Every once in a while we are told that they finally have the proof for Schrödinger’s cat being possible and the quantum multiverse being thus proven. Recently, yet another incarnation of the ‘Finally Proven!!!’ of macroscopic quantum superposition was also hailed as one of the 10 breakthroughs, if not the breakthrough of the year 2010. By Science about an article published in Nature , no less!
If such were true, it would destroy Roger Penrose’s idea about gravity leading to the collapse of quantum superposition. Many a ‘quantum-brain’ proposal would fall along with it. Why not Roger and Co object? I asked him, and it seems he is plainly too busy with interesting science to care about such hype – that’s my man! Anyways, he, and probably anybody even semi-knowledgeable about similar issues, agrees that experiments are still very far from a superposition of states that differ macroscopically.
The “breakthrough of the year 2010” system in question 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 circuit called SQUID and a qubit and so on and so forth.
The article is all about the coupling of a vibration inside 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 what does it tell us regarding the Schrödinger cat issue? Only almost at the very end are we treated to:
“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, no doubt, but it is nowhere close to a macroscopic quantum superposition, and, to the authors’ credit, they do not claim such. 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.
However: It is not so and it will not be so in a looooong while!
There are quite 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, and photons have been entangled over many kilometer long distances.
None of this counts as a Schrödinger cat, because a cat is neither just large nor heavy, nor would both, large and heavy, be enough. Schrödinger’s feline is in two states which differ by a large distance between a heavy object’s possible positions, for example the cat standing versus the cat dead on the floor of the box.
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 us that different mass distributions curve space time differently in the different states, and a superposition of different curvatures spells trouble. 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 survives.
I won’t explain the trouble in detail but just give two scenarios of my own to contemplate; they should make clear that some new physics must happen on principle:
1) The box isolates the cat from all interactions with the outside environment, this being 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. Obviously, no wall can isolate against interactions if it is eaten up by a black hole. So the box can on principle not isolate the cat from gravitational interactions. If there is interaction with the environment, so called ‘decoherence’ sets in.
2) Another scenario involves two entangled particles in a superposition of their spins being ΨUp-Down and ΨDown-Up relative to a certain axis. Once the space in between the particles is curved sufficiently, the axes to be compared by Parallel transport are path dependent and the entanglement collapses (at least in the sense that it would now need information about preferred paths).
A relatively simple formula by Stephen L. Adler  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 (Homework!), 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. I claim you will find that all the experiments are still very far away from probing macroscopic superposition states. The time t is way too long for us to wait and measure whether the superposition has collapsed or not.
But maybe you disagree! 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 hyped aluminum nitride paddle is far below the limit suggested in the Diósi-Penrose criterion  (and Penrose agrees , but maybe for different reasons).
Let me add a clarification: I am not out to poop on Schrödinger cats, on the contrary, however, science should stay with the facts. It happens about once a year now that yet another macroscopic quantum superposition is claimed. The Diósi-Penrose criterion is seldom mentioned. Even if it is incorrect, it at least gives a well defined meaning to the term ‘macroscopic’ in the first place!
 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)
 Stephen L. Adler: “Comments on Proposed Gravitational Modifications of Schroedinger Dynamics and their Experimental Implications ”
 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.
 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.