The “single-slit experiment”: A thought experiment on superposing macroscopic states

After discussion, online and offline, relating to Dilip’s recent post and my rejoinder, here are some further thoughts on the question of putting a cat in a superposition of dead-alive states.

First, quantum mechanically a “superposition of states” is just a state, mathematically as valid as any other. It’s like choosing a different “basis vector” — that is, choosing to tilt your coordinate axes when taking measurements.

Second, a cat is of course in a superposition of states, as are we all — because we are made of quantum particles — but these states are very “nearby” in a sense.

Third, only something that is isolated from its environment is really in a “pure” state. In reality we all, including the cat, interact with our environments, and therefore a “true” quantum mechanical wavefunction must encompass both the cat and the environment. If we choose to focus only on the cat, it is in a “mixed state”.

It is because of this interaction that I asserted strongly that a cat will not be in a superposition of widely-separated (dead and alive) states. And if you did isolate the cat from the environment, by putting it in a vacuum, you’d anyway have a dead cat. But this is not a problem only with cats. The main problem with quantum computing is how to maintain the “coherence” of individual quantum bits, or “qubits”, which — in contrast to a cat — are quantum objects with just two states. If it is difficult to maintain coherence for qubits, it is impossible (in this sense of “impossible”) to do so for a cat.

It seems to me that the cat motif serves only to distract from the real question, of whether it is feasible to put a large macroscopic object in a superposition of states — and show experimentally that it is in fact in a superposition of states. With that in mind, here’s a thought experiment.

As in the Schroedinger cat experiment, you have a radioactive atom inside a closed box. If it decays, a detector swings into action — but instead of killing a cat, it moves a screen with a slit in it. On one side of the slit is a point light source. On the other side is a projection surface which is externally visible. So all that we can see is, initially, a patch of light on one side of the projection surface.

So we set up the experiment. Initially, the atom is supposed to be undecayed. But immediately it gains a finite probability of having decayed. So if the screen is truly isolated from the world, it ought to be in a superposition of states — so the slit in the screen, too, is in a superposition of two possible positions. This is a twist on the double-slit experiment but, if the screen is really in a superposition of states, should yield the same result: we should see an interference pattern on the projection surface. Since, as time goes by, the probability of the atom having decayed goes to 1, we should start with a patch of light on one side of the projection surface, progress through an interference pattern in the middle of the surface, and end with a patch of light on the other side of the surface.

We need to do this in as isolated a manner as possible — in a vacuum, near absolute zero — and even then I doubt very much that it is a feasible experiment. To me, it seems the probability of failure is overwhelming, and a failed experiment will tell us nothing. But if it worked and produced an interference pattern, it would be an astonishing result. Anyone care to try?

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2 Comments

  1. The notion of “macroscopic objects” needs to be defined more clearly. The field of Mesoscopic physics, for instance, involves study of systems systems that are macroscopic in the sense that they do have macroscopic number of degrees of freedom while still retaining quantum properties and number of quanta of energy per degree of freedom can be quite less – this makes them ideal to study macroscopic quantum effects which you allude to in your blog and in fact they are nowadays widely used for quantum information processing like applications (Josephson junctions, quantum dots etc.). In fact, beginning in late 1980s with observation of MQT (macroscopic quantum tunneling) in Josephson junction, there already have been many experiments since then where macroscopic quantum effects have been observed and well documented.

    Reply
    • Rahul Siddharthan

       /  September 28, 2011

      Archana – thanks for the comment (I deleted an identical anonymous comment, but didn’t get around to replying). Indeed, if such an experiment is done, I had mesoscopics in mind — and not necessarily via interference of light either. Macroscopic quantum effects have indeed been observed frequently — superconductivity being the best-known example — but all the examples I know of (including, I believe, the ones you refer to) are purely electronic effects. I don’t know whether an extended solid structure, or even a macromolecule, has been shown to be in a quantum superposition of states. Wikipedia’s article on the cat refers to a proposed experiment on a virus (near absolute zero, in conditions where a cat could not live) but, as far as I can tell, the experiment has not been carried out.

      Reply

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