A Scenario for Strong Gravity
(Without Extra Dimensions)
Why it could happen;
How it might behave;
How it might be tested at LHC.
SCIPP seminar
May 8, 2007
D. Coyne, SCIPP/UCSC
(Oral presentation of limitations of a “scenario”:
not a theory, more than a speculation; discussion.)
Fgravity /FCoulomb = GN Me2/ c  3·10-43

Assumed that some theory of quantum gravity will restore sensibility to the relative
size of gravity and the other forces, when interactions at the Planck mass  1019 GeV
are reached from below (HEP), or from above (22mg) by black hole evaporation.
(Oral discussion of the string
theory scenario for black hole
production at LHC). Note that the
theory is elegant but also presumptuous.
The first step (presumptuous) is to give
the reason why gravity is so small:
IT ISN’T
A Perfectly Elegant explanation already exists for why gravity appears weak
Arkani-Hamed, Dimopoulos & Dvali: hep-ph/9803315
Banks & Fischler: hep-th/9906038
Giddings & Thomas: hep-ph/0106219
Dimopoulos & Landsberg: hep-ph/0106295
MP 
c GNewton
M Pn 
c GBulk

If extra “ large” dimensions exist, then
experiments near MPn confront the merging
of QM and GR into QG; black holes should

be produced in energetic collisions.
Possibility of large dimensions was enabled by the lack of experimental data on
the form of the gravitational potential at small distances.
Classical
Region:
RM
T  M -1
SM2
 M 2
???
???
String Black
Hole Region:
R  M 1/6
T  M -1/6
S  M 7/6
  M 1/3
Adapted from Carr & Giddings, Scientific American, May 2005
The Problems with this Scenario
1.
It’s a scenario, not a theory, so that there are:
2.
Many regions of important experimental phase space where the predictions
are not sharp, and there is no prediction of…
3.
What real size of extra dimensions should be expected, and..
4.
The experimentalists in this field are direct descendents of Genghis Khan.
Genghis Khan Experimentalists!

r
m1m 2
 
V (r)  GN
1 e
r

  10 6 at ~ 1mm
(J.Price, late 1980’s, UCSC seminar )

Reviewed by J.C. Long, SSI 2005
The Problems with this Scenario
And besides…..the
Lyyken criterion, where
thermodynamics rears its
hot head.
A global theory of particles should converge to the
proper entropy in each energy region
In special cases, strings turn into black holes; in others,
there is a string field-QFT duality.
(Long oral presentation) Story from student
days about Feynman lecturing to grad students in
experimental particle physics: how experimental
error misleads theory.
My observation that theory can also mislead:
suggestion that string theory not wrong, but derives
power from degrees of freedom and form of
equations, not from paradigm that extra dimensions
exist. Suggest looking for other basic paradigms
and for other places where large numbers of
degrees of freedom can exist; in particular, use the
same starting presumption for why the gravitational
force is weak:
IT ISN’T
But could there be a different reason that it isn’t?
Historically, how did we “find” the forces?
(oral discussion of how measurement of shielded forces gave wrong
impression of strengths and radial dependences; suggestion that we
have never yet observed true strong gravity because of shielding)
What if gravity is really strong, but shielded?
Where would it be “visible”?
Embark on a program of looking for a critical system in physics where gravity becomes
competitive with all other forces, but where current theory fails us. Also look for preexisting theories which individually work well but appear to fail for this particular limit.
The tiny evaporating black hole is the ideal candidate!
•
J. Bardeen, J. Bekenstein and S. Hawking combined the time-honored theories of
thermodynamics, GR and QFT to come up with a consistent picture of black hole
evaporation which fails only near the Planck mass.
We speculate that strong gravity exists only on or within a new
type of horizon formed in the “endpoint” of black hole evaporation.
1) Why is gravity seen at all from stars and planets, everyday objects and (presumably) from fundamental particles? Why would
the basic underpinnings of cosmology (GR) depend on the leakage of gravity from small black holes, which, it is often
suggested, are rare or may not even exist?
2) Configurations of electric or color charges can both have neutral states, but how can one neutralize (and thus shield) gravity?
Formation of the models for Schwarzschild black holes:
(Hawking, Page, Carr, MacGibbon, Halzen, Zas)
|
P  T A
|
|


2G M 
dMc
c
  M , spin 
4


 
dt
8k G M   c  |
 |
|
|
|
|
|

|
dM

so

t

M
dM

,

dt
M
|

4
2
3
4
o
2
N
M (t)
o
dM

  2 o 2 , where  o   oGN2
dt
GN M
2
N
2
B
(DGC & D.C. Cheng; J.M. Hanna
Senior thesis, UCSC, Aug. 2004)
Mo
2
The key assumption of the strong
gravity model is that G is a variable,
an artifice to simulate the effects of an
unknown theory of quantum gravity.
We use for the Strong Shielded Gravity Scenario:
TP
G(T )  GN
TP T
v
v
dM

  2 o 2 holds
dt
G M
exactly into all mass regions!
and assume
Why would we be so crazy as to introduce
infinities in G when we want to get rid of
infinities in curvature?
Not so crazy: the solution for G(M) is implicit and not a pole at all!
 c 3  

T  

,
and
so
T



P
G(M P )M P G(
8k BGM  GM
v
v
v

c /G )
c /G
This looks messy but the definition for G simplifies in a few easy steps to:
M P 
G
 1 G /GN  
 M 
GN
With all the little v’s gone, and MP back to the usual 1019 GeV. Then, with
g = G/GN and m = M/MP, the solution for g in terms of m
is simply:

The Hawking equation then becomes:
2
 1

1 1
g     2  4 
m

4 m
 ot  M  M g 2 m 2 dm
3
P
M
o
and is exactly integrable!
Fgravity /FCoulomb  GN Me2/(— hc) = 3·10-43
Asymptotic form for G is G/GN = (MP/M)2, so if we blindly apply this to a particle
with mass Me, then:
— hc) =1/ =137, a strong
Fgravity /FCoulomb  Ge Me2/() = GNMP2/(
scale.
Classical
Region:
SSGS SubPlanckian
Region:
RM
T  M -1
SM2
 M 2
R  M-1
TM
S  log M
 M-2
Black Hole Thermodynamics
dU  PdV TdS
First Law:
Second Law:
(A new generalization, too involved for this talk)

Specific Heat:
cBH
1 dU

U dT
Black Hole Thermodynamics
First Law:
dMc  Jd TdS
2

Specific Heat:
cBH
1 dM

M dT
Black Hole Thermodynamics
First Law:
Bekenstein-Hawking
realization:

SSGS realization:
(sub-Planckian)

Specific Heat:

dMc  TdS
2
S

dM
2
 M  horizon area
T
S

dM

T
cBH
 mgdm  ??????
1 dM

M dT
Specific heat solutions:
a) Hawking solution
b) SSGS:Super-Planckian
c) SSGS: Sub-Planckian
•
At slightly less than MP, the specific heat becomes positive and the black hole
can be in stable equilibrium with a thermal bath.
•
At 3 Kelvins, the black hole is in thermal equilibrium with the CMB
at a mass of 6 milli eV, an addition to hot dark matter that has increased with universe age!
Black Hole Thermodynamics
dMc  TdS
2
First Law:
S

dM
2
 M  horizon area
T
SS

dM
dM 
TT
Bekenstein-Hawking
realization:

SSGS realization:
(sub-Planckian)

Specific Heat:

cBH

mgdm ??????
??????
mgdm
1 dM

M dT
The Global Entropy of the SSGS
The super-Planckian asymptotic form is:
The sub-Planckian asymptotic form is:

S
A
4
(in Planck area units
S  SL  8 ln
M
ML
The Lykken criterion is satisfied.

GN
)
3
c
Quantization: the real point of contact with experiment.
For black holes, it’s an old idea and a new idea
J. D. Bekenstein, The Quantum Mass Spectrum of the
Kerr Black Hole, Lett.Nuovo Cimento 11, 467,( 1974).
V. Mukhanov, Are black holes quantized?, JETP Lett.
44, 63 (1986).
C. Rovelli and L. Smolin, Discreteness of area and
volume in quantum gravity, Nucl. Phys. B442 (1995),
593. Erratum: Nucl. Phys. B456 (1995), 734; also at
gr-qc/9411005.
J. Bekenstein and V. Mukhanov, Spectroscopy of the
quantum black hole, Phys.Let. B360,7 (1995);
gr-qc.9505012 .
G. ‘t Hooft, The Scattering Matrix Approach for the
Quantum Black Hole: An Overview, Int. J. Mod. Phys.
A11, 4623 (1996).

G. Immirzi, Quantum Gravity and Regge Calculus, Nucl.
Phys. Proc. Suppl. 57 65 (1997); also at gr-qc/9701052.
S. Hod, Bohr’s Correspondence Principle and the Area
Spectrum of Quantum Black Holes, Phys.Rev.Lett. 81
(1998) 4293; gr-qc/9812002 .
O. Dreyer, Quasinormal Modes, the Area Spectrum, and
Black Hole Entropy, Phys. Rev. Lett. 90, 081301 (2003);
gr-qc/0211076 .
L. Motl, An analytical computation of asymptotic
Schwarzschild quasinormal frequencies, Adv. Theor.
Math. Phys. 6 (2003) 1135-1162; gr-qc/0212096 .
From Bekenstein’s “adiabatic invariant”
to loop quantum gravity’s spin networks,
the quantum of area seems to be:
Ao  4(ln 2) (in units of GN /c2 )
This quantization scheme leads to
dA  MdM  M 1/ M
or, if successive states are steps of nAo ,
Mn 
1 (ln 2)(| n | 1)
MP
2

(n large)
All of this is for super-Planckian masses!
The SSGS Scheme for Quantization
Which makes more
sense, quantizing area
or entropy?
From the point of view of
shielding horizons, quantize
the information needed to
establish the horizon.
(Wheeler’s IT from BIT)
SSGS generalized entropy quantization
for sub-Planckian region (with step size qln2):
M  (e q ln 2 / 8 1)M ,
M n  M Le
q ln 2
( n1)
8
leading to
Are the SSGS spectra discrete or continuous?
A sensible lifetime for a state is:
1
dM
1

n
dt M n  M n1
(how does dM/dt know anything about branching ratios?)
RESULTS:
o !!

For super-Planckian masses, states are discrete for
all masses and both quantization schemes.
For sub-Planckian masses and Area quantization, the states
merge into a continuum at about MP/2, and at the level of ML,
the density of states is absurdly high. LHC/detectors melt.
But, for Entropy quantization, the states are widely-spaced and
always discrete for any spacing more than 1 bit of information.
The SSGS predictions for LHC physics at CERN
Parameters: ML = 100 GeV; quantum of information = 16 bits.
The pattern of the states is the real prediction!
Competing LHC Scenarios
14TeV
Classical
Region:
RM
T  M -1
SM2
 M 2
?
?
SSGS Sub-Planckian Region:
R  M-1
TM
S  log M  M-2
String Black Hole Region:
R  M 1/6
S  M 7/6
T M -1/6
  M 1/3
And when we get to the Planck mass in 2307:
There is no “End of High Energy Physics”!
hep-th/0602183
hep-th/0609097
DGC: A Scenario for Strong Gravity
without Extra Dimensions
DGC & DCC:
Quantization of Black Holes in the
Shielded Strong Gravity Scenario (I. Neutral Scalar States)
We long
have been
important
particlestotohave
find;them
There has
a motivation
don’t
confuse
theyou
situation!
there
(at
least
a
few).
Now
have a to
possible
The SSGS states are uncharged scalars, coupled fundamentally
gravity (i.e., mass).
do you
thinkcame
they could
be?
reason forWhat
where
they
from.
Linear comparison between black-hole Higgs width
and tan = 30 MSSM Higgs width.
Carena & Haber. Prog.Part.Nucl.Phys., 50 ,2003, 71
What is the pertinent variable Planck mass
in the region of elementary particles?
c
MP 

G
v
c
M
2
M P 
GN  
 M 
!!
If black holes become particles via something like the SSGS,
then the Planck scale relevant for those particles is their own mass!
Elementary particle physics is innately governed by
quantum gravity at all mass scales.
The landscape of masses M, with a scale log M/MP; the arrows indicate
the most massive elementary particle (at left) that can be emitted by a
black hole (at right).
The second law of thermodynamics holds separately for intrinsic entropy
of particles; there is no lost-information problem.
A Scenario for Strong Gravity
(Without Extra Dimensions)
Why it could happen;
How it might behave;
How it might be tested at LHC.
SCIPP seminar
May 8, 2007
D. Coyne, SCIPP/UCSC