Editor's Choice: Quantum Upsizing

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hm. largest quantum object...

"Can we start to observe quantum behavior in bigger and bigger objects?"

this reminded me of an article i'd come across about one of Saturn's moons, Hyperion.

found at:

http://cosmicvariance.com/

on October 28, 2008 10:49:56 PM PDT:

Quantum Hyperion

Sean at 7:51 pm, October 23rd, 2008

One of the annoying/fascinating things about quantum mechanics is the fact the world doesn't seem to be quantum-mechanical. When you look at something, it seems to have a location, not a superposition of all possible locations; when it travels from one place to another, it seems to take a path, not a sum over all paths. This frustration was expressed by no lesser a person than Albert Einstein, quoted by Abraham Pais, quoted in turn by David Mermin in a lovely article entitled "Is the Moon There when Nobody Looks?":

I recall that during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I looked at it.

The conventional quantum-mechanical answer would be "Sure, the moon exists when you're not looking at it. But there is no such thing as `the position of the moon' when you are not looking at it."

Nevertheless, astronomers over the centuries have done a pretty good job predicting eclipses as if there really was something called `the position of the moon,' even when nobody (as far as we know) was looking at it. There is a conventional quantum-mechanical explanation for this, as well: the correspondence principle, which states that the predictions of quantum mechanics in the limit of a very large number of particles (a macroscopic body) approach those of classical Newtonian mechanics. This is one of those vague but invaluable rules of thumb that was formulated by Niels Bohr back in the salad days of quantum mechanics. If it sounds a little hand-wavy, that's because it is.

The vagueness of the correspondence principle prods a careful physicist into formulating a more precise version, or perhaps coming up with counterexamples. And indeed, counterexamples exist: namely, when the classical predictions for the system in question are chaotic. In chaotic systems, tiny differences in initial conditions grow into substantial differences in the ultimate evolution. It shouldn't come as any surprise, then, that it is hard to map the predictions for classically chaotic systems onto average values of predictions for quantum observables. Essentially, tiny quantum uncertainties in the state of a chaotic system grow into large quantum uncertainties before too long, and the system is no longer accurately described by a classical limit, even if there are large numbers of particles.

Some years ago, Wojciech Zurek and Juan Pablo Paz described a particularly interesting real-world example of such a system: Hyperion, a moon of Saturn that features an irregular shape and a spongy surface texture.

The orbit of Hyperion around Saturn is fairly predictable; happily, even for lumpy moons, the center of mass follows a smooth path. But the orientation of Hyperion, it turns out, is chaotic -- the moon tumbles unpredictably as it orbits, as measured by Voyager 2 as well as Earth-based telescopes. Its orbit is highly elliptical, and resonates with the orbit of Titan, which exerts a torque on its axis. If you knew Hyperion's orientation fairly precisely at some time, it would be completely unpredictable within a month or so (the Lyapunov exponent is about 40 days). More poetically, if you lived there, you wouldn't be able to predict when the Sun would next rise.

So -- is Hyperion oriented when nobody looks? Zurek and Paz calculate (not recently -- this is fun, not breaking news) that if Hyperion were isolated from the rest of the universe, it would evolve into a non-localized quantum state over a period of about 20 years. It's an impressive example of quantum uncertainty on a macroscopic scale.

Except that Hyperion is not isolated from the rest of the universe. If nothing else, it's constantly bombarded by photons from the Sun, as well as from the rest of the universe. And those photons have their own quantum states, and when they bounce off Hyperion the states become entangled. But there's no way to keep track of the states of all those photons after they interact and go their merry way. So when you speak about "the quantum state of Hyperion," you really mean the state we would get by averaging over all the possible states of the photons we didn't keep track of. And that averaging process -- considering the state of a certain quantum system when we haven't kept track of the states of the many other systems with which it is entangled -- leads to decoherence. Roughly speaking, the photons bouncing off of Hyperion act like a series of many little "observations of the wavefunction," collapsing it into a state of definite orientation.

So, in the real world, not only does this particular moon (of Saturn) exist when we're not looking, it's also in a pretty well-defined orientation -- even if, in a simple model that excludes the rest of the universe, its wave function would be all spread out after only 20 years of evolution. As Zurek and Paz conclude, "Decoherence caused by the environment ... is not a subterfuge of a theorist, but a fact of life." (As if one could sensibly distinguish between the two.)

Update: Scientific American has been nice enough to publicly post a feature by Martin Gutzwiller on quantum chaos. Thanks due to George Musser.

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matt.

Hello,

We've checked the PDF and it is downloading correctly.

Best,

K Rajanna

Dear Sirs

If space-time would be fundamental arena of the universe entanglement and superposition would not be possible. They are possible because fundamental arena of the universe is timeless quantum space that is an immediate energy and information medium between elementary particles.

Sincerely yours amritAttachment #1: 2_TIMELLESS_QUANTUM_SPACE.doc

Dear Colleagues,

I wish to draw the attention of the readers of this forum to the essay that I have written for the current Essay Contest of FQXi, where I explain why one should expect a breakdown of *linear* quantum mechanics, when larger and larger objects are examined. The theory is then replaced by a nonlinear quantum mechanics [applicable for mesoscopic objects] which goes over to classical mechanics for macroscopic objects. Thus the idea is that the mechanics of the mesoscopic domain is different from both classical and quantum mechanics.

In particular, Planck's constant is no longer a constant, but a function of the number of degrees in the system. Can the above experiment be used to infer the value of Planck's `constant', by treating the micro-mirror as a mesoscopic object? The departure from the linear theory is expected to become more and more pronounced as the mass of the mirror becomes closer to Planck mass.

If the authors of the above article/experiment happen to see this post, I will be very much interested in their views.

Many thanks,

Tejinder Singh

It is so nice to see this attempt to check what lies in between current domains of quantum and classical physics. The proposed experiment is highly imaginative. I just wonder about the terms used like laser bombardment causing cooling of the micro-mirrors as more energy gets released than absorbed in the process. I am unable to comprehend the mechanism involved including the nature of laser that is proposed to be used. i wish to interact closely with members of the experimental group and contribute my webit of experience in experimental physics.

In fact i always have wondered about the constancy of physical constants like h, c, e, m, etc. as also about the strengths of force fields eversince these emerged to fulfil the requirements of the universe's evolutionary logical design. i see an interplay between gross randomness in observing physical processses experimentally and the logic that is behind them which has to be an orderly effect! Some cosmological measurements thouugh isolated have already emerged pointing to the higher value of c and a different value for e/m in the light signals coming from far off cosmic objects over 12 billion years away. A closer and precise attempt at accurate cosmological experiments conducted from apparatus in space beyond earth-boundness may well provide us answers to several cosmological mysteries that bedevil present day Physics. LHC expts in comparison appear to me far less fruitful as per this line of thinking. i am on the current FQXI website Essay competition 2009 and will be most happy to sontinue the line of discussions as i feel too that the value of h was smaller in the early universe. Tejinder's proposal for an inbetween region of mesomorphic physics is relevant in this context too.

Hi ,

A very beautiful project with a beautiful collaborations .

I wish them all the best .

Best Regards

Steve

This bold attempt at a tough problem is highly commendable. My personal interest has arisen in this experiment from the desire to test the valdity of possible variation in the value of h above 0 limit for classical objetcs/processes. The interst follows an attempt by Tejinger Singh of TIFR, Mumbai, India who has developed a theory for such a mesomorphic region where neither classical nor quantum mechanics is strictly valid.

I have yet to grasp the full import of the planning being done by the Vienna group of scientists , Keith, Anton & Markus, guided by Nobel Leureate Prof. Tony Leggett.

May i enroll myself with my e-mail Id to be an interested associate from India who would like to contribute whatever little i can towards the success of this experiment right from the stage of planning to its final execution. To start with i wish to have some details about the size of the micro-mirror, the type of laser intended to be used and the limit of low temperatures being considered for conducting the experiment.How it is being planned to change the frequency and power of the laser that is planned to be used.Is it being contemplated to employ a nanostructured material crystal to reflect/refract the laser light?

Narendra Nath, . Kurukshetra, India

A FQXI Essay Contest author of ' What Physics Can & Can't Do? ' 2009

The paper

http://arxiv.org/abs/0711.3773

argues that quantum theory is intrinsically nonlinear, and goes to the standard linear limit for microscopic objects. THe nonlinear theory goes to the classical limit for large objects, but departs from linear quantum mechanics for mesoscopic objects.

Because of the nnlinearity, the lifetime of two superposed states is no longer infinite. It decreases as the number of atoms in the object under study increases, going from an astronomically large value for microsystems, to extremely small values for macrosystems. Thus somewhere in between, the superposition lifetime ought to be measureable in the laboratory.

For the micro-mirror of a billion atoms, the superposition lifetime is predicted to be about ten days. If the number of atoms in the mirror is increased a thousand fold, the lifetime of superposition comes down to about a thousand seconds.

Mesomorphic region experiments are required to be conducted. It may be a difficult regime but human beings are smart enough to generate new design ideas in the minds of prospective physicists to conduct such experiments in the near future. What about High energy Compton scattering using nanostructured crystal of silver or gold! Where to see the effect of change in value of Planck's constant, compton scattered electron or the scattered photon?