AUTHOREA
Log in Sign Up Browse Preprints
BROWSE LOG IN SIGN UP

Public Articles

Back to Browse
A Gender Problem? In Academia?
Jeff Montgomery

Jeff Montgomery

November 07, 2014
Friday, an op-ed piece _actually_ titled “Academic Science Isn’t Sexist” went up on the _New York Times_ blog (a version appeared in the Sunday Review). It was about academic research and the lack of sexism therein. The two editorialists are co-authors on a recently released analysis on the subject (it _is_ beautifully open access, and much of the raw data is available). The piece and the paper claim sexism has largely waned in academic research, the result of shifts from a previously sexist, male-dominated academy. Further, that any remaining incongruities between male and female enrollment, advancement, and achievement are artifacts and anecdotal. Academic research is completely gender-blind now. Any differences are largely the product of society-at-large and earlier life decisions (like the choice to play with dolls/cute animals versus trucks/destructive robots). Huh. The response from the science blogging community and Twittersphere was immediate and is still on-going. Jonathan Eisen responded Halloween night, soon after the piece was posted. His immediate critique was of the acknowledgement of reports of “physical aggression” in the op-ed piece, without ever addressing these in their data or analysis (even the 60+ page research paper is short on coverage). The assumption: they are also anecdotal? So everything is actually fine? Probably not (<- this article details accounts of _sexual misconduct in field work_ involving biology, anthropology, and other social sciences, disciplines the authors above highlight as _largely welcoming and open to women_). Emily Willingham provides excellent analysis of the data presented in the paper and in the broader debate at hand. It turns out there are numerous discrepancies and avoided topics of analysis (e.g. salary figures often had statistically significant differences by gender; women more often reported lack of inclusion; more details in her impeccable post). Likewise, Matthew Francis covered the story, emphasizing the need to actively address these still-existent problems and not ignore them: the importance of even a little explicit encouragement of female students in the face of implicit discouragement (like he sees in his native field of physics) is often all that’s needed. The ever-emphatic PZ Myers rounds out the debate by breaking down the major reasoning and assumptions in the original paper, with characteristic gusto. So what exactly were the original authors thinking? A handful of distributed scientists were able to challenge the key arguments of their paper, using their data and citations, in free time over the weekend. Talk about peer-review. Seriously though, what were they thinking? I would _like to think_ that this was actually a brilliantly orchestrated publicity stunt to get more attention on this critical issue. AFTER ALL, WHO IS GOING TO BLOG/TWEET/COUNTER-OP-ED “ACADEMIC SCIENCE IS SLIGHTLY LESS SEXIST THAN WHEN MALE ACADEMICS COULD STILL SMOKE IN THEIR OFFICES”? Because when you look at the data, the background on this issue, and the immediate response from the community, it’s obvious academic research isn’t now some utopian meritocracy brimming with equality. There is still institutional and systemic biases. Whether its gender, race, sexual-preference, or need related, or tied up in the archaic publishing system that is all too easily gamed, we have a long way to go before things can be considered “fair”. What might a fair system even look like?
Gamma Knife Problem
Michael Retchin
Matthew Retchin

Michael Retchin

and 3 more

October 23, 2014
INTRODUCTION Stereotactic radiosurgery delivers a single high dose of ionizing radiation to a radiographically well-defined, small intracranial 3D brain tumor without delivering any significant fraction of the prescribed dose to the surrounding brain tissue. Three modalities are commonly used in this area; they are the gamma knife unit, heavy charged particle beams, and external high-energy photon beams from linear accelerators. Background Gamma Ray Knife The gamma knife unit delivers a single high dose of ionizing radiation emanating from 201 cobalt-60 unit sources through a heavy helmet. All 201 beams simultaneously intersect at the isocenter, resulting in a spherical (approximately) dose distribution at the effective dose levels. Irradiating the isocenter to deliver dose is termed a “shot.” Shots can be represented as different spheres. Four interchangeable outer collimator helmets with beam channel diameters of 4, 8, 14, and 18 mm are available for irradiating different size volumes. For a target volume larger than one shot, multiple shots can be used to cover the entire target. In practice, most target volumes are treated with 1 to 15 shots. The target volume is a bounded, three-dimensional digital image that usually consists of millions of points. Circle Packing In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that all circles touch another. The associated packing density of an arrangement is the proportion of the surface covered by the circles. In two dimensional Euclidean space, the optimal lattice arrangement of identically-sized circles with the highest density is the hexagonal packing arrangement, a result that was proven by Lagrange. Generalizations can also be made of higher dimensions – this is called “sphere packing,” which usually deals only with identical spheres. We dealt only with circles for our first model for simplicity.
Optimization of hot dog vendor location for college student convenience
Michael Retchin
Liam Spiers

Michael Retchin

and 3 more

October 14, 2014
INTRODUCTION Business site selection has always been high-stakes: the opening of a new business location has extremely large monetary implications. Location can impact margins, response to competition, and effective exploitation of possible market segments . It is also well-established that convenience is a significant factor in consumer decisions, especially those regarding food . In a university setting, decisions such as food vendor placement become particularly important, as daily food is the second highest consumer expenditure for college students . In the present study, these understandings were incorporated into a decision procedure regarding the position of a hypothetical hot dog vendor on a college campus, in which convenience for students was evaluated using spatial information. Assigned problem A map was given of a college campus showing the walking paths and dormitories and approximate distances between the intersections (Figure 1). We were asked to answer questions about the location of a hot dog vender: 1. Where on campus should you set up your stand? 2. How does your location change if you set up two stands? 3. Suppose A and C are female dorms and D, E, and F are male dorms. How would your location change if 30 percent of females and 80 percent of males are likely to eat at your stand? 4. Suppose the path between B and C and the path between E and D go uphill and that it is twice as hard to walk uphill as downhill. How would your choice change? Proposed solution We propose an algorithm that determines the most convenient location as the position that minimizes the distance between the dormitories and the hot dog vendor location.
Supplemental Material for WASP: allele-specific methods for unbiased discovery of mol...
Graham McVicker
Bryce van de Geijn

Graham McVicker

and 1 more

July 29, 2014
UNBIASED READ MAPPING WITH WASP To detect differences in molecular phenotypes from sequencing data it is essential to remove read mapping biases, which are a major source of false positives. The WASP read mapping pipeline accomplishes this task by ensuring that the mapping of each individual read is unbiased.
The formation of filamentary bundles in turbulent molecular clouds
Nickolas Moeckel
Andreas Burkert

Nickolas Moeckel

and 1 more

October 17, 2013
The classical picture of a star-forming filament is a near-equilibrium structure, with collapse dependent on its gravitational criticality. Recent observations have complicated this picture, revealing filaments as a mess of apparently interacting subfilaments, with transsonic internal velocity dispersions and mildly supersonic intra-subfilament dispersions. How structures like this form is unresolved. Here we study the velocity structure of filamentary regions in a simulation of a turbulent molecular cloud. We present two main findings: first, the observed complex velocity features in filaments arise naturally in self gravitating hydrodynamic simulations of turbulent clouds without the need for magnetic or other effects. Second, a region that is filamentary only in projection and is in fact made of spatially distinct features can displays these same velocity characteristics. The fact that these disjoint structures can masquerade as coherent filaments in both projection and velocity diagnostics highlights the need to continue developing sophisticated filamentary analysis techniques for star formation observations.
Human Typology Sustainability Behaviour
Robert Orzanna
Jonas Wolterstorff

Robert Orzanna

and 1 more

October 25, 2014
ABSTRACT This article proposes a typology of four types of individuals who are impeded to engage in sustainable lifestyles.
Social Recommender Systems
Ido Guy

Ido Guy

March 03, 2014
Recommender systems play an increasingly important role in the success of social media websites. Higher portions of social websites’ traffic are triggered by recommendations and those sites rely on the quality of the recommendations to attract new users and retain existing ones. In this chapter, we will introduce the notion of social recommender systems as recommender systems that target the social media domain. After a short introduction, we will discuss in detail two of the most prominent types of social recommender systems — recommendation of social media content and recommendation of people. We will describe the main approaches and state-of-the-art techniques for each of the recommendation types. We will also review related work from the recent years that studied such recommender systems, in order to demonstrate the different use cases and methods applied to take advantage of the unique data. We will conclude by summarizing the key aspects, emerging domains, and open challenges for social recommender systems.
Authorea newsletter. Oct 2014
Alberto Pepe

Alberto Pepe

October 13, 2014
Hi friend, Now that the academic year is back in full swing, we'd like to share with you some of our latest news. First things first: We are happy to announce that we have raised a round of investment from FF Ventures and the New York Angels! We are solidifying and GROWING our team which means that Authorea will get better faster. We will keep working toward our mission to accelerate science, to improve dissemination and quality of research results and to promote Open Science. In terms of technical developments, we have implemented a bunch of new features and bug fixes. We wanted to highlight our SLEEK BRAND NEW COMMENTING INTERFACE - TRY IT NOW! GO AHEAD, HIGHLIGHT SOME TEXT AND CLICK ON THE COMMENT POPUP. It's fast and it will let you discuss your manuscripts with coauthors, reviewers, and the public. We also (finally!) developed a WORD COUNT FEATURE which lets you... uhm... count words! But you know what, different journals have different ways of counting words and we got you covered for all of them. One more feature which will make some of you happy is the MICROSOFT WORD EXPORT. Yeah that's right. Whether you are writing a math-heavy LaTeX manuscript or a student review paper, you can now export your document to Word. As usual, feel free to post your bug reports and feature requests on our feedback page or send us an email at hi@authorea.com with any questions. Happy writing, The Authorea team (oh, we're hiring!)
Representatietheorie
Kasper Peulen

Kasper Peulen

September 05, 2014
WEEK 1 Since v ≠ 0, clearly there exists a basis element b₀ such that b₀*(v)≠0. Since b₀* is in the dual vector space, we are done.
Motivation to join the SENSE programme
Robert Orzanna

Robert Orzanna

September 11, 2014
I am passionate about sustainability. I aim to live sufficiently and enjoy the personal qualities that come along with a lifestyle of reduced consumption. Despite the increasing relevancy and debates around _green growth_ and _socially fair_ conditions in society, the majority of the people are hampered or struggle with adopting more sustainable practices in their day to day life. Thereby the key question for me is: How can we better understand the complex dynamics that play out on individual behaviour in the context of a sustainable transition path? Throughout the first year of my studies, courses such as on _Energy and Material Efficiency_ or _Environmental and Material Policy_ contributed to a better understanding of the technical and institutional side of sustainable development. Aside the classroom, the practical involvement in a number of voluntary initiatives allowed me to explore my interest in grassroots initiatives and the promotion of sustainable lifestyles. They showed me that there is a large transformative potential within people and small communities. Those have achieved a more balanced state within a certain domain, and allow us to learn from their living labs. They are admirable front-runners in that they are willing to fundamentally change their behaviour despite the currently still prevailing systemic incompatibilities, lock-ins and discomforts. Throughout the last weeks I have been attending conferences on sustainability transitions, degrowth and energy efficiency. I came to the conclusion that in all these research fields, a more comprehensive understanding of particularly sufficiency behaviour on an individual level is crucial, and that a better conceptualisation could be a useful addition to the existing theoretical frameworks. Therefore I want to devote my Master thesis to this research area, prospectively in the scope of a wider research project. I am excited about the great challenges lying ahead of us that ask for my and everyone else’s contribution, to bridge practical experiences with scientific research. And I am very enthusiastic to work together with other passionate researchers in programmes such as offered by SENSE, on further exploring the dynamical trias of individuals, behaviour and sustainability.
Spatial Implications of Tax and Expenditure Limitations in Colorado
Marvin Ward Jr.

Marvin Ward Jr.

February 04, 2014
INTRODUCTION The economic potential of any system is not only driven by the presence of natural and/or developed capital, but also the institutions that govern the exploitation of these valuable assets. In this sense, the term economic potential is misleadingly incomplete. The mechanism that drives resource allocation is a function of both the distribution of purely economic value and the feasible range of activities governed by political institutions. The goal in institutional design for economic growth, therefore, ought to be the facilitation of those activities that increase the marginal product of value extraction efforts. If the objective is the maximization of economic growth, this broad goal is unlikely to draw many detractors. The devil, however, is in the details. Among the multitude of policy innovations that have been advanced in service of increasing economic growth, institutional reforms that act on the property tax base have materially altered local government finance for more than a century. As early as the 1880s, these reforms were dominated by efforts to target specific populations via circuit breakers and homestead exemptions. However, starting in large part with the Tax Revolt of the 1970s, more interest has taken root in implementing reforms that target the base in a general way: tax and expenditure limitations. The impact of these and other measures has been noticeable. While property tax revenue remains fairly buoyant with respect to the economy, it has declined in importance, dropping as a percentage of general revenue from 34% to 27% over the 1977-2002 period. This paper is one component of a larger study seeking to understand the unintended consequences of tax and expenditure limitations. The broad study is a three part empirical examination of the differential impact of tax and expenditure limitations in Colorado (henceforth COTELs) on counties of with different economic foundations. Each section is characterized by exploration of three thematic hypotheses: - COTELs create wedges between desired and realized expenditure behavior; - COTELs decrease variation among similarly constrained counties and increase variation among disimilarly constrained counties; and, - COTELs decrease resident and employment growth in constrained counties. The unifying principle across each of these inquiries is the idea that COTELs have constraint levels that vary both cross-sectionally and temporally. This paper explots this variation to explore the extent to which fiscal clustering (measured as fiscal capacity and revenue generation in this context) is driven by this "COTEL intensity" concept.
416492 ORCID iDs and Counting: Uptake by the Astronomical Community
Christopher Erdmann
James Damon

Christopher Erdmann

and 7 more

April 01, 2014
ORCID – an acronym short for Open Researcher and Contributor ID – is an international, interdisciplinary and community-driven effort to create and maintain a registry of persistent, unique identifiers for researchers and scholars. ORCID IDs are extremely important in the disambiguation of non-unique author names. They can also be embedded in key workflows, such as research profile maintenance, manuscript submissions and grant applications. Using several approaches to reach out to our users, we will report on ORCID ID uptake by the astronomical community.
Measurements of Resonance Cones and Cone angle in a Steady State Magnetic Field
Chris Spencer
Michael Morag

Chris Spencer

and 2 more

March 06, 2014
ABSTRACT Resonance Cones were observed in a plasma affected by a steady state magnetic field and their angular distribution was measured over a set of electric radio frequencies from the time varying oscillation of a short antenna. The angles were compared to the theoretical values under the cold electron approximation and found to match within a few degrees. Resonance cones at smaller angles were also observed, as predicted by theory for warm electron temperatures where $}{T_{e}}\ll1$[3].
Evaluating Southern Ocean cloud biases in ACCESS1.3 using hybrid cloud regimes
Shannon Mason

Shannon Mason

June 24, 2014
INTRODUCTION - Cloud biases in representing current climate, and effects for predicting cloud feedback in warming climate. - Use of cloud regimes to aid model evaluation (identifying compensating biases) - Use of ISCCP-style cloud regimes to for observational studies and model evaluation. - Issues relating to identifying ISCCP-style cloud regimes from models: - Identifying inconsistent cloud regimes in each model. - Applying modelled clouds to observed cloud regimes. - In this study we present a hybrid approach, using both observed and modelled cloud to identify cloud regimes that are common to the model and observations, as well as cloud regimes found only in the models. - We evaluate the ACCESS1.3 GCM; a basic comparison of this model against observations using the ISCCP-simulator is given in Figure [fig:hist_sim-obs]: we note that optically thick low and mid-topped cloud are strongly under-represented, while optically thin cloud is over-represented. - NOTE: significant under-estimate in cloud about! May be the same problem noticed by John Haynes. Shit.
Double click to edit the title
Alec Aivazis
Ari Kaplan

Alec Aivazis

and 1 more

July 24, 2014
source  ee  eμ 1 & 50 & 837 & 970 2 & 47 & 877 & 230 3 & 31 & 25 & 415 4 & 35 & 144 & 2356 5  45  300  556
Big Brother is Watching You... To Predict Crashes
Paul St-Aubin
Nicolas Saunier

Paul St-Aubin

and 2 more

July 08, 2014
The age of Big Data is here and many industries have already started embracing it. The transportation industry stands much to gain from large-scale data analysis due to the complexity and pervasiveness of transportation in daily life, which promises smarter roads and a better understanding of our transportation needs and environment. But this inertia is also one of the greatest challenges to big data adoption initiatives. Transitionary technologies may, however, provide the answer to kick-start this migration today. This paper presents, in detail, a practical framework for implementation of an automated, high-resolution, video-based traffic-analysis system, particularly geared towards traffic flow modelling, behavioural studies, and road safety analysis. This system collects large amounts of microscopic traffic flow data from ordinary video cameras and provides the tools for studying basic traffic flow measures as well as more advanced, pro-active safety measures. This paper demonstrates the process step-by-step illustrated with examples and applies it to a case study of a large set of roundabout data. In addition to providing a rich set of behavioural data, the analysis suggests a relationship between flow ratio and safety, between lane arrangement and safety, and is inconclusive about the relationship between approach distance and safety.
Motivation to join the 6^th Sustainable Summer School
Robert Orzanna

Robert Orzanna

July 12, 2014
I am passionate about sustainability. I aim to live sustainably and enjoy the personal qualities that come along with a sustainable way of life. But also outside of my _sustainability club_, in the lives of the common people, I notice an increasing relevancy for _green growth_ and _socially fair_ conditions. However, many people are hampered or struggle with adopting more sustainable practices in their day to day life. What are the reasons? And what can I do as a current Master Student of Sustainable Development to help these people successfully overcoming their individual challenges? Throughout the first year of my studies, courses such as on _Energy and Material Efficiency_ or _Environmental and Material Policy_ contributed to a better understanding of the technical and institutional side of sustainable development. Aside the classroom, the practical involvement in a number of voluntary initiatives allowed me to explore my interest in urban transitions, grassroots initiatives and the promotion of sustainable lifestyles. But they also help me to reflect on who I am: an advanterous young man who sees himself in an experimental playground for the bettering of the life conditions of the people around him. I have devoted this year’s semester vacations to cycle through France, Germany and Czech Republic to visit sustainability communities. I am fascinated by their straightforward bottom-up approach and want to help sharing the success factors of their developments[1]. These encounters showed me the large transformative potential within people and small communities. They have achieved a more balanced state within a certain domain, and allow us to learn from their living labs. They are admirable front-runners in that they are willing to fundamentally change their behaviour despite the currently still prevailing difficulties and discomforts. I am excited about the great challenge lying ahead of mankind that asks for my and everyone else’s contribution, to bridge practical experiences with scientific research. And I am very enthusiastic to work together with other passionate people in projects such as offered by the 6th Sustainability Summer School, on exploring the dynamical trias of individuals, behaviour and sustainability. [1] I am sharing my experiences in form of storylines. An example is the community supported agriculture (CSA) initiative in the Southwest of Paris: https://medium.com/susvoice-showcasing-sustainability/community-supported-agriculture-in-the-region-of-gif-sur-yvette-219ea65d76c9
Extended Authorea LaTeX Cheat Sheet
Robert Orzanna

Robert Orzanna

June 14, 2014
STANDARD TABLE ---------- ------- ------- ------- ------ ------ PHASE TIME M₁ M₂ ΔM P 1 ZAMS 0 16 15 – 5.0 2 Case B 9.89 15.92 14.94 0.14 5.1 3 ECCB 11.30 3.71 20.86 6.44 42.7 4 ECHB 18.10 – 16.76 – – 5 ICB 18.56 – 12.85 – – 6 ECCB 18.56 – 12.83 – – ---------- ------- ------- ------- ------ ------ : SOME DESCRIPTIVE STATISTICS ABOUT FRUIT AND VEGETABLE CONSUMPTION AMONG HIGH SCHOOL STUDENTS IN THE U.S. While bananas and apples still top the list of most popular fresh fruits, the amount of bananas consumed grew from 7 pounds per person in 1970 to 10.4 pounds in 2010, whereas consumption of fresh apples decreased from 10.4 pounds to 9.5 pounds. Watermelons and grapes moved up in the rankings.
CLAS 40 Assignment #2
Alec Aivazis

Alec Aivazis

July 10, 2014
A 1. This is not a good thesis because it is an obvious statement 2. Same with this one. 3. This is a good example of a thesis statement because while it is obvious that Gaia gave advice to Zeus, it is not certain that without her advice Zeus would not have succeeded. Because of this, it sets up a specific provable point that the author can persue. B Through the acceptance of the apple, the “author” of the Garden of Eden myth portrays women as the ultimate source of evil. This thesis is good because it contradicts the normal thinking that the snake is the representation of evil and is something one could look to prove in the text.
Classics 40 Assignment #1
Alec Aivazis

Alec Aivazis

July 03, 2014
A “The mother archetype was repsented on Mt. Olympus by Demeter, whose most important roles were as mother (of Persephone) and as provider of food (as Goddess of Grain) and spiritual sustenance (the Eleusian Mysteries). Although other goddess were also mothers (Hera and Aphrodite), her daughter was Demeter’s most dignificant relationship” (Demeter the Archetype, 1). B “You’ve suffered pain and humiliation. / Your mind wanders into distraction, / like a bad doctor taken ill / and unable to find the cure” (Prometheus Bound, pg 2). C “Every woman who falls in love with someone who is also in love with her at that moment is a personification of the Aphrodite archetype” (Aphrodite the Archetype, 1). “A new feature, interpolated by Plato, is the vision of the structure of the unicerse, in which the ’pattern set up in the havens ... is revealed to the souls before they choose a new life” (Plato, Republic 349). “Ouranos, father of all, eternal cosmic element, / primeval, beginning of all and end of all, / lord of the universe, moving about the earth like a sphere /home of the blessed gods” (Orphic Hymns, 1-4).
Elliptical black hole singularity
Alberto Pepe
Albert Einstein

Alberto Pepe

and 1 more

June 19, 2014
One more edit! Here I can write whatever I like in simple text or in _Latex_ as well. I can use the TOOLBAR above too. Let me paste some text: Astronomers produce and peruse vast amounts of scientific data. Let’s add a citation: . And a medical reference too: Making these data publicly available is important to enable both reproducible research and long term data curation and preservation. Because of their sheer size, however, astronomical data are often left out entirely from scientific publications and are thus hard to find and obtain. In recent years, more and more astronomers are choosing to store and make available their data on institutional repositories, personal websites and data digital libraries. In this article, we describe the use of personal data repositories as a means to enable the publication of data by individual astronomy researchers. And some Latex: By associativity, if ζ is combinatorially closed then δ = Ψ. Since ${S^{(F)}} \left( 2, \dots,-} \right) \to }{},$ $l < \cos \left( \cup P \right)$. Thus every functor is Green and hyper-unconditionally stable. Obviously, every injective homeomorphism is embedded and Clifford. Because 𝒜 > S, $$ is not dominated by b. Thus Tt > |A|. Obviously, WΞ is composite. Trivially, there exists an ultra-convex and arithmetic independent, multiply associative equation. So $\infty^{1} > $. It is easy to see that if v(W) is not isomorphic to 𝔩 then there exists a reversible and integral convex, bounded, hyper-Lobachevsky point. One can easily see that $}} \le 0$. Now if $}} > h' ( \alpha )$ then zσ, T = ν. Clearly, if ∥Q∥∼∅ then every dependent graph is pseudo-compactly parabolic, complex, quasi-measurable and parabolic. This completes the proof.
Convex black holes
Alberto Pepe
Albert Einstein

Alberto Pepe

and 1 more

June 18, 2014
Astronomers produce and peruse vast amounts of scientific data. Making these data publicly available is important to enable both reproducible research and long term data curation and preservation. Because of their sheer size, however, astronomical data are often left out entirely from scientific publications and are thus hard to find and obtain. In recent years, more and more astronomers are choosing to store and make available their data on institutional repositories, personal websites and data digital libraries. In this article, we describe the use of personal data repositories as a means to enable the publication of data by individual astronomy researchers. Here I can type some random text and use the TOOLBAR above.
Analysis of First,Second, and Fourth Sound Modes in a Helium 4 Superfluid
Chris Spencer

Chris Spencer

June 05, 2014
First,second,and fourth sound were successfully found and plotted. Graphs show a lack of steepness in decay as sound modes approach Tλ, this could be due to refilling liquid helium later than recommended leaving less medium for the sound modes to propogate through. Scattering factor,n, was found to be n=1.239 ± .007 and porosity,P, was found to be 0.46 ± 0.02 close to the theoretical value of ≈40% porosity.
Phys 131 Study Guide
Alec Aivazis

Alec Aivazis

June 10, 2014
SPECIAL RELATIVITY Lorenz Boosts For a boost in the x direction, t' = \gamma ( t - v x) \\ x' = \gamma (x - vt) \\ y' = y \\ z' = z \\ Fun with 4 Vectors = (\gamma, \gamma v) \\ \cdot = -1 \\ } \cdot } = 0 \\ E_{obs} = - p \cdot \\ ^2 = m^2 \\ E^2 = p^2 + m ^2 \\ More special relativity l' = {\gamma} \\ \Delta x' = \gamma (\Delta x - v \Delta t) \\ \Delta t' = \gamma (\Delta t - x \Delta x) \\ u' = {1- uv} where \gamma = {} Principle of Equivalence elevators in a feely falling elevator on earth experience the same physics as someone who is not in the elevator. From this you can get the bending of light weight in elevator =m(g + a) so if a = −g then w = 0 so gravity is not a real force and can be seen as a curvature in spacetime
← Previous 1 2 … 335 336 337 338 339 340 341 342 343 Next →
Authorea
  • Home
  • About
  • Product
  • Preprints
  • Pricing
  • Blog
  • Twitter
  • Help
  • Terms of Use
  • Privacy Policy