DOCSLIB.ORG

Confusions of Mass and Size

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Confusions of Mass and Size COMMENTARIES Confusions of Mass and Size THEUNIS PIERSMA• AND NICK C. DAVIDSON 2 Work by Rising and Somers(1989) and Freeman combines information about structural size and nu- and Jackson(1990) has recently emphasized that mul- trient reserve massbut alone cannot provide an in- tiple, and preferably skeletal,measurements provide dicator of structural size. It is the ease with which a more accurateassessment of body sizein birds than body masscan be measured(and not the difficulty; do single, external measurements.We agree. It is re- contra Freeman and Jackson 1990) that has made it a grettable,however, that both papersperpetrate a con- muchused and interestingmeasure. Inclusion of body fusion between two useful and quite distinct vari- mass in structural size-related analysesmay not al- ables:body size and bodymass. In doing so they have ways distort interpretationof the data (e.g. seeCooke ignored several highly relevant published studies, et al. 1990),but it is usually impossibleto determine notably of nonpasserineand Europeanspedes (the this from ambiguousresults. latter bias apparently part of a more general trend By definition structuralsize is independentof the identified by Enckell 1988). nutritional status that varies with time of day and Rising and Somers(1989) and Freemanand Jackson year, reproductivestatus, and habitatquality. For this (1990) are but two recent examplesof a widespread reasonstructural size is the preferred variable in stud- misunderstanding.Smith et al. (1990) provide a fur- ies of geographicalsize variation and perhapsin be- ther instance.Another is the inclusionby Davieset havioral studies of contests. Note, however, that it al. (1988)of massin an analysisof body sizeof Lesser may not be structuralsize per se but rather muscular Snow Geese(Chen c. caerulescens),which was criticized power (possiblyreflected in the protein reservemass) recentlyby Alisauskasand Ankney (1990),although that determines contest outcomes. Whereas studies of in this casethe overall interpretationof a size-related geographicalsize variation regard all this nutritional variation in fecundityof LesserSnow Geesemay not noise as a problem to be removed, studiesof ener- have been affected (Cooke et al. 1990). Even Peters getics and nutrient reserve status require precisely (1984), in his extensive discussionof the ecological this information on reserve mass. For such studies implicationsof body size,provides no cleardefinition body masscan be a useful variable if massvariations of body size and in many instancesdiscusses body due to differences in structural size can be controlled size-relatedphenomena through body mass. (e.g. Davidson1983, Ankney and Afton 1988,Piersma Although not stated explicitly, both Rising and 1988, Piersma and van Brederode 1990). Somers (1989) and Freeman and Jackson(1990) ad- Althoughbody massis readily measured,structural dressedproblems of measuringstructural size. The Ox- size is more difficult, and there have been surpris- ford dictionarydefines structural as "of the (essential) ingly few attemptsto devise practicalmeans of mea- framework" and structuralsize accordinglyas "the suring structural size in birds. One approach is to size of the essential framework" (Piersma 1984). Be- definestructural size as the body massof starvedbirds causeindividual birds have a remarkablecapacity to (i.e. birds that have died after exhaustingall their vary their massand volume dependingon their nu- nutrient reserves[Piersma 1984, 1988; see King and tritional status,we feel it is biologicallymost mean- Ml•rphy 1985 for the distinctionbetween nutrient ingful to define structural size as the "nutrient re- reservesand nutrient stores])and then seewhich body serve-independentsize of a bird." dimensionsstatistically "explain" starvedbody mass Our point is simple.There is an importantbut wide- most accurately.There are, however, pitfalls even in ly ignored distinction that must be made between this approach.Although birds die in natural starva- two concepts:(1) the reserve-independentstructural tion eventsafter substantiallydepleting their fat and sizeand (2) the variableamounts of nutrients(chiefly protein reserves,there is evidence that the precise fat and protein) that permit birds to exerciseand to nutritional state at death is influenced by the envi- survive periodsof negativeenergy and nutrient bal- ronmentalconditions during starvation.This canlead ance, the variable nutrientreserve mass. Body mass to both the fat mass and the nonfat mass of starved birds still including some nutritional reserves,al- though absolute amounts are small (Davidson and ' NetherlandsInstitute for SeaResearch (NIOZ), Evans 1982, Davidson and Clark 1985). P.O. Box 59, 1790 AB Den Burg, Texel, Netherlands, Skeletal measurements of the sternum have been and ZoologicalLaboratory, University of Groningen, used to index pectoralmuscle size (Evansand Smith P.O. Box 14, 9750 AA Haren, Netherlands. 1975, Piersma et al. 1984), but these linear measure- 2Chief ScientistDirectorate, Nature Conservancy ments cover only part of the overall skeletal size. As Council,Northminster House, Peterborough PE1 1UA, suggestedby Wishart (1979), (dry and fat-free) skel- United Kingdom. etal massis almostentirely reserve-independent,ex- 441 The Auk 108: 441-444. April 1991 442 Commentaries [Auk, Vol. 108 cept for small variations in bone marrow mass(see reserves, clutch size, and incubation. Condor 90: Moser and Rusch 1988), and should provide an ac- 459-472. curate estimator of structural size on which linear ALISAUSKAS,R. T., & C. D. ANKNEY. 1990. Body size dimensionscan be regressedto provide an index of and fecundity in LesserSnow Geese.Auk 107: structural size. Moser and Rusch (1988) concluded 440-443. that skeletal volumeß measured by water displace- COOKE,F., J. C. DAvIEs, & R. F. ROCKWELL.1990. Re- ment of excisedbonesß provides an even more precise sponseto Alisauskasand Ankney. Auk 107:444- measureof structuralsize. Finally, the first principal 446. component of a set of linear skeletal measurements DAVIDSON,N.C. 1983. Formulae for estimatingthe likewise provides an appropriate structural size mea- lean weight and fat reservesof live shorebirds. sure (Ankney and Afton 1988, Rising and Somers Ring. & Migr. 4: 159-166. 1989). ß, & N. A. CLARI<. 1985. The effects of severe Most skeletalmeasurements require the sacrificeof weather in Januaryand February 1985on waders birds and are of little help in studies of live birds. in Britain. Wader Study Group Bull. 44: 10-16. Consequently,body-size variation in live birdsis usu- ß& P. R. EVANS.1982. Mortality of Redshanks ally controlledin analysesof body massby the use and Oystercatchersfrom starvationduring severe of one or more easily measured external measure- weather. Bird Study 29: 183-188. ments, typically the lengths of wingß tarsus,body, DAvms,J. C., R. F. ROCk'W•L,& F. COOKE.1988. Body- and bill. Choice of the appropriateexternal dimen- size variation and fitness componentsin Lesser sions to indicate structural size can be made with Snow Geese (Chen caerulescenscaerulescens). Auk appropriatemodels of regressionon starvedor skel- 105: 639-648. etal mass or volume, as outlined aboveß and their ENCKELL,P. H. 1988. Ecology: the (inter)national derivation may hold some surprises.For exampleß science. Br. Ecol. Soc. Bull. 19: 224-228. Moser and Rusch(1988) found that some commonly EvANs, P. R., & P. C. SMITH. 1975. Studies of shore- usedexternal measures were only moderatecorrelates birds at Lindisfarne, Northumberland. 2. Fat and of structural size (measuredby skeletal volume) in pectoral muscleas indicators of body condition Canada Geese (Branta canadensis).Further, the most in the Bar-tailed Godwit. Wildfowl 26: 64-76. appropriateexternal measures may differ interspecif- FromMAN,S., & W. M. JACr,SON. 1990. Univariate met- ically, even between closely related species(e.g. in ricsare not adequateto measureavian body size. Podicepsgrebesß Piersma 1988). Auk 107: 69-74. Future studies must differentiate clearly between KING, J. R., & M. E. MURPHY. 1985. Periods of nu- structural-size and nutritional-mass variation, and tritional stress in the annual cycles of endo- should avoid using body massin exercisesaimed at therms: fact or fiction? Am. Zool. 25: 955-964. describingstructural size. Failure to distinguishbe- MOSER,T. J., & D. H. Ruscrt. 1988. Indices of struc- tween the two can lead to ambiguousand misleading tural size and condition of Canada Geese. J. Wildl. interpretations.For example,the regional differences Manage. 52: 202-208. in flight-surfaceloading of Accipiterhawks described Pgrm•s,R.H. 1984. The ecologicalimplications of by Smith et al. (1990) may be purely structuraland body size. Cambridge,Cambridge Univ. Press. adaptively related to differencesin the relative use PIERSMA,T. 1984. Estimatingenergy reserves of Great of thermal updrafts, as the authors suggestßor they Crested GrebesPodiceps cristatus on the basis of may be a consequenceof differencesin fat-reserve body dimensions.Ardea 72: 119-126. massin relation to the length of the ensuingnonstop 1988. Body size, nutrient reservesand diet flight (seee.g. Smith et al. 1986). of Red-neckedand SlavonianGrebes Podiceps gri- Although easyto define in general, structuralsize segenaand P. aurituson Lake IJsselmeer,The defiesa uniform approximationin termsof a standard Netherlands. Bird Study 35: 13-24. set of external measurementsand should preferably ß N. C. DAVIDSON, & P. R. EvANs. 1984. Esti- be derived for eachspecies under study.Clearly, there
Load more

Recommended publications
  • Chapter 5 Dimensional Analysis and Similarity
    Chapter 5 Dimensional Analysis and Similarity Motivation. In this chapter we discuss the planning, presentation, and interpretation of experimental data. We shall try to convince you that such data are best presented in dimensionless form. Experiments which might result in tables of output, or even mul- tiple volumes of tables, might be reduced to a single set of curves—or even a single curve—when suitably nondimensionalized. The technique for doing this is dimensional analysis. Chapter 3 presented gross control-volume balances of mass, momentum, and en- ergy which led to estimates of global parameters: mass flow, force, torque, total heat transfer. Chapter 4 presented infinitesimal balances which led to the basic partial dif- ferential equations of fluid flow and some particular solutions. These two chapters cov- ered analytical techniques, which are limited to fairly simple geometries and well- defined boundary conditions. Probably one-third of fluid-flow problems can be attacked in this analytical or theoretical manner. The other two-thirds of all fluid problems are too complex, both geometrically and physically, to be solved analytically. They must be tested by experiment. Their behav- ior is reported as experimental data. Such data are much more useful if they are ex- pressed in compact, economic form. Graphs are especially useful, since tabulated data cannot be absorbed, nor can the trends and rates of change be observed, by most en- gineering eyes. These are the motivations for dimensional analysis. The technique is traditional in fluid mechanics and is useful in all engineering and physical sciences, with notable uses also seen in the biological and social sciences.
    [Show full text]
  • Guide for the Use of the International System of Units (SI)
    Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S.
    [Show full text]
  • How Are Units of Measurement Related to One Another?
    UNIT 1 Measurement How are Units of Measurement Related to One Another? I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind... Lord Kelvin (1824-1907), developer of the absolute scale of temperature measurement Engage: Is Your Locker Big Enough for Your Lunch and Your Galoshes? A. Construct a list of ten units of measurement. Explain the numeric relationship among any three of the ten units you have listed. Before Studying this Unit After Studying this Unit Unit 1 Page 1 Copyright © 2012 Montana Partners This project was largely funded by an ESEA, Title II Part B Mathematics and Science Partnership grant through the Montana Office of Public Instruction. High School Chemistry: An Inquiry Approach 1. Use the measuring instrument provided to you by your teacher to measure your locker (or other rectangular three-dimensional object, if assigned) in meters. Table 1: Locker Measurements Measurement (in meters) Uncertainty in Measurement (in meters) Width Height Depth (optional) Area of Locker Door or Volume of Locker Show Your Work! Pool class data as instructed by your teacher. Table 2: Class Data Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 Width Height Depth Area of Locker Door or Volume of Locker Unit 1 Page 2 Copyright © 2012 Montana Partners This project was largely funded by an ESEA, Title II Part B Mathematics and Science Partnership grant through the Montana Office of Public Instruction.
    [Show full text]
  • Quick Guide to Precision Measuring Instruments
    E4329 Quick Guide to Precision Measuring Instruments Coordinate Measuring Machines Vision Measuring Systems Form Measurement Optical Measuring Sensor Systems Test Equipment and Seismometers Digital Scale and DRO Systems Small Tool Instruments and Data Management Quick Guide to Precision Measuring Instruments Quick Guide to Precision Measuring Instruments 2 CONTENTS Meaning of Symbols 4 Conformance to CE Marking 5 Micrometers 6 Micrometer Heads 10 Internal Micrometers 14 Calipers 16 Height Gages 18 Dial Indicators/Dial Test Indicators 20 Gauge Blocks 24 Laser Scan Micrometers and Laser Indicators 26 Linear Gages 28 Linear Scales 30 Profile Projectors 32 Microscopes 34 Vision Measuring Machines 36 Surftest (Surface Roughness Testers) 38 Contracer (Contour Measuring Instruments) 40 Roundtest (Roundness Measuring Instruments) 42 Hardness Testing Machines 44 Vibration Measuring Instruments 46 Seismic Observation Equipment 48 Coordinate Measuring Machines 50 3 Quick Guide to Precision Measuring Instruments Quick Guide to Precision Measuring Instruments Meaning of Symbols ABSOLUTE Linear Encoder Mitutoyo's technology has realized the absolute position method (absolute method). With this method, you do not have to reset the system to zero after turning it off and then turning it on. The position information recorded on the scale is read every time. The following three types of absolute encoders are available: electrostatic capacitance model, electromagnetic induction model and model combining the electrostatic capacitance and optical methods. These encoders are widely used in a variety of measuring instruments as the length measuring system that can generate highly reliable measurement data. Advantages: 1. No count error occurs even if you move the slider or spindle extremely rapidly. 2. You do not have to reset the system to zero when turning on the system after turning it off*1.
    [Show full text]
  • New Varying Speed of Light Theories
    New varying speed of light theories Jo˜ao Magueijo The Blackett Laboratory,Imperial College of Science, Technology and Medicine South Kensington, London SW7 2BZ, UK ABSTRACT We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying c, dispelling the myth that the constancy of c is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying c induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how “doubly special” relativity has emerged as a VSL effective model of quantum space-time, with observational implications for ultra high energy cosmic rays and gamma ray bursts. Some recent work on the physics of “black” holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in c. Finally we describe the observational status of the theory. The evidence is slim – redshift dependence in alpha, ultra high energy cosmic rays, and (to a much lesser extent) the acceleration of the universe and the WMAP data.
    [Show full text]
  • “The Constancy, Or Otherwise, of the Speed of Light”
    “Theconstancy,orotherwise,ofthespeedoflight” DanielJ.Farrell&J.Dunning-Davies, DepartmentofPhysics, UniversityofHull, HullHU67RX, England. [email protected] Abstract. Newvaryingspeedoflight(VSL)theoriesasalternativestotheinflationary model of the universe are discussed and evidence for a varying speed of light reviewed.WorklinkedwithVSLbutprimarilyconcernedwithderivingPlanck’s black body energy distribution for a gas-like aether using Maxwell statistics is consideredalso.DoublySpecialRelativity,amodificationofspecialrelativityto accountforobserverdependentquantumeffectsatthePlanckscale,isintroduced and it is found that a varying speed of light above a threshold frequency is a necessityforthistheory. 1 1. Introduction. SincetheSpecialTheoryofRelativitywasexpoundedandaccepted,ithasseemedalmost tantamount to sacrilege to even suggest that the speed of light be anything other than a constant.ThisissomewhatsurprisingsinceevenEinsteinhimselfsuggestedinapaperof1911 [1] that the speed of light might vary with the gravitational potential. Interestingly, this suggestion that gravity might affect the motion of light also surfaced in Michell’s paper of 1784[2],wherehefirstderivedtheexpressionfortheratioofthemasstotheradiusofastar whose escape speed equalled the speed of light. However, in the face of sometimes fierce opposition, the suggestion has been made and, in recent years, appears to have become an accepted topic for discussion and research. Much of this stems from problems faced by the ‘standardbigbang’modelforthebeginningoftheuniverse.Problemswiththismodelhave
    [Show full text]
  • Sewers, Force Main
    United States Office of Water EPA 832-F-00-071 Environmental Protection Washington, D.C. September 2000 Agency Wastewater Technology Fact Sheet Sewers, Force Main DESCRIPTION insertion and retrieval stations. In most cases, insertion facilities are located within the lift station Force mains are pipelines that convey wastewater and the pig removal station is at the discharge point under pressure from the discharge side of a pump or of the force main. Several launching and retrieval pneumatic ejector to a discharge point. Pumps or stations are usually provided in long force mains to compressors located in a lift station provide the facilitate cleaning of the pipeline. energy for wastewater conveyance in force mains. The key elements of force mains are: APPLICABILITY 1. Pipe. Force mains are used to convey wastewater from a lower to higher elevation, particularly where the 2. Valves. elevation of the source is not sufficient for gravity flow and/or the use of gravity conveyance will 3. Pressure surge control devices. result in excessive excavation depths and high sewer pipeline construction costs. 4. Force main cleaning system. Ductile iron and polyvinyl chloride (PVC) are the Force mains are constructed from various materials most frequently used materials for wastewater force and come in a wide range of diameters. Wastewater mains. Ductile iron pipe has particular advantages quality governs the selection of the most suitable in wastewater collection systems due to its high pipe material. Operating pressure and corrosion strength and high flow capacity with greater than resistance also impact the choice. Pipeline size and nominal inside diameters and tight joints.
    [Show full text]
  • The International System of Units (SI) - Conversion Factors For
    NIST Special Publication 1038 The International System of Units (SI) – Conversion Factors for General Use Kenneth Butcher Linda Crown Elizabeth J. Gentry Weights and Measures Division Technology Services NIST Special Publication 1038 The International System of Units (SI) - Conversion Factors for General Use Editors: Kenneth S. Butcher Linda D. Crown Elizabeth J. Gentry Weights and Measures Division Carol Hockert, Chief Weights and Measures Division Technology Services National Institute of Standards and Technology May 2006 U.S. Department of Commerce Carlo M. Gutierrez, Secretary Technology Administration Robert Cresanti, Under Secretary of Commerce for Technology National Institute of Standards and Technology William Jeffrey, Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. National Institute of Standards and Technology Special Publications 1038 Natl. Inst. Stand. Technol. Spec. Pub. 1038, 24 pages (May 2006) Available through NIST Weights and Measures Division STOP 2600 Gaithersburg, MD 20899-2600 Phone: (301) 975-4004 — Fax: (301) 926-0647 Internet: www.nist.gov/owm or www.nist.gov/metric TABLE OF CONTENTS FOREWORD.................................................................................................................................................................v
    [Show full text]
  • An Overview of Particulate Matter Measurement Instruments
    Atmosphere 2015, 6, 1327-1345; doi:10.3390/atmos6091327 OPEN ACCESS atmosphere ISSN 2073-4433 www.mdpi.com/journal/atmosphere Review An Overview of Particulate Matter Measurement Instruments Simone Simões Amaral 1, João Andrade de Carvalho Jr. 1,*, Maria Angélica Martins Costa 2 and Cleverson Pinheiro 3 1 Department of Energy, UNESP—Univ Estadual Paulista, Guaratinguetá , SP 12516-410, Brazil; E-Mail: [email protected] 2 Department of Biochemistry and Chemical Technology, Institute of Chemistry, UNESP—Univ Estadual Paulista, Araraquara, SP 14800-060, Brazil; E-Mail: [email protected] 3 Department of Logistic, Federal Institute of Education, Science and Technology of São Paulo, Jacareí, SP 12322-030, Brazil; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +55-12-3123-2838; Fax: +55-12-3123-2835. Academic Editor: Pasquale Avino Received: 27 June 2015 / Accepted: 1 September 2015 / Published: 9 September 2015 Abstract: This review article presents an overview of instruments available on the market for measurement of particulate matter. The main instruments and methods of measuring concentration (gravimetric, optical, and microbalance) and size distribution Scanning Mobility Particle Sizer (SMPS), Electrical Low Pressure Impactor (ELPI), and others were described and compared. The aim of this work was to help researchers choose the most suitable equipment to measure particulate matter. When choosing a measuring instrument, a researcher must clearly define the purpose of the study and determine whether it meets the main specifications of the equipment. ELPI and SMPS are the suitable devices for measuring fine particles; the ELPI works in real time.
    [Show full text]
  • The Speed of Light and Pur¯An.Ic Cosmology
    The Speed of Light and Pur¯an. ic Cosmology Subhash Kak Department of Electrical & Computer Engineering Louisiana State University Baton Rouge, LA 70803-5901, USA FAX: 225.578.5200; Email: [email protected] April 18, 1998 Corrected Dec 30, 2000 Abstract We survey early Indian ideas on the speed of light and the size of the universe. A context is provided for S¯ayan. a’s statement (14th cen- tury) that the speed is 2,202 yojanas per half nimes.a (186,000 miles per second!). It is shown how this statement may have emerged from early Pur¯an. ic notions regarding the size of the universe. Although this value can only be considered to be an amazing coincidence, the Pur¯an. ic cosmology at the basis of this assertion illuminates many an- cient ideas of space and time. Keywords: Speed of light, Ancient Indian astronomy, Pur¯an. ic cos- mology Indian texts consider light to be like a wind. Was any thought given to its speed? Given the nature of the analogy, one would expect that this speed was considered finite. The Pur¯an. as speak of the moving jyoti´scakra, “the circle of light.” This analogy or that of the swift arrow let loose from the bow in these accounts leaves ambiguous whether the circle of light is the Sun arXiv:physics/9804020v3 [physics.hist-ph] 15 Jan 2001 or its speeding rays. We get a specific number that could refer to the speed of light in a me- dieval text by S¯ayan. a (c. 1315-1387), prime minister in the court of Emperors Bukka I and his successors of the Vijayanagar Empire and Vedic scholar.
    [Show full text]
  • Relativity Chap 1.Pdf
    Chapter 1 Kinematics, Part 1 Special Relativity, For the Enthusiastic Beginner (Draft version, December 2016) Copyright 2016, David Morin, [email protected] TO THE READER: This book is available as both a paperback and an eBook. I have made the first chapter available on the web, but it is possible (based on past experience) that a pirated version of the complete book will eventually appear on file-sharing sites. In the event that you are reading such a version, I have a request: If you don’t find this book useful (in which case you probably would have returned it, if you had bought it), or if you do find it useful but aren’t able to afford it, then no worries; carry on. However, if you do find it useful and are able to afford the Kindle eBook (priced below $10), then please consider purchasing it (available on Amazon). If you don’t already have the Kindle reading app for your computer, you can download it free from Amazon. I chose to self-publish this book so that I could keep the cost low. The resulting eBook price of around $10, which is very inexpensive for a 250-page physics book, is less than a movie and a bag of popcorn, with the added bonus that the book lasts for more than two hours and has zero calories (if used properly!). – David Morin Special relativity is an extremely counterintuitive subject, and in this chapter we will see how its bizarre features come about. We will build up the theory from scratch, starting with the postulates of relativity, of which there are only two.
    [Show full text]
  • [Physics.Gen-Ph] 23 Dec 2016 Modified Planck Units
    Modified Planck units 1Yu.L.Bolotin, 2,3V.V.Yanovsky January 5, 2017 1A.I.Akhiezer Institute for Theoretical Physics, National Science Cen- ter Kharkov Institute of Physics and Technology, NAS Ukraine, Akademich- eskaya Str. 1, 61108 Kharkov, Ukraine 2 Institute for Single Crystals, NAS Ukraine, Nauky Ave. 60, Kharkov 31001, Ukraine 3 V. N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61022, Ukraine Abstract Planck units are natural physical scales of mass, length and time, built with the help of the fundamental constants ~, c, G. The func- tional role of the constants used for the construction of Planck units is different. If the first two of them represent the limits of the action and the speed of light and underlie quantum mechanics and special relativity, the Newton’s constant G ”only” fixes the absolute value of the gravitational forces. It seems natural to make a set of fundamental constants more consistent and more effective if used to build Planck units only limit values. To this end, in addition to the limit values ~ and c we introduce an additional limit value - a maximum power in nature. On the basis of these values, a modification of the Planck arXiv:1701.01022v1 [physics.gen-ph] 23 Dec 2016 unit system is proposed. The proposed modification leaves unchanged the numerical values of Planck units, however, opens up exciting new possibilities for interpreting the known results and for obtaining new ones. 1 1 Introduction Introduction of the Planck system of units [1] prior to creation of quantum mechanics as well as of special and general relativity theory, was a significant event in physics.
    [Show full text]