A Scenario for Strong GravityA Scenario for Strong Gravity (Without Extra Dimensions) (Without Extra Dimensions)

Why it could happen;Why it could happen;

How it might behave;How it might behave;

How it might be tested at LHC.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/

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 (22g) by black hole evaporation.

€

hc

(Oral discussion of the stringtheory scenario for black holeproduction at LHC). Note that thetheory is elegant but also presumptuous.The first step (presumptuous) is to givethe reason why gravity is so small:

IT ISN’T

A Perfectly Elegant explanation already exists for why gravity appears weak

€

M P = hc GNewton

€

M Pn = hc 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 onthe form of the gravitational potential at small distances.

Arkani-Hamed, Dimopoulos & Dvali: hep-ph/9803315Banks & Fischler: hep-th/9906038Giddings & Thomas: hep-ph/0106219Dimopoulos & Landsberg: hep-ph/0106295

Adapted from Carr & Giddings, Scientific American, May 2005

Classical Region:

R M T M -1 S M 2 M 2

String Black Hole Region:

R M 1/6 T M -1/6 S M 7/6 M 1/3

???

???

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!

Reviewed by J.C. Long, SSI 2005

€

V (r) = GN

m1m2

r1+αe− r

λ[ ]

(J.Price, late 1980’s, UCSC seminar )

€

Δ ≈106 at ~ 1mm

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 intoblack 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 pre-existing 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 newtype 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?

•

€

P = σT 4 A

dMc2

dt= σ M , spin( )

hc3

8πkBGN M

⎛

⎝ ⎜

⎞

⎠ ⎟

4

4π2GN M

c2

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

€

so α ot = M 2dMM o

M ( t )∫

€

dMdt

= −α o

M 2,

Formation of the models for Schwarzschild black holes:

||||||||||||

€

dMdt

= −β o

GN

2 M 2 , where β o = α oGN

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:

€

G(T ) = GN

TPv

TPv−T

€

and assume dMdt

= −β o

G 2M 2 holds

exactly into all mass regions!

Why would we be so crazy as to introduceinfinities in G when we want to get rid ofinfinities in curvature?

(Hawking, Page, Carr, MacGibbon, Halzen, Zas) (DGC & D.C. Cheng; J.M. HannaSenior thesis, UCSC, Aug. 2004)

€

T =hc3

8πkBGM

⎛

⎝ ⎜

⎞

⎠ ⎟≡

κGM

, and so TPv=

κG(M Pv

)M Pv

=κ

G( hc /G ) hc /G

Not so crazy: the solution for G(M) is implicit and not a pole at all!

This looks messy but the definition for G simplifies in a few easy steps to:

€

GGN

=1+ G /GN

M P

M

⎛ ⎝ ⎜

⎞ ⎠ ⎟

With all the little v’s gone, and MP back to the usual 1019 GeV. Then, withg = G/GN and m = M/MP, the solution for g in terms of mis simply:

€

g =14

1m

±1

m 2+ 4

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥

2

€

ot = −M P

3 g2m 2dmM o

M∫

The Hawking equation then becomes:

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:

Fgravity /FCoulomb Ge Me2/() = GNMP

2/(hc) =1/ =137, a strong scale.

—

—

Classical Region:

R M T M -1 S M 2 M 2

SSGS Sub-Planckian Region:

R M-1 T MS log M

M-2

Black Hole Thermodynamics

First Law:

Specific Heat:

€

dU = −PdV +TdS

€

cBH =1U

dUdT

Second Law: (A new generalization, too involved for this talk)

Black Hole Thermodynamics

First Law:

Specific Heat:

€

dMc2 = −JdΩ +TdS

€

cBH =1M

dMdT

Black Hole Thermodynamics

First Law:

Specific Heat:

€

dMc2 =TdS

€

cBH =1M

dMdT

€

S ∝dMT∫ ∝ M 2 ∝ horizon area

Bekenstein-Hawking realization:

SSGS realization:(sub-Planckian)

€

S ∝dMT∫ ∝ mgdm∫ ∝ ??????

At slightly less than MP, the specific heat becomes positive and the black holecan be in stable equilibrium with a thermal bath.

At 3 Kelvins, the black hole is in thermal equilibrium with the CMBat a mass of 6 milli eV, an addition to hot dark matter that has increased with universe age!

a) Hawking solutionb) SSGS:Super-Planckianc) SSGS: Sub-Planckian

Specific heat solutions:

•

•

Black Hole Thermodynamics

First Law:

Specific Heat:

€

dMc2 =TdS

€

cBH =1M

dMdT

€

S ∝dMT∫ ∝ M 2 ∝ horizon area

Bekenstein-Hawking realization:

SSGS realization:(sub-Planckian)

€

S ∝dMT∫ ∝ mgdm∫ ∝ ??????

€

S ∝dMT∫ ∝ mgdm∫ ∝ ??????

The Global Entropy of the SSGS

The sub-Planckian asymptotic form is:

€

S = SL +8π lnMM L

The super-Planckian asymptotic form is:

The Lykken criterion is satisfied.

€

S =A4

(in Planck area units =hGN

c3 )

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 .

Quantization: the real point of contact with experiment.For black holes, it’s an old idea and a new idea

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 hGN /c2 )

This quantization scheme leads to

€

dA ∝ MdM ⇒ ΔM ∝1/ M

or, if successive states are steps of nAo ,

M n =12

(ln 2)(| n | −1)π

M P (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 quantizationfor sub-Planckian region (with step size qln2):

€

ΔM → (eq ln 2 / 8π −1)M , leading to

M n = M Leq ln2

8π( n−1)

Are the SSGS spectra discrete or continuous?

A sensible lifetime for a state is:

€

1τ n

= −dMdt

1

M n − M n+1

(how does dM/dt know anything about branching ratios?) o !!

RESULTS: 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!

Classical

Region:

R M T M -1 S M 2 M 2

Competing LHC Scenarios

SSGS Sub-Planckian Region:

R M-1 T M

S log M M-2

String Black Hole Region:

R M 1/6 T M -1/6

S M 7/6 M 1/3

?

?

14TeV

And when we get to the Planck mass in 2307:

hep-th/0602183 hep-th/0609097 DGC: A Scenario for Strong Gravity DGC & DCC: Quantization of Black Holes in the without Extra Dimensions Shielded Strong Gravity Scenario (I. Neutral Scalar States)

There is no “End of High Energy Physics”!

We have important particles to find;don’t confuse the situation!

The SSGS states are uncharged scalars, coupled fundamentally to gravity (i.e., mass). What do you think they could be?

Carena & Haber. Prog.Part.Nucl.Phys., 50 ,2003, 71

There has long been a motivation to have them there (at least a few). Now you have a possible reason for where they came from.

Linear comparison between black-hole Higgs width

and tan = 30 MSSM Higgs width.

What is the pertinent variable Planck mass in the region of elementary particles?

€

M Pv→

hcG

=hc

GN

M P

M

⎛ ⎝ ⎜

⎞ ⎠ ⎟2 = 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 entropyof particles; there is no lost-information problem.

A Scenario for Strong GravityA Scenario for Strong Gravity (Without Extra Dimensions) (Without Extra Dimensions)

Why it could happen;Why it could happen;

How it might behave;How it might behave;

How it might be tested at LHC.How it might be tested at LHC.

SCIPP seminar May 8, 2007 D. Coyne, SCIPP/UCSC