A Model of Spontaneous Collapse with Energy Conservation
Author
D. W. Snoke
Title
A Model of Spontaneous Collapse with Energy Conservation
Description
Supplemental notebook to "A Model of Spontaneous Collapse with Energy Conservation"
Category
Academic Articles & Supplements
Keywords
quantum field theory, quantum foundations, spontaneous collapse
URL
http://www.notebookarchive.org/2022-07-5la04jb/
DOI
https://notebookarchive.org/2022-07-5la04jb
Date Added
2022-07-12
Date Last Modified
2022-07-12
File Size
66.28 kilobytes
Supplements
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This file contains supplementary data for D. W. Snoke, "A Model of Spontaneous Collapse with Energy Conservation," Foundations of Physics, 51(5), 2021 100. https://link.springer.com/article/10.1007/s10701-021-00507-z.
A Model of Spontaneous Collapse with Energy Conservation
A Model of Spontaneous Collapse with Energy Conservation
D. W. Snoke
(*Thiscalculationgivesasinglerandomwalk,usingaLorentzian(Cauchy)distributionofkicks,andplotsit*)Nsteps=2000;Theta=Pi/2;m2=Table[0,{i,1,Nsteps,1}];m3=Table[0,{i,1,Nsteps,1}];kick=Table[0,{i,1,Nsteps,1}];For[i=1,i≤Nsteps,i++,kick[[i]]=Sign[Random[]-.5]*Min[Abs[RandomVariate[CauchyDistribution[]]]*norm,.2]];m3[[1]]=Cos[Theta];m2[[1]]=Sin[Theta];dt=1;norm=.005;For[i=2,i<=Nsteps,i++,dm=kick[[i]]*Sqrt[1-(m3[[i-1]])^2];m3[[i]]=m3[[i-1]]+dm*m2[[i-1]]*dt;m2[[i]]=m2[[i-1]]-dm*m3[[i-1]]*dt;While[m3[[i]]>1,{m3[[i]]=1;m2[[i]]=0}];While[m3[[i]]<-1,{m3[[i]]=-1;m2[[i]]=0}]]plottable=Table[{i,m3[[i]]},{i,1,Nsteps,1}];ListPlot[plottable,JoinedTrue,PlotRange{-1,1},AspectRatio.25,PlotStyle{RGBColor[0,0,0],Thickness[.0025]},AxesStyle{{RGBColor[0,0,0],Thickness[.0025]},{RGBColor[0,0,0],Thickness[.0025]}},TicksStyleDirective[FontSize14]]
Out[]=
(*Thiscalculationaveragesovermanyrandomwalkstogetthestatisticsofhittingeitherendpoint,forastartingpointbetweenthetwoendpoints,usingaLorentzian(Cauchy)distributionofkicks.TheBornprobabilityruleisreproduced.Changingthestrengthofthekicksisdonebychangingthevariable"norm".TheBornruleisreproducedforawiderangeofvaluesof"norm".*)jtable=Table[0,{j,1,10}];For[j=1,j≤10,j++,Nsteps=2000;Theta=.1+.8*Pi*(j/10);PosSum=0;NegSum=0;For[is=1,is≤1000,is++,m2=Table[0,{i,1,Nsteps,1}];m3=Table[0,{i,1,Nsteps,1}];kick=Table[0,{i,1,Nsteps,1}];norm=.005;For[i=1,i≤Nsteps,i++,kick[[i]]=Sign[Random[]-.5]*Min[Abs[RandomVariate[CauchyDistribution[]]]*norm,.2]];m3[[1]]=Cos[Theta];m2[[1]]=Sin[Theta];dt=1;For[i=2,i<=Nsteps,i++,dm=kick[[i]]*Sqrt[1-(m3[[i-1]])^2];m3[[i]]=m3[[i-1]]+dm*m2[[i-1]]*dt;m2[[i]]=m2[[i-1]]-dm*m3[[i-1]]*dt;While[m3[[i]]>1,{m3[[i]]=1;m2[[i]]=0}];While[m3[[i]]<-1,{m3[[i]]=-1;m2[[i]]=0}]];PosSum=If[m3[[Nsteps]]>0,PosSum+1,PosSum];NegSum=If[m3[[Nsteps]]<0,NegSum+1,NegSum];pfrac=N[PosSum/(PosSum+NegSum)];nfrac=N[NegSum/(PosSum+NegSum)];];jtable[[j]]=pfrac;Print[j," ",.5+N[Cos[Theta]]/2," ",pfrac]];PTable=Table[{.5+N[Cos[(.1+.8*Pi*(k/10))]]/2,jtable[[k]]},{k,1,10}];a=ListPlot[PTable];b=Plot[x,{x,0,1}];Show[a,b,PlotRange{0,1}]
1 0.969458 0.97
2 0.911917 0.908
3 0.828493 0.836
4 0.724429 0.745
5 0.606263 0.608
6 0.48142 0.492
7 0.357745 0.348
8 0.243008 0.246
9 0.144419 0.138
10 0.0681721 0.07
Out[]=
(*Thiscalculationaveragesovermanyrandomwalkstogetthestatisticsofhittingeitherendpoint,forastartingpointbetweenthetwoendpoints,usingaGaussian(Normal)distributionofkicks.TheBornruleisreproducedforsimilarconditionsastheLorentziandistribution*)jtable=Table[0,{j,1,10}];For[j=1,j≤10,j++,Nsteps=6000;Theta=.1+.8*Pi*(j/10);PosSum=0;NegSum=0;NoDec=0;For[is=1,is≤2000,is++,m2=Table[0,{i,1,Nsteps,1}];m3=Table[0,{i,1,Nsteps,1}];kick=Table[0,{i,1,Nsteps,1}];norm=.025;For[i=1,i≤Nsteps,i++,kick[[i]]=Sign[Random[]-.5]*Min[Abs[RandomVariate[NormalDistribution[]]]*norm,.2]];m3[[1]]=Cos[Theta];m2[[1]]=Sin[Theta];dt=1;For[i=2,i<=Nsteps,i++,dm=kick[[i]]*Sqrt[1-(m3[[i-1]])^2];m3[[i]]=m3[[i-1]]+dm*m2[[i-1]]*dt;m2[[i]]=m2[[i-1]]-dm*m3[[i-1]]*dt;While[m3[[i]]>1,{m3[[i]]=1;m2[[i]]=0}];While[m3[[i]]<-1,{m3[[i]]=-1;m2[[i]]=0}]];PosSum=If[m3[[Nsteps]]>=.99,PosSum+1,PosSum];NegSum=If[m3[[Nsteps]]<=-.99,NegSum+1,NegSum];NoDec=If[m3[[Nsteps]]<.99&&m3[[Nsteps]]>-.99,NoDec+1,NoDec];pfrac=N[PosSum/(PosSum+NegSum+NoDec)];nfrac=N[NegSum/(PosSum+NegSum+NoDec)];ufrac=N[NoDec/(PosSum+NegSum+NoDec)];];jtable[[j]]=pfrac;Print[j," ",.5+N[Cos[Theta]]/2," ",pfrac," ",ufrac]];PTable=Table[{.5+N[Cos[(.1+.8*Pi*(k/10))]]/2,jtable[[k]]},{k,1,10}];a=ListPlot[PTable];b=Plot[x,{x,0,1}];Show[a,b,PlotRange{0,1}]
1 0.969458 0.9715 0.0005
2 0.911917 0.916 0.
3 0.828493 0.82 0.
4 0.724429 0.738 0.
5 0.606263 0.607 0.
6 0.48142 0.4875 0.
7 0.357745 0.353 0.
8 0.243008 0.238 0.
9 0.144419 0.1395 0.
10 0.0681721 0.06 0.
Out[]=
Cite this as: D. W. Snoke, "A Model of Spontaneous Collapse with Energy Conservation" from the Notebook Archive (2022), https://notebookarchive.org/2022-07-5la04jb
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