olegt
Posts: 1405
Joined: Dec. 2006
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TP, I'm not going to reply to the first part of your latest comment since I've already commented on those subjects. I'm going to answer the rest and it'll be a long answer.
| Quote | | The brings us to to justifying the default position or, as you say, "Standard QM" while we wait for experimental confirmation. What is the "Standard QM" explanation for why BuckyBalls exhibit coherence but baseballs don't? If the quote from the BuckyBall experimenters is any indication it comes down to assuming there is unexplainable magic behind Heisenberg's pronouncement. |
It looks like magic only if you put it in black-and-white terms: an object either exhibits quantum coherence or it doesn't. But it doesn't work that way. Coherence, quantified through a suitable statistical quantity like the density matrix, decreases to zero gradually as the object is getting wacked by the environment. Experiments show that it usually does so in an exponential fashion, as exp(-t/T), where T is called a decoherence time. You can say that a quantum system possesses coherence over time intervals short to T and doesn't over ones longer than T. While that would only be a qualitative description, it shows that the situation is a bit more complex than you assume.
In light of this fact, the question becomes quantitative: how long is the decoherence time? The answer depends on the particular physical system and its environment. While calculating it is not an easy task, in some cases it has been done in the framework of standard quantum mechanics. For instance, Das Sarma and his collaborators recently computed the decoherence time for a phosphorus spin planted in silicon (a few milliseconds at 8 degrees Kelvin). In this case, decoherence is caused by the hyperfine interaction of the phosphorus electron spin with the spins of silicon nuclei. The calculated value agrees with the experimentally measured one in various settings, thus indicating that perhaps gravity has nothing to do with decoherence in this case, it's all within the reach of standard quantum mechanics.
I don't think anyone computed the decoherence time for a baseball in a typical environment. It's a much more complicated task. However, given the vastly greater number of degrees of freedom (10^23 vs 1) and their strong interaction with the environment, one can reasonably infer that the decoherence time will be much, much shorter than in the case of an electron spin in ultrapure silicon. That, and not exotic gravitational quantum effects, are the likely reason for the lack of quantum coherence for baseballs.
| Quote | So, by "Standard QM" could an isolated planet-size rock in an isolated part of space be in superposition as long as there is no chance anyone could measure both position and momentum?
Penrose has a logical explanation. Mass, whether in superposition or not, curves space. The larger the mass, the steeper the curve. Ergo, coherence is time limited for objects with mass, the larger the mass, the shorter the time.
Coherence of massless photons can be maintained forever.
Coherence of very light electrons have a long time limit.
Coherence of heavier atoms have shorter time limits.
Coherence of BuckyBalls is too short to do much more than interference patterns.
Coherence of Baseballs is so short as to be undetectable.
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I'm afraid I don't find this argument convincing. For starters, not only mass, but also the number of particles involved increases in this sequence. More importantly, standard quantum mechanics provides an excellent account for decoherence in at least some of the physical systems (see the example above), while Penrose's theory remains at this point a speculation.
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