A Stringy Universe
As the age of blogging rolls on, people seem to be more and more enthusiastic about the prospects of string theory. Today kneemo highlights a new paper by Kallosh. Mottle continues to entertain with links to F theory, for experts only, and of course Woit somehow manages to continuously whine.
Meanwhile, I have been looking again at certain stringy black holes in four dimensions whose entropy is measured by quantities that occur very naturally in the study of entanglement. One may well ask where the $d = 4$ comes from in the quantum information theory, because obviously the messy string theory derivation is quite unimportant compared to these more fundamental considerations.
Well, notice that the three spatial dimensions from $d=4$ matches the number of MUBs for a qubit. Similarly, $d=5$ black holes mysteriously require qutrit states, which have four basic MUBs. Moreover, if one correctly accounts for the fourth roots in the Pauli MUB case, one might guess the dimension should be 6, which happens to be the dimension of the compactified piece in type IIB theory. So instead of ridiculous numbers of dimensions in some arbitrary classical space, we just have dimensions of Hilbert spaces.
Later on I might discuss how one can rewrite this entanglement measure for three qubits in terms of symmetric $3 \times 3$ matrices with entries dependent on only 6 of the 8 amplitudes. Of course, Carl Brannen used similar operators in his paper on the hadron masses, but this paper was rejected due to the unfortunate circumstance that it had almost nothing to do with QCD.
Meanwhile, I have been looking again at certain stringy black holes in four dimensions whose entropy is measured by quantities that occur very naturally in the study of entanglement. One may well ask where the $d = 4$ comes from in the quantum information theory, because obviously the messy string theory derivation is quite unimportant compared to these more fundamental considerations.
Well, notice that the three spatial dimensions from $d=4$ matches the number of MUBs for a qubit. Similarly, $d=5$ black holes mysteriously require qutrit states, which have four basic MUBs. Moreover, if one correctly accounts for the fourth roots in the Pauli MUB case, one might guess the dimension should be 6, which happens to be the dimension of the compactified piece in type IIB theory. So instead of ridiculous numbers of dimensions in some arbitrary classical space, we just have dimensions of Hilbert spaces.
Later on I might discuss how one can rewrite this entanglement measure for three qubits in terms of symmetric $3 \times 3$ matrices with entries dependent on only 6 of the 8 amplitudes. Of course, Carl Brannen used similar operators in his paper on the hadron masses, but this paper was rejected due to the unfortunate circumstance that it had almost nothing to do with QCD.
posted by Kea | 6:51 AM
8 Comments:
"As the age of blogging rolls on, people seem to be more and more enthusiastic about the prospects of string theory."
This always happens with the birth of a new religion! Things get easier for the religion as it grows in size and becomes ever more hardened orthodoxy.
I'm excited to have just found online the Fierz-Pauli paper which sowed the seeds for the entire string theory religion fraud, right back in 1939. It is:
M. Fierz and W. Pauli, “On relativistic wave equations for particles of arbitrary spin in an electromagnetic field”, Proc. Roy. Soc. London., volume A173, pp. 211-232 (1939).
It concludes:
“In the particular case of spin 2, rest-mass zero, the equations agree in the force-free case with Einstein’s equations for gravitational waves in general relativity in first approximation ...”
This false claim caused the entire mess of string theory today because:
(1)
"For the last eighteen years particle theory has been dominated by a single approach to the unification of the Standard Model interactions and quantum gravity. This line of thought has hardened into a new orthodoxy ... It is a striking fact that there is absolutely no evidence whatsoever for this complex and unattractive conjectural theory. There is not even a serious proposal for what the dynamics of the fundamental ‘M-theory’ is supposed to be or any reason at all to believe that its dynamics would produce a vacuum state with the desired properties. The sole argument generally given to justify this picture of the world is that perturbative string theories have a massless spin two mode and thus could provide an explanation of gravity, if one ever managed to find an underlying theory for which perturbative string theory is the perturbative expansion." [Emphasis added.]
- Woit, http://arxiv.org/abs/hep-th/0206135, page 52.
and
(2)
‘String theory has the remarkable property of predicting [false, spin-2] gravity.’ - E. Witten (M-theory originator), ‘Reflections on the Fate of Spacetime’, Physics Today, April 1996.
My discussion of the spin-2 graviton error (and of course my correction to the graviton spin, leading to falsifiable predictions) is completely ignored, as predictable in a world obsessed with fashionable ideas that are false:
In the universe, masses that ‘attract’ due to quantum gravity are in fact surrounded by an isotropic distribution of distant receding masses in all directions (clusters of galaxies), so they must exchange gravitons with those distant masses as well as nearby masses (a fact ignored by the flawed mainstream path integral extensions of the Fierz-Pauli argument for gravitons having spin-2 in order for ‘like’ gravitational charges to attract rather than to repel which of course happens with like electric charges; see for instance pages 33-34 of Zee’s 2003 quantum field theory textbook).
Because the isotropically distributed distant masses are receding with a cosmological acceleration, they have a radial outward force, which by Newton’s 2nd law is F = ma, and which by Newton’s 3rd law implies an equal inward-directed reaction force, F = -ma.
The inward-directed force, from the possibilities known in the Standard Model of particle physics and quantum gravity considerations, is carried by gravitons. This works for spin-1 gravitons, because
(a) the gravitons coming to you from distant masses (ignored completely by speculative spin-2 graviton hype) are radially converging upon you (not diverging), and
(b) the distant masses are immense in size (clusters of galaxies) compared to local masses like the planet earth, the sun or the galaxy,
so the flux from distant masses is way, way stronger than from nearby masses; consequently the path integral of all spin-1 gravitons from distant masses reduces to the simple geometry below and will cause ‘attraction’ or push you down to the earth by shadowing (the repulsion between two nearby masses from spin-1 graviton exchange is trivial compared to the force pushing them together).
In the case of electromagnetism, like charges repel due to spin-1 virtual photon exchange, because the distant matter in the universe is electrically neutral (equal amounts of charge of positive and negative sign at great distances cancel). This is not the case for quantum gravity, because the distant masses have the same gravitational charge sign, say positive, as nearby masses (there is only one observed sign for gravitational charge). Hence, nearby like gravitational charges are pushed together by gravitons from distant masses, while nearby like electric charges are pushed apart because they exchange spin-1 photons but are not pushed together by virtual photon exchanges with distant matter, due to that matter being electrically neutral.
The simple geometry for graviton exchange is illustrated in the new diagram here.
[I don't know why I've only just come up with this simple diagram for spin-1 graviton attraction of two masses! The previous illustration (trying to show how the gravitational acceleration field arises around a single mass) is the little diagram beside my name on here, and that was was the one I formulated in a letter to Woit a few years ago - maybe 2005 or 2006 - who evidently wasn't impressed. Before that, I didn't even have a diagram, just some calculations based on an of a reaction force to the cosmological acceleration of matter radially outward from an observer. It's hopeful that I'm still making progress, but very annoying that I didn't come up with this much earlier.]
(R in that diagram is the distance to distant receding galaxy clusters of mass m. The distribution of mass around us in the universe can be treated as a series of shells of receding mass at distance R, and the sum of contributions from all the shells gives the total inward graviton delivered force to masses.)
"Well, notice that the three spatial dimensions from d=4 matches the number of MUBs for a qubit."
Yes, that is no coincidence at all.
I first got involved in MUBs it came from applying geometric algebra to the elementary fermions. There are three spatial dimensions and these correspond to the three basis choices. This is literally true for spin-1/2 but I believe it is also true when you apply MUB theory to QCD. (This violates a no go theorem by Nelson and Mandela but that's another story.)
And when you count the hidden dimensions by comparing the idempotent structure of general complex Clifford algebras with the structure of the elementary fermions, it's natural to conclude that in addition to the Pauli MUB structure, there also needs to be 1 or 2 hidden dimensions.
Don't worry too much about my getting shot down at Phys Math Central. The history of physics (and academia in general) shows that papers that straddle boundaries have to be shopped around a bit.
Kea, I'm glad you're looking into the black hole/entangled qudit correspondence. I haven't stopped working on this and I have some new results that extend those of Borsten et al. Kallosh's new argument for the finiteness of N=8 D=4 SUGRA actually depends on certain MHV twistor results, along with properties of the U-Duality group E_7(7). As Kallosh notes, the extremal black holes are nonperturbative solutions of N=8 D=4 SUGRA, making them all the more interesting to study, especially as a source for new mathematics.
Note: The D=4 comes from M-theory compactified on a 7-torus (T^7), giving D=11-7=4 and U-duality group of the form E_(11-4)(11-4)=E_7(7). Similarly, the dimensionally reduced D=3 theory with E_8(8) symmetry corresponds to M-theory on an 8-torus.
Hi Marni,
2 things:
1.The head of page is wrong. You are not on New Zeland anymore.
2.The humming code of this 4D black hole can be seen as a E(8) group (I don't know why) you just wrote it here:http://kea-monad.blogspot.com/2008/01/m-theory-lesson-150.html
The point is that the Homology Sphere os Poincare sphere, in 4D, is not Piecewise Triangulable manifld. The resulting manifold, although not triangulable, it is the intersection of 8 dodecahedron, face to face identified, whose link is that of the Coxeter E(8) diagram.
What do I mean with this? Well, if you tag a few CP^2 spheres to this system, you get a manifold with infinite number of non diffeomorphic smoothing structures. My personal idea, it is that this E(8)works is as source of randomness in 4D space. If you view every particle as a small blackhole, you might, who knows, make another interpretation of QM arising for GR.
If this looks interesting for you, look for Exotic Smothness & Physics, or The Wild World of 4 manifolds, or 4 manifolds and Kirby Calculus. If you liked the part about quantum mechanics, look at chapter 5 of "How Surfaces Intesect in Space... an Introduction to Topology", and see how generalized radamaister moves can give an idea on how to yield Feinmann diagrams in 4D. This is just speculation of mine, of course.
Daniel, what you say is very, very interesting, and I'd like to get there one day. As for NZ, I don't view the blog header as something that needs constant changing. If I ever actually find a home, I might change it.
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