Still No Schrödinger Cat Jumps The Diosi-Penrose Criterion
    By Sascha Vongehr | March 2nd 2011 02:03 AM | 7 comments | Print | E-mail | Track Comments
    About Sascha

    Dr. Sascha Vongehr [风洒沙] studied phil/math/chem/phys in Germany, obtained a BSc in theoretical physics (electro-mag) & MSc (stringtheory)...

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    Every once in a while we are told that Schrödinger’s cat is now proven. One incarnation of the ‘Finally Proven!!!’ of macroscopic quantum superposition was hailed as one of the 10 breakthroughs, the breakthrough of the year 2010. By Science about an article in Nature [1], no less!

    Such would destroy Roger Penrose’s idea about gravity collapsing quantum superposition. Many a ‘quantum-brain’ proposal would fall, too. I asked Roger why he does not object, and he is plainly too busy to care about such hype. He agrees that experiments are still far from a superposition of states that differ macroscopically.

    The “breakthrough of the year 2010” system is a roughly 20 times 30 micrometer large aluminum nitride paddle (see picture). It dilates and contracts along its 0.74 micrometer thickness. Since aluminum nitride is piezoelectric, these oscillations lead to voltages that can be coupled to a quantum mechanical interference device (SQUID) and thus to a qubit and so on.

    They couple a vibration in the paddle to the excitation of the quantum circuit. The proudest claim is that

    “we have created a single quantum excitation in a macroscopic mechanical object”.

    This is nice, but is it a Schrödinger cat? Almost at the end we read:

    “We also attempted to measure the resonator’s dephasing time […] revealed by the evolution of […] a quantum superposition of the state in which the resonator contains zero phonons and the state in which it contains one phonon.”

    That is also nice, but it is not a macroscopic quantum superposition, and to the authors’ credit, they do not claim such. The journal Science however insinuates such and popular sources like science blogs slurped it up. In the German news and science blogs it was sold straight as a Schrödinger Cat.

    There are heavy objects that have been experimentally related with a quantum superposition, systems with many particles involved, like super fluids flowing clock and counterclockwise at the same time. Photons have been entangled over many kilometers! None of this is a Schrödinger cat, because large or/and heavy is not enough. Schrödinger’s feline is in (a superposition of) two states which differ by a large distance between a heavy object’s possible positions of its mass (e.g. the center of mass), for example the cat standing versus the cat dead on the floor of the box. (Obvious in my understanding, because the space-time curvature is suffitiently different so that the parallel worlds do no longer sufficiently overlap.)

    The limit for a quantum superposition to be possible has been proposed by the Hungarian physicist Lajos Diósi and afterward by Roger Penrose, for example in his 1994 book "Shadows of the Mind".

    General relativity tells that different mass distributions distort space-time differently, and a superposition of different curvatures and thus shapes of regions spells trouble. Since it is space-time that is curved, the synchronization gets lost, and thus the quantum phases dephase. The Diósi-Penrose criterion and similar center-of-mass-displacement criteria predict an upper limit for the amount of time t that a quantum superposition (quantum entanglement over space-time distance) survives.

    I just give two scenarios of my own to make clear that new physics must happen on principle:

    1) The box isolates the cat from all interactions with the environment; this is vital for the superposition. Think of the mechanism that kills the cat as also making a black hole by pressing large, dense masses together near a wall of the box. The space-time curvature will go through the wall for sure, because it is nothing that must penetrate the wall but simply passes by deforming it! Or to make it clear via the extreme black hole: No wall can isolate against interactions if it is eaten up by a black hole. So the box can on principle not isolate against gravitational interactions. Interaction with the environment implies ‘decoherence’ of the quantum superposition.

    2) Another scenario is two entangled particles (e.g. EPR anti-correlated singlet state photons at Alice's and Bob's places) in a superposition of their spins relative to a certain axis. If the space in between the particles becomes curved sufficiently, comparing the axes (a and b) by Parallel transport becomes path dependent and the entanglement in this sense collapses (The angle dependent statistics differs if the observation results were to go this or that path toward Carl in the middle, so if they go both paths, the statistics mix).

    A relatively simple formula by Stephen L. Adler [2] gives t = ħ/E = 109 seconds of decoherence time for an experiment proposed by Marshall and Penrose that involves a tiny mirror. If you like the exercise, try to adapt that formula [E = (4Pi/3) G d2 S3rho2] and the sizes involved in the paddle described (or any of the hyped experiments that come along for the next 20 years). You will find that experiments are far away from probing macroscopic superposition states. The time t is too long for us to wait and measure whether the superposition has collapsed. It would have already collapsed due to experimental noise.

    Adler considered the mass to be homogeneously “smeared out” instead of being concentrated in atomic nuclei. An improved formula would predict a smaller decoherence time. This means that maybe the paddle experiment’s 20 nanoseconds de-phasing has already entered the ‘macroscopic Schrödinger cat’ regime as would be predicted by a better formula.

    I claim the aluminum nitride paddle is far below the limit suggested in the Diósi-Penrose criterion [3], and Penrose agrees [4], but maybe for different reasons. I do not poop on Schrödinger cats, on the contrary, however, stay with the facts. It happens about once a year that macroscopic quantum superposition is claimed. The Diósi-Penrose criterion is seldom mentioned. It should be, because it gives a well defined meaning to the term "macroscopic"!

    [1] A. D. O’Connell, M. Hofheinz, M. Ansmann, Radoslaw C.Bialczak, M. Lenander, Erik Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J.Wenner, John M. Martinis, A. N. Cleland: “Quantum ground state and single-phonon control of a mechanical resonator” Nature 464, 697-703 (1 April 2010)

    [2] Stephen L. Adler: “Comments on Proposed Gravitational Modifications of Schroedinger Dynamics and their Experimental Implications

    [3] The symmetry of the paddle (it dilates rather than swinging up and down) makes this unsuitable for testing macroscopic superposition. The distance d involved in the paddle superposition is tiny. The paddle oscillates at 6 GHz, i.e. the dephasing time is longer than the period.

    [4] Private communication – He mentions that the paddle's states are by no means stationary states. Experiments better suited to the cat issue are the Bouwmeester type. There is one planned to test a superposition of a 10-micron cube being in two locations that differ from each other by about the diameter of an atomic nucleus. Even these experiments will fall short of what is needed to confirm a true Schrödinger cat.


    "The journal Science however insinuates this being the case and most if not all more popular sources like science blogs for instance, slurped it up only too willingly. In the German news and science blogs it was sold straight as a Schrödinger Cat.


    Editors grasping for headlines. Sensational sells almost as well as sex.

    Atta boy, Sasha. Keep them on their toes.


    Decoherence is often brought up as why macroscopic superpositions aren't possible, and a more common theory than Penrose-style "objective collapse" involving e.g. gravity. In my paper at my name link, I explain why decoherence cannot really destroy superpositions (as opposed to simply making them messy), cannot lead to mixtures from such superpositions, and cannot lead to a classical-style world. I propose two experiments, quite doable, to test this claim.

    Indeed, much gets lost and distorted in translations from actual physics to popular renditions. For example, with Schrödinger’s cat, the transition in the thought experiment is not from a Live cat |L> to one that is Dead or alive … or … dead plus alive: |D> + |L>. These are wrong. Instead, the cat becomes Entangled with a Triggering Device or Gun that has some random chance of being Fired |F> or Unfired |U>. We start off with a Live cat |L> and an Unfired gun |U> . The initial state in Dirac’s notation is |LU>. The transformation to the superposition is then written as follows. I have neglected here the all important question as to how long the interference of |LU> and |DF> is maintained (x,y are complex numbers (on a unit circle)). |LU> becomes x|LU> + y|DF> I hope that helps. As indicated by Sascha, the DIFFERENCE from a live cat to a dead cat is a huge separation distance in an abstract Hilbert space. Nonetheless, it is interesting to attempt experiments at nanoscales in which one maintains a superposition of nearby states that are not suddenly undone by one’s surroundings (or heat bath) doing a thousand and one measurements/entanglements. It’s rather difficult, of course, for us regular folk to have access to liquid helium … and even less likely that we can work with it …. so all this talk is …. somewhat academic.
    As indicated by Sascha, the DIFFERENCE from a live cat to a dead cat is a huge separation distance in an abstract Hilbert space.
    The difference is a separation in space, not in Hilbert space, where orthogonal directions have actually no separation at all (except for being 90 degree to each other).
    I was thinking of how Wooters in 1981 associated distinguishability with distance in Hilbert space. Yes, orthogonal states, even with good old Fourier harmonics are orthogonal from each other … something is wrong in the way I have phrased things. Maybe this link is more transparent: My main point is that it is quite a bit harder, both mentally and mathematically, to deal with a tensor product like |LU> in a ket than it is to deal with simple (orthogonal) pairs of state vectors like |U> and |D> . What gets sacrificed in popular renditions is the use of tensors. OK. Now I am going to be told it is not about tensors, yet we are going to parallel transport them around loops and look for deviations in the components … to see if the presence of matter ... matters.

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