Download Chapter 14 Cosmology II

Chapter14
CosmologyII–TheBigPicture
Inchapter3wedeterminedthechangesinenergy,force,voltage,etc.thatarerequiredtokeep
thelawsofphysicsconstantindifferentgravitationalpotentialswherethereisadifferencein
therateoftime.The“normalized”coordinatesystemofchapter3usedtheequationLo Lg.This
doesnotimplythatLoandLgareconstantovertime.Itisnowproposedthatbothoftheseunits
oflengtharesimultaneouslycontractingastheuniverseages.Thissimultaneouscontraction
maintainsLo LgintheCMBrestframeaccordingtoamidpointobserver.
Nowweareattemptingtounderstandtheevolutionoftheuniverse.TodothisIproposethatit
ismostconvenienttouseacoordinatesystembasedonthepropertiesofPlanckspacetimewhen
Гu 1.Eventhoughtheuniversehasalwayshadflatspacetime,therehasbeenacontinuous
increase in Гu since the Big Bang. As previously explained, the current value of Гu is about
Γuo 2.6 1031andthisnumbercontinuestoincrease.Thisaffectsmanythingsincludingour
rate of time, our length standard and our energy standard. The best reference we have to
quantifythesechangesistouseacoordinatesystembasedontheconditionsthatexistedwhen
Гu 1.Anotherwayofsayingthisisthatweshouldreferencetheconditionsthatexistedatthe
startoftheBigBangwhenwehadPlanckspacetime.
RelativetothespatialandtemporalcoordinatesystemthatexistedattheBigBangwhenГu 1,
therehasbeenadecreaseintherateoftimeandadecreaseinastandardizedunitoflengthsuch
asonemeter.Aswillbeexplained,thiscombinationkeepsthelawsofphysicsunchanged.This
hassomesimilaritiestothegravitationaleffectspreviouslydiscussedinchapter3.However,
withtheuniversethebackgroundgravitationalgamma Гu iscontinuouslyincreasing.Oneof
thefewindicationsthatanythingischangingintheuniverseisthatlightthatwasemittedalong
timeagofromdistantsourceshasundergoneobviouschangesinwavelengthandintensity.
Spacetime Transformation Model:Amodeloftheuniversebasedonacontinuouslyincreasing
ГurepresentsanalternativetotheBigBangmodel.Whatweperceiveasanincreaseinthescale
oftheuniverseisactuallyduetoanincreaseinthebackgroundГuoftheuniversechangingthe
spatialandtemporaldimensionsofspacetime.Thisisachangeinthepropertiesofspacetime
thathasaneffectoneverythingintheuniverse.Theradiusofanatomortherotarradiusofa
rotarwoulddecreaserelativetocoordinatelength .AnincreaseofГuresultsinthefollowing:
1 the hybrid speed of light of the universe decreases; 2 proper length contracts relative to
coordinatelength;3 therateofpropertimedecreasesrelativetotherateofcoordinatetime;4 thetotalenergydensityoftheuniverseremainsthesame totalenergyincludesvacuumenergy .
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Perhaps most surprising of these is that the spacetime transformation model says that the
coordinate energy density of the universe has remained constant since the beginning of the
universe sincetheBigBang .Thecoordinateenergydensityutilizescoordinatelength and
coordinaterateoftimedttoquantifycoordinateenergydensity.Theobservableenergydensity
oftheuniverse measuredinproperunitsofenergy hasdecreasedbyafactorofroughly10120
sincethebeginningoftime sincetheBigBang .However,includingthewavesinspacetime
responsibleforvacuumenergy,itwillbeshownthatthespacetimetransformationmodelofthe
universeseesnochangeinthecoordinateenergydensityoftheuniverse.Thisalsoeliminates
thefamous10120discrepancybetweenthe“critical”energydensityoftheuniversederivedfrom
generalrelativityandsupportedbyobservationcomparedtothecalculatedenergydensityof
theuniversederivedfromquantummechanicsandquantumchromodynamics.
Thisspacetimetransformationmodelmightseemlikeanunnecessarycontrarianviewthatis
fundamentallyequivalenttodepictingtheuniverseasexpanding.However,itwillbeshownthat
thismodelisnotequivalenttotheBigBangmodel.Thisproposedmodelgivesthesameredshift
andthesameincreaseinpropervolumeastheBigBangmodel,butthespacetimetransformation
model offers different predictions about the future of the universe. Probably the most
controversialdifferenceisthatthespacetimetransformationmodelpurportstoeliminatethe
needfordarkenergyandacosmologicalconstant.
Observable Universe from Planck Spacetime: As previously stated in chapter 13, Planck
spacetimehadsphericalPlanckenergydensity.Mostimportantly,PlanckspacetimehadГu 1
and all the dipole waves in spacetime had ½ Planck energy about 109 J and ħ angular
momentum.Thismeansthat100%oftheenergyinPlanckspacetimewas“observable” had
quantizedspin .ThevalueofГu 1alsomeansthattherateoftimewasthehighestpossible
andthepropervolumeoftheuniversewasthesmallestpossible.Гu 1alsoimpliesthataunit
of energy such as one Joule was the highest possible value when measured on the absolute
energyscalewhichusescoordinaterateoftimeandcoordinatelength.Incomparison,itwillbe
shownthatoneJouletodayisavastlylowerenergyontheabsoluteenergyscalebecausetoday
Γuo 2.6 1031.Also,thetransformationofspacetimethathastakenplacesincetheBigBang
has resulted in a decrease in the percentage of the energy in the universe that possesses
quantizedangularmomentum.Today,onlyabout1partin10122oftheenergyintheuniverseis
“observable” possessesquantizedangularmomentum All the energy required to form our current universe including vacuum energy would be
containedinasphereofPlanckspacetimeabout15 10‐6meters ~15microns inradius.This
radiusiscalculatedbyreducingthecurrentdistancetoourparticlehorizon ~46billionlight
yearsor4 1026m byafactorofГuo 2.6 1031.OurcurrentuniversehasГuo 2.6 1031
whichgreatlyreducesbothourcurrentstandardofenergyandthefractionoftheenergyinthe
universethatis“observableenergy”
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Itispresumedthattheuniversecurrentlyextendsfarbeyondourcurrentparticlehorizon.This
meansthattheoriginalvolumeofPlanckspacetimewasfarbiggerthanthe15micronradius
spherical volume required to form everything including vacuum energy within our current
particlehorizon.ThisoriginalvolumeofPlanckspacetimemightnothavebeeninfinite,butitis
presumedtobeeffectivelyinfinitebecausethereisnodetectabledifferenceasfarasamodelof
theuniverseisconcerned.Itisalsopresumedthattherearegalaxies,darkmatter,etc.beyond
ourparticlehorizonthathaveasimilarappearanceanddensitytoourobservableuniverse.
The spacetime transformation model of the universe has a fixed not expanding coordinate
system.Forexample,twodistantgalaxiesareconsideredtobeseparatedbyaconstantdistance
when measured in units of coordinate length . The coordinate grid used by the spacetime
transformationalmodelhassimilaritiestothecoordinategridusedbytheΛ‐CDMmodel.Both
gridscorrespondtotheCMBrestframeatalllocationsintheuniverse.Howeverthedifference
isthattheΛ‐CDMmodelhasagridthatexpandswiththepropervolumeoftheuniverseandthe
spacetime transformation model has a grid that remains stationary. In the spacetime
transformationmodel,theexpansioninthepropervolumeoftheuniverseisaccommodatedby
thechangeinΓuovertheageoftheuniverse.
Hubble Parameter and Shrinking Meter Sticks:Today,astronomersdonotrealizethattheir
metersticksarecontractingduetochangesinspacetime.Theterm“meterstick”representsany
meansoflengthmeasurement.Astrophysicistscalculatethatthedistancetodistantgalaxiesis
increasing.However,thisdistanceismeasuredusingcontractingmetersticks contractingunits
oflength .Thedistantgalaxiesthatarestationaryonthestaticcoordinatesystemappeartobe
recedingatavelocitygivenbytheHubbleparameter.
In astronomical terminology, the Hubble parameter is often expressed as about
70.8km/s/MpcwhereMpcismegaparsec,aunitoflengthusedinastronomyequaltoabout
3.09 1022 meters. Converting the Hubble parameter to SI units we have 2.29 10‐18
m/s/m.Thesecondsusedherearetoday’sproperseconds.Thecommoninterpretationofthe
Hubble parameter is that this is the current expansion rate of the universe. The spacetime
transformationmodelinterpretstheHubbleparameterdifferently:
Г
Г
or Г
Г
notethedotsrepresentingtimederivative
Thedotsareshorthandfortimederivatives.Therefore,theHubbleparameter equalstherate
ofchangeofГudividedbythecurrentbackgroundvalueГuo.Alsoauoisthecurrentscalingfactor
oftheuniversewhichisequaltoГuo.
Ameterstick 1meterlong iscontractingatavelocityofabout2.29 10‐18meters/secondwhen
compared to a hypothetical meter stick that is not contracting a meter stick with fixed
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coordinatelengthinunitsof .Asexplainedinchapter13,theHubblesphereisa13.7 109
light year 1.3 1026 m radius imaginary spherical shell where galaxies and space itself are
calculatedtoberecedingawayfromusataboutthespeedoflight.However,itisproposedthat
weareusingacontractingunitoflength,suchasacontractingmeterstick,asreferenceforthis
calculation.TheproperdistancebetweenusandagalaxyattheedgeoftheHubblesphereis
indeed increasing by 3 108 m/s, but that is because we are measuring the distance using a
contractingmeterstick.Ourmeterstickisshrinkingattherateof2.29 10‐18meters/secondso
weobtainanincreaseinproperdistanceof3 108m/s obtainedfrom2.29 10‐18m/s/m 1.3 1026meters .Thisisnotthesameassayingthatthegalaxyisphysicallyrecedingfromus
at the speed of light. The spacetime transformation model says that the calculated speed is
erroneousbecauseitisobtainedwhenwemeasureafixeddistanceusingshrinkingmetersticks.
Thereasonableexplanationisthatspacetimeisundergoingatransformationthatchangesthe
coordinate speed of light while keeping the laws of physics unchanged including a constant
proper speed of light . This is similar to the covariance of the laws of physics in different
gravitationalpotentialsasdiscussedinchapter3.However,withtheuniverseГuincreaseswith
timebutthelawsofphysicsremainunchanged.Oneobservableeffectisthatittakeslongerfor
lighttotravelbetweengalaxiesastheuniverseages.Sincewemeasurenochangeintheproper
speedoflightweinterpretthisasindicatinganexpansion.However,thealternativeexplanation
proposed here is that the change occurring in the properties of spacetime produces a
dimensional contraction. In chapter 3 we saw how the rate of time can change at different
elevationsofagravitationalfieldwithoutbeingdetectablelocally.Gravityalsowasshownto
affect proper volume which implies a difference in the unit of length. The universe is also
producinganomnidirectionalgravitationaleffectthatiscontinuouslyincreasing.Oneresultof
thisiswhatweperceivetobethecosmologicalincreaseinthevolumeoftheuniverse.
Itwasshowninchapter3thatgravityaffectsmanyoftheunitsofphysicsinawaythatkeepsthe
lawsofphysicsunchanged.Itisproposedthatsomethingsimilarishappeningwiththeentire
universeexceptthatthereisanimportantdifference.Withtheuniverseatanyinstantthevalue
ofГuisuniformlyincreasingeverywhere.Thisistheoppositeofthegravityassumedinchapter
3 which was static and had a gravitational gradient. The continuous increase in Гu causes
changesinvariousunitsofphysics energy,force,voltage.etc. whichtogetherpreservethelaws
ofphysics.Onlywhenwelookatdistantgalaxiesdoweobtainahintthatchangeovertimeis
occurring.
No Cosmic Event Horizon: The Λ‐CDM model considers the accelerating expansion of the
universetohaveacosmiceventhorizon.Thisisdefinedasthelargestcomovingdistancefrom
which light emitted now can ever reach the observer in the future1 According to the Λ‐CDM
model,galaxiesthatweobserveashavingaredshiftgreaterthan Z 1.8arecurrentlybeyond
1
Bergström, L.; Goobar, A.: "Cosmology and Particle Physics", WILEY (1999), p. 65.ISBN 0-471-97041-7
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ourcosmiceventhorizon.Lightthatiscurrentlybeingemittedbythesegalaxieswillsupposedly
neverreachusbecausecosmicexpansionofspaceisaddingvolumeatsuchafastratethatthe
distanceincreaseexceedsthespeedoflight.EventheexpansionofourHubblespherecannot
overcometheacceleratingexpansionoftheuniverse.Photonsbeingemittednowbygalaxies
withZ 1.8willbesweptawayfromusbytheacceleratingexpansionoftheuniverse.Theonly
reasonthatwecanseethosegalaxiestodayisthatweareseeingthelightemittedfromalong
time ago before they crossed our event horizon. Once again, that is the Λ‐CDM model
interpretation.
Thespacetimetransformationmodeloftheuniversemakesapredictionthatisdifferentthan
theΛ‐CDMmodel.TheproperdistancebetweenusandtheZ 1.8galaxiesisindeedincreasing
fasterthanthespeedoflight.However,thisisbecauseofthecurrentrateofincreaseinГuis
causing our meter sticks to shrink. The galaxies are actually stationary on the proposed
coordinate grid. The prediction is that light currently being emitted from those galaxies will
eventuallyreachusbutataslowerhybridspeedoflightthantoday.Eventhoughtheuniverse
appearstohaveacceleratingexpansion,thespacetimetransformationmodelsaysthatthereis
no event horizon at a distance corresponding to Z 1.8 or at any other distance in the
foreseeablefuture.
Wecanobtainabetterinsightintothepropertiesofthehybridspeedoflightwithanumerical
example.SinceC≡d /dτu c/Гu,thereforethecurrentvalueofthehybridspeedoflightis:
C c/Гuo 2.6 10 10‐23m/s
divided
Thisisthecurrenthybridspeedoflightwheretheunitsm/sarecoordinatemeters
bypropercomovingseconds noteuseofitalicincoordinateunits .Thehybridspeedoflightis
deceleratingeverysecondatacurrentrateof:
C 10‐23m/s 2.3 10‐18s‐1 2.3 10‐41m/s2decelerationofC
Finally,thecurrentrateoftime dτuo isabout2.6 1031timesslowerthanthecoordinaterate
oftime dt whichassumesГu 1.
Constant Coordinate Energy Density:Theenergydensityofthis15 10‐6msphericalvolume
isequaltosphericalPlanckenergydensity:Ups 5.5 10112J/m3.Atthebeginningoftime the
BigBang thisenergywasintheformofdipolewavesinspacetimewiththeuniqueproperties
ofPlanckspacetimepreviouslyenumerated.Todaythecharacteristicsofthedipolewavesin
spacetimethatformbothvacuumenergyandtheobservablemass/energyinouruniversehave
changed their characteristics compared to Planck spacetime. Almost all the energy in the
universetodayisintheformofvacuumenergy–dipolewavesinspacetimethatdonotpossess
angular momentum. Only an extremely small part is in the form of observable energy that
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possesses angular momentum. However, it will be shown that not only the proper energy
density includingvacuumenergy butalsothecoordinateenergydensityoftheuniversetoday
isstillthesameasPlanckspacetime.Therehavebeenchangesrelatingtothedistributionof
quantizedangularmomentum,therateoftime,properlength,etc.butthetotalenergydensity
has not changed even when measured using coordinate energy density that assumes Гu 1.
Therefore,itispossibletoadoptacoordinatesystembasedonthesecoordinatevaluesthatdoes
notexpandovertime.Thisisthestationarycoordinatesystemofthespacetimetransformation
model.
ItmightseemthattheBigBangmodelisultimatelyequivalenttothespacetimetransformation
modelwithitsstationarycoordinatesystem.However,thisisnotacaseofsimplecoordinate
transformation.Forexample,thetwomodelsmakedifferentpredictionsabouttheexistenceof
aneventhorizonaspreviouslynoted.Also,theBigBangmodelcannotaccommodatethefact
thatnewvolumebeingaddedtotheuniversemustalsopossessthevacuumenergywithenergy
density exceeding 10112 J/m3. Where did this additional energy come from? The spacetime
transformation model can accommodate this requirement as will be explained later in this
chapter.
Illustration of Slowing Hybrid Speed of Light: Figure 14‐1 illustrates the concept of a
stationarycoordinatesystemwithaslowinghybridspeedoflight.Thisfigureusescoordinate
length,thereforethedistanceincoordinatelengthunitsbetweenPointAandthefurthestcurved
surface 16billionyears isroughly10‐5m.Point“A”canbeimaginedasinitiallyaPlancksphere
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withinPlanckspacetimeatthebeginningoftime.ThisspherecontainedaboutabillionJoules,
sowhentimebegantoprogressthegravitationalinfluenceofthisenergybegantopropagate
awayfrompointAattheproperspeedoflightc.However,therateofpropagationasmeasured
usingthehybridspeedoflightdecreasesasГuincreases.After4billionyearsthegravitational
influence had reached the propagating particle horizon designated 4 billion years. The term
“propagatingparticlehorizon”isusedheretodesignatetheexpandingsphereofinfluenceofa
pointofmass/energy Similarly,thepropagatingparticlehorizonsfor8,12and16billionyears
areshown.
The purpose of this figure is to illustrate the slowing rate of propagation as indicated by the
decreasingdistanceseparatingthecurvedsurfacesastimeprogressesandГuincreases.There
isnotendencyforthisprogressiontobesweptbackwardsbycosmicexpansion.Therateof
progresswillcontinuetodecrease,butthereisnoeventhorizonwheretheprogressisstopped.
ItisspeculationwhetherГueverreachessuchalargevaluethataquantummechanicaltransition
occurs.Thespacetimetransformationmodeloftheuniversepredictsthatfortheforeseeable
future,wewillcontinuetoseenew,moredistantgalaxiesappearinthesky.Thegalaxiesthat
wecurrentlyseewillgetdimmer lessphotonspersecondperm2 butalsoparadoxicallybeless
redshiftedthantoday.
Redshift:Thespacetimetransformationmodelisalsothebestmodeltoseewhyanincreasing
backgroundГuproducesaredshiftonthelightthatweseefromadistantgalaxy.Thepresence
of a redshift in cosmology is counter intuitive when it is realized that the spacetime
transformationmodelclaimsthattherateoftimewasfasterwhenthelightwasemitted dτem than when the light is observed Гem Гobs and dτobs dτem . For example, Schwarzschild
assumedasinglestationarymassinanemptyuniverse.Thisassumptionpresumeda“mature
gravity” condition no time dependence . Under these conditions, light propagating from a
locationfarfromthemass smallgravitationalГ toalocationnearthemass largegravitational
Г ,undergoesa“gravitationalblueshift”.Thiswaspreviouslydiscussedandshownthatadistant
observerusingasinglerateoftimeperceivesnochangeintheenergyofthephoton.Thelocally
observedapparentincreaseinenergyisduetotheslowrateoftimeingravity largeГ .
When the background Гu of the universe increases uniformly everywhere, this is completely
differentthanaphotonpropagatingfromalocationwithasmallvalueofГtoalocationwitha
largervalueofГ.ItwillbeshownbelowthatanincreaseinthebackgroundГuoftheuniverse
producesaredshiftwhichincludesanincreaseinproperwavelengthandadecreaseinproper
frequencyandadecreaseinproperenergy.
Coordinate Wavelength Constant: When the background Гu of the universe is increasing
homogeneouslythroughouttheuniverse,thismeansthatthehybridspeedoflightisdecreasing
homogeneouslyas:C c/Гu.Lightinflightjustslowsdownhomogeneouslyeverywhere.This
homogeneousslowingmaintainsthesamecoordinatewavelengthforalightwave.Theentire
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wavejustslowsdownwithoutchangingitssizewhenmeasuredusingcoordinatelength.Ifthe
lightinflightisconstantwavelengthwhenmeasuredinunitsofcoordinatelength,whatresult
willweobtainwhenwemeasurethewavelengthinunitsofproperlengthusingacontracting
meterstick?Wewillobtaintheresultthatthelightisincreasingitswavelengthrelativetothe
contractingmeterstick.Inotherwords,wewouldseearedshift anincreaseinwavelength .
Redshift – Wavelength Analysis:Toanalyzethiswewillassumethatlightisemittedinlocation
#1atanageoftheuniverset1andabackgroundgravitationalgammaГ1.Theemissionisat
coordinate wavelength λ which can be converted to proper wavelength λ1 at the time of
emission. At a later time age of the universe t2 and background gamma Г2 the coordinate
wavelengthisstillthesame buttheproperwavelengthis λ2relativetothecontractedmeter
stick.Allwehavetodoiscompare λ1to λ2whichmeansthatweneedtoconvert λwhichis
always in units of coordinate length into wavelength λ expressed in proper length at two
different times. The coordinate wavelength λ does not change; it only slows down due to a
changeinthehybridspeedoflightCwhenГuincreases C c/Гu .Thereforewemustconvert
betweencoordinatelengthandproperlengthattwodifferentvaluesofbackgroundgamma:Г1
andГ2.Fromchapter13weknowthattheconversionofunitsofcoordinatelength tounitsof
properlengthisL Гu .Whenweexpressthisconversionintermsofwavelengthsymbolswe
have λ Гuλ.Thissaysthatagivenwaveappearstohaveabiggerwavelength moreunitsof
properlength whenitismeasuredwiththecontractedmeterstickusedforproperlengththan
when it is measured with the coordinate scale meter stick that is not contracted. Since λ is
independentofthebackgroundГuwehave:
λ wavelengthoflightwhenmeasuredinunitsofcoordinatelength.
λ1andλ2 wavelengthoflight properwavelength attimet1andt2wheret2 t1
Г1andГ2 backgroundГuoftheuniverseattimet1 andt2wheret2 t1
aem cosmologicalscalefactoratemission aem attime t1
aobs cosmologicalscalefactoratobservation aobs attime t2
1
Г1
Г
Г
andλ
Г
conversionofλtoλ1andλ2
sinceГ2 Г1thereforeλ2 λ1 wavelengthsinunitsofproperlength SinceГuisincreasingwithtime,thereforeГ2 Г1andλ2 λ1.Thisallsaysthatλ2isredshifted
longerwavelength comparedtoλ1.Theamountoftheredshiftis:λ2/λ1 Г2/Г1whichcanalso
be expressed in terms of the ratio cosmological scaling factors at emission aem a1 and
observation aobs a2 orintermsofredshift1 Z.
Г
Г
1 Z
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Since λ1 is the proper wavelength at emission time t1 and λ2 is the proper wavelength at
observation timet2 ,thereforetherelationshipcanbewrittenas:
1 Z
This answer, obtained from the spacetime transformation model agrees with the answer
obtainedfromtheBigBangmodelthatassumescosmicexpansionoftheuniverse.
Redshift – Frequency Analysis:Therefore,ithasbeenshownthatlookingjustatwavelength
there is the correct redshift when we presume that the redshift is caused by a change in the
backgroundГuratherthananexpansionoftheuniverse.Itispossibletoworkthissameproblem
lookingatthefrequencyoftheradiationratherthanatthewavelength.Inthiscasewewould
expectalowerfrequencyatalatertimewhenweexpressfrequencyrelativetopropertime.
Wewillstartoffbyworkingthisproblemusingcoordinatevalues.Asbefore,thereisnochange
inwavelengthexpressedintermsofcoordinatelengthbetweentheemissionandobservation.
Thenewsymbolsare:
C1andC2 hybridvelocityoflightattimest1andt2respectively
λ wavelengthexpressedinunitsofcoordinatelength–thisdoesnotchangeatt1andt2
υ1andυ2 properfrequencyoflightattimest1andt2respectively
properfrequencyhasaredshiftsinceυ1 υ2andГu2 Гu1
Since υ1canbeconsideredthefrequencywhenthelightwasemitted υ1 υem and υ2 canbe
considered the frequency when the light was observed υ2 υobs , therefore the following is
anotherwayofstatingtheseresults:
Thereforethespacetimetransformationmodelgivesthesameredshift properwavelengthand
proper frequency as the Big Bang model. However, this analysis leaves one question
unanswered.Iftherateoftimewasfasterinthepastthanitistoday,whydon’tweobservea
blue shift on light from distant galaxies? The answer to this question is not obvious in the
previous analysis because that analysis used the “hybrid speed of light C d /dτu. This
definitionincorporatestheproperrateoftimeintheuniverse dτu whichhidesthequestion
about the blue shift. This question can only be answered if we compare proper values to
coordinatevalues.Thiscomparisonrequiresthatwereworktheproblemusingcoordinaterate
oftime dt ,coordinatespeedoflight andcoordinatefrequency υc .
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Tobegin,wewillreturntotheexamplepreviouslystatedandexaminelightemittedatlocation
#1atanageoftheuniverse tu1whichhadabackgroundgravitationalgammaГu1.Thislightis
laterobservedatlocation2withtheageoftheuniversetu2andbackgroundgammaГu2.Again,
the wavelength of the light measured in units of coordinate length is λ. This coordinate
wavelengthdoesnotchange;thelightmerelyslowsasthecoordinatespeedoflightdecreases.
Thecoordinatespeedoflightatagesoftheuniverse tu1and tu2willbedesignatedas 1and 2
respectively.
1
Г
and 2 Г
Wewillnowstatethefrequencyofthislightusingtherateofcoordinatetimedtasourstandard.
Recallthatdt Гudτu.Frequencyobtainedusingthecoordinatetimestandardwillbedesignated
νc.Theparticularcoordinatefrequencyproducedbywavelengthλ willbedesignatedν1cwhen
thebackgroundgammaisГu1andν2cwhenthebackgroundgammaisГu2.Therefore:
λ set 1
Г
and 2
Г
Г
Г
Г
Г
ratioofcoordinatefrequencies
Thissaysthatusingcoordinatefrequencyresultsinaredshiftproportionaltothesquareofthe
ratioofgammas.Thismeansthatthecorrectionduetotheslowingrateoftimedoesnotproduce
anobservableblueshift,butinsteadthisblueshiftisusedtoreduceacoordinateredshiftthatis
proportionalto Гu1/Гu2 2toaproperredshiftproportionaltojust Гu1/Гu2 .Thisisshownby
makingthesubstitution
Г
and
Г
toobtaintheratiooffrequenciesexpressedin
properfrequenciesυ1andυ2.
Г
Г
ratioofproperfrequencies
Rotar’s Frequency:SincephotonsloseproperfrequencyasГuincreases,whydoestheproper
Comptonfrequencyofrotarsremainconstant?Toputthisquestioninperspective,weshould
firstacknowledgethatonthecoordinatetimescalethatassumesГu 1theComptonfrequency
ofarotardoesdecrease.Therefore,allfundamentalrotarsarecontinuouslyslowingdownon
anabsolutetimescale.Wedonotnoticethisslowingbecauseourcosmicclockisalsoslowing.
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Thereforewe are using a continuouslyslowing clock totime the frequency of a continuously
slowing rotar such as an electron. This is a moving standard, but each secondan electron is
losingabout282HzifwemeasuredtheComptonfrequencyusingtherateoftimethatexistedin
theprevioussecond ωc /2π 282Hz/s .
Therefore,onanabsolutetimescale,whydoesaphoton’sfrequencydecreaseproportionalto
Гu1/Гu2 2 while a rotar’s frequency scales with just Гu1/Гu2 ? The answer is that the
propagationrateoftherotar’sdipolewavedecreasesproportionalto Гu1/Гu2 2butthisispartly
offsetbyadecreaseintherotar’scircumference measuredontheabsolutescaleof .The
reducedcircumferencedistanceandreducedrotarradius bothmeasuredontheabsolutescale
of means that a dipole wave with quantized angular momentum propagates around the
shortened circumference measured in units of . The decrease in a rotar’s circumference
resultsinarotar’sfrequencyscalingwith Гu1/Гu2 whichmatchestherateoftimedecreaseon
anabsolutescale.Therefore,therotar’sComptonfrequencyappearstobeconstantwhilethe
frequency of a photon decreases when measured using proper rate of time. The standard
explanationofthecosmicredshiftbasedonexpansionoftheuniverseisproposedtobewrong.
Wavelengths are not being stretched. There are no point particles. Particles with finite
dimensions are also affected by the transformation of spacetime. However the effects on
particles are not noticeable because there are offsetting effects on the rate of time, on the
standardofenergyandonotherunitsofphysics.
Maintaining the Vacuum Energy Density:Throughoutthisbooktherehavebeennumerous
referencestotheenergydensityofthespacetimefieldbeingontheorderof10113J/m3 timesan
unknown numerical constant near 1 . The problem is that throughout the history of the
expandinguniverse,theproperenergydensityofvacuumenergywouldhavetoremainconstant.
Theexpandingvolumewouldappeartorequireamechanismtocontinuouslyaddatremendous
amount of new energy to the expanding universe. For example, the Hubble parameter of
2.3 10‐18 m/s/m indicates that each cubic meter in the universe is expanding and
increasing its volume by ~ 10‐53 m3/s. If the vacuum energy density required to fill this
additional volume is Uvac 10112 J/m3, then the additional volume generated by EACH cubic
meter in the universe requires additional 1059 Joules/second. To put this in perspective, the
E mc2totalobservableenergyoftheMilkyWaygalaxyisalsoabout1059Joules.Thereforeit
wouldappearthateachcubicmeterofvolumeintheuniversemustbesuppliedwithabout1059
Joulesofenergyeachsecond.
Therefore, the problem of supplying the universe with dark energy each second is trivial
comparedtotheproblemofsupplyingtheuniversewithnewvacuumenergyeachsecond.This
allseemstobeimpossible,somostphysicistspresumethattheremustbesomemechanismthat
cancels out almost all the implied vacuum energy density in the universe. However, this
hypothetical cancelation mechanism has several problems. 1 Zero point energy, vacuum
fluctuations,andtheuncertaintyprinciplemustremainandtheseallimplythatvacuumenergy
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hasnotbeencanceled.2 Thecancelingmechanismmustbecarefultoleavetheonepartin10122
thatconstitutesourobservableuniverse.3 Theeffectcapableofcanceling10113J/m3mustbe
equallyaslarge.4 Nomechanismhasbeensuggestedthatiscapableofcausingthisenormous
cancelation.
Thespacetimetransformationmodelsaysthatthereisnocancelingmechanism.Theenormous
vacuumenergyispresentinspacetime.Itisdipolewaveenergythatlacksangularmomentum
andthereforeonlyinteractswithourobservableuniverse fermionsandbosons throughsubtle
quantummechanicalmechanisms.Thisvacuumenergyisthemostperfectsuperfluidpossible.
Itformsthesingleuniversalfieldthatisresponsibleforallotherfields.Italsogivesthefollowing
propertiestospacetime:Zs,c,εo,µo,ħ,G,lp,tp,etc.
NewTransformationsofUnits:Recallthatinchapter3wemadeatableoftransformationsof
theunitsofphysicsshowingthedifferencebetweena“zerogravity”locationandalocationwith
gravity. In chapter 3 we designated the “zero gravity” location as having Г 1. Now it is
necessarytorealizethatthisdesignationincorporatedasimplification.Wewereignoringany
changeinthebackgroundgravitationalgammaoftheuniverseΓu.Anotherwayofsayingthisis
thatwedefineda“zerogravitylocation”ashavingΓ 1.Nowthatwearetalkingaboutthe
evolution of the universe it is necessary to be more precise. The length transformation was
previouslyexpressedas:Lo Lg.However,toputthisinthebiggerperspectivethatincorporates
Γuand ,wecannowsay:
Lo Lg /Γu
Thisequationsaysthatwhatwewerepreviouslycalling Loand Lgwerebothchangingrelative
to our absolute lengthstandard that waspresentat thestart oftheuniverse when Γu 1.
When we are dealing with the universe and time scales where the effects of a changing
background Гu are significant, then it is no longer possible to adopt proper length as the
coordinate unit of length. A different coordinate length transformation is required to
characterizetherelationshipbetweentheunitsofphysicswhentheyarecomparedatthesame
locationbutatsubstantiallydifferentagesoftheuniverse.ThevalueofГuincreaseswiththeage
oftheuniverse.
Inchapter3wewereabletoobtainalltheothertransformationsusingdimensionalanalysis
once we had the transformations for length, time and mass. Previously these three
transformationswereexpressedas:
Lo Lgunitoflengthtransformation
To Tg/Гunitoftimetransformation
Mo Mg/Гunitofmasstransformation
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InthesetransformationsthesymbolsLo,ToandMorepresentedcoordinate zerogravity units
of length, time and mass respectively. Now it is necessary to adopt new coordinate units to
representaunitofcoordinatelength,coordinatetimeandcoordinatemassatthestartoftheBig
Bang when the universe was one unit of Planck time old τu 1 and had Гu 1. We have
previouslybeenusing torepresentoneunitofcoordinatelengthinauniversewhereГu 1.
However,nowitisnecessarytoaddasubscript“1”tothisdesignationtoconformtoapattern
whereallunitsofphysicsneedtobespecifiedwhenГu 1.Forexample, E1, Q1and U1willbe
used to specify a unit of energy, charge and energy density respectively when Гu 1. The
symbols 1and 1willbeusedtospecifyaunitofmassandtimerespectivelyatthestartofthe
BigBangwhenΓu 1.
Inchapter3thesubscript“g”wasusedtospecifyalocationingravity.Theanalogouscondition
whendealingwiththeevolutionoftheuniverseistospecifytheunitofphysicswhenitfeelsthe
effectofabackgroundgravitationalgammathatisgreaterthan1 Γu 1 .Thisconditionwill
bespecifiedbythesubscript“u”.Forexample,aunitoflength,timeandmasswhenΓu 1will
bedesignatedasLu,TuandMurespectively.Fortheevolutionoftheuniversethetimeandmass
transformations are similar to those in chapter 3 but with new symbols. Only the length
transformation equation is not analogous to Lo Lg from chapter 3. The new length
transformationequationneeds tospecifythefactthatwearenowrecognizingthechangeina
unitoflengththatscaleswithΓu.Thereforewehave:
1 ГuLuunitoflengthtransformation
1 Tu/Гuunitoftimetransformation
1 Mu/Гuunitofmasstransformation
Inutilizingthemasstransformation 1 Mu/Гu,itisimportanttorecalltheassumptionstated
inchapter3thatthesamerateoftimemustbeusedtoquantifyboth 1and Mu.Massisa
measurementofinertia,whichinturninvolvesforceandacceleration.Alloftheseimplytheuse
of a rate of time. Mass is not synonymous with matter. In chapter 3 we often assumed that
coordinatetimewouldbeused.However,inthecurrentuniversewithГuo 2.6 1031,therate
ofcoordinatetimeontheГ 1clockisabout2.6 1031timesfasterthantherateoftimeonthe
cosmicclock,soitmightnotbeconvenienttousecoordinaterateoftime.Allthatisimportant
isthatwerememberthatthetransformationofunitsrequiresthatweusethesamerateoftime
toexpressboth 1andMuorotherunitsofphysicsatdifferentagesoftheuniversewithdifferent
valuesofГu.
Because of the change in the length transformation, it is necessary to recalculate the other
transformationsusingthedimensionalanalysisproceduresestablishedinchapter3.Usingthe
abovetransformationsforunitsoflength,timeandmassweobtain:
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Impedance of Spacetime Zs :Zs1→
1/
1
Г
→Zsu
Zs1 Zsuimpedanceofspacetimetransformation
Energy E:E1→1
2
1 /
1
Г
Г
→Г3Eu
Г
E1 Гu3Euunitsofenergytransformation
Energy Density U:U1→1/
1
2
1 /Г Г
/Г
→Uu
U1 Uuunitsofenergydensitytransformation
Coordinate Speed of Light : 1→
1/
1
Г
→Г2 u
/Г c 1 Γu2 ucoordinatespeedoflighttransformation
Thesearethemostimportanttransformationsandsomeofthemwillbeusedtodeterminethe
currentvacuumenergydensityandanalyzethe10120mystery.First,theimpedanceofspacetime
shouldbeunaffectedbyachangeinГu.Thefactthatthetransformationgave Zs1 Zsu shows
that the length, time and mass transformations are correct. This acts as a check on the
transformationprocess.Aboveweassumedthemasstransformationwasthesameaschapter3.
In truth, this was not a foregone conclusion. However, the impedance of spacetime should
remainconstant.Assumingthelengthandtimetransformations,thereisonlyonepossiblemass
transformationthatachievesaconstantimpedancetransformation.
Energy and Energy Density Transformations: Next, the units of energy transformation
E1 Гu3Eu will be illustrated with an example. Suppose that there was an electron in a
hypotheticaluniversewithГ 1.TheenergyoftheelectronintheГu 1universewouldbe
8.19 10‐14Joulesmeasuredlocallywhichisthesameenergywewouldmeasurefortheelectron
inourcurrentuniverse.However,themeasurementintheГu 1universeusedalocalclockthat
isrunning2.6 1031timesfasterthanthecosmicclockinourcurrentuniverse.Furthermore,a
meterintheГu 1universeis2.6 1031timeslargerthanameterinourcurrentuniverse.Both
ofthesefactorscombinetomake1JouleintheГu 1universeequivalenttoГuo3 1.8 1094
joules in our current universe. Therefore, even though both electrons have the same energy
measured locally, different standards of energy are being used. When we correct for this
difference,theelectronintheГu 1universehasГuo3 1.8 1094moreenergy.
Using the rotar model, suppose that we wanted to compare the energy density of the Гu 1
electronandanelectronintheuniversetoday.Thetransformationofunitsoflengthis 1 ГuLu.
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ThissaysthatameterintheГ 1universewouldbeabout2.6 1031timeslongerthanameter
stickinourcurrentuniversebecausewearelivinginauniversewithГu 2.6x1031.Therefore,
therotarradiusoftheelectronintheГ 1universewouldbe2.6 1031timesbiggerandthe
rotarvolumeofthatelectronwouldbeГuo3 1.8 1094timesgreaterthantherotarvolumeof
anelectroninouruniverse.Theresultisthatbothelectronswouldhavethesameenergydensity
because the 1.8 1094 difference in the electron’s energy is offset by the factor of 1.8 1094
differenceinthesizesoftherotarvolumes.Thetransformationofenergydensityisshownabove
andresultsinU1 Uu.
This illustrates how the proper energy density of the universe (including vacuum energy)
remains constant even when the universe experiences a vast increase in Гu.
This is a fantastic result because it is a key component in solving the mystery of the 10122
differencebetweenvacuumenergydensityandcurrentlyobservedenergydensity.Whenthe
universe was Planck spacetime, it had energy density of 5.53 10112 J/m3. The spacetime
transformation model of the universe views the current universe as the same size and same
energydensityasPlanckspacetime.Therefore,thetransformationU1 Uusaysthattheproper
energy density of the universe equals the tremendously large energy density of the universe
obtainedwhentheenergydensityisexpressedincoordinateunits.Itisnotnecessarytoadd
energytotheuniversetokeeptheenergydensityofvacuumenergyconstant.Instead,nature
usestwodifferentstandardsforaunitofproperenergy inadditiontodifferentstandardsof
length,force,therateoftime,etc. Thisdifferenceinenergystandardsexactlyoffsetthechange
in proper volume thereby maintaining a constant energy density. The total proper energy
densityoftheuniverse includingvacuumenergy hasremainedconstantat5.53 10112J/m3
sincethebeginningoftime sincetheBigBang .Todayalmostallofthisenergyoftheuniverse
isintheformofvacuumenergy.
Additional Transformations: If we carry these transformations further, we obtain a few
counter‐intuitiveresults.Forexample,thetransformationsofcharge Q andmomentum p are:
Q1 ГuQuunitofchargetransformation
p1 Гupuunitofmomentumtransformation
Atfirstthesetransformationsseemtobesayingthatneithercharge Q normomentum p is
conservedwhentheuniverseagesandГuincreases.However,thesearethetransformations
requiredtopreservecharge,momentumandthelawsofphysicswhenmeasuredlocally proper
measurement andassumingaCMBrestframewhichhasthedistancebetweenpointsincrease
withtheHubbleflow.Themomentumtransformation p1 Гupu willbeusedtoillustratethis
point.
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Wewillstartwithathoughtexperiment.Supposethatthereisahydrogenatominanexcited
statethatisatrestrelativetotheCMBandalsoatrestattheoriginofacoordinatesystem.The
hydrogen atom emits a photon in the Y direction and the photon’s momentum causes the
hydrogen atom to recoil in the – Y direction carrying the opposite momentum. As shown in
chapter5,themomentumimpartedtotheatombytheemissionofaphotonresultsintheatom
havingadeBrogliewavelengththatequalsthewavelengthoftheemittedphoton.Ifweview
thisfromarigidframeofreferencethatdoesnotexpandwiththeHubbleflow,thenthereisno
lossofmomentumovertime.However,ifweviewboththerecoilingatomandthepropagating
photon from a coordinate system that expands with the Hubble flow, then relative to this
coordinatesystemthereisalossofmomentum.BoththephotonandthedeBrogliewavesofthe
atomundergoaredshift losemomentum relativetoacoordinatesystemthatexpandswiththe
Hubbleflow.Thecoordinatesystemusedbythespacetimetransformationmodelisrigidbut
the effect of an increasing Γu produces effects similar to adopting an expanding coordinate
system. Therefore the equation p1 Гu pu is merely expressing this difference in perceived
momentumbetweenthetwocoordinatesystems.Similarly,thechargetransformationQ1 ГuQu
keepstheproperlawsofphysicsunchangedinbothanexpandingcoordinatesystemandinthe
spacetimetransformationcoordinatesystemasГuincreases.
10120 Calculation:Nowwearegoingtocalculatethecurrentratioofvacuumenergydensityto
observableenergydensity.APlancksphereoriginallycontainedaboutabillionJoulesmeasured
usingthecoordinateenergystandardofenergybecausetheuniversestartedasPlanckspacetime
withГu 1.ThePlanckspherestartedwithradiusofPlancklengthandtodaythepropervalue
of this radius has increased by a factor of Гuo 2.6 1031 to 0.42 mm radius or a volume of
3.1 10‐10m3.The109JofcoordinateenergywhenГu 1hashadanapparentincreasesothat
currentlythismuchenergywouldappeartohaveincreasedbyafactorofГuo3.Theobjectiveof
thefollowingcalculationistofindthecurrentvacuumenergydensityUvac.
109J Гuo3 1.8 10103Jconversionofcoordinateenergytoproperenergy
4π/3 lp3Гuo3 3.18 10‐10m3currentpropervolumeofPlancksphere
1.8 10103J/3.18 10‐10m3 5.5 10112J/m3 Uvac
Ignoringvacuumenergy,thecurrentcriticalenergydensityoftheuniversedependsonthevalue
of the Hubble parameter used. Using 70.8 km/s/Mpc the critical energy density of the
universeUcritisabout8.5 10‐10J/m3ifweincludehypotheticaldarkenergy.Ifweexcludedark
energy which represents about 72.1% of the total energy density, then we have observable
energydensityUobsofabout2.36 10‐10J/m3.
Uvac/Ucrit 5.5 10112J/m3/8.5 10‐10J/m3 6.5 10121ratioincludingdarkenergy
Uvac/Uobs 5.5 10112J/m3/2.4 10‐10J/m3 2.3 10122ratioexcludingdarkenergy
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Either of these numbers qualifies as the famous 10120 discrepancy between the theoretical
energy density of the universe and the observed energy density. Here is how we achieve
sphericalPlanckenergydensityusingoneofthe5wave‐amplitudeequations U H2ω2Z/c .
Usingtheproperrateoftimeonthecosmicclock,thefrequencyappearstobePlanckangular
frequency ωp.Furthermore,strainamplitudeisadimensionlessnumberthatdoesnotchange
withГu.ThereforewewillinsertH 1.Finallywemustinserttheconstantk’toconvertfrom
cubictosphericalwiththefactorof½associatedwithzeropointenergy.
U H2ωp2Zs/csetωp 1.855 1043s‐1;Zs 4.038 1035kg/s;H 1andaddk’ 3/8π
Ups k’H2ωp2Zs/c 3/8π 12 1.855 1043 2 4.04 1035 /3 108
Ups 5.53 10112J/m3
Ups Uvac Uobs
Thespacetimetransformationmodeloftheuniverseproposesthatovertheageoftheuniverse
therehasbeennochangeinthetotalenergydensityoftheuniverse.Todayvirtuallyallofthe
energydensityoftheuniverseisintheformofvacuumenergyUvacwhichlacksquantizedangular
momentum.However,atthestartoftheBigBangalltheenergydensityofPlanckspacetimeUps
was observable energy density Uobs because all the energy possessed quantized angular
momentum.Overtimethetransformationofspacetimehasresultedinadramaticdecreasein
theobservableenergydensityoftheuniverseandanequalincreaseinvacuumenergydensity
of the universe. Today Uvac 10122Uobs but the total energy density has not changed:
Uvac Uobs Ups.
Todayweperceivethemaximumfrequencyofthewavesthatformvacuumenergytobeequal
to Planck angular frequency. However, this is a proper frequency that has been slowed by a
factorofГuo 2.6 1031comparedtothecoordinatefrequencythatoccurredwhentheuniverse
wasPlanckspacetime.Howisitpossiblefortoday’svacuumenergytopossessvirtuallythesame
energydensityasPlanckspacetimeifthecurrentmaximumfrequencyofthedipolewavesisa
factorofabout2.6 1031timesslowerthanthedipolewavesthatformedPlanckspacetime?The
answertothisquestionisanalogoustotheanswergivenpreviouslyinthesectiontitled“Energy
andEnergyDensityTransformations”.Thereitwasshownhowtheenergydensityofanelectron
remainsconstantevenwhenthereisabigincreaseinГu.Theenergyscalesproportionalto1/Гu3
butthevolumealsoscaleswith1/Гu3sotheenergydensityoftheelectronremainsconstant..
This holds true for any dipole wave in spacetime that has a specific frequency and strain
amplitude.ThehighestfrequencydipolewaveshaveaproperfrequencyequaltoPlanckangular
frequencyωpandapropervolumethatisPlancklengthinradius.However,thisvolumeis1/Гu3
times smaller than it was in Planck spacetime. The wavelets that form vacuum energy are
continuously forming new wavelets as previously explained. These wavelets adapt to the
changingscaleoflength.
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Illustrations Showing the Effect of Гu on Waves:Next,wewanttoseewhathappenstothe
wavesinspacetimethatformvacuumenergywhenthereisanincreaseofГu.Themysterytobe
explainedishowthewavestructureofvacuumenergychangestoresultinanincreaseinproper
volumeastheuniverseages.Infigure14‐2wehavetwosinewavesdesignatedwave#1and
wave #2. These are crude representations of the dipole waves in spacetime responsible for
vacuumenergy.Sincethenonlinearityisparticularlystrongintheearlypartoftheevolutionof
theuniverse,insteadimaginetheseasrepresentingvacuumenergyatmorerecenttimes.Infact,
wave#2canbethoughtofasrepresentingvacuumenergytodaywithГuo 2.6 1031andwave
#1 representing vacuum energy when the comoving grid was 1/3 its current size which is
equivalent to Гu 1031 . Therefore, it is important to remember that there is a factor of 3
differencebetweenthevalueofГuforwave#1comparedtothebackgroundgammapresentfor
wave#2.Thisiswrittenas3Гu1 Гu2.
Bothofthesewaveswouldbeexactlythesameiftheyweredrawnusingproperunitsoflength.
ThedisplacementamplitudeofbothwavesisdynamicPlancklengthwhenthedisplacementof
spacetimeisexpressedinunitsofproperlength.However,figure14‐2usescoordinatelength
forboththe andYaxis.Therefore,thespatialdisplacementamplitudeofwave#1is3times
largerthanthespatialdisplacementamplitudeofwave#2becauseofthefactorof3difference
betweenГu1andГu2.Thedisplacementamplitude Yaxis issetsothatwave#1hasamplitude
of 1. This makes the coordinate amplitude of wave #2 equal to 0.333. If the displacement
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amplitudewasexpressedusingtheabsolutecoordinatescalewherePlancklengthequals1when
Гu 1,thenwave#1wouldhaveadisplacementamplitudeof10‐31.Thisisbecausewave#1is
presumedtoexistinauniversewithabackgroundvalueofГu 1031.ThislargevalueofГu
contractsproperlengthcomparedtoaunitofcoordinatelength 1.
Themaximumslopeofasinewaveoccurswhenthesinewavecrossesthezeroline.Thearrow
showsoneofmanypointswherethetwowaveshavethe“samemaximumslope”.Thisslopeis
adimensionlessnumberthatisthestrainamplitudeofthesinewave.Thepointofthisfigureis
toshowthatthemaximumslopeisthesameeventhoughthewaveshaveadifferentscale.The
strainproducedbywavesinspacetimeisproportionaltothemaximumslope.Thereforeboth
waveshaveastrainamplitudeofH 1.Naturally,theslopewouldalsobethesameifthewaves
were drawn using proper length because both waves would then be exactly the same in
displacement, wavelength and maximum slope. The waves that form vacuum energy can
maintainthesamestrainamplitudeevenwhenГuisincreasing.Thefrequency,measuredlocally,
remainsthesamesotheproperenergydensityalsoremainsconstantwhenГuincreases.The
pointisthatthestrainamplitudeisalwaysH 1forallvaluesofΓu.Thisisakeycomponentin
maintaining the total energy density of the universe at 10113 J/m3 throughout the age of the
universe.
Itisinterestingtonotewhatthesewaveswouldlooklikeiftheywereplottedinthetemporal
domain rather than the spatial domain. The Y axis would be labeled “Coordinate Temporal
DisplacementAmplitude”andthe axiswouldbelabeled“CoordinateTime”.Thefigurewould
physicallylookthesameasfigure14‐2exceptthatthelabelsforwave#1and#2wouldbe
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reversed.Wave#2 largervalueofГu wouldhavethelargertemporaldisplacementamplitude
whenmeasuredincoordinateunitsoftime.Thiscomparisonhelpstoillustratehowachangein
Гuexchangesthetemporalpropertiesofspacetimeforthespatialpropertiesofspacetime.
Figures 14‐3 shows a 3‐dimensional plot of wave #1 in figure 14‐2 and figure 14‐4 shows a
3‐dimensionalplotof3layersofwave#2infigure14‐2 originaldefinitionsofГu .Thesetwo
figures are oversimplified. The wave structure should be more chaotic and unsymmetrical.
Imaginethewavesinfigure14‐4asoscillatingat 1/3thefrequencyofthewavesinfigure14‐3.
Thegridpatterninfigure14‐4isonly 1/3thecoordinatelengthsoeachgridcubehasonly 1/27
thecoordinatevolumeofthegridcubeinfigure14‐3.However,eachgridcubealsoonlycontains
1/ thecoordinateenergyasthegridcubeinfigure14‐3,sotheenergydensityisthesameno
27
matter whether it is assessed using the proper standard of energy density or the coordinate
standardofenergydensity.
Quantummechanicshasbeentellingusthatthevacuumenergydensityshouldbeconstanteven
as the universe ages and the proper volume increases. Now it is possible to see that the
spacetimebasedmodeloftheuniverseshowsthatthisispossible.Infact,inorderforthelaws
ofphysicstoremainconstant,itisnecessarythatthevacuumenergydensityremainsconstant.
Ifthevacuumenergydensitydecreasedasthepropervolumeoftheuniverseexpanded,thenthe
highfrequencyvirtualparticlepairswouldeventuallybelostandthiswouldbedetectable.
Does Dark Energy Exist? Darkenergyissupposedlyahomogeneousformofenergythatforms
asthevolumeoftheuniverseexpands.Everythingabouthypotheticaldarkenergyconflictswith
the concepts presented in this book. There is no single explanation for dark energy, but the
simplestexplanationgivenfortheexistenceofdarkenergythatscaleswithvolumeisthatdark
energyis“thecostofhavingspace”.Eachtimecosmicexpansionsomehowcreatesanadditional
cubicmeterofspacetime;thisvolumeissupposedlyleftwithanenergydeficitofabout6 10‐10
Joulesof“negativeenergy”thatisconsideredtobedarkenergy.Intheearlyuniverse,whenthe
energy density of matter and photons washigher, 6 10‐10 J/m3 was insignificant. However,
todaythepropervolumeoftheuniversehasincreased.Thedensityofmatterandlighthasfallen
sothattodaydarkmattersupposedlymakesupabout73%oftheenergydensityoftheuniverse.
Inthisconcept,gravityisattemptingtocollapsetheuniverse,butdarkenergyopposesgravity
andcausesanacceleratedexpansionoftheuniverse.Theexactmechanismusedtoaccomplish
thisacceleratingexpansionisvague.Ifitistheoppositeofgravity,thenthiscreatesaproblem
forthemodeloftheuniverse.Recallthatitwaspreviouslyshownthatgravitationalacceleration
requiresagradientintherateoftime.Therefore,anythingthatcausesananti‐gravityrepulsion
mustaccomplishthisbyarateoftimegradientthatopposesgravity.However,theobserved
redshiftofgalaxieswouldrequirealargescalegradientintherateoftime.Theproblemisthat
alargescaletimegradientintheuniverseisincompatiblewiththeconceptthattheuniverseis
homogeneousbothspatiallyandtemporallyonthelargescale.
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TheΛ‐CDMmodeldoesnotrespecttheconditionsthatmustbemettocreateacubicmeterof
“new”space.Creatingevenacubicmeterofnewspacerequiresalotofconditionstobemet.
This new space must have the impedance of spacetime Zs c3/G and the interactive bulk
modulusofspacetimeKs Fp/λ2.Thenewspacemustbefilledwithzeropointenergyatenergy
density of 10113 J/m3. Therefore, each new cubic meter requires more energy than the
annihilation energy of entire observable universe. As before, the problem is in the physical
interpretationofobservationsandequations.Iftheproperdistancebetweengalaxiesincreases,
thiscanbeinterpreteddifferentways.Themodelproposedhereisactuallythesimplestbecause
itdoesnotdemandanynewphysicsornewenergytobeaddedtotheuniverse.Itdoesnot
requiremysteriousdarkenergy.
Thereisnodirectexperimentalevidencethatdarkenergyexists.Darkenergyisatheoretical
conceptispostulatedtoexplaintheapparentaccelerationoftheexpansionoftheuniverseand
also to explain that the energy density of the universe has fallen below the “critical density”.
Baryonic matter, dark matter and radiation only achieve about 28% of the energy density
calculatedtobenecessarytoachieveflatspacetime.However,thiscalculationdependsonthe
accuracyofthemodeloftheuniversebeingused.Theconceptof“criticaldensity”oftheuniverse
assumesthattheuniversepossessesagravitationalgradient.Thisdoesnotexistinthecondition
previously described as “immature gravity”. It does not make any difference whether the
immaturegravityoccursinthelowgravitationalГofthedustcloudthoughtexperimentorthe
highgravitationalГuoftheuniverse.Theimportantpointisthatimmaturegravityproducesan
increasinggravitationalГuandauniforminstantaneousrateoftimeintheCMBrestframe.If
thereisnolargescalerateoftimegradientfromthemidpointobserverperspective,thenthere
is no large scale gravitational acceleration and nothing that demands an explanation that
incorporatesanti‐gravity.
Theconceptofcriticaldensityoftheuniverseassumesthatthereisagravitationalacceleration
thatisattemptingtocollapsetheuniverse.Iftheuniverseispicturedasthehomogeneousand
static distribution of galaxies with proper volume increase because of the spacetime
transformationoftherateoftimeandofproperlength,thentheuniverseisnotstrugglingto
expand against gravity. There is no such thing as a critical density. The dust cloud thought
experimentdidnotmeettheconditionsof“criticaldensity”andyettherewasnogravitational
accelerationinthefirstfewmillisecondsaftergravitywas“turnedon”.
As long as the universe has no detectable boundary no edge , the mature gravity condition
cannotbeestablished.Ittakesadensitychangeataboundarytoestablisharateoftimegradient
and gravitational acceleration. The proposed model of the universe started with Planck
spacetimethathadauniformrateoftime.Atspeedoflightcommunication,westillhaveno
detectableboundary.Therateoftimehassloweddownbuttherestillisnolargescalerateof
time gradient. Gravitational acceleration and curved spacetime both require a rate of time
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gradient. Therefore, the universe has never possessed large scale curved spacetime or
gravitationalacceleration.Newmass/energywillcontinuetoappearontheparticlehorizonof
theobservableuniverse.ThebackgroundГuoftheuniversewillcontinuetoincreasetowards
infinityandtherewillbenorateoftimegradientonthescaleofuniversalhomogeneityunless
one day we become aware of a large scale density discrepancy that is the equivalent of a
boundaryconditionthatgivesan“edge”totheuniverse.
Dark Energy Not Needed:Whatisbeingproposedisthatthespacetimetransformationmodel
doesnotrequiretheinventionofdarkenergytoprovidethemissingcriticaldensityanddoes
not need any mysterious force with anti‐gravity properties that is causing the apparent
expansionoftheuniversetoaccelerate.Whenviewedfromtheproposedcoordinaterateoftime
and coordinate unit of length, there is no expansion of the universe. No work is being done
againstgravity.Theimmaturegravityconditionpreviouslydiscussedeliminatesthetendency
fortheuniversetohaveagravitationalcontraction.Thecoordinatevolumeoftheuniversehas
never changed and the coordinate energy density including vacuum energy has remained
constantatthelargescaleof300,000lightyears.Atasmallerscalematterhasformedstarsand
galaxies which distort the homogeneous energy density of vacuum energy. We call this
distortion “curved spacetime”. Our perception of the volume of the universe indicates
continuousexpansion.However,thisistheresultofacontinuousincreaseinthebackgroundГu
of the universe. What we perceive as acceleration of the expansion is due instead to an
accelerationintherateofchangeofdГu/dτu.
AllthefactorsthatdeterminedГu/dτu therateofchangeofГuinpropertime arenotknown.
This would be a function the age of the universe, but it probably also includes other factors
relating to the composition and the observable energy density of the universe. For example,
whentheuniversewasradiationdominated,asubstantialamountoftheobservableenergywas
beingconvertedtovacuumenergy.ThisprocessresultedindГu/dτubeingproportionaltoτ1/2.
Duringthematterdominatedepochtheelectromagneticradiationwasasmallpercentageofthe
observable energy of the universe and dГu/dτu was proportional to τu2/3. Today we have an
increaseinpropervolumethatisacceleration.Ifthisisviewedasanaccelerationintherateof
changeofdГu/dτu,thenamysterystillexists,butitdoesnotdemandtheinventionofdarkenergy
foranexplanation.Thesolutionistobefoundinthepropertiesofspacetimethatcreatethe
accelerationofdГu/dτuforthecurrentconditionoftheuniverse.
Offsetting the Rate of Change of Гu:ReturningtotheincreaseinГu,howfastwouldanobject
needtoberaisedintheearth’sgravitationalfieldinorderforthedecreaseintheearth’sГto
offset the increase in Гu of the universe? In other words, what rate of increase in elevation
achieves dГ/dt /Г 2.29 10‐18s‐1intheearth’sgravitationalaccelerationof9.8m/s2?
g c2
c2
Г
Г
set
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Г
Г
set
Г
Г
andg 9.8m/s2
.021m/s
verticalvelocity
Thereforeanelevationvelocityofabout2.1cm/sorabout75metersperhourintheearth’s
gravityoffsetsthetemporaleffectsofanincreaseintheГuoftheuniverse.Obviouslythisisonly
atemporaryreprievemadepossiblebecauseanobjectintheearth’sgravitystartsoffatalower
energystate largertotalГ thanthesameobjectifitwasisolatedonthecomovingcoordinate
system.Still,thisexamplegivesaphysicalfeelfortherateofchangethatiscurrentlytakingplace
intheuniverse.
Allphysicalobjectsarelosingenergyeachsecondwhenmeasuredwithanabsoluteenergyscale
thatdoesnotdecreaseasΓuincreases.Forexample,thesuniscurrentlyradiatingabout4 1026
wattsofelectromagneticradiationbutthesunislosingabout1000timesthisenergypersecond
astheenergyinthesun’srotar’sisbeingconvertedtovacuumenergy.Thisisanundetectable
effectusingtheproperenergystandardwhichdoesnotacknowledgetheeffectofanincreasing
Γuoneverythingintheuniverse.
Thereisanotherinterestingwayoflookingatthechangingrateoftimeastheuniverseages.An
electronhastwodifferentratesoftimeinitstwolobesasexplainedinchapter5.Theseratesof
timedifferbyαβ 4.18 10‐23.HowmanysecondsdoesittakeforΓutochangebyafactorof
4.18 10‐23?Inotherwords,whatdifferenceintheageoftheuniverseproducesarateoftime
differenceequaltotherateoftimedifferenceinanelectron?
Aβ/ 4.18 10‐23/2.29 10‐18s‐1 1.8 10‐5second
Time’s Arrow:Theequationsofphysicsseemtobereversibleintime.Exceptforentropy,it
appearsasifitshouldbepossibletogobackwardsintime.However,ifthebackgroundГu ofthe
universeisincreasingcontinuouslyandallmatterisconvertingenergyintovacuumenergy,then
itisnotpossibletogobackwardsintime.Yesterdayalltherotarsandphotonsintheuniverse
hadmoreenergythantheypossesstoday measuredonthescaleofcoordinateenergy .Also,
thelowerbackgroundГuofyesterdayalsoaffectsmanyotherthingssuchastheunitsofforce,
velocity,voltage,etc.Eventhoughthelawsofphysicsarethesametodayandyesterday,allthe
components that makeup the universe are different. The universe is undergoing a
transformationandthismakesTime’sarrowonlypointonedirection–tothefuture.
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Black Holes: Thefollowingdiscussionofblackholesismorespeculativethantherestofthis
book.Thereforethefollowingshouldbeconsideredjustafewpreliminarythoughtsaboutblack
holes.
Doblackholeshaveadifferentstructureinaspacetimebaseduniversethantheywouldhaveif
theuniverseispopulatedbypointparticles?Sofarthegeneralrelativityanalysisofblackholes
hasindirectlyassumedthestandardmodelofparticles.Withthepointparticleassumption,a
blackholehasanaccretiondisk,aneventhorizon,avolumeinsidetheeventhorizonandfinally
asingularityatthecenter.Thissingularitysupposedlyhasinfiniteenergydensity thesameas
point particles . The volume inside the event horizon supposedly has modulation of the
propertiesofspacetimethatwouldrequireinexcessof100%depthofmodulationofspacetime.
Clearly these conditions cannot be achieved by the spacetime based model of the universe
proposedhere.Theeventhorizonofablackholesupposedlyhasarateoftimethatisstopped
andacoordinatespeedoflightequaltozero.Itisquestionablewhetheracompletestoppageof
therateoftimeandstoppingthepropagationoflightcanbeachievedbythewave‐basedmodel
ofhadronsandbosonsproposedhere.
Ifyourmodelofafundamentalparticleisapointparticlewithnophysicalsizeandnostructure,
thensuchaparticlewouldbeabletosurvivetheplungepasttheeventhorizonofablackhole.
However,ifweassumetherotarmodelofmatter,thenapreliminaryanalysisseemstoindicate
adifferentanswer.Aspreviouslyexplained,arotarisjustaslightdistortionofspacetimethat
hasaspecificfrequency,rotarradius,anddisplacementamplitude.Itseemsasifaspacetime
basedexplanationoftheuniversecannotformatrueblackholeeventhorizon.Thisisbecause
suchaneventhorizonwouldeliminatethewavesinspacetimerequiredforitsformation.Ifa
masscollapsedtoadegreethattherateoftimeissloweddownbyanenormousamountsuchas
1020 or more compared to the comoving rate of time , then externally this would be
indistinguishablefromaconventionalblackhole.Inthisscenario,afterablackholeforms,all
additionalmass/energythatfallstowardstheblackholeaddstotheorbitingaccretiondiskand
neverreachesaneventhorizon.Thespacetimewavepropertiesofrotarsandphotonswould
have to be taken into consideration in order to properly characterize the accretion disk that
neverquitereachesaneventhorizon.Ifhadronsandbosonsneverquitereachatrueevent
horizon,thenthiswouldexplainhowitispossibleforinformationabouttheblackhole’scharge,
magneticfield,massandrotationaldirectioncanbecommunicatedtotherestoftheuniverse
outsideoftheblackhole.
Likeanygravitationalcapture,massmustshedsomeenergyinordertobecapturedbyapseudo
black hole. This sheading of energy is done by the emission of radiation and by the energy
emittedbythepolarjetsassociatedwithblackholes.Theenergythatiscapturedcanchangeits
formbutitsgravitationaleffectremainsconstant.Recalltheexamplepreviouslygivenofaplanet
inahighlyellipticalorbitaroundastar.Thetotalgravitationaleffectofthecombinationofthe
starandtheplanetisconstanteventhoughtheenergyintheplanetchangesform.Similarly,a
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photonfallingintoapseudoblackholewouldappeartobeblueshiftedifthephotoncouldbe
observedlocallyinaregionwithahighgravitationalgammaГ.Arotarwouldgainkineticenergy
tooffsetthelossofinternalenergyassociatedwithahighГ.Inneithercasedoestheenergypass
aneventhorizonwherecontactwiththeoutsideuniversewouldbelost.
Themodelofspacetimecurrentlyacceptedisthattheeffectsofcurvedspacetimecansomehow
transcendaneventhorizon.Wecanobviouslyaccuratelymeasurethemass,spinandchargeof
ablackhole.Theseareexamplesofcommunicationthatappearstobecomingfrominsidean
eventhorizon.Thespacetimebasedmodelofgravityrequireswavesinspacetimetoproducea
nonlinearinteractioninspacetime.Whentheenergydensityofmatterandradiationapproaches
the energy density that would require 100% modulation of the spacetime field then we are
approachingtheconditionsofablackhole.However,thespacetimebasedmodelneveractually
reaches100%modulationofspacetime.Timeneverquitestopscomparedtocoordinatetime
and length never quite contracts to zero compared to coordinate length. The singularity
associatedwiththeconventionalblackholerequiresenergydensityinexcessofPlanckenergy
density. This is usually “explained” by saying that “the laws of physics break down”. The
spacetimebasedmodeloftheuniverseneverrequiresthatthelawsofphysicsbreakdown.
Ivisualizethevolumenearthecenterofawavebasedblackholetobeprimarilyphotonsthat
havebeenhighlyblueshiftedrelativetothelocalrateoftime.Matterfallingintotheaccretion
diskwillundergohighlyenergeticcollisions.Whilenewparticleswouldbeformed,repeated
collisionsanddecompositionswouldeventuallyresultinahighpercentageoftheenergybeing
photons. Therefore, photon density would increase with depth. There would be no event
horizon,butenergyintheaccretiondiskwouldcausethegravitationalgammaГtoapproach
infinity.Forexample,supposethatthisenergydensityachievesarateoftimethatis1020times
slower than the surrounding volume of the universe. This would look like a black hole, but
information about charge, mass and rotational direction could still be communicated to the
surroundingspace.
The Spacetime Transformation Model Versus The Inflationary Model:Inchapter13we
performed several calculations to find the value of Гuo. However, the same data can be
rearrangedtosupportthecontentionthattheproposedspacetimetransformationmodelofthe
universeiscorrectandthattherewasnotaninflationaryphase.Hereisthereasoning.When
wecalculatethechangeinscalefactorstartingfromoneunitofPlancktime ~5 10‐44s and
endingwith13.7billionyears,weobtainedscalingfactorsof2.1,2.6,2.95andanupperlimitof
3.4 all 1031 .Thesenumbersareapproximatelythesameyettheywereobtainedfromdiverse
sources such as the currently observable energy density of the universe, the observed CMB
temperatureandtheCMBphotonenergydensity.
Nowwewillreversethethoughtprocessandextrapolatebackintimetowhentheuniversewas
5 10‐44 seconds old 1 unit of Planck time . Starting with the currently observable energy
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density,CMBtemperatureandCMBphotonenergydensityoftoday’suniversewealwaysarrive
at the properties of Planck spacetime using an average value of Γuo 2.6 1031. This
extrapolationmakestheassumptionthattherewasnoinflationaryphaseintheexpansionofthe
propervolumeoftheuniverse.
However, suppose that we include inflation in this backwards extrapolation. Between about
10‐35secondsand10‐32secondswehavetodeviatefromtheradiationdominatedconditionthat
scaleswithτu1/2andinserttheinflationaryexponentialscalingfactor.Thisinflationfactoris
unknown, but it is usually considered to be in excess of 1025. At an age of 5 10‐44 second,
includinginflationimpliesthattheenergyperphotonexceedsPlanckenergybyafactorofat
least1025.SimilarlytheimpliedtemperatureexceedsPlancktemperaturebymorethan1025and
theimpliedenergydensityexceedsPlanckenergydensityalsobyasimilarfactor.Theseare
impossibilitiesaccordingtotheknownlawsofphysics.Thereforephysicistscasuallydisregard
thisbysayingthatthelawsofphysicsmust“breakdown”undertheseconditions.Eventheidea
thattheinflationaryexpansiongreatlyexceededthespeedoflightrequiresabreakdownofthe
lawsofphysics.
Thereisnoexperimentalproofthatitispossibleforthelawsofphysicsto“breakdown”.Thisis
merelyatermusedwhenaparticulartheorygivesanimpossibleansweraccordingtotheknown
lawsofphysics.Instead,whenatheoryrequiresabreakdowninthelawsofphysics,thisshould
beastrongindicationthatthetheoryiswrong.Thebeautyofassumingthattheuniverseisonly
spacetimeisthatthereshouldbenocaseswherethetheoryneedstoreverttosayingthatthe
lawsofphysicsmustbreakdowninordertoexplainaparticularimpliedresult.
Cosmicinflationisanadhocsolutionrequiredbyamodeloftheuniversethathaspointparticles
andforcescarriedbytheexchangeofvirtualparticles.Iftheuniverseisonlyspacetime,thenit
wasonlyspacetime thecompositequantummechanicalandrelativisticspacetimemodel even
at the beginning of the Big Bang. Extrapolating backwards from today results in the “Planck
spacetime”homogeneousstate.Thisisthehighestobservableenergydensitythespacetimefield
cansupport.Thelawsofphysicsneverbreakdown.Forexample,therearenosingularitiesin
thisspacetimebasedmodeloftheuniverse.Allthestepsareconceptuallyunderstandableand
accessible to physicists today. Planck spacetime is as homogeneous as quantum mechanics
allows,sothereisnoneedforinflationtoexpandspacetimetoachievelocalhomogeneity.
Unity and Entanglement Revisited: It was previously proposed that quantized waves in
spacetimesuchasrotarsandphotonscanhaveinternalcommunicationfasterthanthespeedof
light.Thispropertyalsoextendstocommunicationbetweentwoentangledphotonsorrotars.
Noinformationcanbeimposedonthisinternalcommunicationsothereisnoviolationofthe
prohibition against faster than light communication. Still there is a question about how
spacetimeaccomplishesthefasterthanspeedoflightinternalcommunication.Onepossibility
isthatthisinternalcommunicationmightbetakingplaceatthespeedoflightcharacteristicof
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Planckspacetime.Thisspeedwouldbeabout2.6 1031timesfasterthantheproperspeedof
light. At this speed, internal communication within a photon distributed over one light year
wouldonlytakeabout10‐24secondandaCMBphotongenerated380,000yearsaftertheBig
Bangwouldcollapsewithinabout10‐14seconds.ThemicrowavephotonsthatmakeuptheCMB
haveapeakfrequencyofabout1.6 1011Hz.Thereforeacollapsewithatimedelayofabout10‐
14 s would meet the conditions of being virtually instantaneous. Perhaps the internal
communicationisactuallyinstantaneous,butcommunicationat2.6 1031timesfasterthancis
indistinguishablefrombeinginstantaneous.
Are All Frames of Reference Really Equivalent?Abasicassumptionofrelativityisthatall
frames of reference are equivalent. The CMB rest frame is clearly the preferred frame for
cosmologicalpurposes,butthelawsofphysicsarepresumedtoworkequallywellinallframes
of reference. Experimental observations have not detected any preference for frames of
reference,butdoesthismeanthatultra‐relativisticframesrelativetotheCMBrestframeare
equivalent?Recallthatinchapters4and11thesubjectofthespectralenergydensityofzero
pointenergy quantizedharmonicoscillators wasdiscussed.Itwasstated:
“Thisspectrumwithitsω3dependenceofspectralenergydensityisuniqueinas
muchasmotionthroughthisspectraldistributiondoesnotproduceadetectable
Doppler shift. It is a Lorentz invariant random field. Any particular spectral
componentundergoesaDopplershift,butothercomponentscompensatesothat
allcomponentstakentogetherdonotexhibitaDopplershift.”
Thereisoneproblemwiththisconcept.Vacuumfluctuationshaveacutofffrequencyequalto
Planckfrequency ωp.IfthiscutofffrequencyissymmetricalwhenviewedfromtheCMBrest
frame,thentheremustbeanultra‐relativisticframeofreference relativetotheCMB where
theasymmetrybecomesobvious.Anexamplewillhelptodefinethisquestion.Wecancurrently
accelerateanelectrontoenergyof50GeV.ThisisarelativisticLorentzfactorofγ 105relative
totheCMBrestframe.However,aframeofreferencewithγ 105doesnotcomeclosetotesting
thequestionsrelatedtothelimitsofextremeultrarelativisticframesofreference.Imaginean
electronwithanultra‐relativisticspeedwithγ 2.4 1022asseenfromtheCMBrestframe.This
istheLorentzfactorwheretheelectron’sdeBrogliewavelengthλdwouldbeshorterthanPlanck
1 .Thisisveryclosetothespeedoflightbut
length λd λc/γapproximationvalidwhenγ
itdoesnotequalthespeedoflight.Therefore,itishypotheticallyapermittedframeofreference
foranelectron.
However, in the CMB rest frame the electron would have a de Broglie wavelength less than
PlancklengthanddeBrogliefrequencyexceedingPlanckfrequency.Accordingtothepremise
ofthisbook,spacetimeisnotcapableofproducingthiswavelengthandfrequency.Also,inthe
electron’sframeofreferencetherewouldbeanextremeredshiftinonedirectionofthedipole
waves in spacetime required to stabilize the energy density pressure of the electron. This
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redshiftwouldpreventthevacuumenergyfromexertingthepressurerequiredtostabilizean
electroninthisframeofreference.Iftheuniverseisonlyspacetime,thenthisframeofreference
isnotpermittedforanelectron.InstabilitywouldappearasanelectronapproachedthePlanck
length/frequencylimitasseenfromtheCMBrestframe.Theelectronwouldexhibitproperties
inthisultra‐relativisticframeofreferencethattheelectrondoesnotpossessintheCMBrest
frame. Other particles would exhibit unusual properties and instabilities at different
ultra‐relativisticframesrelativetotheCMBrestframe.
Foranotherexample,inchapter9wedeterminedthatphotonsarequantizedwavespropagating
inthemediumofthespacetimefield.Thisimpliesthataphotonisnotpermittedinanyframeof
referencewhichwouldappeartohaveawavelengthshorterthanPlancklengthintheCMBrest
frame.Thereisonlyonespacetimefieldforallframesofreference.Thisfieldisnotcapableof
propagatingwavesshorterthantheshortestwavelengthwaveinthefield.Thecurrentrecord
for the highest energy photon ever observed is a 12 TeV gamma ray ∿ 2 10‐6 J which has
wavelengthofabout10‐19m.Thisenergyphotonispermittedinourframeofreference,butit
wouldnotbepermittedinanyframeofreferencewhichexceededaboutγ 1016relativetothe
CMB. The reason is that this photon would have a wavelength less than Planck length when
viewedintheCMBrestframeandtheenergywouldexceedPlanckenergy.Thisimpliesthatthe
lawsofphysicschangeintheseextremeframesofreference.
String theory is based on three starting assumptions which are expressed as mathematical
equations.Theseare1 Lorentzinvariance, thelawsofphysicsarethesameinalluniformly
moving frames of reference 2 analyticity a smoothness criteria for the scattering of high
energyparticlesafteracollision and3 unitarity allprobabilitiesalwaysadduptoone .The
speedoflightisthesameinalluniformlymovingframesofreference,butthelawsofphysicsare
not. Therefore the contention is that Lorentz invariance is not a valid assumption for all
uniformly moving frames of reference. String theory incorporates this erroneous assumption
andalltheconclusionsbasedonthisassumptionarequestionable.
Lorentz Was Correct:EventhoughtodayweoftenassumethatEinsteindidnotbelieveinthe
aether,heactuallycontinuedtorefertotheaetheror“physicalspace”untilhisdeath2.Hemerely
declaredthattheaethermusthaverelativisticpropertieswithnopreferredframeofreference.
Lorentzalsobelievedintheaether,buthiscalculations Lorentztransformations assumedthat
the aether had a preferred frame of reference. Lorentz transformations did not confer and
detectable special properties to this preferred frame of reference since the transformations
madethelawsofphysicsthesamein“all”framesofreference.However,EinsteinandLorentz
disagreed about whether the aether had some special reference frame which served as the
standardforallotherreferenceframes.
2
L. Kostro, Einstein and the Ether, (2,000) Apeiron, Montreal, Canada
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Thespacetimefieldcanbethoughtofasatypeofaether.Sinceallparticles,forcesandfieldsare
madefromthisspacetimefield,thereisaconceptuallyunderstandablereasonwhyexperiments
usingcurrentlytechnologycannotdetectmotionrelativetothespacetimefield.Theparticles
and forces merely undergo the transformations required to achieve Lorentz invariance.
However,Lorentzwascorrect.Thespacetimefielddoeshaveapreferredframeofreference.It
is the CMB rest frame. No experiment capable of being performed using current technology
wouldbeabletoexperimentallyprovethisbecauseitwouldrequireacceleratingaparticletoa
speedwhereitsdeBrogliewavelengthapproachesPlancklength.Forexample,anelectroncould
beacceleratedtoaspecialrelativitygammaofγ 2.4x1022iftheexperimentisdoneintheCMB
restframe.Theelectronwouldthenhaveλc Lp.Theelectron’sinternalpressurewouldbeequal
toPlanckpressureandtheabilityofthespacetimefieldtostabilizetheinternalpressureofthe
electronwouldbeatitslimit.Allotherframesofreferencewouldnotbeabletoachievethis
value of γ because theelectron would become unstable at a lower value of γ. Therefore, the
spacetimefielddoeshaveapreferredframeofreference,butitiscurrentlyundetectable.
The Fate of the Universe:Thecurrentlyacceptedmodeloftheuniversehasmysteriousdark
energybecomingmoredominantandacceleratingtheexpansionoftheuniverseuntilwelose
sight of distant galaxies. In the most extreme extension of this process, a Big Rip eventually
occurs when the expansion becomes so extreme that gravitationally bound objects such as
galaxiesandstarsaredispersedbytheexpansionofspace.Finallyevenatomsarerippedapart
andtheuniversediesassubatomicparticlesareeventuallyconvertedtophotons.
Themodelproposedherehasnotbeendevelopedsufficientlytohaveaclearpredictionabout
theeventualfateoftheuniverse.However,aspreviouslyexplained,thenearterm afewbillion
years has distant galaxies getting dimmer but also the currently observed redshift of any
particular distant galaxy will decrease. This counter intuitive prediction is actually a
continuationoftheprocessthathasoccurredthroughoutthehistoryoftheuniverse.
Overthelongertermthespacetimetransformationmodeloftheuniverseoffersanintriguing
possibility. The total energy density of the universe observable energy vacuum energy remainsthesameoverthelifetimeoftheuniverse.Presentlyobservableenergy includingdark
matter representsonlyabout1partin10122ofthetotalenergyintheuniverse.Aspreviously
explained, we only can observe and interact with waves in spacetime that possess quantized
angularmomentum fermionsandbosons .Furthermore,thefractionofthetotalenergythat
possesses angular momentum 10‐122 is dropping daily and the rate of change of dГu/dτu
appearstobeaccelerating.
Iffundamentalparticleseventuallydecayintophotonsinthefardistantfutureoftheuniverse,
then an intriguing possibility exists. When the quantized angular momentum of the photons
becomeshomogeneouslydistributedthroughouttheuniverse,thenthisconditionofspacetime
beginstolooklikePlanckspacetime.Theenergydensityisthesameandtheaveragedistribution
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ofthequantizedangularmomentumisthesame.ThemajordifferenceisthatPlanckspacetime
hasГu 1andthisfinalstateoftheuniversehasГuapproachinginfinity.
Perhapstheenergyinthesephotonsbecomessuchasmallfractionofthevacuumenergydensity
oftheuniversethatquantummechanicsallowsthebackgroundgammaoftheuniversetoround
offtoГu ∞.Therateoftimewouldstopandthehybridspeedoflightwouldstop.Thisisa
discontinuity that would allow a rebirth of the universe. All that has to happen is that the
backgroundgammaoftheuniversehastochangefromГu ∞toГu 1.Nocollapseisrequired
becausetheuniverseisalreadyattherequiredenergydensity.Also,therequiredquantizedspin
unitswouldbepreservedandevenlydistributed.Allthathastochangeistherateoftimeand
thespatialcharacteristicsmustrevertbacktotheГu 1condition.ThiswouldproducePlanck
spacetimeandtheuniversewouldstartanewcyclewithanew“BigBang”.
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Closing Thoughts: Einstein’s greatest contributions to science happened when he combined
insightfulnewassumptionswithmathematicalanalysis.Laterinhislifehetendedtowardsmore
advancedmathematicalanalysisofthesameoldassumptionsandhiscontributionstoscience
diminished.Iseeananalogytoallofphysics.Thegreatestadvancesinphysicsoccurredwhen
insightfulnewassumptionswerefirstintroduced.Thisintroductionofnewideaswasfollowed
by“goldenages”ofphysics.However,overtimethepaceofadvancementslowedwhenthesame
assumptionswerejustmathematicallyanalyzedinmoredetail.Theobjectiveofthisbookisto
proposeaseriesofnewideasbasedonthesimpleststartingassumption:Theuniverseisonly
spacetime.
Whileworkingontheideascontainedinthisbook,thereweretimesthatIquestionedwhetherI
should be undertaking this large project. Was there really a conceptually understandable
solutiontoaparticularproblem?WhyshouldIbetheoneattemptingtofindthissolution?At
those times I thought about and received encouragement from the following quote by John
ArchibaldWheeler.Predictinganewrevolutioninphysics,hesaid:
“Andwhenitcomes,willwenotsaytoeachother,Oh,howbeautifulandsimpleitallis!How
couldweeverhavemisseditsolong?”
–JohnArchibaldWheeler
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