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A Step Closer to Quantum Theory of Gravity
ruszka writes "PhysicsWeb has an article on two condensed matter theorists that have come up with a new way of looking at the Quantum Hall effect.. It says this could go to be "a small step towards one of the ultimate goals in theoretical physics - a quantum theory of gravity""
Will someone please explain what a quantum hall effect is, and how it relates to superconductivity and/or electron spin?
The next Slashdot story will be ready soon, but subscribers can beat the rush and slashdot the links early!
Anyway, my understanding of this article (haven't read the paper in Science), is that the theory they have come up with is perfectly computable - a four-dimensional analogon to general relativity if you will. If they manage to extend it into a full theory of quantum gravity, that would not only be amazing, but it would show full computability as well.
That would mean Penrose is toast.
Ceci n'est pas une sig
It's really hard to tell what's going on from this article directly - it mostly just points out that some research is going on in this field. (And I haven't read the original article)
What I can read into it is that by working out the equations for a condensed matter system with where the interactions between individual particles are strong enough to influence the larger properties of the material - the authors have recognized that the equations look very similar to standard equations found in the classical fields of physics (E&M, Relativity, etc.)
If this is the case, then assuming that the basic assumptions are portable (that these types of quantum interactions are important on a macroscopic scale) then you have basically derived classical physics from Quantum mechanics.
This would hint (at least) that Quantum theory is scientifically more fundamental than classical physics. It gives a motivation for the observation that Quantum equations tend to reduce to classical equations when the systems get large.
Pretty cool if it all pans out. Lovely philosphical shift in thinking...
In illa quae ultra sunt
With Quantum you at least need Fourier Series and partial Diff. Eq. to solve basic problems. In classical physics you can often get by with just Algebra.
I really think you have that backwards. The only kind of classical physics you can do without calculus is the sort where you plug numbers into equations. $x=(1/2)at^2$. You can do that just as well with QM: the energy states of the hydrogen atom are given by $E=-\frac{\mu Z^2 e^4}{2 \hbar^2 n^2$, what are the first three when Z=2?
On the other hand, the fundamental mathematics of QM is linear algebra, and in its discrete version (matricies) you can go a long long way. Matrix Algebra is commonly taught as part of second-year calculus, but really has little to with the rest of that subject and you could easily teach it first.
I do agree that the cognitive dissonance many students get from the historical progression we use in physics education is unnecessary. I'm not even sure qm is especially counter-intuitive if you haven't just spent a couple years learning to think classically; from a practical point of view they're equally abstract.
Actually a wonderful Quantum Gravitational Theory has been put forward by Superstring theory.
1 1/ qid=1004615200/sr=2-1/ref=sr_2_11_1/103-5726037-41 19066
In the mid 90's, the 5 seemingly disparate String theories were united by a common, unifying theoretical structure that included 11 Dimensional Quantum Gravity.
The problems that have beset String theory since are the limitations of perturbative methods of mathematical solutions in providing exact answers in the extreme arena of string theory.
If you've not already read it, the book "The Elegant Universe" by Brian Greene gives a great explanation of this area of theoretical physics, even if it is 5 years out of date now.
http://www.amazon.com/exec/obidos/ASIN/03757081
if you're interested, priced 9 of your US Dollars.
Chris.
Fractional quantum hall effect