Lecture 10
Comment 19: Is Smolin’s paper the end of the story?
“Establishing the existence of a semi-classical limit, in which classical spacetime and the Einstein field equations are supposed to emerge, is widely regarded as the main open problem of this approach.”
In other words the Loop Quantum Gravity theorists are not really able to derive Einstein’s 1915 equation
Guv + kTuv = 0
As a limiting case.
I am able to do this in my emergent gravity theory from
L ~ (dTheta)(Phi) – (Theta)(dPhi)
Where Theta and Phi are the two Goldstone phases of the vacuum Planck Higgs field whose bare vacuum manifold is S2 excluding Calabi-Yau parameters. B is the curved piece of the Einstein-Cartan invariant 1-form tetrad field. Einstein’s metric field is obtained trivially from the mathematical form the equivalence principle.
Excerpts & my commentaries on:
AEI-2006-004 hep-th/0601129 January 18, 2006
arXiv:hep-th/0601129 v1 18 Jan 2006
Loop and Spin Foam Quantum Gravity: A Brief Guide for Beginners
Hermann Nicolai and Kasper Peeters
Max-Planck-Institut f¨
ur Gravitationsphysik Albert-Einstein-Institut Am M¨
uhlenberg 1 14476 Golm, GERMANY
hermann.nicolai, kasper.peeters@aei.mpg.de
“Abstract:
We review aspects of loop quantum gravity and spin foam models at an introductory level, with special attention to questions frequently asked by non-specialists.
Contributed article to “An assessment of current paradigms in theoretical physics”.
1. Quantum Einstein gravity
The assumption that Einstein’s classical theory of gravity can be quantised non-perturbatively is at the root of a wide variety of approaches to quantum gravity. The assumption constitutes the basis of several discrete methods [1], such as dynamical triangulations and Regge calculus, but it also implicitly underlies the older Euclidean path integral approach [2, 3] and the somewhat more indirect arguments which suggest that there may exist a non-trivial fixed point of the renormalisation group [4, 5, 6]. Finally, it is the key assumption which underlies loop and spin foam quantum gravity. Although the assumption is certainly far-reaching, there is to date no proof that Einstein gravity cannot be quantized non-perturbatively, either along the lines of one of the programs listed above or perhaps in an entirely different way.
In contrast to string theory, which posits that the Einstein-Hilbert action is only an effective low energy approximation to some other, more fundamental, underlying theory, loop and spin foam gravity take Einstein’s theory in four spacetime dimensions as the basic starting point, either with the conventional or with a (constrained) ‘BF-type’ formulation. 1 These approaches are background independent in the sense that they do not presuppose the existence of a given background metric. In comparison to the older geometrodynamics approach (which is also formally background independent) they make use of many new conceptual and technical ingredients. A key role is played by the reformulation of gravity in terms of connections and holonomies. A related feature is the use of spin networks in three (for canonical formulations) and four (for spin foams) dimensions. These, in turn, require other mathematical ingredients, such as non-separable (‘polymer’) Hilbert spaces and representations of operators which are not weakly continuous. Undoubtedly, novel concepts and ingredients such as these will be necessary in order to circumvent the problems of perturbatively quantised gravity (that novel ingredients are necessary is, in any case, not just the point of view of LQG but also of most other approaches to quantum gravity). However, it is important not to lose track of the physical questions that one is trying to answer.
The present text, which is based in part on the companion review [7], is intended as a brief introductory and critical survey of loop and spin foam quantum gravity2, with special focus on some of the questions that are frequently asked by non-experts, but not always adequately emphasized (for our taste, at least) in the pertinent literature.
[1 In the remainder, we will follow established (though perhaps slightly misleading) custom and summarily refer to this frame•work of ideas simply as “Loop Quantum Gravity”, or LQG for short.
2 while our review [7] is focused on the ‘orthodox’ approach] to loop quantum gravity — to wit the Hamiltonian framework — the present text also addresses the more recent spin foam developments. Even though the connections between these approaches are not as strong as one might expect, they do share some historical background and philosophy.
These concern in particular the definition and implementation of the Hamiltonian (scalar) constraint and its lack of uniqueness. Another important question (which we will not even touch on here) concerns the consistent incorporation of matter couplings, and especially the question as to whether the consistent quantisation of gravity imposes any kind of restrictions on them. Establishing the existence of a semi-classical limit, in which classical spacetime and the Einstein field equations are supposed to emerge, is widely regarded as the main open problem of this approach. Explaining the emergence of classical space-times is also a prerequisite for understanding the ultimate fate of the non-renormalisable UV divergences that arise in the conventional perturbative treatment. The latter question also arises in the ‘covariant’ spin foam approach in the form of the existence (or nonexistence) of a proper ‘continuum limit’.
A further question in any canonical approach to quantum gravity is whether one has succeeded in achieving (a quantum version of) full space-time covariance, rather than merely covariance under the diffeomorphisms of the three-dimensional slices. For someone unfamiliar with the concepts of LQG, it is not easy to see whether and how this requirement is met. In the presently known canonical set-up of LQG, it is only possible to establish on-shell closure of the constraint algebra, which means that partial use of the (diffeomorphism) constraint must be made in checking the commutator of two Hamiltonian constraint operators. In [7] we have argued that this is not enough, and that it is rather the off-shell closure of the constraint algebra that should be made the crucial requirement in establishing quantum space-time covariance. Space-time covariance is also an issue in discrete approaches, and thus spin foam quantum gravity, although the problem appears in a different guise. Whereas in conventional lattice discretisation the main question was whether and in which sense it is possible to ‘approximate’ general coordinate transformations on discrete sets of points and links, the key question in modern approaches which work with reparametrisation invariant quantities (proper lengths, etc.), as in Regge calculus, is now whether it is possible to obtain results which do not depend on the way in which the discretisation and the continuum limit are performed.
In view of our continuing ignorance about the ‘true theory’ of quantum gravity, the best strategy is surely to explore all possible avenues, including non-string approaches to quantum gravity. LQG, just like the older geometrodynamics approach [8], addresses several aspects ofthe problem that are currently outside the main focus of string theory, in particular the question of background independence and the quantisation of geometry.”
Comment 20: In my alternative theory the curved space-time geometry should not be quantized top -> down because it is a “More is different” bottom -> up emergent structure from the “organizational order” macro-quantum vacuum ODLRO Goldstone phases of the first Higgs field that forms at 10^-33 inflation to the edge of the ledge on the cosmic landscape before the final plunge off the ledge to make the hot big bang. Quantizing geometry is a silly as quantizing temperature, or quantizing elasticity. The ODLRO is already non-perturbative and background independent. There are still spin 2 quanta relative to the dynamical curved ODLRO spacetime of course. This explains why no giant Schrodinger Cats, why macro-spacetime physics is local and what the correspondence principle really is.
Appendix: Measuring dark energy and dark matter as virtual vacuum stuff locally in the laboratory with the Casimir force.
On Jan 24, 2006, at 9:28 PM, Jack Sarfatti wrote:
PS I trivially proved below that the electromechanical Casimir force in a closed spherical conducting cavity should be repulsive not attractive as for parallel plates! This is in fact observed!
This only happens of course because of the controversial mechanism that causes
/\ ~ 0.7 critical density to make our pocket universe spatially flat
Given that, my proof goes through when the ZPF energy density's effective micro /\ inside is more negative than the cosmological constant is positive. Therefore, in principle, we can use spherical Casimir cavities as TINY LOCAL DARK ENERGY DETECTORS in the lab! (In principle) so far this is a Gedankenexperiment. This is my DARK ENERGY GRAVITOMETER! It also LOCALLY detects DARK MATTER if it is simply negative /\.
That is, inside the spherical shell we have /\(cosmic) - /\(Casimir) when we exclude enough long wave spherical modes. The fact that repulsion is actually seen shows that this is not hard to do.
On Jan 24, 2006, at 9:04 PM, Jack Sarfatti wrote:
On Jan 24, 2006, at 8:12 PM, Figaro wrote:
The ZPE/ZPF fields are real as Hal mentioned many times not virtual
That's why every one of the top-rank physicists in the field reject the Haisch-Puthoff ZPE theory because it's based on the "SED" theory of Trevor Marshall that has been completely discredited. Also that SED theory is only for electromagnetic waves it says nothing about vacuum polarization of virtual fermion-antifermion pairs. Says nothing about the weak and strong forces. Hal's theory not only rejects Einstein's general relativity but he rejects quantum field theory! Therefore, it is completely inconsistent for Hal to cite Bryce De Witt's quantum field theory calculation of the ZPF tensor! Hal is not able to derive that result in his theory. So Hal is simply hiding the pea in a shell game.
but some still like to say virtual.
"Virtual" means "off-mass-shell," i.e. not the poles in Feynman propagators. It means stuff inside the vacuum. "Real" means stuff excited outside the vacuum.
E^2 = (pc)^2 + (mc^2)^2
dpdx > h
for real quanta excited outside the vacuum
E^2 =/= (pc)^2 + (mc^2)^2
dpdx < h
for virtual quanta inside the vacuum
As for w = -1 that's for no boundaries.
That's correct.
Then there are places out there in space where w = + 1/3..
No!
What you have for EM virtual quanta between the parallel plates where rotational and translational symmetry is broken is diagonal terms in the tensor that are
- 1, +1, +1, -3
The - 3 is the space direction perpendicular to the parallel uncharged conducting plates separated by tiny distance a
In this case the Casimir energy density is negative between the plates because long wave modes between the plates are excluded and in QED they take the space outside the plates to be "zero energy".
Now in fact for gravity purposes you cannot do that.
The naive energy density outside the plates is ~ hc/Lp^4 > 0 and the energy density inside the plates is ~ hc(1/Lp^4 -1/a^4)
Note if there were no plates at all, or for a small spherical cavity, the same tensor would be for virtual photons
+1 - 1 -1 - 1
In general the Newtonian 00 limit of GR is the Poisson equation
Laplacian of potential energy per unit test mass of any source ~ (G/c^2)(Source Energy Density)(Trace of Matrix)
In the case of virtual photons without any boundaries this is
(G/c^2)(Source Energy Density)(1 - 1 -1 -1) = -2(G/c^2)(Source Energy Density)
Therefore, a positive energy density isotropic ZPF distribution will repulsively anti-gravitate from the negative pressure!
In contrast, it will electrically attract from that same negative pressure.
It will do so at different coupling strengths of course.
If, instead, the isotropic ZPF energy density is negative, the positive pressure causes attractive gravity and electrical repulsion on a thin spherical shell (like ordinary gas in a piston)
Next consider the case of the anisotropic Casimir plates.
The negative pressure perpendicular to the plates will electro-mechanically attract (suction), but gravitationally repel. Note the negative longitudinal pressure - 3 acts with the negative energy density in that direction of space with rotationally broken symmetry.
The 2 positive transverse pressures will electro-mechanically repel, but will have no gravity effect because of the cancelation from the equal and opposite negative energy density.
Defining Trace of Matrix = 1 + 3
is not a useful measure when boundary conditions dominate. It is only useful in the homogeneous isotropic cosmological situation.
Jack Sarfatti wrote:
Yes, I am obviously not the only physicist putting 1 + 1 + 1 together to make 1. ;-)
The cosmic energy and the Lamb shift and Casimir force energy are all basically the same virtual zero point vacuum energy. w, of course, need not always be -1 when boundary conditions break isotropy and homogeneity which is assumed in the large-scale cosmological limit.
On Jan 24, 2006, at 7:39 PM, Gary S. Bekkum wrote:
How about:
"... we discuss the relevance of experiments at the interface of astrophysics and quantum field theory, focusing on the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions..."
" C. Vacuum energy and Casimir effect in gravitational and cosmological contexts
Another approach is to think of a situation or an experiment where the validity of the cosmological constant-vacuum energy identification can be put to the test. A geometrical cosmological constant has no quantum properties while vacuum energy has both gravitational and quantum properties. Also, is it possible to learn more on how vacuum energy contributes to the cosmological constant? Some of these questions started to be addressed in the literature as we cite further.
It is perhaps relevant at this point to recall the Casimir effect which is a purely quantum field theory phenomena...
The Casimir effect results from a change in the zero-point oscillations spectrum of a quantized field when the quantization domain is restricted or when the topology of the space is non- trivial. For example, a Casimir force appears as the result of the alteration of the vacuum energy by some boundaries...
BTW topological defects enter here where the Higgs field vanishes and the possibly several Goldstone phases are undefined.
Now, related to our question on how the vacuum energy may fit within the EFE, it has been argued in some papers, see for example [42, 43, 44], that as the measured Casimir effect is related to vacuum energy differences, the vacuum energy may not contribute to the cosmological dynamics via some fixed cutoff energy but rather via energy differences as in Casimir energy. This Casimir energy can be produced from some compact extra dimensions [42, 43, 44] or non-trivial topology of the spacetime..."
Those papers are suspect. They violate the equivalence principle.
SEE:
http://www.arxiv.org/abs/astro-ph/0504416
Remarks on the formulation of the cosmological constant/dark energy problems
Authors: Mustapha Ishak (Princeton University)
Comments: 10 pages, 5 figures
Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. Motivated by some theorems, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. Next, we evaluate how much fine tuning the cosmic coincidence problem represents. We discuss some implications of the simplest solution for the principles of General Relativity. We stress the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions. Also, we discuss the relevance of experiments at the interface of astrophysics and quantum field theory, focusing on the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions
Sent: Tuesday, January 24, 2006 8:16 PM
Subject: Re: On the true relation of zero point energy to gravity (Robert Laughlin)
Jack Sarfatti wrote:
Robert Laughlin, a Nobel Prize physicist, also a professor of physics at Stanford like Lenny Susskind, makes it clear that all mainstream physicists essentially think that the vacuum energy of the cosmological constant and the vacuum energy of the Lamb shift and the Casimir force are the SAME PHENOMENON at vastly different scales. Thus on the relation of the Lamb shift's "/\zpf" to Einstein's cosmological constant "/\(Dark Energy)" - both are the same vacuum virtual "stuff" mentioned below by Laughlin (off-mass- shell).
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