J: Yes.
Z: "Do you really want to go there?"
J: Allah Akbar! Do we have a choice? ;-)
"Mach" does make some sense only in a Wheeler-Feynman retro-causal theory without the total future absorber boundary condition.
On Nov 1, 2007, at 12:53 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On 10/29/07, Jack Sarfatti
The problems of interest are:
1. Dark energy
2. Dark matter
3. Multiverse? WAP as explanation for the arbitrary parameters of the standard models of both quarks, leptons & gauge bosons and the precision cosmology of the accelerating universe.
4. Extra dimensions?
5. Practical warp drive & time travel to past seen in UFOs - I take that as established fact for the sake of argument at least, e.g. data base in http://www.nidsci.org/
On Oct 31, 2007, at 4:21 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On Oct 30, 2007, at 3:13 PM, Paul Zielinski wrote:
Jack Sarfatti wrote:
On Oct 30, 2007, at 10:47 AM, Paul Zielinski wrote:
"I'm trying to understand tetrads. I'm particularly interested in Rovelli's and others' explanations of the relationship between the Einstein-Cartan tetrad model and the 1916 metric field model for GR."
Good! Remember my basic idea here that seems to be completely original compared to Visser's, Chapline's, Volovik's et-al approaches. The key idea is in superfluid helium
v = (h/m)(dTheta)
v = coherent velocity field (here a closed 1-form in 3D Euclidean space)
Theta = single macro-quantum ground state ODLRO Goldstone phase
PSI = (Higgs Field)e^i(Goldstone Phase)
"OK, but you need to explain in intuitive physical terms:
(1) How your macro Higgs-Goldstone field is established and controlled by matter;"
Vacuum instability is already part of inflation cosmology folklore.
"OK."
BTW NO ONE (Visser, Chapline, Volovik) can yet answer (1)
"So far no one can answer this basic question with a condensate model? Hmmm.
Well, then I suppose I shouldn't just pick on you, should I?"
See Rocky Kolb's latest, I think he mentions this?
http://arxiv.org/PS_cache/arxiv/pdf/0709/0709.3102v1.pdf
The situation in string theory is far worse. See Lee Smolin's "The Trouble With Physics". It should be sub-titled: "The Good, The Bad and The Bogus."
"String theory is a mathematical template for the kind of "theory of everything" that some theorists in high positions would *like* to exist. It is aggressively unfalsifiable. If there are 10^500 ways to fold up 6 extra spatial dimensions and make them invisible, float the modest hypothesis that there are 10^500 parallel universes to match. Problem solved!"
True enough, on the other hand this is consistent with WAP (Weak Anthropic Principle) in a multiverse of actual material parallel universes. This is testable with metric engineering of warp and wormhole plus signal nonlocality to actually travel and communicate with ET/ED advanced beings in the universes next door in the sense of mainstream eternal chaotic inflation. I mean Max Tegmark's "Level 2" below
http://www.acceleratingfuture.com/michael/blog/images/multiversethumb.JPG
Note that Level 2 is Wheeler's "IT"
Level 3 is Wheeler's "BIT" as a Bohm pilot wave in Wheeler's Super Space.
"IT FROM BIT"
http://www.metanexus.net/ultimate_reality/zeilinger.pdf
"It is mathematical *a priorism* run amok. IMHO."
OK ;-)
The two battle-tested organizing principles are:
1) localize both internal and space-time symmetry groups of matter source fields
"The difference here is that you are doing it with "external" gauge symmetries."
Yes, but Utiyama did it in 1956 with 6-parameter space-time Lorentz rotation group. He had to stick Einstein's GCT's in adhoc. Kibble redid it in 1961 with 10-parameter Poincare group that is 1905 Special Relatvity and out pops Einstein's 1916 General Relativity curvature field equation driven by the stress-energy current density source matter tensor with ADDITIONAL torsion field equations driven by the 4D angular momentum density matter field tensor. Virtual sources (zero point energy) inside the vacuum must contribute directly with real sources excited out of the vacuum! That's from the EQUIVALENCE PRINCIPLE - the ORGANIZING IDEA! But why stop there? At least play same trick with 15-parameter Penrose conformal TWISTOR group!
a) only some source fields carry internal charges
b) all source fields carry the 4 space-time charges (4-momentum) of the translation group T4 equally universally and that is the EQUIVALENCE PRINCIPLE!
"The Noether conserved quantities of T4, right?"
Yes, of course.
"Doing this with a group like T4 could also shed some additional light on the workings of the Standard Model."
I have already done it. Not localizing global rigid T4 to local elastic T4(x) is the unstable pre-inflation false massless Minkowski globally flat vacuum like super-saturated steam ready to nucleate liquid inflationary bubbles, i.e. Tegmark "Level 2." Each bubble is an infinity of our pocket universes limited by past and future causal horizons broken by "signal nonlocality" (A. Valentini). Localizing T4 alone gives precisely Einstein 1916 General Relativity provided that you ad-hoc impose the zero torsion field constraint. This via Rovelli eq. (2.89) gives a dummy spin connection in terms of the T4(x) induced tetrads which which to get Einstein's 1916 equations.
It is extended up to the 15-parameter conformal TWISTOR group at least. The additional group parameters act like extra space dimensions and the supersymmetry is inherent in Roger Penrose's mapping of world tensors to spinor-twistor QUBITS as in J. A. Wheeler's
IT FROM BIT
"Do you think this could explain why string theory seems to "work" at a certain level of abstraction? That it captures this kind of mathematical structure?"
Not sure if "work" is the right word.
It's obvious that the 4 dimensions of space-time are simply the "phases" of T4(x) local translations
It's equally obvious that the 6 dimensions of Calabi-Yau space of string theory are simply the "phases" of SO(1,3) the local space-time translations. This is precisely Gennady Shipov's "oriented point."
It's also obvious that 3D+1 boson <-> fermion "supersymmetry" is simply Roger Penrose's spinor formulation of Einstein 1916 GR made fancy by the mythamaticians. ;-)
You use Roger Penrose's spinor-tensor diagrams in his "Road to Reality" to get that. I don't mean here his conformal spacetime diagrams. Penrose has all sorts of diagrammatic techniques.
Basic 2-component spinor is a "line" qubit
a world vector (spin 1) is an entangled EPR pair
Obviously 2 spinor lines fuse to a boson etc.
If one of the two entangled spinor lines moves to a parallel universe it looks like the boson has morphed to a fermion. It moves through a wormhole connecting the two universes?
The T4 momentum generators Pa are world vectors obviously.
The spinor supersymmetry generators are their "square roots" - commutators of supersymmetry generators are the T4 generators essentially. Hence T4 has a supersymmetry "deep structure" (N. Chomksy) or "substratum" (Dirac).
with 2) "condensates" "ODLRO" "spontaneous symmetry breaking" "hidden symmetry" "More is different" i.e. the principle of bottom - up EMERGENCE as distinct from top-down REDUCTIONISM gives long wave "effective field theories" like gravity - we get
IT FROM QBIT + BIT FROM IT = spontaneous self-organizing strange loops across different levels of complexity as well as self-creating loops in time - signal nonlocality (Antony Valentini's "sub-quantal non-equilibrium) http://www.fqxi.org/aw-valentini.html
"So do you think that Lorentz symmetry is itself also only an equilibrium property of the post-inflation vacuum?"
Huh? Define "equilibrium". Global Lorentz symmetry in the pre-inflation false vacuum is extended to local Lorentz symmetry in the post-inflation truer vacuum. Local Lorentz symmetry is a larger symmetry group than global Lorentz symmetry which is one of its subgroups! I mean here symmetries of the actions of all matter fields still preserved in the post-inflation Higgs-Goldstone vacuum ODLRO fields. Spontaneously breaking (or hiding) this local Lorentz symmetry is a separate problem also possible - same for T4(x) of course.
http://arxiv.org/PS_cache/arxiv/pdf/0710/0710.4474v1.pdf
inflation phenomenology fits the facts
"But I hope you agree that a satisfactory condensate model for the gravitational vacuum should explain the
basic features of Einstein's theory."
Earth to Paul, come in Paul. That's exactly what I have done!
A^a = M^a^a curved tetrad
S^a^b = M^[a,b] spin connection
M^a^b = (dTHETA)^a(PHI)^b - (THETA)^a(dPHI)^b
THETA^a & PHI^b are THE EIGHTFOLD Goldstone coherent vacuum "hologram phases" of THE NINE real Higgs scalar fields. ;-)
e^a = I^a + @A^a Minkowski + curved tetrad
ds^2 = guv(LNIF)dx^udx^v = e^aea(LIF)
is exactly that!
"OK, so your BEC Higgs-Goldstone field is a macro-quantum model for Einstein's unified "gravitational-inertial field", that automatically implements the equivalence principle? "
That's what I said a jillion times to deaf ears. ;-)
"If so, then of course the explanation for the equality of inertial and gravitational mass will be the same as Einstein's."
Yup.
If you read about spontaneous broken symmetry order parameters in say a book on "Soft condensed matter physics" you should understand that the EXACT MICROSCOPIC DYNAMICS is largely IRRELEVANT to the effective emergent field theory! You do not need to know electron-pairing to get most of the gross features of superconductors like the Meissner effect, quantized magnetic vortex filaments in type II phase etc.
"OK."
It's nice to have a micro-model of course - but it is not required to make important progress.
"Right."
String theorists have even less than this if you read Smolin and Woit and that has not stopped NSF & all the major private foundations from putting all their eggs into the string theory basket - now the eggs are broken and All The King's Men ... ;-)
"That is quite a syndrome -- basically a sociological phenomenon. There appears to have occurred a serious institutional breakdown in American science. The blind leading the gullible. Although I'm not sure Smolin went far enough with his critique. I guess he knows he is walking on eggs."
Yes.
As another example, 19th century crystallography was very successful even before atomic theory, even before quantum theory. One age's fundamental theory is the future's phenomenology. ODLRO is semi-phenomenology, but it works and suffices to answer most of the questions of precision cosmology.
"Sure. I don't see a problem there."
note from http://arxiv.org/PS_cache/arxiv/pdf/0709/0709.3102v1.pdf
http://www-conf.slac.stanford.edu/ssi/2005/lec_notes/Kolb1/default.htm
My pre-inflation unstable false vacuum is massless standard model in global Minkowski spacetime without any vacuum ODLRO in the inflation instability virtual bosons form condensates and virtual fermion-antifermion pairs form condensates in the COMs.
"OK, so does this mean zero inertial and zero gravitation mass for all standard model particles in the pre-inflation vacuum?"
Yes of course.
This sucks up most of the random ZPF of the false vacuum into the coherent fabric given by the c-number tetrads e^a and the spin connections S^a^b!
"OK. I can see that this is an attractive feature of the model."
Understatement.
e^a = I^a + @A^a
@ = probability to cut and fuse strings? ~ N^-1/3 see Lee Smolin "Trouble With Physics"
@ is actually a variable
"OK."
A^a = M^a^a
S^a^b = M^[a,b]
M^a^b = (dTHETA)^a(PHI)^b - (THETA)^a(dPHI)^b
ds^2 = guv(LNIF at P)dx^udx^v = e^aea(LIF at P) EQUIVALENCE PRINCIPLE
P (gauge orbit) defined in Rovelli
(2) How your Higgs-Goldstone field sets up inertial resistance to accelerating motion;
this question is ill-posed.
"But doesn't the standard Higgs field do just that? Don't elementary particles acquire inertial mass by way
of a Higgs mechanism? Isn't that why the Higgs field is regarded as a "quantum ether"?"
Partly. The Higgs provides the rest masses to the weak W bosons. The strong gluons and photons have no rest mass. The quarks also get small rest mass. Most the the mass of nucleons is KINETIC energy inside the "bag" of IR CONFINEMENT, i.e. dark zero point energy creates an effective quark-quark string potential
"Of course we're talking about *rest* mass here. Of course kinetic energy itself endows elementary particles
with inertial mass."
NO! You do not get the idea. This is trapped kinetic energy inside the "bag" of "quark confinement" - actually it may be mostly zero point "dark matter" of positive pressure and negative energy density if w = -1. In any case Frank Wilczek discusses this point in several of his popular articles on QCD for which he shared a Nobel Prize. Most of the 1Gev nucleon rest mass is "kinetic" or, more precisely, "zero point vacuum jiggling." The quark rest masses are in the MEV range.
V(quark-quark) ~ +c^2r/Lp*^2
Lp* ~ 10^-13 cm
hc/Lp* ~ 1Gev
r ~ h/p
p = 3-momentum transfer in a basic quark-quark Feynman scattering diagram
as p -> 0 (IR) V(quark-quark) -> + infinity
that's CONFINEMENT Watson!
Standard model gives rest masses m from electro-weak Higgs that may correspond to my GMD point monopoles with 3 real Higgs and 2 Goldstone phases projected into 3D + 1 from 9D + 1.
"But shouldn't your theory actually *predict* the observed inertial masses, based on some interaction with the Higgs fields?"
"Of course here I meant rest masses."
I never promised you a Rose Garden nor a Tree in Flatbush! Go ask Ed Witten. It's the Weak Anthropic Principle on Lenny Susskind's "Cosmic Landscape" in the Multiverse.
"It is only reasonable to expect that any theory that claims to explain the origin of inertia and its relationship to gravitation will have the capability of predicting the rest masses of elementary particles. Isn't that exactly what quantum (or macro-quantum) gravity should be about?"
No. The multiverse populated cosmic landscape is a viable alternative. You are imposing a Red Herring on the the theory. What's important is that you get 4D elastic distortion dislocation field tetrads A^a and twisting 6D dislocation spin connections S^a^b in precisely the same way that you get 3D superfluid frictionless flow. That's the important really new idea here.
"Or are you doing physics more in the style of the string theorists?! :-)"
Not everything they say is NOT EVEN WRONG. I make predictions. Strong ones - no dark matter particles on mass shell as a matter of fundamental principle! LHC can knock me out of being a contender! ;-)
http://www.youtube.com/watch?v=prXXOxCPNek
"Yes, but if a physical model for gravitation and inertia can really explain the origin of inertia of elementary particles, then why shouldn't it also predict values for the particle rest masses? Or at least have the potential to do so? I guess this is the Holy Grail."
Not necessarily. Lenny Susskind explains this rather well in his pop book "Cosmic Landscape". You cannot impose the idea that there is one universe with all numbers determined. It may be so, but so far the evidence seems to point that it's not so. This is John A. Wheeler's "Law without law."
http://www.bigear.org/vol1no4/wheeler.htm
http://adsabs.harvard.edu/abs/1988bqc..book..583D
http://en.wikipedia.org/wiki/John_Archibald_Wheeler
Now as far as inertial resistance is concerned since I derive the tetrads and spin connections as emergent macro-quantum vacuum condensate fields, therefore we have the action principle for test particles that answers your question exactly like Einstein would.
"Well, that could mean more than one thing.
Do you mean you can get Machian long-range interactions with remote masses from your model?"
No of course not! "Who ordered that?" (I. Rabi) When do I ever even use the word "Mach"?
"OK, good. Because as far as I am concerned that is a DEAD DUCK."
It's a COOKED GOOSE! "Physics is simple when it's local." (John A.Wheeler). Local gauging is basically local causality - classically prior to post-quantum signal nonlocality of course.
"Or do you mean that both inertia and gravitation are built into the Einstein-Cartan tetrad model, being "fused together" in that model by the Einstein principle?
Obviously. Tried and true. If it ain't broke, don't fix it. The wheel has already been invented.
"OK."
Dx^u(test particle)/ds^2 = (external force)^u/m
"OK, so you get the tetrads from the Goldstone phases, and the tetrad model automatically requires a non-gravity force to be applied in order to push a test particle off a spacetime geodesic?"
Obviously, yes.
"OK."
my
A^a = M^a^a
is exactly like
v = (h/m)dTHETA
for the frictionless flow of superfluid Helium 4.
A^a is physically an elastic distortion of the 4D world hologram crystal lattice
"OK, this makes sense. So is it fair to say that in this "world crystal" model the lattice spacing determines the metric intervals between spacetime points? And that this is directly related to your M^a^a = A^a?"
Wait - the GMD point monopoles are the literal nodes of the 3 post-inflation real Higgs scalar fields that live on 3D spacelike hypersurfaces. The other 6 are in "Calabi-Yau" space, i.e. G. Shipov's "oriented point." These point nodes are like the atoms in the crystal lattice. Equilibrium is when there are no torsion dislocation and no curvature disclination defects in the arrangement of these nodes. A^a(P) is the distortion field of a node at P.
The wavelet resolution dependent mean spacing between these nodes is
&L = (Lp^2L)^1/3 = N^1/6Lp
where L is scale of a dominating null horizon i.e. future retrocausal dark energy driven de Sitter horizon.
L = 10^28 cm
&L = 10^-13 cm
N ~ 10^122 Bekenstein BITS
There are N area quanta on the horizon with exactly N volume-without-volume quanta.
whose equilibrium NODES are separated by the quantum foam scale
&L ~ (Lp^2L)^1/3 ~ N^1/6Lp Jack Ng's papers http://tinyurl.com/2pfvdj
Lp ~ 10^-33 cm
N ~ 10^122 in our pocket universe on the cosmic landscape of the multiverse of parallel worlds without end
The NODEs are the GMD monopole defects (2nd homotopy group of wrapping integers is non-trivial) when the 8 Goldstone phases project from 9D + 1 to 3D + 1 leaving 2 Goldstone phases in 3D space, the extra 6 Goldstone phases are the dimensions of 6D Calabi-Yau space.
"OK."
Quantum Foam}, gr-qc/0401015, to appear in the Proceedings of the Tenth Marcel Grossman Meeting on General Relativity.
{Spacetime Foam, Holographic Principle, and Black Hole Quantum Computers} (with H. van Dam), gr-qc/0403057, to appear in the Proceedings of the 2003 Coral Gables Conference.
{Quantum Foam and Quantum Gravity Phenomenology}, gr-qc/0405078, to appear in the Proceedings of the 40th Karpacz Winter School on Theoretical Physics.
{Spacetime Fluctuations}, to appear in the Proceedings of the Vulcano Workshop on Frontier Objects in Astrophysics and Particle Physics, ed. by F. Giovannelli and G. Mannocchi.
"Is it correct to say that your Higgs-Goldstone field directly controls the metric properties of the physical spacetime, which in turn determine the physical geodesics?"
Yes, but there is also a back-reaction of the geometrodynamic field on the Goldstone phases. It's a self-organizing creative strange loop.
"OK. So in your model, as in GR, the geometrodynamic field has a life of its own."
Yes, maybe a conscious GAIA "Star Maker" (Stapledon) "Black Cloud" (F. Hoyle) "GOD(D)"(I.J. Good) "Participatory" (Wheeler) "Intelligent Universe" (F. Hoyle, 1983).
http://qedcorp.com/APS/ureye.gif
The Higgs fields obey a Landau-Ginzburg equation - it's local nonunitary in the GMD field of the tetrads and spin connections in a globally self-consistent loop.
"OK."
"(3) Why the inertial mass is precisely equal to the gravitational mass in your model?"
This is not an appropriate question "why"? Why is it for any model? I take Einstein's premises as "true," i.e. pragmatically useful. Your questions are basically ill-posed.
"Well, Einstein of course had an explanation for this in terms of the "unity of nature" of gravitation and inertia based on a unified gravitational-inertial field. So I suppose if you can recover Einstein's geometrodynamic field via the tetrad model based on your BEC Goldstone phases, then you have everything you need. Inertia is then in essence a physical resistance of the Higgs-Goldstone field to acceleration away from gravitationally determined geodesics of locally interacting test particles."
By Jove, I think he's got it? ;-)
If this interpretation is accurate, then I don't see the need for any "Mach's principle" in your model.
Red Herring. I never mentioned "Mach's principle". We don't need no stink'n Mach's principle! ;-)
http://www.youtube.com/watch?v=M3YpdMxrIXg
"OK, good. But then it's still not clear to me what your theory has to do with "general relativity". Geometrodynamics, fine, but not "general relativity"."
Now you have gone off the deep end.
1916 GR is in a nutshell
ds^2 = e^aea
T^a =de^a + S^ac/\e^c = 0 no torsion dislocation
curvature disclination R^a^b = dS^a^ab + S^ac/\S^cb =/= 0 possible
gravity action density ~ R^a^b/\e^ce^d
I derive S^a^b from M^[a,b]
and the important new compensating T4(x) gauge tetrad part of e^a, i.e. A^a from M^a^b that uses all 9 effective space dimensions if you want to think "superstring theory."
"Of course if you can show in your model that one effect of a macro-quantum gravitational field is to "accelerate " the geodesics at each spacetime point (according to a metrically determined action principle),"
This sentence you wrote Paul is nonsense. By definition a timelike geodesic for a massive test particle has zero covariant acceleration. There are no g-forces on that test particle. The rest observer sitting on the test particle is weightless.
d^2x^u(test)/ds^2 + {LC}^uvw(LNIF)(dx^v(test)/ds)(dx^w(test)/ds) = 0
If you think "Newton" NOT "Einstein" then
d^2x^u(x)/ds^2 is the Newtonian "acceleration" compensated by the "inertial force"
{LC}^uvw(LNIF)(dx^v(test)/ds)(dx^w(test)/ds) on the parabolic path of the cannon ball
that is not a Newtonian geodesic in flat spacetime, but is a Einstein geodesic in curved spacetime. Therefore, "inertial compensation" is strictly a Newtonian concept.
In a LIF the geodesic test particle obeys d^2x^u/ds^2 = 0, but in a coincident LNIF it obeys for the observed test particle
d^2x^u(test)/ds^2 = - {LC}^uvw(LNIF)(dx^v(test)/ds)(dx^w(test)/ds)
but it is the observer frame that has the acceleration from a non-gravity force! The RHS is determined by the non-gravity force in the LNIF rest frame of the observer.
"then I suppose you do recover the defensible core of the Einstein principle (limited analogy with the locally observable effects of frame acceleration)."
You are not making sense to me here.
in this simplest of "More is different" emergence from Sid Coleman's "hidden symmetry" (goes back to Brout-Englert - PW Anderson). PS Robert Brout was one of my tutors at Cornell (in group theory) I saw him again in Brussels when Jagdish Mehra invited me to Prigogine's institute when I was with Abdus Salam in Trieste 1973-4. That's when I suggested
Hadronic Resonance Spin = (1Gev)^-2(Energy)^2 + Jo
as a strong short-range gravity G* - 10^40G(Newton) as a kind of Kerr "black hole" - decay by Hawking radiation. Also wrote about making miniblack holes in accelerators & baby universes in ICTP internal memos 1973-4. Also did a paper on Dirac Eq in curved spacetime David Finkelstein I think published it? - or maybe it was Foundations in Physics? I forget which.
"Fine, but how does you macro Higgs-Goldstone field result in inertia? And how is it controlled by the matter distribution?"
Guv = kTuv how else? Again an ill-posed question not really relevant. Too broad - ask same question of any model and even so it is not really an interesting question within the context of the theory.
"That doesn't make sense to me in view of the fact the standard Higgs mechanism is supposed to result in inertia, based on a direct interaction of the Higgs field with elementary particles. Doesn't this apply to your macro Higgs fields? If not, why not?"
The Higgs mechanism in standard model has NO GRAVITY.
"Inertia only. OK."
Yes, but that is a contradiction - violating the equivalence principle. Since there is no gravity in that limit there is no gravity mass - serious incompleteness.
It's in Minkowski spacetime. It purports to get rest masses.
"Right."
However, that is obviously inconsistent with Einstein's GR!
"I can see how it doesn't *give you* Einstein's GR, but how is it inconsistent with it?"
It violates
m(inertial) = m(gravity)
because in Minkowski spacetime with 1905 SR since there are no gravity fields in the GIF
m(gravity) = 0.
Note that 1905 SR only allows GIFs. As soon as you allow GNIF's it's the first baby step to 1916 GR and then you do have
m(inertial) = m(gravity) in the GNIF
m(gravity) =/=0
Do you mean that inertial and gravitational mass of W bosons need not be the same in the Higgs model?
gravity mass = 0 strictly in all special relativistic quantum field "point" theory limited to the rigid Poincare group. There is no room for even Newton's gravity field
g = -GM/r^2
because G = 0 in all 1905 SR limited field theories.
In my theory I assume the standard model as the pre-inflation unstable false vacuum, but without any Higgs mechanism - there are no rest masses in my false vacuum.
"OK. So no Higgs rest masses in your pre-inflation vacuum."
Yes.
The Higgs mechanism comes into being only post-inflation with the emergent tetrads and emergent spin connections from the Goldstone phases - the weak Higgs fields derive from that with parity violation - is the idea.
"So you only have a macro-quantum Higgs field. OK."
Since my 8 Goldstone phases essentially have the 6 extra space dimensions in them, I then ask Ed Witten how he would do it. Dump it on Witten's lap! ;-)
"Wait a minute. Do these have to be actual spatial dimensions? Or could they simply be additional abstract structure without any direct geometric interpretation?"
Not the latter. There is always a direct geometrodynamic interpretation as an EXTENDED TEST PARTICLE.
That's why it fits string theory. The simplest extended structure is two point particles connected by a spring.
The center of mass has 4 coordinates with 4 displacements. There are 4 relative coordinates with 6 space-time rotations. It's the 6 space-time rotations that form the "extra space" dimensions of Calabi-Yau space. Note that there is also a dilation - changing distance between the two ends - so 11DIM, i.e. fiber bundle 4D T4 base + 7D fiber in the group parameter space. Then when you include the elastic string field you have a infinity of new degrees of freedom. But the basic idea is that you no longer have a point object, but a spatio-temporally extended object. Then when you include constant acceleration conformal boosts from GIFs to GNIFs you get an additional 4 configuration dimensions so we have the 15D fiber bundle.
"How would you hide the additional spatial dimensions? By folding them up, like the string theorists?"
Yes.
"Do you really want to go there?"
Allah Akbar! Do we have a choice? ;-)
Note that Gennady Shipov's 6D "oriented point" in curvature + torsion theory is essentially a 6D Calabi-Yau space for us peasants. ;-)
"OK. That's interesting. I still think you should look for a way to predict rest masses."
I don't think so. I think the Cosmic Landscape multiverse is probably correct - it's retro-causal "Law without law" teleological natural selection - signal non-locality. All rest masses exist in other worlds along with all other values of all the couple of dozen coupling parameters etc - and in principle we can detect these other worlds.
in any case the vorticity vanishes locally:
dv = 0 means irrotational curl-free flow (2-form)
nevertheless first homotopy group is non trivial for stable string (line vortex) quantized circulation defects where the two real Higgs scalars making single-valued complex order parameter vanish, so that THETA is undefined on the string vortex (healing coherence length with string at center - random zero point energy self-trapped inside the core!).
Effective integral of dv on singular area surrounded by closed non-bounding cycle enclosing a stable string defect i.e. circulation integral of v = N(h/m), N = 0, +-1, +-2 .... first homotopy group
OK for the world crystal lattice on 3D spacelike slice we have 2 Goldstone phases THETA & PHI with three real Higgs fields giving stable point "monopole defects" of the EMERGENT GeoMetroDynamic GMD
field.
"So you go from your Goldstone-Higgs fields via a Kleinert-type world lattice model to the emergent GMD field?"
Yes.
What are you asking? I wrote the equations.
e^a = I^a + @A^a
A^a = M^a^a
S^a^b = M^[a,b]
M^a^b = (dTHETA)^a(PHI)^b - (THETA)^a(dPHI)^b
ds^2 = guv(LNIF at P)dx^udx^v = e^aea(LIF at P) EQUIVALENCE PRINCIPLE
What don't you get? ;-)
"I'll take that as a "yes"."
LENGTH 1-FORM is not closed
L = Lp[(dTHETA)(PHI) - (THETA)(dPhi)]
Define closed AREA 2-FORM A
A = LpdL ~ 2Lp^2(dTHETA)/\(dPHI)
dA = 0 is WORLD HOLOGRAPHY of
Volume without volume.
Integral of A over closed surrounding non-bounding 2-surface enclosing N stable elementary GMD monopole point defects is ~ NLp^2 i.e. Bekenstein area quantization from non trivial 2nd homotopy group.
N area quanta (HOLOGRAM) project to N interior volume-without-volume quanta (HOLOGRAM IMAGE)
consistent with Jack Ng's
&L = (Lp^2L)^1/3 = N^1/6Lp
&L is lattice spacing of Kleinert World Crystal Lattice = quantum foam bubble size
L is scale of a null horizon
1-1 map of horizon area bit quanta to volume-without-volume bit quanta = HOLOGRAM PRINCIPLE
"So is this how you connect your Goldstone-Higgs fields to the Kleinert lattice?"
Partly.
"OK."
OK now to TETRADS
THETA^2 = (THETA)^a(THETA)a
PHI^2 = (PHI)^b(PHI)b
e^a = I^a + @A^a = Einstein-Cartan emergent gravity tetrad field
@ = dimensionless string coupling field - environmentally dependent probability to cut and fuse strings.
I thought you had e^a = I^a + A^a? This is true only for N^-1/3 = 1?
You thought wrong! I sometimes may not bother to write in @.
"Well, this is an additional wrinkle in the relationship between the tetrad model for GR and your Higgs-Goldstone field quantities, isn't it?"
Not at all.
e^a = I^a + B^a
B^a = @A^a = @M^a^a
"OK."
this is only notation - no wrinkle unless you mean that as pun "wrinkle" as "curvature"
"No."
A^a is a "wrinkle" in that sense.
"OK."
I had in one model
@ = N^-1/3
ranges from 0 to 1 like a probability N = 1 is min out to infinity.
ds^2 = guvdx^udx^v = e^aea
A^a = M^a^a
M^a^b = (dTHETA)^a/\(PHI)^b - (THETA)^a/\(dPhi)^b
How did you arrive at this expression and how is it justified based on your ODLRO condensate model?
My act of intuition!
"Inscrutable."
God moves in mysterious ways.
Spin connection is
S^a^b = - S^b^a = M^[a,b]
How did you arrive at this expression and how is it justified based on your ODLRO condensate model?
Ditto - to my mind it is obvious.
"OK..."
This is where intuition comes into play. It came from the future in a self-creating loop in time! Signal nonlocality in action!
"In other words, it is a "free creation of the Humean intellect"?"
It's the free invention of the Sarfattian Mind!
http://www.youngfrankensteinthemusical.com/
"Try and and you'll like it"?
That's the way all physics is when theoretical physicists remember their's is an empirical pragmatic science not the Circe of pure mathematical seduction by Pied Pipers.
"Tell that to Witten."
Pure mathematics is the opiate of theoretical physicists who have not had a good physical idea in decades. The experimentalists have taken the lead and it's a good thing.
"Yet you cannot proceed mechanically from empirical data to theory. So I suppose your intuition may have a legitimate part to play here."
Free invention of the human imagination to paraphrase Einstein. How did Leonardo Da Vinci recognize that vortices in the blood flow of the heart are essential to its operation and he designed an aortic heart valve that works perfectly in human's if made with the proper modern material? Leonardo was 500 years ahead of his time - perhaps he met a time traveller from the future? 3/4 of his work was destroyed by the Church! See NOVA on this.
Lobo
This requires 9 real Higgs scalars.
"OK."
Stable defects needs one space dimension for each Higgs field.
"OK."
This give branes with 6 extra space dimensions (e.g. Shipov's oriented point -> Calabi-Yau).
Basically one HYPERSPACE dimension for each generator in the Lie algebra of the space-time symmetry group -
"Tell me more about this "spacetime symmetry group" and its Lie algebra."
Ask Carlos Castro, read Penrose on twistors.
"OK. Standard stuff I guess. That was really supposed to be a rhetorical question."
this would be 15D for Conformal Penrose Twistor Group! 10 for Lorentz group.
Supersymmetry is trivial from Penrose map of nth rank Poincare group tensors to 2nth rank spinors.
This becomes TWISTORS for Conformal Group!
I am answering key issues about real observations.
"Doesn't your model put any constraints at all on the number and type of Higgs fields -- other than that there be one hyperspace dimension per Lie generator?"
no - that's all that topological defect stability demands
"OK."
Z: "Considering this relationship with reference to both the inertial compensation and Einstein equivalence paradigms could be very illuminating."
I don't think so.
"I know you don't."
"However, once I have a precisely defined covariant measure of gravitational geodesic deformation, I think I will also have the tetrad model cracked, in addition to the traditional metric-connection model featured in the 1916 theory."
Promises, promises ...
"Getting closer to product rollout every day."
Will there be any glaciers and fish in the sea on that day? ;-)
"Well, I'll have the last laugh when Hell freezes over. I guess you haven't heard about climate change?"
That's what I alluded to in the melting of the glaciers Holmes.
I imagine it will make more sense to physicists to described the gravitational field as a geometric deformation field, as opposed to a set of coordinate transformations, one for each spacetime point, specified by the Jacobian matrices e^a_u.
e^au is a physical field in my theory same as v = (h/m)dTheta in superfluid helium - this is a non-problem.
"Yes, but you've already agreed that according to Rovelli the e^a_u specify frame transformations that only mirror the actual field at each spacetime point -- they do not and cannot themselves directly represent the gravitational field. The key here is the precise relationship between the tetrad transformations on the one hand and the metric field of 1916 GR on the other, as discussed for example by Rovelli."
"Inertial compensation" is a Newtonian idea making no sense at all in Einstein's GMD theory.
"It makes no sense in Einstein's theory of "general relativity", I agree. But geometrodynamics is another matter."
Wrong. The GMD fields are simply e^a and S^a^b - end of short story.
"Since the so-called "spin" connection determines curvature and torsion in the tetrad model?"
The tetrads by themselves in 1916 approximation are forced by adhoc constraint to have zero torsion dislocation defects in the world hologram (volume without volume 1-1 map of area quanta to volume quanta where Bekenstein BITs N = # GMD monopoles). They still have curvature disclination defects with dummy spin connections as in Rovelli's eq. (2.89). But that is simply step 1 not enough to explain the 96% of the dark stuff of the universe.
"OK."
It's an inappropriate concept taken out of its proper context.
Just sayin' it don't make it so.
Practice what you preach.
"Fair enough."
I agree that the idea is iconoclastic, and certainly runs against almost everything we've been taught about Einstein's theory. But then again, read for example Vladimir Fock's preface in his "Space, Time and Gravitation" (1952) for a contrary view.
If you read Lee Smolin you will see why you are hitting your head against a stone wall.
"I *have* read Smolin. His account of the current situation in academic physics rings true, and is pretty
scary. Total lockstep group think. String theorists want to change the definition of physics -- and even science in general -- to legitimize the speculative hypergeometric oregami of M-theory. Nice work if you can get it."
Read how John Schwarz (JS) did not get tenure & Pierre Ramond et-al.
"Yeah"
JS did get it at Cal Tech after 1984 "First superstring revolution". Feynman dies in 1986 and he hated string theory.
"Yes, I'll have to look into that."
Maybe Feynman held back JS's tenure?
"Interesting to speculate, but how could you verify that?"
Ask Murray Gell-Mann. I am sure plenty of people left who know.
There is no loose string in Einstein's equivalence principle, which in fundamental for is SIMPLY
ds^2 = guv(LNIF)dx^udx^v = e^aea(LIF)
"It's not clear to me (at least yet) that Rovelli's tetrad transformations are the exact mathematical equivalent
of the metric field model for GR. Does that mean that Einstein's principle is only an approximation? Or does it mean that Einstein's principle only works for uniformly accelerating motion?"
Neither.
"Rovelli is slippery on this. How can the tetrad model be a more faithful representation of the gravitational field of GR, if it's mathematically exactly equivalent to the metric field model? Doesn't make sense. What's wrong with Rovelli's picture?"
No because:
1) you need tetrads to couple to spinor matter source fields
"OK, that makes sense."
2) since tetrads are simply local T4 gauge potentials you get more GMD fields by locally gauging bigger spacetime symmetry groups.
"Mathematically, yes of course you do. My questions are directed more at the physics."
The physics is that those fields must be there by parsimony and they must explain the dark energy and the dark matter.
"What makes you think this is an exact representation of the Einstein field?"
All theories are approximations.
"Well, I want to know what the precise relationship between the two models is, both mathematically
and physically. At this point at least it Rovelli's analysis in Section 2.2 doesn't seem so clear and
obvious to me."
It's the best I have seen so far.
with universal minimal coupling to source matter fields Psi
Du = e^auPa + S^a^bPab
"OK, but what exactly does this mean physically? How does this affect the meaning of Einstein's principle?"
It is the principle of local gauge invariance. Read "The Dawning of Gauge Theory." It's spelled out in Rovelli Ch 2.
"Again, I think I understand the meaning of local gauge invariance as it is applied in Yang Mills and the Standard Model. What I am questioning is the physical meaning of local gauge invariance as it is applied in Utiyama, Kibble, et al."
Those papers are in that book.
"In the standard gauge field model, working with internal gauge symmetries, I have no objection. My problem is with the application of the gauge field model to what I regard as ill-defined *external* symmetries.
Of course I understand that Yang-Mills forms the basis for the Standard Model in elementary particle physics.
But here we are dealing with external symmetries apparently defined with reference to coordinate invariance groups."
{Pa,Pab} is Lie algebra of Poincare( -> Conformal Group)
"This is a coordinate invariance group?"
Meaning what? It's a physical symmetry.
"You can interpret the Lorentz or Poincare group as a group of spacetime coordinate transformations, or as a group of geometric transformations. They are not the same thing."
"So the machinery of Noether's theorem -- Lie algebras, Lie generators, and so on -- is being applied here
to groups of coordinate transformations? Which latter are being treated as physical symmetries?"
Poincare group is displacements & rotations of detectors - independent of local coordinates
"In the tetrad model. OK. Yes of course the tetrads are covariant objects (vectors), even in a coordinate basis. But this is a very tricky concept as I've said."
In your approach, is Lorentz invariance a physical symmetry of the vacuum, or is it a property of a
particular choice of coordinates?
neither! It's a physical symmetry of the actions of all physical fields.
"OK, good answer. And this symmetry also holds locally for the tetrads in any local inertial frame, right?"
In any local frame period, both inertial and non-inertial. When you localize the global Poincare symmetry (translation + Lorentz) you include the local non-inertial frames as well beyond 1905 SR.
"I'm not sure about this. I thought that in the tetrad model LLT invariance only applies in LIFs?"
You thought wrong. GR works in all LFs.
in a matrix representation in which the source matter field components forms a basis
e.g. 2-component Weyl spinors
4-component Dirac spinors
spin 0 Poincare group scalars
spin 1 Poincare group vectors ...
Pa generate T4 (total momentum 4-vector)
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