total anthropogenic CO$_2$ emission (including the cement carbonation sink) of 10.9 ± 0.8 GtC yr$^{−1}$ (40.0 ± 2.9 GtCO$_2$). Also, for 2021, G$_{ATM}$ was 5.2 ± 0.2 GtC yr$^{−1}$ (2.5 ± 0.1 ppm yr$^{−1}$), S$_{OCEAN}$ was 2.9  ± 0.4 GtC yr$^{−1}$, and S$_{LAND}$ was 3.5 ± 0.9 GtC yr$^{−1}$, with a B$_{IM}$ of −0.6 GtC yr$^{−1}$ (i.e. the total estimated sources were too low or sinks were too high). The global atmospheric CO$_2$ concentration averaged over 2021 reached 414.71 ± 0.1 ppm. Preliminary data for 2022 suggest an increase in E$_{FOS}$ relative to 2021 of +1.0 % (0.1 % to 1.9 %) globally and atmospheric CO$_2$ concentration reaching 417.2 ppm, more than 50 % above pre-industrial levels (around 278 ppm). Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959–2021, but discrepancies of up to 1 GtC yr$^{−1}$ persist for the representation of annual to semi-decadal variability in CO$_2$ fluxes. Comparison of estimates from multiple approaches and observations shows (1) a persistent large uncertainty in the estimate of land-use change emissions, (2) a low agreement between the different methods on the magnitude of the land CO$_2$ flux in the northern extratropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set. The data presented in this work are available at https://doi.org/10.18160/GCP-2022 (Friedlingstein et al., 2022b)

Global Carbon Budget 2023

Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFOS) are based on energy statistics and cement production data, while emissions from land-use change (ELUC), mainly deforestation, are based on land-use and land-use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly, and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) is estimated with global ocean biogeochemistry models and observation-based f CO2 products. The terrestrial CO2 sink (SLAND) is estimated with dynamic global vegetation models. Additional lines of evidence on land and ocean sinks are provided by atmospheric inversions, atmospheric oxygen measurements, and Earth system models. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and incomplete understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the year 2022, EFOS increased by 0.9 % relative to 2021, with fossil emissions at 9.9 ± 0.5 Gt C yr−1 (10.2 ± 0.5 Gt C yr−1 when the cement carbonation sink is not included), and ELUC was 1.2 ± 0.7 Gt C yr−1, for a total anthropogenic CO2 emission (including the cement carbonation sink) of 11.1 ± 0.8 Gt C yr−1 (40.7±3.2 Gt CO2 yr−1). Also, for 2022, GATM was 4.6±0.2 Gt C yr−1 (2.18±0.1 ppm yr−1; ppm denotes parts per million), SOCEAN was 2.8 ± 0.4 Gt C yr−1, and SLAND was 3.8 ± 0.8 Gt C yr−1, with a BIM of −0.1 Gt C yr−1 (i.e. total estimated sources marginally too low or sinks marginally too high). The global atmospheric CO2 concentration averaged over 2022 reached 417.1 ± 0.1 ppm. Preliminary data for 2023 suggest an increase in EFOS relative to 2022 of +1.1 % (0.0 % to 2.1 %) globally and atmospheric CO2 concentration reaching 419.3 ppm, 51 % above the pre-industrial level (around 278 ppm in 1750). Overall, the mean of and trend in the components of the global carbon budget are consistently estimated over the period 1959–2022, with a near-zero overall budget imbalance, although discrepancies of up to around 1 Gt C yr−1 persist for the representation of annual to semi-decadal variability in CO2 fluxes. Comparison of estimates from multiple approaches and observations shows the following: (1) a persistent large uncertainty in the estimate of land-use changes emissions, (2) a low agreement between the different methods on the magnitude of the land CO2 flux in the northern extra-tropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living-data update documents changes in methods and data sets applied to this most recent global carbon budget as well as evolving community understanding of the global carbon cycle. The data presented in this work are available at https://doi.org/10.18160/GCP-2023 (Friedlingstein et al., 2023)

Particles in Quantum Field Theory and Non-inertial Reference Frames

In this thesis I discuss various topics relating to the definition of particles and vacuum states in quantum field theory in general, and apply it to non-inertial reference frames in Minkowski spacetime. The particle concept in quantum field theory is shown to be rather ambiguous and subjective. I discuss generally what particles are and how they should be defined in quantum field theories. I then discuss what ambiguities are inherent in such a definition and in particular what ambiguities there are for observers in different stationary non-inertial reference frames in Minkowski spacetime. I use this to gain a broader perspective on the Unruh effect, the effect by which an accelerated observer will view the vacuum state of an inertial reference frame as being filled by a thermal ensemble of particles. I conclude that the effect actually depends on how the solutions of the field equation are joined across the event horizon that is present in hyperbolicly accelerated reference frames, and that the effect is really more subjective than is commonly assumed in the literature. Finally, I investigate the behaviour of a model particle detector. I conclude that it does not necessarily reflect the spectrum of particles that is present in the reference frame of the detector, because the excitation spectrum of the detector may be distorted by particle states with negative energy, which are present in many non-inertial reference frames. The results of detection experiments will therefore not generally agree with the usual definition of particles in quantum field theory. Along the way I provide explicit calculations of all possible Killing vector fields and stationary trajectories in Minkowski spacetime, discussions of what the corresponding reference frames look like, as well as solutions of the Klein-Gordon equation in coordinates appropriate to the different reference frames

Technical report: Nordic Green to Scale

This technical analysis for the Nordic Green to Scale report was commissioned to CICERO (Center for International Climate and Environmental Research – Oslo), which is Norway’s foremost institute for interdisciplinary climate research. The report illustrates the scaling potential of 15 proven Nordic low-carbon solutions and presents an analysis of the greenhouse gas emissions reductions of these solutions and their scalability internationally