Exploring the Relationship between Size and Quantum Phenomena

[MetalBunnyLove]

I'd like to say first off, that I'm not a physics student, so if an idea of mine sounds bizarre or ridiculous, please forgive me, but don't keep back any criticism.

From my understanding, quantum phenomena is restricted to the 'quantum realm', and can be found to exist in measurement no smaller than Planck's scale, and conversely, no larger than...well, I guess that's what I'm unsure of.

As an entity increases in size, then the corresponding size of its wavelength will decrease in size, correct? If this is correct, then could we further generalize, and say that the size of an entity is inversely correlated to the extent of its potential quantum phenomena?

 

[ZapperZ]

I'd like to say first off, that I'm not a physics student, so if an idea of mine sounds bizarre or ridiculous, please forgive me, but don't keep back any criticism.

From my understanding, quantum phenomena is restricted to the 'quantum realm', and can be found to exist in measurement no smaller than Planck's scale, and conversely, no larger than...well, I guess that's what I'm unsure of.

As an entity increases in size, then the corresponding size of its wavelength will decrease in size, correct? If this is correct, then could we further generalize, and say that the size of an entity is inversely correlated to the extent of its potential quantum phenomena?

This is not quite right.

We know that quantum phenomena are clearly present in the scale you are talking about, and we know that at our classical scale, we do not see them... or do we?

The whole issue here is what is known as "coherence" and the scale of such coherence. The destruction of such coherence when a system has coupled to such a large degree of freedom has been used as the source on why we lose such quantum phenomenon as the macroscopic scale. And it is easy for a system to couple to such large external influences. That is why it isn't easy for quantum phenomenon to manifest itself to us.

However, it does mean that if you can maintain such coherence, you can actually maintain quantum behavior even at "large" scales. Superconductivity is one such example. The gazillion particles making the supercurrent maintain their coherence with each other, producing a macroscopically detectable phenomenon in which there are no classical description. In fact, according to Carver Mead[1]:

Although superconductivity was discovered in 1911, the recognition that superconductors manifest quantum phenomena on a macroscopic scale came too late to play a role in the formulation of quantum mechanics. Through modern experimental methods, however, superconducting structures give us direct access to the quantum nature of matter. The superconducting state is a coherent state formed by the collective interaction of a large fraction of the free electrons in a material. Its properties are dominated by known and controllable interactions within the collective ensemble. The dominant interaction is collective because the properties of each electron depend on the state of the entire ensemble, and it is electromagnetic because it couples to the charges of the electrons. Nowhere in natural phenomena do the basic laws of physics manifest themselves with more crystalline clarity.

Not only that, the Schrodinger Cat-type experiments of Delft/Stony Brook[2] showed that one can create a system consisting of [itex]10^{11}[/itex] particles that maintain a coherent superposition of states - the Schrodinger Cat states - in which this quantum phenomenon can be detected.

So no. From all indications, it isn't the SIZE that matters, it is whether we can maintain the coherence of the "wavefunction" that describe each part of the system. While it is true that the larger the size of the system, the more difficult it is to maintain such coherence, it isn't impossible, and all these experiments are starting to be performed to show quantum effects at larger and larger sizes.

Zz.

[1] C.A. Mead, PNAS v.94, p.6013 (1997); or you may be able to access it http://www.pnas.org/cgi/content/abstract/94/12/6013?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&fulltext=carver+mead&searchid=1&FIRSTINDEX=0&resourcetype=HWCIT".

[2] C.H. van der Wal et al., Science v.290, p.773 (2000); J.R. Friedman et al., Nature v.406, p.43 (2000).[ArXiv version can be found http://arxiv.org/abs/cond-mat/0004293" ]

 

[MetalBunnyLove]

Very informative response as usual, Z. Thank you for your time.

So, in how large of a system have we successfully managed to maintain wave coherency? Is the superconductor it?

If by large, we're speaking of something along the lines of [itex]10^{11}[/itex], I'm going to have a hard time getting excited. But if we're talking about the possibility of approaching the necessary technological advancement so that we could use chairs in place of photons in the double-slit experiment, while still maintaining coherency...

Aside from the obvious act of observation, and also size, are there any other factors which govern a wave's ability to maintain coherence as size increases? For example, a system enclosed inside a certain molecular compound, such as a crystal.

 

[ZapperZ]

Very informative response as usual, Z. Thank you for your time.

So, in how large of a system have we successfully managed to maintain wave coherency? Is the superconductor it?

Probably. Note that there's no limit to the size of a superconductor. However, to be accurate, the size of the coherence is only limited to the "size" of the supercurrent, i.e. the number of electrons (or holes) that have condensed into this coherent state.

If by large, we're speaking of something along the lines of [itex]10^{11}[/itex], I'm going to have a hard time getting excited.

But considering that originally, you thought that this number is just "1" (or a few", I'd say the jump from that to [itex]10^{11}[/itex] is rather significant, don't you think?

This number, btw, is still low compare to the number in a typical conventional superconductor. Roger Penrose and company have proposed another Schrodinger Cat-type experiment using a series of mirrors[1] in which the number of atoms involved are even larger than this. We'll see if anyone attempts such an experiment.

Aside from the obvious act of observation, and also size, are there any other factors which govern a wave's ability to maintain coherence as size increases? For example, a system enclosed inside a certain molecular compound, such as a crystal.

I'm not sure if this is relevant, but people such as David Pines and Phil Anderson have discussed at length the concept of "quantum protectorate"[2], in which for a many-body system, the emergent property seems immune to microscopic variation in the system. Superconductivity, for example, once it sets in, is pretty immune to local inhomogeneity of the bulk material, and therefore able to maintain its long-range coherence. So this property is more of a behavior of many-body system. What would cause such quantum protectorate to kick in, I have no idea.

Zz.

[1] http://arxiv.org/abs/quant-ph/0210001

[2] http://arxiv.org/abs/cond-mat/0002281; http://arxiv.org/abs/cond-mat/0007287.

 

[David Burke]

It's been a while since I've studied but I've heard of Bose Einstein condensates being created at macroscopic volumes in labs at MIT.