Wavefunctioncollapse,gravityandspace

RencontresdeMoriondGravitation

23th–30thMarch2019

(AngeloBassi–UniversityofTrieste&INFN)

“Thetroublewithquantummechanics”Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. Albert Einstein

I’m not as sure as I once was about the future of quantum mechanics. Steven Weinberg

Ifyouthinkyouunderstandquantum

mechanics,youdon’tunderstand

quantummechanicsRichard

Feynman

if you push quantum mechanics hard

enough it will break down and something else will take over – something we can’t

envisage at the moment.

Anthony J. Leggett

StandardQuantumMechanics

Quantumworld Classicalworld

Thewavefunctiongivestheprobabilitiesofoutcomesofmeasurements

TheCopenhageninterpretationassumesamysteriousdivisionbetweenthemicroscopicworldgovernedbyquantummechanicsandamacroscopicworldofapparatusandobserversthatobeysclassicalphysics.[…]S.Weinberg,Phys.Rev.A85,062116(2012)

Whynotsimplyremovingthedivision?

LinearityèSuperpositionPrincipleèItpropagatesfromthemicrotothemacro

Schrödinger’scat

Spontaneouswavefunctioncollapse

TheycombinetheSchrödingerevolutionandthecollapseofthewavefunctioninasingleunifieddynamics,accountingforthequantumpropertiesofatomsandmolecules,theclassicalpropertiesofmacro-objects,andexplainingwhyquantummeasurementoccurtheywaytheyoccur.èModificationoftheSchrödingerequation

Spontaneouswavefunctioncollapse

J.S.BellSpeakableandUnspeakableinQuantumMechanics

E.P.Wignerin:QuantumOptics,ExperimentalgravityandMeasurementtheory,Plenum,NY(1983)

A.J.LeggettSupplementProgr.Theor.Phys.69,80(1980)

H.P.StappIn:QuantumImplications:EssayinHonorofDavidBohm,Routledge&KeganPaul,London(1987)

S.WeinbergPhys.Rev.Lett.62,486(1989).

R.PenroseIn:QuantumConceptsofSpaceandTime,OxfordU.P.(1985)

S.L.AdlerQuantumTheoryasanemergentphenomenon,CUP(2009)

G.C.Ghirardi,A.Rimini,T.WeberPhys.Rev.D34,470(1986)

P.PearlePhys.Rev.A39,2277(1989)

L.DiosiPhys.Rev.A40,1165(1989)

HowtomodifytheSchrödingerequation?

Theno-faster-than-lightconditionheavilyconstraintsthepossiblewaystomodifytheSchrödingerequation.

Inparticular,itrequiresthatnonlineartermsmustalwaysbeaccompaniedbyappropriatestochasticterms.

N.Gisin,Hel.Phys.Acta62,363(1989).Phys.Lett.A143,1(1990)

N.GisinandM.Rigo,Journ.Phys.A28,7375(1995)

J.Polcinski,Phys.Rev.Lett.66,397(1991)

H.M.WisemanandL.Diosi,Chem.Phys.268,91(2001)

S.L.Adler,“QuantumTheoryasanEmergentPhenomenon”,C.U.P.(2004)

A.Bassi,D.DürrandG.Hinrichs,Phys.Rev.Lett.111,210401(2013)

L.Diosi,Phys.Rev.Lett.112,108901(2014)

M.Caiaffa,A.SmirneandA.Bassi,Phys.Rev.A95,062101(2017)

DiffusionProcessinHilbertSpaceL.Diosi,Phys.Rev.A40,1165(1989)

Wt = standard Wiener process

d t =

� i

~Hdt+p�(q � hqit)dWt �

�

2(q � hqit)2dt

� t

hqit = h t|q| ti nonlinearity

stochasticity

REVIEW:A.BassiandG.C.Ghirardi,Phys.Rept.379,257(2003)

A.Bassi,K.Lochan,S.Satin,T.P.SinghandH.Ulbricht,Rev.Mod.Phys.85,471(2013)

Theequationinducestherandomcollapseofthewavefunction,whichisthestronger,thelargerthesystem

(Mass-proportional)CSLmodelP.Pearle,Phys.Rev.A39,2277(1989).G.C.Ghirardi,P.PearleandA.Rimini,Phys.Rev.A42,78(1990)

Twoparameters

� = collapse strength rC = localization resolution

M(x) = ma†(x)a(x) G(x) =1

(4⇡rC)3/2exp[�(x)2/4r2C ]

d

dt| ti =

� i

~H +

p�

m0

Zd3x (M(x)� hM(x)it) dWt(x)

� �

2m20

Z Zd3xd

3y G(x� y) (M(x)� hM(x)it) (M(y)� hM(y)it)

�| ti

� = �/(4⇡r2C)3/2 = collapse rate

Theoperatorsarefunctionofthespacecoordinate.Thecollapseoccursinspace.

Theoverallpicture

Microscopicsystems

Macroscopicobjects

Macrosuperpositions

Hilbertspace

BECs,SQUIDs,superfluids…

Unstable!Nλlargeandd>>rC

Stable.λtoosmall

Stable.Alreadylocalized(d<<rC)

Stable.Nocat-likesuperposition

CollapseandgravityFundamentalpropertiesofthecollapse&thepossibleroleofgravity

Itoccursinspace

Itscaleswiththemass/sizeofthesystem

REVIEWARTICLE:A.Bassi,A.GrossardtandH.Ulbricht,“GravitationalDecoherence”,Class.QuantumGrav.34,193002(2017).ArXiv1706.05677

Thepossibilityisopenforgravitynottobequantum,thuspossiblyprovidingthenonlinearcouplingnecessaryforthecollapse

Then,thenoisecouplestothemassdensity(thestress-energytensor,inarelativisticframework).Gravitynaturallyprovidessuchacoupling

Diosi – Penrose model…forthesuperposedstateweareconsideringherewehaveaseriousproblem.Forwedonotnowhaveaspecificspacetime,butasuperpositionoftwoslightlydifferingspacetimes.Howarewetoregardsucha‘superpositionofspacetimes’?...Itwillbeshownthatthereisafundamentaldifficultywiththeseconcepts,andthatthenotionoftime-translationoperatorisessentiallyilldefined.

R. Penrose, Gen. Rel. Grav. 28, 581 - 1996

Penrose’sidea:quantumsuperpositionèspacetimesuperpositionèenergyuncertaintyèdecayintimePuttinghisreasoningintoequations,PenrosecomeoutwithbasicallythesameequationsasDiosi’s

564 Found Phys (2014) 44:557–575

Fig. 6 Schrödinger’s lump gives space-time bifurcation

τ ≈ h/EG

where the quantity EG is taken as some fundamental uncertainty in the energy of thesuperposed state see [12], and the above formula is taken to be an expression of theHeisenberg time-energy uncertainty relation (in analogy with the formula relating thelifetime of a radioactive nucleus to its mass/energy uncertainty).

The quantity EG is the gravitational self-energy of the difference between the mass(expectation) distributions of the two stationary states in superposition. (If the twostates merely differ from one another by a rigid translation, then we can calculate EGas the gravitational interaction energy, namely the energy it would cost to separatetwo copies of the lump, initially considered to be coincident and then moved to theirseparated locations in the superposition.) The calculation of EG is carried out entirelywithin the framework of Newtonian mechanics, as we are considering the massesinvolved as being rather small and moved very slowly, so that general-relativisticcorrections can be ignored.

Nevertheless, we are to consider that regarding EG as an energy uncertainty comesfrom considerations of general-relativistic principles. In Fig. 6, I have schematically

123

The Diosi – Penrose modelL. Diosi, Phys. Rev. A 40, 1165 (1989)

LikeCSL(fewslidesago),theonlydifferencebeinginthecorrelationfunctionofthenoise,whichis

G(x) =G

~1

|x|Gravity.Andnootherfreeparameter(almost…)

Remarks:

•  Thegravityeffectisnotderivedfrombasicprinciples,butassumedphenomenologically

•  Ifthereistruthinthemodel,thenquantumgravityasweknowitiswrong

Diosi – Penrose model

Itleadstothecollapseofthewavefunction.Tomeasurehowstrongitisonecanconsiderthe(single-particle)masterequation.

ItisoftheLindbladtype,andimplies

⇢(x,x0, t) = e�t/⌧(x,x0)⇢(x,x0, 0)

⌧(x,x0) =~

U(x� x0)� U(0)U(x) = �G

Zd3rd3r0

M(r)M(r0)

|x+ r� r0|

Penrose’sidea Itdivergesforpoint-likeparticles

L. Diosi, Phys. Rev. A 40, 1165 (1989)

(Quantum)gravitydoesnottoleratequantumsuperpositions

Oneneedsaregularizingcutoff

Diosi – Penrose modelThemodelneedstoberegularized(particleswithfinitesize)

Penrose:SolutionoftheSchrödinger-Newtonequation

Diosi:Comptonwavelength

Inbothcases:R0about10-15m,foranucleon

Point-likeparticle

R0

Extendedparticle

Non-interferometrictests

+

= center of mass

A localization of the wave function changes the position of the center of mass Collapse-induced Brownian motion Also theoretical reasons for that

colla

pse

Constraintsonthecutoff

10-15 10-14 10-13 10-12 10-11 10-10 10-9

R0[m]

X-rays[Workinprogress]

Coldatoms[T.Kovachyetal.,Phys.Rev.Lett.114,143004(2015)]

Cantilever[A.Vinanteetal.,Phys.Rev.Lett.116,090402(2016)]

Diosi/Penrose

NonInterferometrictests

AlsoPenroses’sideaimpliesacollapse-inducedBrownianmotiononparticles.(A.BassiandS.Donadi,inprogress)

Adler’sideaS.Adler,inQuantumNonlocalityandReality:50YearsofBell’sTheorem.CambridgeUniversityPress(2016)

Collapsemightbeinducedbygravity.

Themetrichasanirreduciblycomplex,rapidlyfluctuating,component,besidestheusualrealone.Thiscomponentisresponsibleforthecollapse.

(Realfluctuationswouldleadtodecoherence,nottoarealcollpase)

Thecorrelationfunctionofthenoiseisleftunknown.Thismeansthatgravityisnotquantum–Adlerprovidesmotivationsforthat.

ThemodelshasbeendevelopedbyGasbarrietal.Everythingworkswell:

•  CollapseinspacelikeCSL(withsomeapproximationsonthecorrelationfunction)

•  Amplificationmechanism

G.Gasbarri,M.Toros,S.Donadi&A.Bassi,Phys.Rev.D96,104013(2017)

Adler’sideaS.Adler,inQuantumNonlocalityandReality:50YearsofBell’sTheorem.CambridgeUniversityPress(2016)

G.Gasbarri,M.Toros,S.Donadi&A.Bassi,Phys.Rev.D96,104013(2017)

Picture:boundsonthemagnitudeξofthecomplexfluctuations.

itisinterestingtoseethatweakcomplexfluctuations–weakerthanrealwavesrecentlymeasuredbyLIGO(10-21)-aresufficientforanefficientcollapse

3.3⨯10-19 3.3⨯10-17 3.3⨯10-15 3.3⨯10-13 3.3⨯10-11

10-26

10-24

10-22

10-20

10-10 10-8 10-6 10-4 10-2

τ0 / s

ξ

rc / m

Requirementthatthemodelcollapsesmacro-objects

Gravitationalwaves

Howtomeasureamacroscopicsuperposition?

Matter-waveinterferometry(Viennagroup)

1999(720au) 2013(10123au)

Howfarcanwepushit?

Sowecangouptomassesof10-21Kg=attogram

Ribosome

Bromemosaicvirus

Althoughtheexperimentwillbetechnologicallyverychallenging,theobjectssuperimposedarestillrathersmall.

Performingdiffractionexperimentswithsmallviruseswouldrepresentthefirsttypeofexperimentwithalivingobject.

It’stimeforSpace

Inouterspaceonecancreateconditionsofalmost0gravity.

Experimentscanberunforlongertimes(<100stechnologicallimit).

Masseslargerby2-3ordersofmagnitude(femtogram)canbeused

MAQROProposal:http://maqro-mission.orgCOSTActionQTSpace:www.qtspace.eu

AcknowledgmentsTheGroup(www.qmts.it)•  Postdocs:M.Carlesso,L.Ferialdi•  Ph.D.students:L.Asprea,C.Jones,J.Reyes

www.infn.itwww.units.it

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