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Wave Function Collapse and Gravity Wave function collapse and gravity Is Quantum Theory Exact? The quest for the spin-statistics connection violation and related items Frascati – IT 2nd - 5th July 2018 (Angelo Bassi – University of Trieste & INFN) In memory of GianCarlo Ghirardi (1935 - 2018) Decoherence • The Schrödinger equation is correct • Take system + environment • Let them interact for a while, for correlations to be diluted in the environment • Trace over the degrees of freedom of the environment • Output: classicality (in some sense) Quantum micro world Quantum macro world (but looks classical) Wave function collapse (models) • The Schrödinger equation is not 100% correct. • Correction are negligible for micro systems and relevant for macro objects • At the macroscopic level one recovers classicality Progressive breakdown of quantum linearity with increasing mass Quantum micro world “Classical” macro world Gravitational decoherence Schrödinger equation (at the Newtonian level) d i = H + V (x, t) dt t 0 t <latexit sha1_base64="ofnFfoibR07koi1ESsTyGrYy5t0=">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</latexit> | i − | i ~ Gravitational potential = the environment “OR” Decoherence: impossibility to detect quantum coherence Gravitational potential news & views GRAVITY Gravitational decoherenceWanna be quantum Superpositions of massive objects would be hard to spot on Earth even in well-isolated environments because of the decoherence induced by gravitational time dilation. Being a standard quantum effect, it does not affect the foundations of quantum Angelo Bassi mechanics (the measurement problem), in spite of its “unavoidability” ho wouldn’t like to experience quantum properties do not survive when Every experimentalist trying to measure a quantum life? We could do they combine to form macroscopic objects. quantum delocalization of material systems Wmany things in parallel: working, Why so? (the situation in which a quantum system There are interesting theoretical aspect to clarify: playing, doing sports, having a meal and Writing in Nature Physics Igor Pikovski is in a superposition of two diferent sleeping. All at the same time — at least as and colleagues1 argue that Earth’s locations at the same time) faces the same A. What is the correct form of the deocherencelong as no one is watchingB. us.Stochasticity We could gravitational is feldnot causes any delocalized state annoying problem: environmental noise, instantly teleport ourselves far away when of a quantum system to decohere and lose its technically known as decoherence2. Te annoyed with a situation. Many childhood quantum properties — even if the system is system’s position very rapidly couples with effect? dreams would come true.necessary However, it seems for isolateddecoherence from the rest of the world. And this the surrounding environment: its quantum we are bound to be classical; (I. Pikovski not a boring et al . Nature Physics efect seems- 2015) strong enough to be signifcant behaviour is diluted and ultimately lost upon life, but less exciting than a quantum one. A for objects on human scales. Te new element measurement. Delocalization of complex much-debated question among physicists is: is that this decoherence is triggered by time systems has only been observed when the • Decoherence in position why so? In the end, we are made of atoms, dilation — one of the striking predictions of system is not too big and is well isolated3,4, (B. Lamine et al., PRL 96, 050405 - 2006) which are quantum. But their most amazing general relativity. Here is how it goes. otherwise it only occurs on extremely short time scales5. [Au: ok?] For larger systems, Beamsplitter like humans, any quantum feature is rapidly • Decoherence in energy Mirror lost in the environment we live in. Hence no (M.P. Blencowe, PRL 111, 021302 - 2013) one will see us taking a quantum jump. However, there is always the possibility to clean the environment better and better, to reduce, and ideally fully remove, its è Toll for gravitational wave detection (since infuence. Tis is a technological problem, a very difcult one, that will keep physicists quantum coherences are fragile) Detector busy for a long time. Meanwhile, we can ask the question: can we eventually reach an almost perfectly clean environment, Beamsplitter where even large massive objects are free Mirror to behave quantum mechanically (if they C. What is the difference between decoherence really do so)? For example, we can think of removing all particles foating around with from gravitons and decoherence from a classical a powerful ultra-vacuum pump. We can imagine shielding the object from all sorts of stochastic gravitational background? è Toll for radiations. We can even succeed in cooling Earth everything down with the best available refrigerator. We can imagine doing many graviton detection (speculation) such amazing things. Still, something will remain: the Earth’s gravitational feld. Suppose that we create a superposition of two diferent spatial locations, separated by a distance Δx. Ten each term of the superposition feels two slightly diferent gravitational potentials: V(x) = mgx, where x is the vertical position, m is the total mass Figure 1 | Decoherence triggered by the Earth’s gravitational field. [Au: ok? caption must begin and g is the acceleration due to the Earth’s with a brief introduction sentence] A quantum system — even if isolated from the surrounding gravity. [Au: ok?] Now, and this is the environment — will decohere due to the presence of the Earth’s gravitational field because its internal crucial point of the work by Pikovski et al.1, degrees of freedom vibrate diferently depending on their position with respect to the field (clocks run the internal state of the system, in each of slower closer to massive objects, according to the general theory of relativity). When the system is in the two terms of the superposition, will a superposition of two diferent locations, such as traveling along the two arms of an interferometer, as evolve diferently. Tis is because, according shown here, its internal structure becomes entangled with the position of its centre of mass, which then to the general theory of relativity, clocks decoheres. [Au: ok?] run slower closer to a massive object, and NATURE PHYSICS | VOL 11 | AUGUST 2015 | www.nature.com/naturephysics 1 (Mass-proportional) CSL model P. Pearle, Phys. Rev. A 39, 2277 (1989). G.C. Ghirardi, P. Pearle and A. Rimini, Phys. Rev. A 42, 78 (1990) d i pγ = H + d3x (M(x) M(x) ) dW (x) dt| ti − m h it t ~ 0 Z γ d3xd3yG(x y)(M(x) M(x) )(M(y) M(y) ) −2m2 − h it h it | ti 0 ZZ 1 2 2 M(x)=ma†(x)a(x) G(x)= 3/2 exp[ (x) /4rC ] (4⇡rC ) − The operators are function of the space coordinate. The collapse occurs in space. Two parameters γ = collapse strength rC = localization resolution 2 3/2 λ = γ/(4⇡rC ) = collapse rate REVIEW: A. Bassi and G.C. Ghirardi, Phys. Rept. 379, 257 (2003) A. Bassi, K. Lochan, S. Satin, T.P. Singh and H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013) The overall picture Stable. λ too small Hilbert space Microscopic Stable. Already localized (d << rC) systems Macroscopic objects Unstable! Nλ large and d >> rC Stable. No cat-like superposition BECs, SQUIDs, superfluids … Macro superpositions Collapse and gravity It is an attempt to answer the question: why should the wave function collapse? Fundamental properties of the collapse & the possible role of gravity • It occurs in space • It scales with the mass/size of the system The obvious way to describe it mathematically, is to couple the noise field to the mass density (the stress-energy tensor, in a relativistic framework). Gravity naturally provides such a coupling. Moreover The possibility is open for gravity not to be quantum, thus possibly providing the nonstandard (anti-hermitian, nonlinear) coupling necessary for the collapse. REVIEW ARTICLE: A. Bassi, A. Grossardt and H. Ulbricht, “Gravitational Decoherence”, Class. Quantum Grav. 34, 193002 (2017). ArXiv1706.05677 The Diosi – Penrose model L. Diosi, Phys. Rev. A 40, 1165 (1989) It is like the CSL model, the only difference being in the correlation function of the noise, which is G 1 G(x)= Gravity. And no other free parameter (almost…) ~ x | | Remarks: • Model not derived from basic principles, but assumed phenomenologically • There is no justification as to why gravity should be responsible for the collapse • It is not clear with the correlation function should be Newtonian • If there is truth in the model, then quantum gravity as we know it is wrong Diosi – Penrose model L. Diosi, Phys. Rev. A 40, 1165 (1989) It leads to the collapse of the wave function. To measure how strong it is one can consider the (single-particle) master equation. It is of the Lindblad type, and implies t/⌧(x,x0) ⇢(x, x0,t)=e− ⇢(x, x0, 0) ~ 3 3 M(r)M(r0) ⌧(x, x0)= U(x)= G d rd r0 U(x x ) U(0) − x + r r − 0 − Z | − 0| Penrose’s idea It diverges for point-like particles (Quantum) gravity does not tolerate One needs a regularizing cut off quantum superpositions 564 Found Phys (2014) 44:557–575 Diosi – Penrose model R. Penrose, Gen. Rel. Grav. 28, 581 - 1996 We have to consider carefully what a ‘stationary state’ means in a context such as this. In a stationary spacetime, we have a well-defined concept of ‘stationary’ for a quantum state in that background, because there is a Killing vector T in the spacetime that generates the time-translations. Regarding T as a differential operator (the ‘∂/∂t’ for the spacetime), we simply ask for the quantum states that are eigenstates of T, and these will be the stationary states, i.e. states with well-defined energy values. [...] However, for the superposed state we are considering here we have a serious problem.
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