For a Hawking Radiation

Home , Alexei Starobinsky, George Smoot, Jacob Bekenstein, Robert Wald

Baocheng Zhang Qing-yu Cai Ming-sheng Zhan

The information loss paradox

2014/3/19

Roger Babson

The Gravity Research Foundation, established in 1948 by businessman Roger Babson (founder of Babson College), was an organization designed to find ways to implement gravitational shielding. It closed in the late 1960s, although it has maintained an annual contest rewarding essays by scientific researchers on gravity-related topics. It is mentioned on stone monuments located at more than a dozen American universities.

Stephen Hawking, who won in 1971, Roger Penrose, who won in 1975, and astrophysicist and Nobel laureate George Smoot, who won in 1993. Notable award winners include Jacob Bekenstein, Sidney Coleman, Bryce DeWitt, Julian Schwinger (Nobel Prize in Physics, 1965), Dennis Sciama, Robert Wald, John Archibald Wheeler and Frank Wilczek (Nobel Prize in Physics, 2004).

2014/3/19

Stephen Hawking

史蒂芬·霍金（1942-），英国理论物理学家。牛津大学毕业后，又在剑桥大学获得哲学博士学位。曾在剑桥大学任引力物理学教授，主要从事宇宙学和黑洞理论的研究。从20多岁起，因患有渐进性的神经疾病，

2014/3/19 一直困在轮椅上从事艰难的科学研究。 Hawking’s (in)famous bets

 1975 against Kip Thorne: black holes do not exist subscription to Private Eye/Penthouse  1991 against Thorne and John Preskill: naked singularity outside a black hole not exist/unobserved  1997 with Thorne against John Preskill: Information loss paradox/firewall paradox (Gerard ‘t Hooft, Leonard Susskind, Juan Maldacena) the Ultimate Baseball Encyclopedia  2000 against Gordon Kane: the existence of Higgs $100

2014/3/19 Correlation: dependence/independence

Entropy: Gibbs or thermodynamic

Information (Entropy/k_b): Shannon/von Neumann Information Loss/Gain: entropy not conserved

No Information Loss/Gain: unitary, reversible, or constant entropy

2014/3/19 Entropy & information

熵代表着系统的不确定度，是信息的最大容量，maximal capacity。系统B能够编码信息的上限是S(B)。

A从B能够获取的信息，受 Holevo bound 的限制，或者简单一些，是受到S(A:B)的限制。 A从B获得的信息等于A和B之间相对熵的减少。

在黑洞问题上，黑洞熵的增加，意味着不确定度增加了，也就是说，相对熵增加了，因此，可以获得的信息减少了。

另一方面，熵增是一个不可逆的过程，标志着可以从系统获取的信息减少了。

2014/3/19 Hawking paradox: black hole information loss

 The paradox of black hole information loss  Unsuccessful resolutions & controversies  Hawking radiation as tunneling  Invisible messengers: quantum correlations  The spectroscopic features of a black hole  Hawking radiation from manmade event horizon  Summary & discussion

2014/3/19 A black hole A black hole is often defined classically as an object whose gravity so strong that the light can not escape. Its two distinct characteristics are the event horizon 1 mM E mv2 G and its thermodynamic effect. 2 r 1783, John Michell and Pierre-Simon Laplace

E  0, v, c

2M R  Schwarzschild c2

Schwarzschild radius 3km for M_sun 9mmfor M_earth 2014/3/19 Event horizon: the point of no return

8G G  g   4 T  2014/3/19 c Hawking radiation Stephen Hawking provided a theoretical argument for its existence in 1974, and sometimes also after Jacob Bekenstein, who predicted that black holes should have a finite, non-zero Classical black hole temperature and entropy.

Hawking's work followed his visit to Moscow in 1973, where the Soviet scientists Yakov Zeldovich and Alexei Starobinsky showed him that according to the quantum mechanical uncertainty principle, rotating black holes should create and emit particles.

Quantum black hole 1 HawkingT ; 60 nanoK for M_sun M 2.7K for M _moon 2014/3/19 Hawking radiation is thermal ? S. W. Hawking, Nature 248, 30 (1974); Commun. Math. Phys. 43, 199 (1975)

The initial scalar field

The later scalar field

The Bogolubov transformation

The observable in infinity

2014/3/19 a fixed background geometry is adopted and the result is inconsistent with energy conservation.

No energy for spacetime? Unruh effect (Hawking-Unruh temperature)

The hypothetical Unruh effect (or sometimes Fulling–Davies–Unruh effect) is the prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none.

a T  2ckB

gHorizon TH  2ckB

It was first described by Stephen Fulling in 1973, Paul Davies in 1975, and W. G. Unruh in 1976.

2014/3/19 The information loss paradox

 Irrespective of what initial state a black hole starts with before collapsing, it evolves eventually into a thermal state after being completely exhausted into emitted radiations.

 The thermal state implies (a) there is no correlation among Hawking radiation and (b) the total entropy increases*.

 Entropy increase implies information loss in Hawking radiation.

Hawking radiation is nonunitary!

*W. H. Zurek, Phys. Rev. Lett. 49, 1683 (1982), D. N. Page, ibid, 50, 1013(1983). 2014/3/19 What is the information loss paradox?

Hawking radiation

our work

ntropy E

0 time

2014/3/19 Information conservation is fundamental  Liouville's theorem: Classically, the conservation of phase space volume, guarantees the conservation of entropy or information under Hamiltonian dynamics.

 Unitarity Quantum physics ensures information conservation, no cloning, no deleting, and no splitting String theory, ADS/CFT, holographic principle

A nonunitary Hawking radiation causes contradiction between gravity and quantum mechanics

2014/3/19 Hawking paradox: black hole information loss

2014/3/19 Failed resolutions: quantum entanglement

Since the emitted particles are not correlated, the paradox will appear soon after half of a black hole is emitted. Quantum hair *S. W. Hawking, Phys. Rev. D 14, 2460 (1976) J. Preskill, arXiv: hep-th/9209058.

limited in the interior by the methods

Baby universe

2014/3/19 Failed resolutions: quantum information

Whether the projection exists or not is unknown and the information transferred outside is incomplete in any situation

G.T. Horowitz, J. Maldacena, J.High.Energy Phys.02,008 (2004)

2014/3/19 Failed resolutions: the remnants *Y. Aharonov, A. Casher, S. Nussinov, Phys. Lett. B 191, 51 (1987).

The remnant has an infinite degrees of freedom to preserve the initial information of a black hole.

2014/3/19 Failed resolutions: no-hiding theorem S. L. Braunstein and A. K. Pati, Phys. Rev. Lett. 98, 080502 (2007).

• The possibility that information about infallen matter could hide in the correlations between the Hawking radiation and the internal states of a black hole is ruled out.

• This implies that the paradox arises immediately after the black holes starts to emit thermal radiations!

2014/3/19 The real puzzle for thermal Hawking radiation

• Either Hawking’s semiclassical predication or unitarity must break down!

2014/3/19 ------by L. Susskind, Scientific American (1997)

------by S. Lloyd and Y. J. Ng, Scientific American (2004) The bet on information loss (1997/2004)

Hawking: 信息真的丢了 Preskill: 信息不会丢失

赌局尚未结束！ Hawking paradox: black hole information loss

2014/3/19 Energy conservation in Hawking radiation

S. W. Hawking, Nature 248, 30 (1974); Commun. Math. Phys. 43, 199 (1975)

• In Hawking’s original treatment, a fixed background geometry is adopted and the result is inconsistent with energy conservation.

• Energy conservation prohibits a fixed background geometry.

2014/3/19 The back reaction

P. Kraus and F. Wilczek, Nucl. Phys. B433, 403 (1995) Back reaction is considered, continued With the radiation null geodesics,

We can get the imaginary part of the action for s-wave outgoing positive particles

Changes the variable from momentum to energy with

outgoing particle Instantons of both particles and antiparticles

An ingoing negative energy particle has

Both particle and antiparticle tunneling-contribute to Hawking radiation Understanding (Schwinger mechanism) ?

Virtual pair becomes real particles: with gravitation field doing the work

Hence the mass of a black hole decreases Parikh-Wilczek conjecture: information-carrying correlation? Hawking paradox: black hole information loss

2014/3/19 Three progressive questions

 If correlations exist among Hawking radiations?

 Does correlation carry off information in a hole ?

 Can all information in a hole be carried off by correlations among Hawking radiations ? Dependent or independent or correlated ?

We should verify whether two successful emissions are dependent or not.

With the standard statistical method, we find that They are correlated

From

We find that The amount of information (equivalent)

mutual information between two subsystems A and B in composite quantum system is defined as

For two emissions with energy E1 and E2, we find that The correlation chain we used

 N-体的总关联==所有独立的inclusive两体关联之和

1 2 3 4 5 6 7

蔡庆宇等的文章。 Counting the total entropy

The entropy of the first emission with energy E1 is

The conditional entropy of the second emission with energy E2 after E1 is

The total entropy of two emissions E1 and E2 becomes

Step by step, we have that Conservation of entropy for a Schwarzschild black hole

A detailed calculation shows that, after a black hole is exhausted,

which exactly equals to the initial Bekenstein-Hawking entropy for a black hole,

Entropy is conserved in Hawking radiation!

45 Interpretation of the BH entropy

For a Hawking radiation (E) from a black home of mass M SEEME  8   4 E 2 S (0)   S (0) precollapsed configuration which reveals the information about the matter that will collapse into a black hole, about self-collapsed configuration which reveals the inaccessible information about how to collapse correlation or the partial information about inter-collapsed configuration which reveals the inaccessible information about the interaction among different collapsed holes

22 S14 m 1 , S 2  4  m 2 , S 12  8  m 1 m 2 2 S4  m1  m 2  S 1  S 2  S 12 Hawking radiation microstates and BH entropy

Number of N exp(S ) microstates ……

Define a microstate

Microcanonical ensemble: all microstates of an isolated system are equally likely, so the number of microstates of black hole are

Thus non-thermal spectrum is consistent with quantum interpretation！ Hawking paradox: black hole information loss

2014/3/19 Spectra compared

The normalized thermal spectrum

The normalized nonthermal spectrum Averaged quantities Emission energy variance Emission energy co-variance

B. Zhang, Q.-y. Cai, M.-s. Zhan, and L. You, Toward experimentally testing the paradox of black hole information loss, Phys. Rev. D 87, 044006 (2013). Hawking paradox: black hole information loss

2014/3/19 54 Hawking radiation in LHC Possible LHC observation

Energy scale in LHC and extra dimension

Our estimation for the observation of non-thermal spectrum:

Hawking paradox: black hole information loss

2014/3/19 References

1, ``Hidden Messenger Revealed in Hawking Radiation: a Resolution to the Paradox of Black Hole Information Loss,” Baocheng Zhang, Qing-yu Cai, L. You, and M. S. Zhan, Phys. Letters B 675, 98 (2009). 2, `Àn interpretation for the entropy of a black hole,” Baocheng Zhang, Qing-yu Cai, M. S. Zhan, and L. You, Gen. Relativ. Gravit. 43, 797 (2011). 3, `Èntropy is conserved in Hawking radiation as tunneling: a Revisit of the Black Hole Information Loss Paradox," Baocheng Zhang, Qing-yu Cai, M. S. Zhan, and L. You, Annuals of Phys. 326, 350 (2011). 4, ``Noncommutative information is revealed from Hawking radiation as tunneling," B. Zhang, Q. Y. Cai, M. S. Zhan, and L. You, Euro. Phys. Lett. 94, 20002 (2011). 5, ``Towards experimentally testing the paradox of black hole information loss," Baocheng Zhang, Qing-yu Cai, Ming-sheng Zhan, and L. You, Phys. Rev. D 87, 044006 (2013). Erratum, Phys. Rev. D 88, 049901(E) (2013). 6, `Ìnformation Conservation Is Fundamental: Recovering the Lost Information in Hawking Radiation," Baocheng Zhang, Qing-yu Cai, Ming-sheng Zhan, and Li You, International Journal of Modern Physics D (IJMPD), Vol. 22, No. 12, 1341014 (2013). First award in the 2013 Awards for Essays on Gravitation, by GRAVITY RESEARCH FOUNDATION. 7, ``Correlation, Entropy, and Information Transfer in Black Hole Radiation," Baocheng Zhang, Qing-yu Cai, Ming-sheng Zhan, and Li You, 《科学通报》(Chinese Science Bulletin), (in press, 2014). 8，arXiv:1210.2048, Comment on "What the information loss is not” by Mathur Qing-yu Cai, Baocheng Zhang, Ming-sheng Zhan, Li You Comments: We submit this comment in order to prevent any further propagation of the misconceptions of the paradox.

2014/3/19 Summary & discussions

 Information is physical and obeys conservation laws of physics  Information loss paradox resolved to the 0-th order, extended by us to other types of black holes, recently to all orders by others  概念清楚  锲而不舍, 不能浅尝即止  …

2014/3/19