Origin of inertia: extended Mach's principle and cosmological consequences

161 Pages·2000·0.885 MB·English

by  Ghosh, Amitabha

Origin of Inertia
Extended Mach’s Principle and

Cosmological Consequences
Amitabha Ghosh

Apeiron
Montreal
Published by Apeiron
4405, rue St-Dominique
Montreal, Quebec H2W 2B2 Canada
http://redshift.vif.com
© Amitabha Ghosh
First Published 2000
Canadian Cataloguing in Publication Data
Ghosh, Amitabha, 1941 Dec. 3-
Origin of inertia : extended Mach’s principle and cosmological
consequences

Includes Index
ISBN 0-9683689-3-X

1. Inertia (Mechanics) 2. Mach’s principle. 3. Celestial
mechanics. I. Title.

QC137.G48 2000 521 C00-900906-X

Cover design by Priyadarshi Patnaik
Contents
1 Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 MeanRestFrame . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 LawsofMotionandUniversalGravitation . . . . . . . . . . . . . . . 5
1.3.1 Thediscoveryofdynamics . . . . . . . . . . . . . . . . . . . 5
1.3.2 Thelawsofmotionanduniversalgravitation . . . . . . . . . 6
1.3.3 Thebasicnatureofmotion . . . . . . . . . . . . . . . . . . . 7
2 DifficultieswithNewton’sLawsofMotion 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 DifficultiesAssociatedwiththeLaws . . . . . . . . . . . . . . . . . 10
2.3 DifficultieswiththePredictions . . . . . . . . . . . . . . . . . . . . 13
2.4 ProposedModifications . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Mach’sPrincipleandInertialInduction 23
3.1 TheOriginofInertia . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 QuantifyingMach’sPrinciple. . . . . . . . . . . . . . . . . . . . . . 26
3.3 RelativeContributionstoInertiaandMassAnisotropy . . . . . . . . 30
4 ExtensionofMach’sPrinciple 33
4.1 ExtensionofMach’sPrinciple . . . . . . . . . . . . . . . . . . . . . 33
4.2 DynamicGravitationalInteraction . . . . . . . . . . . . . . . . . . . 34
4.3 InertialInduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5 UniversalInteractionandCosmicDrag 39
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 ModeloftheUniverse . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3 LawofMotionandCosmicDrag . . . . . . . . . . . . . . . . . . . . 41
5.4 MagnitudeofCosmicDrag . . . . . . . . . . . . . . . . . . . . . . . 45
iii
iv CONTENTS
6 CosmicDrag:CosmologicalImplications 49
6.1 CosmicDragandtheFirstLawofMotion . . . . . . . . . . . . . . . 49
6.2 CosmicDragandCosmologicalRedshift. . . . . . . . . . . . . . . . 50
6.3 HubbleAnisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.4 RotatingBodiesinSpace . . . . . . . . . . . . . . . . . . . . . . . . 54
7 LocalInteractionofphotonswithmatter 57
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
7.2 GravitationalRedshift. . . . . . . . . . . . . . . . . . . . . . . . . . 57
7.3 RedshiftsinWhiteDwarfs . . . . . . . . . . . . . . . . . . . . . . . 61
7.4 ExcessRedshiftofSolarSpectrumattheLimb . . . . . . . . . . . . 64
7.5 RedshiftofPhotonsGrazingaMassiveObject . . . . . . . . . . . . . 71
8 InteractionofMatterwithMatter 77
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
8.2 InertialInductioninSomeIdealConfigurations . . . . . . . . . . . . 77
8.2.1 Forceonaparticleduetoarotatingring . . . . . . . . . . . . 77
8.2.2 Forceonaparticleduetoarotatingsphericalshell . . . . . . 79
8.2.3 Forceonaparticleduetoarotatingsphere . . . . . . . . . . 81
8.2.4 Torqueonarotatingsphereinthevicinityofalargemassive
body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8.3 SecularRetardationoftheEarth’sRotation . . . . . . . . . . . . . . 83
8.4 ExplanationfromVelocityDependentInertialInduction. . . . . . . . 86
8.4.1 Secular retardationof Earth’s spin due to velocitydependent
inertialinductionoftheSun . . . . . . . . . . . . . . . . . . 88
8.5 SecularRetardationofMars . . . . . . . . . . . . . . . . . . . . . . 94
8.6 SecularAccelerationofPhobos. . . . . . . . . . . . . . . . . . . . . 95
8.7 TransferofSolarAngularMomentum . . . . . . . . . . . . . . . . . 100
8.8 MatterDistributioninSpiralGalaxies . . . . . . . . . . . . . . . . . 111
9 Extra-galacticPhenomena 119
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.2 TrueVelocityDispersion . . . . . . . . . . . . . . . . . . . . . . . . 119
9.2.1 Determinationoftruevelocitydispersion . . . . . . . . . . . 122
9.2.2 Effectoflocalvariationin andshapedistortion . . . . . . . 124
9.2.3 Dependenceofapparentma(cid:20)gnitudeonredshift . . . . . . . . 127
9.2.4 AnalysisofComaandPerseusclusters . . . . . . . . . . . . 128
9.3 AConceptofPotentialEnergyinanInfiniteUniverse . . . . . . . . . 131
9.4 TheProblemoftheGreatAttractor . . . . . . . . . . . . . . . . . . . 134
9.5 TheNatureoftheUniverse . . . . . . . . . . . . . . . . . . . . . . . 135
Epilogue 139
References 141
Foreword
NEOFthe enduringmysteries of classical and modernphysics arises from the
factthatthevalueobtainedforthegravitational-massratiooftwoparticlescom-
O
paredinaweighingexperimentisidenticaltothevalueobtainedfortheinertial-mass
ratioofthesametwoparticlescomparedinacollisionexperiment(towithinexperi-
mentalerror). Forthisreasonwespeakoftheequivalencebetweeninertialandgrav-
itationalmass,andtendtousetheconceptsinterchangeably. However,whilstpracti-
tionersof science andengineeringhave beencontentto accept this equivalenceas a
matteroffact,therehasbeenlittlerationalunderstandingofit. AmitabhaGhosh,the
authorofthisbook,providesuswithaparticularunifyingperspectiveforthisbaryonic
dichotomy—and,intheprocess,unifiesmanyotherdisparatephenomenaaswell.
Amitabha Ghosh is a very fine mechanical engineer, as can be judged from his
positionsasaSeniorFellowoftheAlexandervonHumboldtFoundation,inGermany,
from1977to1995,asaFellowoftheInstitutionofEngineers(India)andofthethree
majoracademiesinIndia—theIndianNationalAcademyofEngineering,NewDelhi,
theIndianNationalScienceAcademy,NewDelhiandtheIndianAcademyofScience,
Bangalore;furthermore,heisfluentinGerman,English,BengaliandHindiinaddition
to (he says!) having a working knowledgeof the very old language, Sanskrit. Any
conversationwithAmitabhawill,soonerorlater,comeroundtoadiscussion(actually,
moreofa one-way‘dialogue’fora secondpartylikemyself!) ofthis language,and
ofhowithasalltheappearanceofbeingalanguagethatwasdesignedfromitsbasics
upwards—ratherthan,asisvirtuallyeveryotherlanguage,beinganevolvedlanguage.
IwouldimaginethatitisAmitabha’sattentiontotheintellectualdetail—asexem-
plifiedbyhisinterestinSanskrit—thathasinformedhislife’sworkasanoutstanding
mechanical engineer and more recently, his directorship of IIT Kharagpur, and the
contentsofthisbook.
Butfirst,considertheIITs(orIndianInstitutesofTechnology):untilmyfriendship
withAmitabha,Ihad(tomyinsularshame)neverheardoftheIITs—butameasureof
theiramazingqualitycanbehadbyconsideringthefollowingstatistics: Everyyear,
about140,000ofthebestschoolstudentsinthewholeofIndia(population1billion)
applyforabouttwothousandplacesinsixIITs(Iprefernottomakeanycomparison
withwhathappensintheUK).IITKharagpur(est. 1951)wasthefirstandthelargest
of the six IITs, and so, by the primary measure of student quality, Amitabha is the
directorofoneoftheworld’sleadinghigher-educationalinstitutions.
v
vi Foreword
And so tothe book! I wouldbeginbysayingthat it standsas a timelyreminder
to all of us that fundamental thought in ‘mathematical physics’ does not have, as a
pre-requisite,necessaryknowledgeofgrouptheory,quantummechanics,generalrela-
tivity,stringtheory,quantumalgebras,knottheory,etcetc.Whatfundamentalthought
does require is a thoroughfamiliarity with the phenomena, combinedwith a proper
appreciationofthewaysinwhichthereceivedviewsfailtoaddressthesephenomena,
further combined with a willingness to suppose that, perhaps, those who have gone
before, no matter how revered, have managed to overlooksome crucial point. This
bookprovidesavividillustrationofhowsuchbraveandsidewaysthinkingcanwork
inthegeneralareaofspace,time,inertiaandgravitation.
The material developedhereconformsclosely to Tom Phipp’s philosophyofthe
‘coveringtheory’—theideathatthemoststableandreliablewayforphysicaltheoryto
progressistomovefromasuccessful(butlimited)theorytoatheorywhich‘covers’(or
includesasaspecialcase)theearlierlimitedtheory.Inessence,Amitabhahasadopted
the position that Newtonian Mechanics (that veritable Queen of sciences) is a good
theory(afterproperattentionispaidtotheideaof‘inertialframe’)andthatitschild,
Newtoniangravitationtheory,isalsogoodatfirst-order.Thatis,Amitabhashowsthat,
inordertoobtainagravitationtheorywhichworksonthelargestspatialandlongest
temporalscales,weemphaticallydonotneedtoscrapthewholeNewtonianparadigm,
replacingthiswholewithacompletelynewconceptualbasis;onthecontrary,allthat
isneededisacreativetweakwhichinvokesthespiritofMachandincorporatesalittle
thinkingofakindwhichmanyengineersmightseeaspurecommonsense.
The resultis a simple andeleganttheorywhichat onceprovidesa rationalbasis
for understanding Newton’s second law (for those who don’t see it as a definition)
and,simultaneously,givesMachagenuineandbelated‘engineeringrole’inthefiner
gravitationalphenomena.
Indetail,thebookbeginswithanexcellentoverviewofNewtonianideas,andfol-
lows this with a brief but accessible discussion on, usually overlooked,fundamental
difficulties associated with these ideas. This is followed by a discussion of Mach’s
PrincipleandofDennisSciama’s1950sideasofacceleration-induced‘inertialinduc-
tion’as a meansof realizingthePrinciple. Finally, in this developmentalphase, the
shortcomings of the Sciama approach are described and a means of circumventing
these is proposed—thenotionof a velocity-inducedinertial inductionmechanismin
additiontotheSciamamechanism.Therethenfollowsdetailedanalysesofmanytypes
ofgravitationallyinteractivesystems.
Apartfromthelucidsimplicityofthe book’sarguments,what impressesmost is
the ability of such a simple no free-parametermodel to explain a very wide variety
of phenomena—some of which are currently anomolous and not explained by any
other theory (e.g., the secular acceleration of Phobos), some of which have ad-hoc
explanations in the standard theories (e.g., the flat rotation curves of spiral galaxies
and the invocationof ‘darkmatter’ as the cure-all) and some of which have a ready
explanationinstandardtheory(e.g.,thecosmicredshiftseenas evidenceofthebig-
bangtheoryofuniversalorigin).
In short, this workdoes whatany goodtheoryshould—itprovidesa simpleuni-
Foreword vii
fyingmechanismtoexplainawidevarietyofphenomenaandmakesstronglytestable
predictions—IhaveinmindthesecularretardationofMars(actuallypredictedinthe
text)and the new generationof gyroexperimentscurrentlyplannedas the definitive
testofthatmuchunder-testedstandardtheory,generalrelativity—which,ofcourse,by
thelightsoftheungenerous,hasalreadyfailedthegalacticdynamicstest!
Asafinalseriouspoint,whatamuchfinerworlditwouldbeifbookslikethiscould
findtheirwayeasilyintoundergraduatephysicsandmathematicalphysicscoursesas
thedefinitiveinoculationagainstthediseaseofhubriswhichisthecurseofcontempo-
raryUniversitytheoreticalphysicsaroundtheworld.
Readandcontemplate!
DavidRoscoe
AppliedMathematicsDepartment
SheffieldUniversity
SheffieldUK
viii Foreword
Preface
The preface of a scientific work is usually considered unimportantby most readers.
Onlyafew(notnecessarilytheseriousreaders)maytakeinterestinthisprelude,pri-
marilytoseehowtheauthorwasmotivatedtowritethebook.Somemayalsowantto
checkiftheirnamesfigureintheacknowledgements.Thisisnotausualsortofscien-
tificpresentation. Thisisamonographinwhichamechanicalengineerhasventured
toextendandmodifyfundamentalconceptsofphysicswithaviewtosolvingsomeof
thelongstandingunresolvedproblemsofastrophysicsandcosmology.Thismakesthis
prefacenotonlyverymuchinorder,butperhaps,absolutelyessential.
LetmeexplainhowImadethisadventurousdigressionfrommyownprofessional
fieldofstudy. Thisunusualvolumecontainstheresultsofabouttwelveyears’(1983-
1995)workandsolitaryeffortonmypart. Itstartedwithadesiretoexplaintheori-
gin of inertia to the students of my second year Dynamics class. Some anticipatory
attempts to introducecertain modifications to the existing formalism led to startling
results, which surprised my colleagues in the Physics Department of the Indian In-
stitute of Technology, Kanpur. They foundthe results to be very intriguing, though
difficult to reconcile with the frameworkof conventionalphysics. As soon as a few
initial conclusions were corroboratedthrough existing experimental and/or observa-
tionalresults,somereputablecosmologistsandastronomerssuggestedthatIapplythe
proposedmodificationsto moreand morecases. I persisted, andfoundthat thethe-
orywasnotonlyabletoyieldquantitativelycorrectresultsineachcase,butinmany
casesresolvedcertainunexplainedphenomena.ThenIrealisedforthefirsttimethatI
couldnotsetthewholematterasidebutshouldtrytodevelopasystematictheoryon
thebasisofwhatIproposeandwhatIhaveaccomplished. However,Imustmention
thatonlyrarelydoesoneencounterclearphenomenainnaturewhereonlyonemech-
anismisoperative. Sincethemagnitudesinvolvedinsuchphenomenaareverysmall,
it is difficultto come to a definite conclusion. It has beenpossible to identifya few
caseswhereconclusionscanbedrawnwithareasonabledegreeofconfidence,andthe
observationssupporttheproposedtheory.
TheprimarythemeofthismonographisatheoryinwhichNewton’sstaticgravita-
tionalinteractionhasbeenreplacedbyanewdynamicmodel.Accordingtothistheory
theinteractivegravitationalforcebetweentwoobjectsdependsnotonlyonthesepa-
ix
x Preface
rationbutalsoontherelativevelocityandaccelerationbetweentheinteractingbodies.
In a sense it is an extensionof Mach’s Principle, and couldbe termedthe Extended
Mach’sPrinciple.AccordingtoMach’sPrincipleaforceactsonanacceleratingobject
duetoitsinteractionwiththematterpresentintherestoftheuniverse.IntheExtended
Mach’s Principle such an interactive force acts on a body due to its velocity (in the
meanrestframeoftheuniverse)also. ThisforcehasbeentermedtheCosmicDrag.
The initial Chapters offer some general discussions and highlight certain interesting
featuresofthefundamentalproblemofmotion. Ithasbeendemonstratedthatinare-
lationalframeworkanabsolutecharactercanbeassignedtodisplacement,andhenceit
ismeaningfultotalkaboutanabsoluteframeofreferenceinaninfinite,non-evolving
andquasistaticuniversesatisfyingthePerfectCosmologicalPrinciple.Abriefaccount
ofthebasicdifficultiesintheNewtonianformulationofmechanicsisthenpresented,
followedbyahistoricalaccountofhowtheearlierresearcherstriedtoresolvetheseis-
suesthroughvarioussuggestionsformodificationsinNewton’slaws.Thenextchapter
presentsSciama’sattempttoquantifyMach’sPrincipleandhismodelofacceleration
dependentinertialinduction.Next,thisisextendedtoincludeavelocity-dependentin-
ertialinductionterm. Thoughverysmall,theeffectofthevelocitydependentinertial
inductiontermintroducessomefundamentalchangesin thebasic frameworkofme-
chanics,leadingtoamodifiedlawofmotion. Theexactequivalenceofgravitational
and inertial masses emerges as a natural consequence of the dynamic gravitational
interaction.
Anotherstartlingresultofthismodificationistheemergenceofacosmicdragterm,
wherebyallobjectsaresubjectedtoadragforcedependingonthevelocitywithrespect
tothemean-rest-frameoftheinfinite,homogeneousandquasistaticuniverse. Though
noteasilyopentodetectionbyanyexperimentbecauseofitsextremelysmallmagni-
tude, this cosmic drag term gives rise to the observedcosmologicalredshiftwithout
invoking any expansion hypothesis. This eliminates the need for introducing a Big
Bang tostart the universe. Here I anticipatea criticism that I am questioninga cos-
mologicaltheoryacceptedbythemajorityofmainstreamphysicistsaroundtheworld.
TheBig Bang Theoryhas becomeso popularnowthat veryfew rememberit is still
onlyahypothesis. ScientistswhobelievethatthesearchforalternativestoBigBang
cosmology should not be restricted are quite fewer in number. I am presenting this
alternativemodelwiththebeliefthatthescopeofscientificresearchisalwayswider
than many people think. The proposed model yields very good results in a number
of other phenomena of different types. This is very important, as these phenomena
areunrelated,andtheproposedmodeldoesnothaveanyadjustablefreeparameters.
Theproposedtheoryandanymodeloftheextendedversionofinertialinductioncan
befurthertestedonnewobservationswithhigheraccuracy. Sincethismodelislikely
to open new vistas, other researchers can take up the necessary work to verify the
correctnessoftheproposedtheory.
Themostdifficultpartofthewholeexerciseisdecidingonanappropriatetitleof
thismonograph.Anattempttomakeittechnicallyprecisecanrenderitunfamiliarand