solidspin

Norman has shared with me his solution of a root tensor basis expressed as a sum in equal magnitudes, of the three Pauli spin matrices of a spin 3/2 object. Alexander Burinskii responded with a lively answer as to how these may be quaternions. He prefers a complexification leading to supersymmetry. I personally believe complexification is fine, but a supersymmetry strategy might not necessarily prove fruitful. I LOVE the fact that 1st and 2nd order quadrupolar effects must, by definition, be included, which forces a re-examination of nuclear shell theory and its implications for GR.

Norman - since the metric g_ab is, effectively, acting as a K. delta, doesn't the metric need to be modified, as you will now (at least w/ ds, not ds^2) have a 3rd option, that of i, in addition to 0,1 for the K. delta view?

so, yes - you at least have to be in the same dimensionality as the system in which you're working - that's what I would assert. Since you're in 4-space, you should be in a 4-space basis set. Since, according to Cartan, Einstein (and NOT Minkowski, it appears), you should be in hyperbolics. Additionally, since the conformal projection of the null geodesic toward a "+H", if you will, or into conditional future in the light cone is path-dependent (for example, according to Weyl convention), then hyperbolic elliptical may offer the best "illumination", as Norman eloquently puts it.

so, I, unfortunately, did NOT coin the term spassitude. That said, Norman and I appear to be correct that, provided the proper basis set is selected, Clifford-style 4-space rotations of the photon-coupled graviton vector should be perfectly reasonable. If one re-examines the Maxwell equations in their Hodge dual/anti-self dual forms...the Stepper operators naturally fall out: F(+/-) = 1/2(F +/- i*F). Hoult and Bhakar in Conc. Mag. Res. 9 (1996) lay out the framework. Although strictly in an NMR context, it doesn't matter, as far as I can tell, provided the modifications I'm thinking of are consistent...

hello, norman - why does an imaginary part indicate absorption? I understand it from an operator point of view, but could you expound upon that. Further, do you envisage a mapping of a typical superconductor (like YBCO) in terms of polarizability? It might look like the difference of the electron density in a YBCO, w/ the added difficulty of long-range shapes as you back away, above and below, the CuO2 planes...hmmmm

safety regs: really HUGE effing sign in red, yellow and black that says "High magnetic field. Authorized persons only." locked door - (somebody left a wood block in it to keep it ajar). Yep, I'm submitting a PRT to get beamtime @ one of the beamlines @ the light source, which should again be accelerating and decelerating electrons @ ~0.6C on or about 1.15.09. They dumped the electron "bunch" last month so they could do maintenance. They've drastically reconfigured the beamlines since you were there - they have a "button-key-button-key" scenario, which forces you 2x to be out of the hutch before the beryllium window is opened.

hey, - really? It's: PRD 74, 085002 (2006). Were you post-doc-ing under him??? He's the only author on the paper. Could you be more specific? What did you do? I'm prepping a research proposal for my advisor on this stuff...I just have this driving need to do this as quickly as possible - couldn't be the worst time, either - some idiot delivering N2(g) to our lab this am quenched our 400Mhz magnet this morning by walking right into the B field w/ the tanks. 80L of He(l) to He(g) in under 5 seconds - had the LN2 also boiled off, it could have killed him. It's a $50,000 error - my advisor is completely pissed. Had his helper been in between the tanks and the magnet, they would have crushed him - huge dent in the hull of the magnet - it's now a VERY expensive paper weight.

Greetings, Gentlemen - Steve, yes, it's quite relevant - this is what Holstein @ UMass-Amherst theorized, not citing the work you just posted - but thank you very much for it! Notice the decay? Also, this adds fuel to my proverbial fire, as I have cited above in both my assertions and the papers I've proffered. Norman, definitely high-E, but I am skeptical of extra dimensions - remember that limit equation I came up with??? I'd bet a dollar that that's how the "extra" dimensions are actually handled - spassitude, baby! That limit equation offers a perfectly reasonable way, since the curve is piecewise-smooth, of either line-integralling it or linearly recombining it, no? See, for example, the Einstein-Cartan-sciama-Kibble theorem and their treatment of torsion in GR curvature - outstanding... S Merged post follows: Consecutive posts mergedGentlemen - Steve - the paper you referenced is EXCELLENT. While I fundamentally disagree w/ their String derivations (since 1. they're derivable from simple CE^4 rotation symmetry group and ii) they largely already exist from NMR theory; see: Conc. Mag. Res. 9 (1996) by Hoult, Bhakar (pp277-98), for example. Secondly, and it may simply be a typo, but they represent a transition as |2> -> |2>, which isn't physically possible. A resonance is a transition from |r> -> |s>; |r>-> |r> makes no sense; |r> -> |-r> is a DQ (double quantum) transition, which in NMR theory is classically "forbidden" and therefore has to be moderated by a SQ transition, which according to NMR theory, as applied here, cannot occur, as there's obviously no dipole-dipole transition here (i.e., |1/2> -> |-1/2>. In their defense, however, they DO get the angles correct for theta (see Table 1)!!! They correspond PERFECTLY to the NMR standard 3cos^2theta - 1 = 0. Ironically, I think they missed the rest of the term, however, as the 2nd term in Table 1 is only part of the P4 term...maybe another typo?

hey, norman! so, as Elie Cartan elucidated in the 50's (I think) - GR is density dependent, not mass dependent. So, I'm going to be governed by the density of the object, and the B field I use. Just like we do in NMR, the B field determines the Larmor frequency of your equipment, but the quarks and the gamma determine the absolute frequency of the nucleus of interest and how difficult it's going to be to get a signal. For example, tungsten (183W) should be easy - it's |1/2> and pretty abundant isotopically, BUT it's sensitivity relative to proton is five orders of magnitude away from proton! Ugh!

Martin - well, it's funny but NOBODY has approached it from a spin perspective. Even the original GR observations (the eclipse in 1921) can assert that fundamental coupling occurs b/t the photon and the graviton so [p^hat,g^hat] = not 0, meaning some crude commutator b/t the photon and the graviton, right? So, you're right about my advisor, of course. I will tell you that we are in the same lab here @ Stony Brook Univ. where MRI was discovered - we are in the same basement lab that Paul Lauterbur developed his "zeugmatography" which is what he originally called it - funny, right? Fascinating that somebody on this side of the pond is getting into "gravitational radiation" - perhaps you know the really clever story about the JPL researchers who were building Gravity Probe B? Janet something was the lead PI's name...at any rate they needed to measure changes in the three spheres spinning in x,y,z to measure the changes according to GR, based on the curvature tensors, but the obviously couldn't make any marks on the surface. They chose Nb as a surface metal, exploiting the fact that it's spin active (|9/2>), but that @ 4K, Nb^0 superconducts and they saw a "blip" that they couldn't explain on their accelerometer (since the sphere was obviously spinning), but they were under deadline, so they put it aside. Fast forward to 1999 w/ Tajmar and de Matos, two physicists who last I looked were still w/ the Euro. Space Agcy - they reproduced these exp'ts and determined that the "blip" was trillions of times greater than from normal radial acceleration of a spinning object (even superC). Personally, my guess would be that the electrons in Fock space are coupling to the local gravitons... HOOOOOOOOLY cow!!! Thank you thank you!!! I just arXived Chiao!!! His paper for his superC test mass is 12GHz!!!!!!! HOOOLY cow this provided strong evidence to my concept!!! I will definitely take your advice on Olaf Dreyer as well, but this rocks!!! Here's Chiao's paper: http://arxiv.org/abs/0710.1378 this is great!!! thank you thank you - he proved my point!!!! jeez this is fun! Merged post follows: Consecutive posts mergedoh, and Norman (norman albers) and I have been fiendishly going on his stuff that he's been producing which dovetails quite well w/ what I've been saying - he's just looking at it from the null geodesic p.o.v., which bends my brain to no end - he is an awesome friend and colleague!

well, martin - I very much appreciate the suggestion...I'm going to get up the gumption to email him...I would just be floored if I could get a post-doc to pursue this...my advisor thinks I'm daft - she's British (D.phil, Oxford, etc.), but she can't see anything wrong w/ the NMR part and she understands the nature of the tensors b/t the 2 gravitons to achieve a resonance condition (they are purported to be bosons, after all!), as there is a useful pulse sequence we use all the time which is analogous (except the construction of the tensors is dramatically different, but same general formula structure). Awesome - thx again! I'll keep you posted?

Martin - thx for the response - I will surely take your suggestions as to contact persons...but, even theoretically, do you think there's a shot? I know that looking at graviton spin as a perturbable object is kind of out-of-the-box, but I haven't been able to figure out any shortcomings - what do you think about the theoretical underpinnings (apart from the experimental part). If a particle or nucleus is spin-active, then you can write a Hamiltonian for it, particularly if you treat it as a density operator. Optics guys do it for the photon and if the gamma for the graviton really is 2, then the EM field to couple to its spin is clearly somewhere in the Ghz range - any thoughts?

hello, Maybe I can try to unstick this thread? Maybe it needs a new thread? Anyway, several groups (Univ. of Minn., UMass Amherst - I am happy to post the links if needed) have coincidentally and perhaps serendipitously offered some pretty interesting information regarding this topic. Further, Grandinetti, et al. just published a great paper on superadiabicity of spin ensembles. I'm finishing my PhD in chemical physics and I hit upon an idea - why not TEST LQG by finding the resonance frequency of the graviton, given an easy test mass (sphere, homogeneous material like boron nitride)? Kalnins, et al. (U of Minn.) and Holstein (UMass) have separately offered very reasonable math for a 4-space version of r x p (in other words, 4-space spin angular momentum) and a gamma of 2 for the graviton, respectively. Since GR provide for torsion-free curvature, that basically eliminates the possibility of getting odd off-diagonal matrix values or additional (rank-2+n) tensors following each tangent bundle. The first Hamiltonian is, obviously, the test mass itself, as that provides the first perturbation. The second Hamiltonian is placing the test mass in an appropriate B field, to remove spin degeneracy. About 1.2T and as homogeneous as possible. Third would be (depending on, as Cartan brilliantly elucidated in the 50's) adiabatically sweeping the field based on the density of the object, not the mass, but using the reconstructed spin AM tensors created by the U of Minn. group. I've got the magnet, the frequency synthesizers, access to a test mass (I have boron nitride powder and a press) and I can cobble together the spectrometer from parts to which I have access. I already know how I want to write the pulse sequence I want to write, but I REALLLLLLY need help in 2 spots: 1) how do I carefully rewrite the spin |2> density matrix to reflect the linear combinations of the coherences, which are going to be manifested in the off-diagonal terms and 2) how can I cleverly incorporate the phase cycling inherent to NMR in the pulse sequence to exploit the off-diagonal terms? OK, where are the flaws?

you and me both, brother! I do know that Gell-Mann's F4 (describing all of QCD) is precisely subsumed by E8 and Lisi's paper shows it flawlessly. if we humans as a whole don't end up slaughtering ourselves, then some of us w/ slightly less feeble brains will continue to enjoy the immense beauty offered by Lisi, Smolin, Cartan and others. Quickly, now!!

I agree - so, to flesh out your concept, as an exercise, think of all the means by which light is absorbed/reflected - gorgeous colors from transition metals are absorbing "white" light, but their d electrons (think cadmium yellow, cobalt or prussian (Fe) blue, etc.) are transmitting only the wavelengths of the color we see so vividly w/ our horribly wavelength-restricted eyes. Then, think about radio antennae absorbing all of those photons at a particular, favorite radio station, right? then a more QM picture comes into view, of the plasmons on the surface of the metal being polarized and resonating according to the initial polarization and resonant frequency (90.7Mhz out here in NYC!!) - though this is largely only absorption. Coincidentally, it's the same frequency on my magnet for 79bromine, to which I'm tuning right now. Of course, then the classic mirror example comes into maybe a more mature view, right? The mirror is just silver-backed glass, but the same plasmon phenomena are occurring, as noted above, w/ Brewster's angle. Do a simple experiment - take some polarizing mylar, shine regular flashlight and look at how effective the polarized light 1) comes through and 2) the efficiency w/ which the polarized light is subsequently reflected off the mirror, onto a surface where you can observe the results...

Mr. Danoyan - So far, you've only introduced a method of calculating discrete symmetries. For continuous symmetries, you will need to develop a series of matrices by which your discrete kets and/or bras (using your discrete symmetry metrics) will end up demonstrating coherences, exhibiting continuously symmetric manifestations of your discrete symmetries. But, why waste your time? Just read A.R. Edmonds, Ernst, et al. who already have developed a beautiful formalism for this which is the basis of Nuclear Magnetic Resonance!!!

Mr. Skeptic - recall that <x>cross<p> >= hbar/2. meaning the expectation value of the total momentum - p - cross the expectation value of position - x - This means that mathematically, you can't know all components both simultaneously, yet they clearly are there. Further, you CAN know some of the components, just not all of them. It's DEFINITELY not "inherently" uncertain, as you say. They're there, but QM doesn't allow them to be observed due to commutation rules... I seem to recall that Bell actually relied on "hidden variables" to justify his inequality. Yet, I sincerely believe he did not fully grasp the beautiful foundation of GR, such that a simple, non-local operator solves his so called "hidden variable" conundrum - particularly w/ his exp't which used photons - gauge bosons where the "|0> spin state" - which doesn't necessarily exist w/ a photon, could, in fact, be mathematically represented as the non-local transition b/t the |1> and -|1> states. great question - I offer an answer by analogy...in NMR, you place a compound in a large B field - you've effectively placed a Hamiltonian operator on your system (the Zeeman effect), since you've killed the degeneracies of your system and you're ready to start doing your exp'ts, since roughly 1/2 of all the spins in your system are now precessing around B(z). The fact that only roughly 1/2 of your spins are pointing up (slightly less than 1/2 are pointing down) is directly due to kT, and that is the slight inhomogeneity. Ultimately, we NEED that slight inhomogeneity to get our data... Here's a 2nd example where inhomogeneity is BAD. - Same as above, except our material now has Iodine in it - a nucleus whose angular momentum is so strong that it fights w/ the Bfield of our magnet and DOESN'T point toward B(z) like all the other spins in your material - now, we have 2 B fields, the one created by the magnet AND the one created by the local iodine - now, we have 2 Hamiltonians in our system and each is going to have its own solutions to Schroedinger - this gives weird off diagonal terms in our matrices, since the spins now feel 2 B fields - Schroedinger breaks down - ugh!!!! This led to the field of NQR (nuclear quadrupole resonance) where you use the naturally occurring iodine (or other strong quadrupole) as its own B-field, then use that w/o a magnet and pulse (apply operators to get solutions) accordingly...

science (math) already did - read A. Garrett Lisi's paper here: http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.0770v1.pdf

hello - Fred - you may be referring to F2 - a subset of E8...you most likely found a typo. Lisi found the rules for colour/QED inside F2 - it's mesmerizing - see the Nov. issue of New Scientist for the story. It's sooooo simple, I still can't believe it. Martin - the matrices he presents are, in fact, quantized, since they are normalized rotations and the extreme off-diagonals are all zeroes - only the Trace and the minor off-diags are left - gorgeous. This is the Clifford of rotations which we use in solid-state NMR. Same commutation rules apply, except that the rotational deconstructions are then manipulated (like |I> = Ix + Iy + Iz), since the whole spin, upon rotation, obviously does NOT commute, but the components do...so, for example, IxSy doesn't commute (standard commutation, right?), but IxSz of course, does. IzSz does, too, since L^2 is an observable - see Angular Momentum in Quantum Mechanics by A. R. Edmonds (ISBN 0691025894) No singularities, no infinities - the (this) universe is a closed set. It's then likely that E(8) is, itself, part of a closed superset, with each E(n) representing a different set of rules...Read Munovitz for some practicals on rotations used in NMR and you'll see what I mean...

I concur, Norm - beautiful - solidspin