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Ek is op soek na 'n teorie wat aantoon of twee verbygaande hemelliggame in 'n wentelbaan gaan of nie.
Ek neem aan dat daar 'n kritieke punt moet wees waar die aantrekkingskrag sterker is as die traagheid van bewegende liggame.
Die liggame wentel dan totdat hulle bots, of word beïnvloed deur 'n krag om agter die kritieke punt te val en om die baan te ontsnap.
Ek is op soek na 'n teorie wat stel dat voorwerpe verby hierdie kritieke punt van gravitasie-aantrekking onmiddellik moet bots of in 'n baan moet gaan nadat hulle binne 'n sekere afstand geval het.
As daar net twee liggame is, sal hulle nooit 'n wedersydse baan betree nie. Vir twee voorwerpe aanvanklik swaartekrag ungebonde, moet u energie uit die stelsel verwyder om swaartekraggebonde te word. Met slegs twee lyke (wat nie bots nie), gebeur dit nie. Hulle sal versnel na mekaar toe, rigtings verander na gelang van hoe naby hulle is, en mekaar dan weer agterlaat met presies dieselfde totale energie en momentum as voorheen, maar in die algemeen gedeel in 'n ander verhouding (byvoorbeeld as 'n klein liggaam teëkom 'n groot liggaam, hoe kleiner sal dit energie kry en met 'n groter snelheid vertrek).
Aan die ander kant, as u drie (of meer) liggame het, kan een met 'n hoë snelheid uitgeslinger word en sodoende energie uit die twee ander onttrek, wat dan in 'n wentelbaan kan gaan. Maar helaas, daar is geen vergelyking hiervoor nie; die sogenaamde N-liggaamsprobleem het geen analitiese oplossing nie, en moet in die algemeen numeries opgelos word.
Hoe Einstein se algemene relatiwiteitsteorie gesonde verstandfisika doodgemaak het
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Swaartekrag bind ons liggame aan die planeet Aarde, maar dit definieer nie die grense van die stygende menslike verstand nie. In November 1915 - presies 'n eeu gelede - is dit bewys dat dit waar is toe Albert Einstein, in 'n reeks lesings aan die Pruisiese Akademie vir Wetenskappe, 'n teorie voorgehou het wat 'n rewolusie sou maak vir die beskouing van swaartekrag - en die fisika self.
Vir twee eeue blyk dit dat Newton se opvallend eenvoudige en elegante teorie oor universele gravitasie die saak goed verklaar het. Maar, soos dit toenemend waar is vir fisika, sny eenvoudig dit net nie meer nie.
Einstein se beginpunt vir algemene relatiwiteit was sy teorie van spesiale relatiwiteit, gepubliseer in 1905. Dit het verduidelik hoe die wette van fisika in die afwesigheid van swaartekrag geformuleer kan word. In die middel van albei teorieë is 'n beskrywing van ruimte en tyd wat verskil van die een wat gesonde verstand sou voorstel.
Die teorieë verduidelik hoe om beweging te interpreteer tussen verskillende plekke wat teen konstante snelhede beweeg - in plaas van relatief tot 'n soort absolute eter (soos Newton aangeneem het). Alhoewel die wette van die fisika universeel is, sê verskillende kykers die tydsberekening van gebeure anders, afhangende van hoe vinnig hulle reis. Dit lyk of 'n gebeurtenis 1000 jaar neem as dit vanaf die aarde gesien word, net 'n sekonde neem vir iemand in 'n ruimtetuig wat vinnig beweeg.
In die middel van Einstein se teorieë is die feit dat die snelheid van die lig onafhanklik is van die beweging van die waarnemer wat die snelheid meet. Dit is vreemd, want gesonde verstand dui daarop dat as u in 'n motor langs 'n treinspoor sit, dit lyk asof 'n trein wat verbygaan, baie vinniger sal beweeg as as u dit in dieselfde rigting sou volg. As u egter sit en kyk hoe 'n ligstraal verbygaan, sal dit ewe vinnig beweeg, ongeag of u dit volg of nie - 'n duidelike aanduiding dat iets verkeerd is met gesonde verstand.
Einstein se spesiale en algemene relatiwiteit.
Die implikasie van hierdie teorie is dat ons die idee dat daar 'n universele tyd is, moet laat vaar en moet aanvaar dat die tyd wat deur 'n horlosie geregistreer word, afhang van die trajek wat dit deur die heelal beweeg. Dit beteken ook dat die tyd stadiger verbygaan as u vinnig gaan, wat beteken dat 'n tweeling wat na die ruimte gaan stadiger sal verouder as hul broer of suster op aarde. Hierdie 'tweelingparadoks' mag 'n wiskundige eienaardigheid lyk, maar dit is in 1971 eksperimenteel geverifieer in 'n eksperiment wat atoomklokke op kommersiële vlugte neem.
Spesiale relatiwiteit werk slegs vir traagheidsraamwerke wat relatief tot mekaar beweeg as hulle teen konstante snelheid beweeg - dit kan nie beskryf wat gebeur as hulle versnel nie. Einstein het gewonder hoe om dit uit te brei om sulke versnelling in te sluit en swaartekrag moontlik te maak, wat versnelling veroorsaak en per slot van rekening oral is.
Hy het besef dat die effek van swaartekrag verdwyn as 'n mens dit nie probeer oorkom nie. Hy het mense in 'n hysbak voorgestel wie se kabel in vrye val gebreek het en uitgewerk het dat die mense nie swaartekrag sou voel nie, aangesien die voorwerpe roerloos of met konstante snelheid sou sweef. Maar deesdae weet ons dat dit waar is, want ons het dit self gesien by mense by die internasionale ruimtestasie. In beide gevalle is daar geen kragte wat die effek van swaartekrag teenwerk nie, en die mense ervaar geen swaartekrag nie.
Geboë ruimtetyd. Mopie
Einstein besef ook dat die effek van swaartekrag dieselfde is as die effek van versnelling wat met 'n hoë spoed wegjaag, ons agteruit stoot, net asof swaartekrag ons trek. Hierdie twee leidrade het Einstein tot algemene relatiwiteit gelei. Terwyl Newton swaartekrag gesien het as 'n krag wat tussen liggame voortgeplant is, word Einstein beskryf as 'n pseudokrag wat ervaar word omdat die hele verweefde weefsel van ruimte en tyd rondom 'n massiewe voorwerp buig.
Einstein het self gesê dat sy pad ver van maklik is. Hy het geskryf dat 'ek my hele lewe lank nie so hard gewerk het nie, en dat ek baie respek vir wiskunde gekry het, en die subtiele deel wat ek tot nou toe as 'n luukse beskou het.'
Die Godsvergelyking: die soeke na 'n teorie van alles
'N Baie oppervlakkige oorsig van die geskiedenis van die fisika - met die laaste hoofstuk wat 'n oppervlakkige oorsig gee van die veld van strykteorie. 'N Laaste hoofstuk bespreek God in die lig van die moderne fisika.
'N Mors van tyd as u 'n ander gewilde boek oor fisika lees. Hierdie genadiglike kort boek voel asof dit vir die geld geskryf is.
2-sterre. 20ste boek vir 2021.
'N Baie oppervlakkige oorsig van die geskiedenis van die fisika - met die laaste hoofstuk wat 'n oppervlakkige oorsig gee van die veld van strykteorie. 'N Laaste hoofstuk bespreek God in die lig van die moderne fisika.
'N Mors van tyd as u enige ander gewilde boek oor fisika gelees het. Hierdie genadiglike kort boek voel asof dit vir die geld geskryf is.
Toe die fisikus Leon Lederman sy boek oor die ontwykende Higgs boson & apos The Goddam Particle & apos wou noem, het sy uitgewer beswaar gemaak en dit eerder The God Particle gemaak. Hierdie gebruik het sedert die populêre wetenskap 'n paar keer opgeduik, veral The God Effect on quantum entangel, en nou pas Michio Kaku dit toe op die konsep van 'n sogenaamde Theory of Everything - 'n meganisme wat die fundamentele kragte van natuur insluitend swaartekrag. Daar is geen sekerheid dat so 'n teorie pos is nie. Toe fisikus Leon Lederman sy boek oor die ontwykende Higgs-boson 'The Goddam Particle' wou noem, het sy uitgewer daarteen beswaar gemaak en dit eerder The God Particle gemaak. Hierdie gebruik het sedert die populêre wetenskap 'n paar keer opgeduik, veral The God Effect on quantum entanglement, en nou pas Michio Kaku dit toe op die konsep van 'n sogenaamde Theory of Everything - 'n meganisme wat die fundamentele kragte van natuur insluitend swaartekrag. Daar is geen sekerheid dat so 'n teorie moontlik is nie, maar as dit wel sou bestaan, sou dit die grondslag van die fisika verskaf. Tog lyk dit onwaarskynlik dat dit die bewering in die publisiteit van die boek sou eerbiedig dat dit 'die oudste en basiese menslike begeertes sou vervul - om die betekenis van ons lewens te verstaan'.
Kaku werk sedert die sestigerjare aan snaarteorie - die teorie wat hy glo, sal ons die teorie van alles gee - en is sterk daarin belê. Hy belowe ons 'n 'gebalanseerde, objektiewe analise van die deurbrake en beperkings van die stringteorie' - maar aangesien dit hierna volg, sê hy dat dit die 'voorste (en volgens my enigste) kandidaat' is vir 'n teorie van alles, is dit nie heeltemal verbasend nie dat dit nogal 'n subjektiewe siening voel. Byvoorbeeld, op 'n stadium word ons meegedeel dat die tekort aan bewyse vir die vereiste 10 of 11 dimensies bekommerd is oor snaarteorie. Kaku wys daarop dat, indien dit bestaan, dit 'n klein impak op die swaartekrag oor klein afstande moet hê. Hy beskryf 'n eksperiment. waar die resultate negatief is. Maar eerder as om dit te sien as 'n meer aanduiding van die twyfelagtige aard van die teorie, gee hy die wegwerplyn 'Maar dit beteken net dat daar geen bykomende dimensies in Colorado is nie.'
Wanneer Kaku weet wat die stringteorie eintlik is (wat eers op bladsy 141 uit 198 plaasvind), gee hy 'n goeie oorsig op hoë vlak voordat hy in 'n paar handwuiwende pogings gedompel word om aan te toon waarom dit eintlik saak maak (beslis voorstel dit gee ons die kans om die betekenis van ons lewens te verstaan). Wat ek teleurstellend vind, is dat daar geen poging is om stringteorie binne konteks van mededingende benaderings te plaas nie. Ek weet dat lus-kwantum-swaartekrag byvoorbeeld nie 'n teorie van alles is nie, maar hulle kan nie albei hou nie - tog word dit nooit genoem nie. Aan die positiewe kant is Kaku eerlik oor die probleme van die stringteorie en die gebrek aan bewyse - maar as hy byvoorbeeld sê dat die ontdekking van supersimmetriese deeltjies dit sou ondersteun, maar dit is nog nie gevind nie, weet hy nie Ek sal nie sê dat entoesiaste oor stryteorie verwag het dat hulle deur die Large Hadron Collider gevind sou word nie.
Dit is ook jammer hoe min detail daar is oor die ontwikkeling van snaarteorie, wat dit sê en waarom dit byvoorbeeld soveel dimensies verg. Vir 'n boek oor 'n teorie van alles, lyk dit asof ons byna alles behalwe die teorie self het. Die rede waarom ons eers op bladsy 141 kennis maak met snaarteorie, is dat die grootste deel van die boek 'n opsomming is van die geskiedenis van fisika. In sy gewone flambojante styl blaas Kaku deur die geskiedenis van die wetenskap wat gelei het tot die ontwikkeling van snaarteorie. Ongelukkig volg hy 'n benadering wat wetenskaphistorici, kersies pluk en soms onakkuraat sou bekommer.
Ons begin met 'n baie outydse voorstelling van die konsep van die donker tydperke wat nou ontslaan is, toe klassieke wetenskaplike 'filosofiese besprekings en debatte verlore gegaan het ... Duisternis versprei oor die Westerse wêreld en wetenskaplike ondersoek is grootliks vervang deur geloof in bygeloof, towery en towery. ' Kaku draf die bekende mite uit dat die 'hoofmisdaad' in Giordano Bruno se dwaalproses was 'Die verklaring dat die lewe op planete rondom ander sterre mag bestaan', impliseer dat Galileo die teleskoop uitgevind het en die kerk die skuld gee vir standaard Aristoteliese teorieë soos die onveranderlike hemel en beweging veroorsaak deur natuurlike neigings.
As ons oor die kwantumfisika gaan, is daar 'n paar eienaardighede. Kaku vertel dat kwantumeffekte selde direk gesien kan word 'omdat die konstante van Planck 'n baie klein getal is en slegs die heelal op die subatomiese vlak beïnvloed' - maar dan draf hy die Schrödinger se kateksperiment uit asof dit betekenisvol was. Hy gee onbetwis die idee dat die Kopenhagen-interpretasie 'waarneming (wat bewustheid vereis) behels'. Hy het ook gesê dat Kopenhagen verontwaardig geraak het, met die interpretasie van baie wêrelde wat nou 'gewilder' is - iets wat nie deur ondersoeke van fisici bevestig word nie.
Oor die algemeen is dit dan 'n boek wat 'n vinnige, ligte, leesbare, maar ietwat beperkte inleiding tot fisika gee. Soos altyd skryf Kaku met energie, duidelike entoesiasme en 'n verrukking in die wonders wat die wetenskap ontbloot. Maar die boek slaag nie daarin om te oortuig dat die stringteorie geldig is nie, of dat dit enigiets van die soort betekenis kan lewer wat Kaku belowe deur dit te vergelyk met die innovasie wat ontstaan het uit die begrip van die Newtonse fisika, elektromagnetisme en kwantumteorie. . meer
Vrye val binne die aarde.
Kan ons soortgelyke effekte in ruimtetyd vind? Dan sou ons kromming gevind het. Ons soek dus 'n vel ruimtetyd waarin ons konvergerende of uiteenlopende krommes vind. Soos ons sal sien, is dit maklik om te vind. 'N Versameling massas in vrye val in 'n swaartekragveld sal presies die soort kurwes bied wat ons benodig.
Om ons aan die gang te kry, sal ons die eenvoudigste saak neem wat die kromming betref, hoewel die opstelling fisies 'n bietjie rommeliger is.
| Stel jou voor dat ons 'n gat deurboor na die middel van die aarde en na die ander kant toe. Dit sal ongeveer 7900 myl lank wees. Ons ontruim die resulterende buis en bedek dit sodat die liggame wat in die gat val, kan val sonder enige lugweerstand. |
| 'N Klein bal wat van die oppervlak afgeval het, sou na die middelpunt val en binne 21 minute daar aankom, verby jaag en na die ander kant gaan en nog 21 minute later aankom. Dit sou dan terugval na die kant toe dit begin het. As niks ingegryp het nie, sou dit heen en weer beweeg en dit 42 minute neem om elke reis van die een kant na die ander te voltooi. | Natuurlik moet ons die rotasie van die aarde ignoreer. Andersins kan die rotasie die wande van die buis met die valbal in botsing bring. |
Een van die eienaardighede van swaartekrag is dat hierdie periode van 84 minute (= 42 minute daar + 42 minute terug) vas is, ongeag waar die bal eers losgelaat mag word. Stel jou voor dat dit vrygestel word van rus halfpad tussen die oppervlak en die middel. Dit sal dieselfde 42 minute neem om die sentrum oor te steek en tot stilstand te kom op die ooreenstemmende punt aan die ander kant van die sentrum en dan nog 42 minute om die rit terug te neem na sy beginpunt.
As u hierdie ruimtetyddiagram vergelyk met die vorige figuur van reisigers op die aardoppervlak, sal u sien dat hulle in die wesenlike aspek saamstem. Hulle toon albei saamtrekbane, die kenmerk van positiewe kromming. Dit stel ons in staat om die swaartekragbewegings op 'n nuwe manier te interpreteer.
Die versoeking is om hierdie konvergensie 'geodesiese afwyking' te noem. Ons moet hier 'n bietjie versigtig wees, aangesien die trajekte in die ruimtetyd nie noodwendig geodesika is nie, dit wil sê kurwes van die kortste afstand. Dit is nie volgens die Newtonse teorie nie. In relatiwiteit, beide spesiaal en algemeen, is dit tydagtige geodesika. Dit wil sê, hulle is kurwes van die grootste regte tyd, wat die analoog is van die reguit lyne van die Euklidiese meetkunde, die kurwes van die kortste afstand. Ons kan dus toegee aan die versoeking en sodoende tot die wesenlike idee van Einstein se teorie kom.
. Herinterpreteer
Hier is hoe ons oorgaan na die wesenlike idee van Einstein se teorie.
Ons noem dit 'n vel ruimte-koppelteken-tyd om aan te dui dat die blad een ruimtelike en een tydelike dimensie het.
Probeer dit nie eens voorstel as ekstrinsieke kromming, die buiging van 'n oppervlak in 'n hoër dimensie ruimte nie. Daardie manier lei tot waansin! Dink aan die kromming intrinsiek, dit wil sê as 'n geometriese effek wat geheel en al binne die oppervlak ontstaan.
Hierdie geval van vrye val binne die aarde blyk 'n baie eenvoudige geval te wees wat kromming op twee maniere betref.
| Eerstens, die kromming van die ruimtetydvelle wat deur hierdie dalende massas ondersoek is, blyk konstant in die hele blad te wees. Dit volg, aangesien die snelheid waarmee naburige balle in die blad saamvloei dieselfde is deur die hele vel. | Hierdie bestendigheid is nie te moeilik om te sien nie. As 'n mens die Newtoniaanse gravitasieteorie uitwerk, blyk dit dat die versnelling as gevolg van die swaartekrag van 'n bal in die buis lineêr groei met afstand vanaf die middelpunt van die aarde. Dit beteken dat ons met elke afstand van elke ekstra kilometer dieselfde toename by die versnelling van die bal voeg. As twee balle op enige plek in die buis een kilometer hoog geskei word, sal hul relatiewe versnelling dieselfde wees. Aangesien die relatiewe versnelling die tempo van konvergensie bepaal, sal die tempo oral dieselfde wees. Aangesien die kromming die kromming bepaal, volg die kromming oral dieselfde. |
Tweedens, is die grootte van die kromming nie afhanklik van die massa of grootte van die aarde nie, dit hang slegs af van die massadigtheid van die aarde. (Dit is nie vanselfsprekend nie. 'N Maklike berekening in die Newtonse teorie kan dit egter toon.)
Hierdie laaste twee punte is belangrik genoeg om in 'n verhouding te wees wat naby is (maar nie heeltemal nie) wat baie algemeen geld:
In hierdie formule is Newtonse "massadigtheid" vervang deur die vaagere "materie-digtheid" in afwagting van wat in die algemene relatiwiteit sal plaasvind, waar die digtheid van die materie 'n ingewikkelder hoeveelheid is wat energie en momentumdigthede sowel as spanning omvat.
Die analise kan veralgemeen word. Ons het net een ruimte-tydblad oorweeg, die een wat deur die tyd gevee is deur die gat wat ons voorgestel het deur die aarde geboor. Niks in die ontleding het afhang van waar ons die gat geboor het nie. Ons kon baie gate geboor het. Elkeen vee 'n ander vel in die ruimtetyd waarop hierdie analise van toepassing is. Oor die algemeen is daar drie onafhanklike ruimtelike rigtings wat ons sou kon kies, ooreenstemmend met die drie asse van 'n driedimensionele ruimte. Om die kromming in die drie resulterende velle te vind, sou voldoende wees om die kromming vas te stel in alle moontlike velle wat gegenereer word deur gate wat ons mag grawe.
Uitdagingsprobleme
- 'N Tunnel word deur die middel van 'n perfek bolvormige en luglose planeet met 'n radius R gegrawe. Gebruik die uitdrukking vir g afgelei in Gravitation Near Earth & rsquos Surface vir 'n eenvormige digtheid, en toon dat 'n massa deeltjie m wat in die tonnel val, eenvoudige harmoniese beweging sal uitvoer . Lei die oscillasieperiode van m af en toon aan dat dit dieselfde periode het as 'n baan aan die oppervlak.
- Volg die tegniek wat gebruik word in Gravitation Near Earth & rsquos Surface, en bepaal die waarde van g as 'n funksie van die radius r vanaf die middel van 'n bolvormige dopplaneet met konstante digtheid ( rho ) met innerlike en buitenste radius Rin en Ruit. Vind g vir beide Rin & lt r & lt Ruit en vir r & lt Rin. Gestel die binnekant van die dop word lugloos gehou, beskryf die reis binne die bolvormige dopplaneet.
- Toon aan dat die oppervlaktesnelheid van 'n sirkelvormige wentelbaan van 'n radius r rondom 'n massa M ( frac < Delta A> < Delta t> = frac <1> <2> sqrt
). Gee u uitdrukking die korrekte waarde vir die Aarde en die oppervlaktesnelheid van die son? - Toon aan dat die wentelperiode vir twee massas, m1 en m2, in sirkelvormige wentelbane van radius r1 en r2, onderskeidelik, oor hul gemeenskaplike massamiddelpunt, word gegee deur (T = 2 pi sqrt < frac
- Toon aan dat vir klein veranderinge in hoogte h, sodat h & lt & lt RE, Vergelyking 13.4 verminder tot die uitdrukking ( Delta ) U = mgh.
- Gebruik Figuur 13.9 om 'n vryeliggaamdiagram noukeurig te skets vir die geval van 'n eenvoudige slinger wat op breedtegraad lambda hang, en merk alle kragte wat op die puntmassa inwerk, m. Stel die bewegingsvergelykings vir ewewig op, stel een koördinaat in die rigting van die sentripetale versnelling (in die rigting van P in die diagram), en die ander loodreg daarop. Toon aan dat die afbuigingshoek ( epsilon ), gedefinieer as die hoek tussen die slingersnaar en die radiale rigting na die middelpunt van die aarde, gegee word deur die onderstaande uitdrukking. Wat is die afbuighoek op die breedtegraad 45 grade? Neem aan dat die aarde 'n perfekte sfeer is. ( tan ( lambda + epsilon) = frac
<(g & minus omega ^ <2> R_ )> tan lambda ), waar ( omega ) die hoeksnelheid van die Aarde is. - (a) Toon dat die getykrag op 'n klein voorwerp met massa m, gedefinieer as die verskil in die gravitasiekrag wat op m uitgeoefen word op 'n afstand naby en aan die ander kant van die voorwerp, as gevolg van die gravitasie op 'n afstand R vanaf M, word F gegeegety = ( frac <2GMm>
- Vind die Hohmann-oordrag snelheid, ( Delta ) vEllipseEarth en ( Delta ) vEllipseMars, benodig vir 'n reis na Mars. Gebruik Vergelyking 13.7 om die sirkelvormige wentelsnelhede vir Aarde en Mars te bepaal. Gebruik vergelyking 13.4 en die totale energie van die ellips (met semi-hoofas a), gegee deur E = & minus ( frac<>
> <2a> ), vind die snelhede op Aarde (perihelion) en by Mars (aphelion) wat nodig is om op die oordrag-ellips te wees. Die verskil, ( Delta ) v, is op elke punt die snelheidsverhoging of oordrag snelheid wat benodig word.
Die mislukte eksperiment wat die wêreld verander het
Die oorspronklike opset van die Michelson-Morley-eksperiment, vanaf 1887.
Case Western Reserve-argiewe
In die wetenskap doen ons nie bloot eksperimente nie. Ons sit dinge nie lukraak saam nie en vra: 'Wat gebeur as ek dit doen?' Ons ondersoek die verskynsels wat bestaan, die voorspellings wat ons teorieë maak en soek maniere om dit in groter detail te toets. Soms gee hulle buitengewone instemming met nuwe presisie, wat bevestig wat ons gedink het. Soms stem hulle nie saam nie en wys dit die weg na nuwe fisika. En soms slaag hulle daarin om glad nie 'n nul-resultaat te gee nie. In die 1880's het 'n ongelooflike presiese eksperiment presies op hierdie manier misluk en die weg gebaan vir relatiwiteit en kwantummeganika.
Die wentelbane van die planete en komete, onder andere hemelse voorwerpe, word deur die wette van. [+] universele gravitasie.
Kay Gibson, Ball Aerospace & amp Technologies Corp.
Kom ons gaan nog verder terug in die geskiedenis om te verstaan waarom dit so 'n groot saak was. Gravitasie was die eerste van die kragte wat verstaan moes word, aangesien Newton sy wet van universele gravitasie in die 1600's uiteengesit het, wat die bewegings van liggame op aarde en in die ruimte verduidelik het. 'N Paar dekades later (in 1704) het Newton ook 'n teorie oor lig voorgestel - die korpuskulêre teorie - wat verklaar dat lig uit deeltjies bestaan, dat hierdie deeltjies rigied en gewigloos is en dat dit in 'n reguit lyn beweeg, tensy iets veroorsaak om te reflekteer, te breek of af te breek.
Die eienskappe van die lig, soos weerkaatsing en breking, lyk asof dit korpuskulêr is, maar daar is wel. [+] golfagtige verskynsels wat dit ook vertoon.
Wikimedia Commons-gebruiker Spigget
Dit was verantwoordelik vir baie waargenome verskynsels, waaronder die besef dat wit lig die kombinasie van alle ander kleure van lig was. Maar met verloop van tyd het baie eksperimente die golfaard van lig onthul, 'n alternatiewe verklaring van Christiaan Huygens, een van die tydgenote van Newton.
Wanneer enige golf - watergolwe, klankgolwe of liggolwe - deur 'n dubbele gleuf beweeg, word die. [+] golwe skep 'n interferensiepatroon.
Wikimedia Commons-gebruiker Lookang
Huygens het eerder voorgestel dat elke punt wat as 'n bron van lig beskou kan word, ook van 'n liggolf wat eenvoudig vorentoe beweeg, soos 'n golf moet optree, met 'n bolvormige golffront wat uit elk van hierdie punte voortspruit. Alhoewel baie eksperimente dieselfde resultate sou lewer, ongeag of u Newton se benadering of Huygens se benadering gevolg het, was daar 'n paar wat begin het in 1799 wat regtig begin wys hoe kragtig die golfteorie was.
Lig van verskillende golflengtes vertoon dieselfde golfagtige as dit deur 'n dubbele gleuf beweeg. [+] eienskappe wat ander golwe doen.
MIT Tegniese Dienstegroep Departement Fisika
Deur verskillende kleure lig te isoleer en deur enkele splete, dubbele splete of afbreekroosters te lei, kon wetenskaplikes patrone waarneem wat slegs geproduseer kon word as lig 'n golf was. Die patrone wat geproduseer is - met pieke en bakke - weerspieël inderdaad die van bekende golwe, soos watergolwe.
Die golfagtige eienskappe van lig word nog beter verstaan danksy Thomas Young se tweespalt. [+] eksperimente, waar konstruktiewe en vernietigende inmenging hulself dramaties vertoon het.
Maar watergolwe - soos dit bekend was - het deur die medium van die water beweeg. Neem die water weg, en daar sal geen golf wees nie! Dit geld vir alle bekende golfverskynsels: klank, wat 'n kompressie en skaarsheid is, het ook 'n medium nodig om deur te beweeg. As u alle materie wegneem, is daar geen medium vir klank om deur te beweeg nie, en daarom sê hulle: 'In die ruimte kan niemand u hoor skree nie.'
In die ruimte sal geluide wat op Aarde geproduseer word nooit na u reis nie, aangesien daar geen medium vir is nie. [+] klank om tussen die aarde en jou deur te beweeg.
NASA / Marshall Space Flight Centre
Die redenasie het dus gegaan, as lig 'n golf is - alhoewel, soos Maxwell in die 1860's getoon het, 'n elektromagnetiese golf - moet dit ook 'n medium hê waardeur dit beweeg. Alhoewel niemand hierdie medium kon meet nie, is dit 'n naam gegee: die gloeilamp.
Klink nou na 'n lawwe idee, is dit nie? Maar dit was glad nie 'n slegte idee nie. In werklikheid het dit al die kenmerke van 'n wonderlike wetenskaplike idee gehad, omdat dit nie net voortgebou het op die wetenskap wat voorheen vasgestel is nie, maar dat hierdie idee nuwe voorspellings gemaak het wat toetsbaar was! Laat my verduidelik aan die hand van 'n analogie: die water in 'n vinnig bewegende rivier.
Die Klamath-rivier, wat deur 'n vallei vloei, is 'n voorbeeld van 'n vinnig bewegende watermassa.
Blake, Tupper Ansel, Amerikaanse vis- en wilddiens
Stel jou voor dat jy 'n rots in 'n woedende rivier gooi, en kyk na die golwe wat dit maak. As u die golwings van die golf na die oewers volg, loodreg op die rigting van die stroom, sal die golf teen 'n bepaalde snelheid beweeg.
Maar sê nou jy kyk hoe die golf stroomop beweeg? Dit gaan stadiger beweeg, want die medium waardeur die golf beweeg, die water, beweeg! En as jy kyk hoe die golf stroomaf beweeg, sal dit vinniger beweeg, weer omdat die medium beweeg.
Alhoewel die gloeiende eter nog nooit opgespoor of gemeet is nie, was daar 'n vernuftige eksperiment deur Albert A. Michelson wat dieselfde beginsel op die lig toegepas het.
Die aarde, wat in sy wentelbaan om die son beweeg en op sy as draai, moet 'n ekstra bydrae lewer. [+] beweging as daar 'n medium is waardeur lig beweeg.
Larry McNish, RASC Calgary
U sien, alhoewel ons nie presies geweet het hoe die eter in die ruimte was nie, wat die rigting daarvan was of hoe dit vloei, of wat dit ten opsigte van rus gehad het, vermoedelik - soos die Newtonse ruimte - was dit absoluut. Dit het onafhanklik van materie bestaan, aangesien dit in ag moet neem dat lig kan beweeg waar klank nie kan nie: in 'n lugleegte.
As u in beginsel die snelheid meet waarmee die lig beweeg terwyl die aarde "stroomop" of "stroomaf" beweeg (of dit loodreg op die "stroom" van die eter is, kan u nie net die bestaan van die aether, jy sou kon bepaal wat die rusraamwerk van die heelal was! Ongelukkig is die snelheid van die lig ongeveer 186,282 myl per sekonde (Michelson het geweet dat dit 186,350 ± 30 myl per sekonde is), terwyl die wentelende snelheid van die aarde slegs ongeveer 18,5 myl per sekonde is, iets wat ons was ' t goed genoeg om in die 1880's te meet.
Maar Michelson het 'n truuk in die mou gehad.
Die oorspronklike ontwerp van 'n Michelson interferometer.
Albert Abraham Michelson, 1881
In 1881 ontwikkel en ontwerp Michelson wat nou bekend staan as 'n Michelson-interferometer, wat absoluut briljant was. Wat dit gedoen het, was gebaseer op die feit dat lig - wat van golwe gemaak is - met homself inmeng. En in die besonder, as hy 'n liggolf neem, deel dit in twee komponente wat loodreg op mekaar staan (en dus verskillend beweeg ten opsigte van die eter), en laat die twee balke presies dieselfde afstande beweeg en weerkaats dit dan terug na mekaar, sou hy 'n verskuiwing in die steuringspatroon wat deur hulle gegenereer is, waarneem!
U sien, as die hele apparaat stilstaan ten opsigte van die eter, sal daar geen verskuiwing wees in die interferensiepatroon wat hulle gemaak het nie, maar as dit enigsins meer in die een rigting beweeg as die ander, sou u 'n skuif kry.
As u lig in twee loodregte komponente verdeel en weer bymekaar bring, sal dit doen. [+] inmeng. As u in een rigting teenoor 'n ander rigting beweeg, sal die interferensiepatroon verander.
Wikimedia gebruik die gebruiker Stigmatella aurantiaca
Michelson se oorspronklike ontwerp kon geen verskuiwing opspoor nie, maar met 'n armlengte van net 1,2 meter was sy verwagte verskuiwing van 0,04 rande net bokant die limiet van wat hy kon opspoor, wat ongeveer 0,02 rande was. Daar was ook alternatiewe vir die idee dat die eter suiwer stilstaan - soos die idee dat dit deur die aarde gesleep is (alhoewel dit nie heeltemal kon wees nie, as gevolg van waarnemings van hoe sterre aberrasie werk) - daarom het hy die eksperiment uitgevoer op verskeie kere gedurende die dag, aangesien die roterende aarde onder verskillende hoeke ten opsigte van die eter moet wees.
Die nulresultaat was interessant, maar nie heeltemal oortuigend nie. Gedurende die daaropvolgende ses jaar het hy 'n interferometer met Edward Morley tien keer so groot (en dus tien keer so presies) ontwerp, en hulle twee het in 1887 uitgevoer wat nou bekend staan as die Michelson-Morley-eksperiment. Hulle het 'n byvoordrag gedurende die dag verwag tot 0,4 franse, met 'n akkuraatheid tot 0,01 franse.
Danksy die internet is hier die oorspronklike 1887-uitslae!
Die gebrek aan 'n waargenome verskuiwing, ondanks die nodige sensitiwiteit en die teoretiese voorspellings,. [+] was 'n ongelooflike prestasie wat gelei het tot die ontwikkeling van moderne fisika.
Michelson, A. A. Morley, E. (1887). "Oor die relatiewe beweging van die aarde en die gloeiende eter". Amerikaanse Tydskrif vir Natuurwetenskap 34 (203): 333–345
Hierdie nul resultaat - die feit dat daar geen ligter eter was nie - was eintlik 'n groot vooruitgang vir die moderne wetenskap, want dit het beteken dat die lig inherent moes verskil van alle ander golwe waarvan ons geweet het. Die resolusie het 18 jaar later gekom, toe Einstein se teorie van spesiale relatiwiteit gekom het. And with it, we gained the recognition that the speed of light was a universal constant in all reference frames, that there was no absolute space or absolute time, and — finally — that light needed nothing more than space and time to travel through.
Albert Michelson won the Nobel Prize in 1907 for his work developing the interferometer and the . [+] advances made because of his measurements. It was the most important null result in scientific history.
Nobel foundation, via nobelprize.org
The experiment — and Michelson’s body of work — was so revolutionary that he became the only person in history to have won a Nobel Prize for a very precise non-discovery of anything. The experiment itself may have been a complete failure, but what we learned from it was a greater boon to humanity and our understanding of the Universe than any success would have been!
Belangrike konsepte en samevatting
Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. Their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the three-dimensional position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. Atomic wavefunctions are also called orbitals. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in space. Therefore, atomic orbitals describe the areas in an atom where electrons are most likely to be found.
An atomic orbital is characterized by three quantum numbers. The principal quantum number, n, can be any positive integer. The general region for value of energy of the orbital and the average distance of an electron from the nucleus are related to n. Orbitals having the same value of n are said to be in the same shell. The angular momentum quantum number, l, can have any integer value from 0 to n – 1. This quantum number describes the shape or type of the orbital. Orbitals with the same principle quantum number and the same l value belong to the same subshell. The magnetic quantum number, ml, with 2l + 1 values ranging from –l to +l, describes the orientation of the orbital in space. In addition, each electron has a spin quantum number, ms, that can be equal to ±12.±12. No two electrons in the same atom can have the same set of values for all the four quantum numbers.
Chemistry End of Chapter Exercises
- How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different?
- What are the allowed values for each of the four quantum numbers: n, l, ml, en ms?
- Describe the properties of an electron associated with each of the following four quantum numbers: n, l, ml, en ms.
- Answer the following questions:
(a) Without using quantum numbers, describe the differences between the shells, subshells, and orbitals of an atom.
(b) How do the quantum numbers of the shells, subshells, and orbitals of an atom differ?
(a) What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)?
(b) How many orbitals of type (x) are found in a shell with n = 2? How many of type (y)? How many of type (z)?
(c) Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n = 4. Of an orbital of type (y) in a shell with n = 2. Of an orbital of type (z) in a shell with n = 3.
(d) What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)?
(e) What are the possible l en ml values for an orbital of type (x)? Of type (y)? Of type (z)?
Artificial Intelligence Solves Schrödinger’s Equation, a Fundamental Problem in Quantum Chemistry
A team of scientists at Freie Universität Berlin has developed an artificial intelligence (AI) method for calculating the ground state of the Schrödinger equation in quantum chemistry. The goal of quantum chemistry is to predict chemical and physical properties of molecules based solely on the arrangement of their atoms in space, avoiding the need for resource-intensive and time-consuming laboratory experiments. In principle, this can be achieved by solving the Schrödinger equation, but in practice this is extremely difficult.
Up to now, it has been impossible to find an exact solution for arbitrary molecules that can be efficiently computed. But the team at Freie Universität has developed a deep learning method that can achieve an unprecedented combination of accuracy and computational efficiency. AI has transformed many technological and scientific areas, from computer vision to materials science. “We believe that our approach may significantly impact the future of quantum chemistry,” says Professor Frank Noé, who led the team effort. The results were published in the reputed journal Nature Chemistry.
Central to both quantum chemistry and the Schrödinger equation is the wave function – a mathematical object that completely specifies the behavior of the electrons in a molecule. The wave function is a high-dimensional entity, and it is therefore extremely difficult to capture all the nuances that encode how the individual electrons affect each other. Many methods of quantum chemistry in fact give up on expressing the wave function altogether, instead attempting only to determine the energy of a given molecule. This however requires approximations to be made, limiting the prediction quality of such methods.
Other methods represent the wave function with the use of an immense number of simple mathematical building blocks, but such methods are so complex that they are impossible to put into practice for more than a mere handful of atoms. “Escaping the usual trade-off between accuracy and computational cost is the highest achievement in quantum chemistry,” explains Dr. Jan Hermann of Freie Universität Berlin, who designed the key features of the method in the study. “As yet, the most popular such outlier is the extremely cost-effective density functional theory. We believe that deep “Quantum Monte Carlo,” the approach we are proposing, could be equally, if not more successful. It offers unprecedented accuracy at a still acceptable computational cost.”
The deep neural network designed by Professor Noé’s team is a new way of representing the wave functions of electrons. “Instead of the standard approach of composing the wave function from relatively simple mathematical components, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around the nuclei,” Noé explains. “One peculiar feature of electronic wave functions is their antisymmetry. When two electrons are exchanged, the wave function must change its sign. We had to build this property into the neural network architecture for the approach to work,” adds Hermann. This feature, known as “Pauli’s exclusion principle,” is why the authors called their method “PauliNet.”
Besides the Pauli exclusion principle, electronic wave functions also have other fundamental physical properties, and much of the innovative success of PauliNet is that it integrates these properties into the deep neural network, rather than letting deep learning figure them out by just observing the data. “Building the fundamental physics into the AI is essential for its ability to make meaningful predictions in the field,” says Noé. “This is really where scientists can make a substantial contribution to AI, and exactly what my group is focused on.”
There are still many challenges to overcome before Hermann and Noé’s method is ready for industrial application. “This is still fundamental research,” the authors agree, “but it is a fresh approach to an age-old problem in the molecular and material sciences, and we are excited about the possibilities it opens up.”
Reference: “Deep-neural-network solution of the electronic Schrödinger equation” by Jan Hermann, Zeno Schätzle and Frank Noé, 23 September 2020, Nature Chemistry.
DOI: 10.1038/s41557-020-0544-y
Repulsion or attraction between two magnetic dipoles
The force between two wires, each of which carries a current, can be understood from the interaction of one of the currents with the magnetic field produced by the other current. For example, the force between two parallel wires carrying currents in the same direction is attractive. It is repulsive if the currents are in opposite directions. Two circular current loops, located one above the other and with their planes parallel, will attract if the currents are in the same directions and will repel if the currents are in opposite directions. The situation is shown on the left side of Figure 7 . When the loops are side by side as on the right side of Figure 7 , the situation is reversed. For two currents flowing in the same direction, whether clockwise or counterclockwise, the force is repulsive, while for opposite directions, it is attractive. The nature of the force for the loops depicted in Figure 7 can be obtained by considering the direction of the currents in the parts of the loops that are closest to each other: same current direction, attraction opposite current direction, repulsion. This seemingly complicated force between current loops can be understood more simply by treating the fields as though they originated from magnetic dipoles. As discussed above, the B field of a small current loop is well represented by the field of a magnetic dipole at distances that are large compared to the size of the loop. In another way of looking at the interaction of current loops, the loops of Figure 7 (top) and 7 (bottom) are replaced in Figure 8A and 8B by small permanent magnets, with the direction of the magnets from south to north corresponding to the direction of the magnetic moment of the loop m. Outside the magnets, the magnetic field lines point away from the north pole and toward the south pole.
It is easy to understand the nature of the forces in Figures 7 and 8 with the rule that two north poles repulse each other and two south poles repulse each other, while unlike poles attract. As was noted earlier, Coulomb established an inverse square law of force for magnetic poles and electric charges according to his law, unlike poles attract and like poles repel, just as unlike charges attract and like charges repel. Today, Coulomb’s law refers only to charges, but historically it provided the foundation for a magnetic potential analogous to the electric potential.
The alignment of a magnetic compass needle with the direction of an external magnetic field is a good example of the torque to which a magnetic dipole is subjected. The torque has a magnitude τ = mB sin ϑ. Here, ϑ is the angle between m en B. The torque τ tends to align m met B. It has its maximum value when ϑ is 90°, and it is zero when the dipole is in line with the external field. Rotating a magnetic dipole from a position where ϑ = 0 to a position where ϑ = 180° requires work. Thus, the potential energy of the dipole depends on its orientation with respect to the field and is given in units of joules by 
Equation (7) represents the basis for an important medical application—namely, magnetic resonance imaging (MRI), also known as nuclear magnetic resonance imaging. MRI involves measuring the concentration of certain atoms, most commonly those of hydrogen, in body tissue and processing this measurement data to produce high-resolution images of organs and other anatomical structures. When hydrogen atoms are placed in a magnetic field, their nuclei (protons) tend to have their magnetic moments preferentially aligned in the direction of the field. The magnetic potential energy of the nuclei is calculated according to equation (7) as −mB. Inverting the direction of the dipole moment requires an energy of 2mB, since the potential energy in the new orientation is +mB. A high-frequency oscillator provides energy in the form of electromagnetic radiation of frequency ν, with each quantum of radiation having an energy hν, where h is Planck’s constant. The electromagnetic radiation from the oscillator consists of high-frequency radio waves, which are beamed into the patient’s body while it is subjected to a strong magnetic field. When the resonance condition hν = 2mB is satisfied, the hydrogen nuclei in the body tissue absorb the energy and reverse their orientation. The resonance condition is met in only a small region of the body at any given time, and measurement of the energy absorption reveals the concentration of hydrogen atoms in that region alone. The magnetic field in an MRI scanner is usually provided by a large solenoid with B of one to three teslas. A number of “gradient coils” insures that the resonance condition is satisfied solely in the limited region inside the solenoid at any particular time the coils are used to move this small target region, thereby making it possible to scan the patient’s body throughout. The frequency of the radiation ν is determined by the value of B and is typically 40 to 130 megahertz. The MRI technique does not harm the patient because the energy of the quanta of the electromagnetic radiation is much smaller than the thermal energy of a molecule in the human body.
The direction of the magnetic moment m of a compass needle is from the end marked S for south to the one marked N for north. The lowest energy occurs for ϑ = 0, when m en B are aligned. In a typical situation, the compass needle comes to rest after a few oscillations and points along the B field in the direction called north. It must be concluded from this that Earth’s North Pole is really a magnetic south pole, with the field lines pointing toward that pole, while its South Pole is a magnetic north pole. Put another way, the dipole moment of Earth currently points north to south. Short-term changes in the Earth’s magnetic field are ascribed to electric currents in the ionosphere. There are also longer-term fluctuations in the locations of the poles. The angle between the compass needle and geographic north is called the magnetic declination (sien Earth: The magnetic field of the Earth).
What Dark Matter is
What Dark Matter is, and why it behaves the way that it does Abstract: I am proposing that the fundamental forces are not dependent upon the distances between objects. Instead, each force is dependent upon a specific angle. Once the forces are calculated using this angle rather than distance as input, many of the mysteries plaguing modern Physics are elegantly solved. One of the implications of this new theory is that at a certain distance, each force will reverse direction. “Dark Matter” then becomes revealed as the repulsive gravitational force between galaxies. Besides showing how the physical laws might be re-worked, later in the article I explain how number theory suggests WHY they behave this way. I ask that the reader not dismiss my theory until my reasoning in number theory is explained at the end of the article. That explanation justifies why space behaves in this way.
I will begin with the gravitational forces between galaxies. I propose that the form of the equation for this gravitational force should look something like this: F = (1.047 X 10 -17) m1m2 [-cos(Θ)] / r 2 where tan Θ = r / (1.419 X 10 22)
Here, force is in Newtons, mass in kg, distance in m. I am taking the distance (1.419 X 10 22) meters as the diameter of the largest known galaxy. I will, in the future call this distance “L”. (1.047 X 10 -17) is a constant that may be adjusted when this idea is fitted to actual data. Before explaining my reasoning, I will first insert a disclaimer: This is my first amateurish attempt at suggesting the form that a real equation for gravity should take. I may have made serious errors in the particular numbers, but I am insisting that an astrophysicist would be able to derive an accurate equation that fits the data of galactic motion. The main point that I am trying to stress is when the equation is put in final form, it will be shown that gravitational force is only dependent upon the masses involved and the angle. It is not dependent upon the distance between objects except in the sense that the distance is itself dependent upon L and Θ.
The way that I derived this particular equation:
Draw a line between the two masses and find the midpoint of this line. Call this line j, and the midpoint E. At this midpoint, draw another line perpendicular to the first line. Call this perpendicular line w. On the perpendicular, move L meters away from the original line and plot a point. Call this point C.
Draw two more lines connecting C with m1 and m2 respectively. Θ is the angle between the lines m1 C and m2 C .
My work in number theory (explained later) suggests that the direction of the gravitational force is actually based upon m1m2 cos (Θ) looking at m1 for example, this suggests a torque force operating at an angle of 90° to the line m1 C.
If this is the case, then why don’t the two masses move towards each other along the arc of a circle? Why do they move at each other along a straight line? It is because this calculation must be repeated 3 more times i.e. we must find another point like C on w, on the opposite side of j. Then we must draw a third line f that is perpendicular to both w and j, through E, and then repeat our calculation 3 more times. This means that the gravitational force is actually a sum of four distinct “torque-like” forces, balancing each other so that the final direction is a straight line. I use the words “torque-like” or “sum”, but I am not entirely certain that this force is a sum, or an area calculation, or a volume calculation. The only thing that I am certain about is that the final form of the equation will be dependent upon the masses, L, and Θ. It will not be dependent upon the distance except indirectly, since the distance is dependent upon L and Θ. I would like now to explore some of the implications of this theory:
The force of gravity is a property of space. It is not caused by matter instead, it acts on matter. This property pushes matter such that the “torque-like force” between masses is minimized. At certain distances this means gravity will be attractive, but at greater distances the “torque-like force” will be minimized if gravity is repulsive.
It will be argued that my selection of some point “C” out in space is arbitrary, but so is the speed of light. I can only assume that some talented physicist will, in the future, be able to explain this angle in a way that relates to the interior of the system m1 and m2 perhaps related to a constant like the Planck’s constant somehow.
This suggests that there is a center to the universe and the effects of dark matter are merely the effects of the negative gravity of galaxies upon each other. Galaxies near the center will be more regular shaped as they have this force more uniformly surrounding them. Galaxies near the edge will be deformed probably their “disc” will be concave with the concavity pointing towards the center of the universe.
More objects must mean more angles, which must mean more “torque-like” forces. Objects are pushed in the direction that leads to a lower energy state. Thus, objects are either going to be pushed together because one single “perspective” is lower energy than many competing perspectives. Or else objects will be pushed so far away that their effect upon each other is near zero. Either way can reduce the energy state.
Relativity: If linear motion is thus understood as compromise between competing torque-like forces, then there are always 4 opposing centrifugal forces perpendicular to the line of motion. At non-relativistic speeds they have no detectable effect. As one tries to accelerate the object closer and closer to the speed of light, more and more of the energy is diverted to the 4 mutually opposing vectors. Since these opposing vectors are pressing upon every part of the object simultaneously, the only way they can be detected is in noting the increase in energy of the object sometimes expressed as an increase in mass. At the speed of light, 100% of any force along the line of travel will be diverted to the perpendicular vectors.
Particles do not generate “fields”. Physical laws are dependent upon the angles between two objects. Force operates to minimize the “torque-like” force caused by these angles, NOT to minimize the distance. This is why forces can “flip.” This means that a lone electron in space, if there is no other object in space, would NOT be generating an electric field around itself, i.e. force, by definition, is a property of space that operates between two objects. Though “field” is obviously a useful mathematical tool, it does not represent anything real. Since an angle needs two objects to cause the force, if there are not two objects, then there is no angle, and there is no force.
Since light seems to be a self-propagating force, understanding how light is dependent upon the angle between emitter and recipient is something to work on. Perhaps it is a particle while in motion and only takes on wave properties when detected? Ek weet nie.
In any case, since space mandates 3 dimensions (see my explanation below), there is an interesting investigation ahead to determine just how and why the magnetic force, the electric force, and the direction of travel are all perpendicular to each other when light travels.
I suspect that gravity acts upon total energy, i.e. the “mass” of an object is the total sum of all the energy contained by that object. This total energy includes all the energy from the actions of the other 3 fundamental forces.
I suspect that the other 3 forces are capable of “flipping” at a certain distance as well. This would explain several things.
There is no “anti-matter.” There are only positrons and electrons. At normal atomic distances, positrons are attracted by the strong force and electrons are repelled by it. This is why positrons reside in the nucleus and electrons don’t. The normal electron distance from the nucleus in an atom of hydrogen must be where the electric force of attraction to the positive nucleus perfectly balances with the repulsion caused by the strong force. I suspect that in an atom of hydrogen the positron is tightly bound in a strong force orbital to the neutron.
There are not “protons” and “neutrons” in the nucleus. There are just neutrons with positrons. At what distance the strong force “flips” and begins to repulse positrons and attract electrons I do not know.
Time is not a single dimension. A dimension is a direction. A direction is a proportion. Time is a proportion between the change in one thing as compared to a change in something else. Thus, the potential dimensions of time are practically infinite, since any two objects being compared create their own particular dimension of time. The idea of time is thus caused and manifested by the physical laws. It is not a cause of the physical laws. The only way in which the concept of time as a cause can make sense is if the unit of time is presented as dependent upon the objects under consideration I call this “causal time.” One source of misconceptions in physics is putting time on an axis as if the variables were dependent upon it in some way. To be accurate, the physical laws should be defined without reference to time.
Since particle physics suggests that ultimately physical measurements are quantized, then continuity is an illusion and it breaks down when you try to apply equations based on continuity to values which can only be discrete. At that point calculations must express continuity in the form of statistical probabilities. The illusion of continuity can only be maintained for relatively large objects and relatively large distances.
I suspect the mysterious effects of “spooky action at a distance” occur because the entangled objects are dependent on a shared angle, NOT dependent on a distance.
Bose-Einstein condensates, taking super-cooled helium as an example: How and why does it climb the walls of a container to pool below it? A noble gas, helium minimizes electro-static interference with atomic motion. When it is super-cooled, motion becomes minimal as well, and the atoms become entangled and take on the characteristics of a single particle. One of these characteristics is some ambiguity about the particle’s precise “location.” Gravity forces motion in a direction minimizing the angle between two objects gravity forces the super-particle along a path leading it closer to Earth. I suspect that microscopic deformations in the shape of the Helium in the container enable enough energy to be borrowed to enable one atom of the Helium to get up and over the edge. Once a single atom gets over the edge, it gives back energy to the particle. It is able to do this because it is still entangled with the super particle.
I must include one fantasy / science fiction speculation along with the more concrete speculations that I’ve given. Since Bose-Einstein condensate behavior suggests that energy may be transferred between entangled particles, and since motion is dependent upon angle, not distance, then instantaneous faster-than-light travel might be accomplished by entangled masses “switching places” i.e. if I could somehow instantaneously switch places with an identical mass in a distant solar system, no energy law would be broken. Hopefully I would end up somewhere able to sustain my ample mass.
I will now explain the geometric reasoning that led me to speculate that motion in space is based upon angle rather than distance: Abstract: Flatland, by Edwin Abbott (1884 Seely & Co.), tells the story of a square that attempts to prove to one-dimensional people the reality that two dimensions are possible. Later, a sphere appears to him and convinces him of the possibility of 3 dimensions. Then the square suggests to the sphere that maybe 4 or even more dimensions are possible. This article begins informally by showing how and why a 1-dimensional person might suspect there are 2-dimensions, and likewise why a 2-dimensional person might theorize about three dimensions. Then it will be shown why a 3-dimensional person may suspect that there are no further dimensions. Some characteristics of geometric space: If we assume that movement in space must be continuous i.e. that any movement can be infinitely subdivided (temporarily setting aside quantum Physics), we find an inconsistency about movement on a number line (i.e. one-dimensional movement). The inconsistency is in the direction of movement. While it is easy for us to conceptualize a partial change in magnitude, direction gives us only two discrete choices: + or -. A one-dimensional mathematician might notice how quantity of movement can be sometimes analogous to the variation of a variable, such as how much money he has. If he further speculates on the relationship between two variables, supposing for example where x = quantity of money, and y = the numbers of apples he can buy, he might be able to come up with the equivalent to our Cartesian plane, and he would understand each point in that plane as having two coordinates: (# of dollars, # of apples). He would then have to come up with explanations of positive and negative slope, and he might arrive eventually at all of our theorems regarding plane geometry. This is where he would learn that change of direction can be partially positive and partially negative. I.e. if facing in the positive direction on the x axis (dollars), he can rotate counter-clockwise to achieve a direction that is partially positive in the x direction and partially positive in the y direction. If he continues to rotate 360 degrees, he will find that there are four pairs of signs, and he can move through all of these signs continuously. The four pairs of signs match up with our traditional quadrants:
+, - +, - -, + - At this point, he might begin speculating about the existence of a 2nd dimension after noticing that travel in his artificially constructed plane is more continuous than travel in his one-dimensional existence. This is because every positive change of direction can be described partially and continuously instead of a simple discrete choice of + or -. Because of this, he might make a bold prediction that there may be a 2nd dimension. But there is a problem in that discontinuity still exists: In the plane, rotations (continuous change of direction) must still be described as + (counter-clockwise) or – (clockwise). The initial reaction to this fact might be a suspicion that proceeding further will result in an infinite process, i.e. if we introduce another dimension to allow partially positive or partially negative changes in the rotation in the plane, then we will have a repeated problem dealing with the discrete dichotomous choice of + up or – down rotation in the third dimension. Upon reflection however, we find that this is not the case, because any rotation in any plane existing in 3 dimensions can always be described continuously as partial rotations in the other two perpendicular planes. It is much easier to visualize with an example. Let us imagine standing on flat ground and facing East. I can describe any rotation continuously by imagining I can rotate in the following 4 quadrants: (South, Up), (North, Up), (North, Down), (South, Down). Thus, any directional change can be expressed as a continuous fraction.
If I lie flat on my back looking upward with my head in the North direction, I can look into space straight up. Doing this, I can see that any change of direction can be described continuously and fractionally by rotating the following 4 quadrants: (West, North), (East, North), (East, South), (West, South). Lastly, if I stand up again and face North, then rotations can be described as (East, Up), (West, Up), (West, Down), (East, Down). Thus, if I consider myself as the origin, then all possible rotations (change of direction) can be continuously and fractionally described with 3 dimensions, or axis. This suggests the following theorem:
Any change of magnitude of a single continuous variable is necessarily and completely described as 3-dimensional. Less than 3 dimensions are incomplete, and more than three dimensions are superfluous.
It also means that any magnitude, to be fully defined, must use a sign convention that designates what Octant it is in. Or if it is on an axis. If we define the three axis as x, y, and z, then these are the 8 sign conventions: (+x, +y, +z) (-x, +y, +z) (-x, -y, +z) (+x, -y, +z) (+x, +y, -z) (-x, +y, -z) (-x, -y, -z) (+x, -y, -z) Our regular sign convention of + or – is thus incomplete when defining magnitudes of a variable. This is most easily demonstrated by considering the mathematical statement -2 X -2 = +4. This statement is ambiguous in that it precisely defines the magnitude of an area, but the location of this area has several different possibilities. One thing we may say is that it CAN NOT mean a multiplication exclusively on the x axis for example. Let me explain why. It is traditional when teaching multiplication to children to use a table of values. I will restrict the first multiplication that I am going to show you to two dimensions. I am going to multiply a negative x value times a negative y value. Notice how I must conserve the proportion of signs in order to designate that this will be in quadrant III in the x / y plane:
Looking at this chart tells me that when I multiply -2 in the x direction times -2 in the y direction I get 4 square units. The designation (-x/-y) is in slope form because directions are being defined as slopes. This particular slope tells me that my 4 square units will be located in quadrant III. Now, what if I multiply two numbers that are each in the same direction?
Since all the slopes are fractions, and since anything over itself is just one, then:
This means that any multiplications of vectors in the same direction results in pure dimensionless magnitudes i.e. numbers that have no implied direction. This means that a negative x times a negative x does NOT equal a positive x. It equals a dimensionless magnitude. Using this procedure, a positive x times a positive x gives the same result. Using the same procedure, we can see that a negative 2 in the x direction times a positive 2 in the x direction will yield an ambiguous, difficult to interpret, perhaps contradictory result: (-x/+x) 4. What this means, I do not know. I suspect it means that any multiplication in a single dimension must be understood as a dimensionless magnitude.
Here are some of the implications of this line of thinking:
Since 3 dimensions are implied in any geometric space, much of our mathematics has an ambiguity at the very heart.
Every continuous magnitude, to be entirely accurate, should have 3 directional components attached to it.
There are 3 and only 3 geometric dimensions. Any less is ambiguous, any more are superfluous.
De Moivre’s theorem works because the square root of -1 is a real number. It is not imaginary. There is no imaginary plane the square root of negative one is ambiguous, but real.
Since the very definition of continuous motion mandates 3 and only 3 dimensions, this suggests that any continuous motion in real space must be completely defined in 3 dimensions to be accurately understood.
Since any motion in space is defined as being 3 dimensional, then the laws of motion in space might be dependent upon angle rather than upon distance. I suspect that this is the case.
Because time is a proportion between changes in any two arbitrary things, time should not be treated as if it is a “dimension” associated with geometric space except in the sense where causal time is rigorously defined as some rate of change between objects where that rate of change is dependent upon physical laws. Time is a product of the laws, it is not a cause of them. In a physics sense, it may be loosely defined as a record of the changes in the local energy of a system. We tend to associate time with the direction that changes tend to go, but this is informal and ambiguous.
Various functions in mathematics like the trigonometric functions should be rigorously re-defined to remove all ambiguity. In my work on the “torque-like” force of gravity upon galaxies I kept on getting results showing it to be perpetually positive when it should have been negative, because the sine function was yielding a consistently positive result, and it is usually the function associated with torque. When I switched to the cosine of the supplement I started getting correct results.
I would like to include below my attempt at a proof that got me started on this train of thought. I thought of a proof that there are only three dimensions and I sent it in to a mathematics journal and it was rejected. They would not give any feedback, so I assumed that it must be trivial. But trying to figure out why it was trivial caused me to go into all the investigations that I outlined up above:
A proof that more than 3 dimensions are redundant in a geometric space.
Space is defined as the set of all possible points.
To locate a point means to state dimensional measurements that describe this one point and exclude all other points.
This paper intends to prove there are a maximum of three dimensional measurements required to locate any point in space.
One and only one point is located at the intersection of two lines. Any additional lines drawn through the point are superfluous and are not necessary in locating the point.
Observe that this is true in 2-dimensional space as well: An infinite number of lines can be drawn through a point, but only two are required to precisely locate the point.
Any point in space can be located on a straight line.
A straight line can be drawn from any point in space to any other point in space.
Two points can be defined as being one and only one specific distance from each other on a straight line. This distance is the shortest distance between these points.
The specific straight-line segment between two points is the one and only one shortest distance between them.
Any point in space not on a flat plane may be located a certain perpendicular distance from the plane. This perpendicular distance is the shortest distance from the point to the plane.
From any point on a plane, treating this point as the vertex of an angle, an angle can be drawn between the plane and any point that is not on the plane.
Any point in space may be arbitrarily labelled as the origin and/or point A.
Any other point in space may be arbitrarily labelled point B, and the line AB may be drawn.
A third point in space that is not on the line extending from the origin to point B may be labelled as point C.
An angle can be formed using the origin as a vertex and any other two points if they are not all on the same line.
There is one and only one smallest angle whose vertex is point A and is formed by the rays AB and AC.
There is one and only one flat plane that contains angle BAC.
Any other point in space, that is not on plane BAC, may be labelled point D.
Point E can be arbitrarily located on plane BAC such that the smallest angle formed by DE and plane BAC can take on any value from 0 to 90 degrees. Specifically, E can be arbitrarily located such that this angle is 90 degrees, so that DE is perpendicular to plane BAC.
To locate point D, we need only three measurements: 1. we can use the degree angle of BAE within plane BAC. 2. Then we can note the degree angle of DAE. This will define the line AD. 3. Lastly, we can note the degree angle of DBE. This will define the line BD.
Since lines AD and BD can intersect at one and only one point, point D is located.
Alternatively, if the distance AD is known, then point D can be located thus: 1. We can use the degree angle of BAE within plane BAC. 2. Then we can note the degree angle of DAE. This will define the line AD. 3. If we travel the specific distance along line AD, From A to D, then point D will be located.
The same procedure can be used to locate any point in space. Using similar logic, all points in space could be located using 3 or less rectilinear coordinates.
Since any and all geometric points can be located using at most 3 measurements, Geometric space has at most 3 necessary dimensions any other dimensions added are superfluous.
Note on Non-Euclidean geometries: A triangle located on the surface of a sphere or some other solid does not have angles that add up to 180 degrees. I have not researched it, but I might suppose that other such geometries may suggest contradictions to my proof. My first inclination would be to disagree with this, since all examples of Non-Euclidean geometry, to my knowledge, can be translated into shapes and/or motion describable with Euclidean geometry.
Note on the implications of this proof on Physics: Although I am a layman when it comes to modern Physics, I would like to make a few observations. Since objects approaching the speed of light cause lengths (and, I assume, angles) to deform, I assume that geometric space is not a good representation of Real Space, and the two should not be confused.
In a similar vein, the fact that subatomic particles simply disappear and reappear in different places shows that they do not “travel” through “space” in the way represented by objects drawn in geometric space. This suggests to me that Real Space may be an artificial construct we have invented along geometric lines to describe the “motion” of macro objects, but that our research at the subatomic level suggests that motion and space might be an illusion – the behavior of subatomic particles might better be described by a system of logic rather than by traditional motion in coordinate axes. In the game of chess, for example, bishops and rooks move in a way that might be described as geometric motion, whereas the “motion” of the knight is rather a logical definition. The bishops and rooks might be described as moving through intermediate stages that can be obstructed by other pieces, whereas the knights cannot be described as moving in this fashion.
Lastly, a note on popular ideas as regards “dimensions”: There is the old example of some two dimensional being unable to imagine a 3rd dimension, and it is posited that there might be other dimensions and we just can’t imagine them. I hope my proof shows clearly how for this to be possible, then we would have to assume that a point cannot be defined by the intersection of two lines. Notice how even a point in two dimensions can have infinite lines drawn through it, yet it still only needs two lines drawn through it to define it. The same goes for any point in any number of dimensions.
So what the popular notion of dimensions more-than-3 has come to mean is objects that are not detectable, motions that are not detectable – in short, it means ghosts and inexplicable shortcuts, which is the stuff of fantasy – my comments about particle physics notwithstanding.
It basically means: “Imagine some point in space that you cannot draw a direct line to from other points in that same space.” I think that this is nonsense.
In light of new evidence I have substantially re-worked my theory as regards Gravity. It is to be found here:
