Fine Tuning the Cosmological Constant

Don't miss the article by Raphael Bousso and Joseph Polchinski in the September, 2004 issue of Scientific American. Entitled "The String Theory Landscape", this article presents a user friendly discussion of the existence of a huge number of environments allowed by string theory, each one of which can be the "vacuum state" of a universe. The vacuum energy of each such universe, existing in different 3D spatial parts of the "megaverse", would be the local measured "cosmological constant". The graphics in this article are very helpful in getting some intuition going.

Recall that the simplest explanation for the origin of the dark energy which is driving the accelerated expansion of the universe is a spatially constant positive vacuum energy proportional to the "cosmological constant" which exerts a negative pressure tending to drive clusters of galaxies apart. As the 3D space of our universe has expanded from the moment of the "big bang", the spatial density of matter and radiation has steadily decreased, while the spatial density of the vacuum energy has remained constant and now dominates the energy density of space.

The "fine tuning problem" is that the measured cosmological constant in our universe is tiny but not zero, and if it were much larger, galaxies could not have formed and galaxies are needed to provide an environment for successive generations of stars to form and die, some of their deaths resulting in the crucial production of chemical elements necessary for our (carbon based) form of life to evolve on suitable planets formed together with second generation stars (like our sun).

The other part of this fine tuning problem is that it would be incredible that one could ever find some deep physics reason (related, say, to some symmetry principle) for there being one unique solution allowed for the vacuum state of any universe such that the cosmological constant was close to the tiny positive value we measure.

A good review of the general "problem" of a non-zero cosmological constant is given by Sean Carroll in his Living Reviews in Relativity (Dec. 99) article: "The Cosmological Constant" (also available at arxiv.org here ).

In the Sept. Sci. Amer. article, Bousso and Polchinski review how recent "countings" of string theory vacua have revealed astoundingly large numbers, like 10^(500) (ie. 1 followed by 500 zeros) vacua having positive vacuum energy. They also discuss how such vacua are unstable to decay to vacua with other values of the cosmological constant (mainly lower values but still positive), allowing a universe to nucleate a baby universe (like a bubble starting somewhere) which expands at a lower rate (if its cosmological constant is smaller than its parent), and this process can continue with the baby universe nucleating out grandchildren universes contained within the prior universe boundaries (a concrete version of "eternal inflation" and the "self-reproducing universe").

String theory suggests that we can regard the "dark energy" component of our universe to be the metastable value of an effective scalar field potential energy density, spatially constant in our local universe, but taking different values in each subuniverse.

If one imagines some effective semi-classical scalar field starting out at a high value of potential energy (but in a local minimum of the effective 3D potential energy), and take into account the quantum fluctuations which can allow the scalar field to tunnel to other minima with lower values of the effective potential energy, eventually the metaverse is populated by a "hierarchy of nested bubbles, or subuniverses."

"In each bubble, an observer conducting experiments at low energies (like we do) will see a specific four-dimensional universe [3 spatial and one time dimension(s)] with its own characteristic laws of physics. Information from outside our bubble cannot reach us, because the intermediate space is expanding too rapidly for light to outrun it."

We are here (ie., life and human life has evolved) because "We live where we can" (to quote Leonard Susskind). The basic physics parameters (including the cosmological constant) of our universe are in the "sweet spot" where life is possible.

No one "ordered" this particular sweet spot for us, but there must be a huge number (actually an infinite number ) of other "pocket universes" (which we cannot communicate with) which also have the requisite physics parameters suitable for the evolution of intelligent life, capable of eventually doing physics and developing a gradual understanding of the universe and meta-universe of which our universe is a part. (And of course also gaining the requisite understanding to develop nuclear weapons and toxic pathogens, etc, which can easily end the local human experiment before long.)

If you have broadband internet service, you might enjoy seeing and listening to Leonard Susskind presenting an informal discussion of these ideas to a group of experts on Friday, Oct. 24, 2003, during one of the sessions of the Conference on Superstring Cosmology (10-20 thru 10-24) at the Kavli Institute for Theoretical Physics at UC Santa Barbara. Susskind's talk can be viewed and heard using Real Player software. You can also download the audio alone and listen at your leisure. Note that there was also a semester long "Program" in Superstring Cosmology at KITP which extended from Aug. 4 to Dec. 19 (2003), which has much of interest.

Don't miss the interview with Susskind on the Edge website. Some of the flavor is suggested by the following Susskind quote from that website:

"The beginning of the 21st century is a watershed in modern science, a time that will forever change our understanding of the universe. Something is happening which is far more than the discovery of new facts or new equations. This is one of those rare moments when our entire outlook, our framework for thinking, and the whole epistemology of physics and cosmology are suddenly undergoing real upheaval. The narrow 20th-century view of a unique universe, about ten billion years old and ten billion light years across with a unique set of physical laws, is giving way to something far bigger and pregnant with new possibilities.

"Gradually physicists and cosmologists are coming to see our ten billion light years as an infinitesimal pocket of a stupendous megaverse. At the same time theoretical physicists are proposing theories which demote our ordinary laws of nature to a tiny corner of a gigantic landscape of mathematical possibilities

"This landscape of possibilities is a mathematical space representing all of the possible environments that theory allows. Each possible environment has its own laws of physics, elementary particles and constants of nature. Some environments are similar to our own corner of the landscape but slightly different. They may have electrons, quarks and all the usual particles, but gravity might be a billion times stronger. Others have gravity like ours but electrons that are heavier than atomic nuclei. Others may resemble our world except for a violent repulsive force (called the cosmological constant) that tears apart atoms, molecules and even galaxies. Not even the dimensionality of space is sacred. Regions of the landscape describe worlds of 5,6…11 dimensions. The old 20th century question, 'What can you find in the universe?' is giving way to 'What can you not find?' "

A deeper look at these ideas can be found in Susskind's "The Anthropic Landscape of String Theory": preprint available here. ( http://arxiv.org/archive/hep-th, or archive/gr-qc, or
archive/astro-ph are full of fascinating physics. )

If you go to this hep-th section of arXiv.org and use an author search on Susskind, you will get 542 hits (as of today: Mon. Aug 30, 2004), and hit number 5 is this paper. I recommend the Adobe Acrobat "PDF" version.

Scientists Have Been Ignored by Bush

Space.com posted an AP report on August 14 which details why many leading scientists are fed up with President Bush.

Science, Politics Collide in Election Year
By Matt Crenson
Associated Press
posted: 14 August 200405:55 pm ET


"With more than 4,000 scientists, including 48 Nobel Prize winners, having signed a statement opposing the Bush administration's use of scientific advice, this election year is seeing a new development in the uneasy relationship between science and politics.

In the past, individual scientists and science organizations have occasionally piped up to oppose specific federal policies such as Ronald Reagan's Star Wars missile defense plan. But this is the first time that a broad spectrum of the scientific community has expressed opposition to a president's overall science policy.

Last November, President Bush gave physicist Richard Garwin a medal for his "valuable scientific advice on important questions of national security." Just three months later, Garwin signed the statement condemning the administration for misusing, suppressing and distorting scientific advice."

See the article for more details...

Christians Should Support John Kerry for President

One of my high school classmates (Stony Brook School, Stony Brook, L.I., N.Y., class of '53) has copied to me a straight from the heart argument that true Christians should be supporting John Kerry for President in 2004. Mike has agreed to let me place it in this blog. Dick is another of my Stony Brook classmates. Stuff in [...] is my addition.

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Hi Dick,

Some friendly banter to you on the John Kerry / VietNam issue. It was found out recently (and probably John McCain knew it first) that those contesting the crew of Kerry's river boat were a group of ardent Republicans dead-set on contesting anything positive about Kerry.

Significantly also about them is that, yes, some of them may have served in the same general area there as Kerry, and maybe in his military unit, but NONE of them were in his crew on the boat and there to see his valor under fire. But ALL but one of his crew who are alive today were there by his side at the convention affirming his character and courage.

Let me share something with you, Dick, about our support for Kerry and the Democratic Party. This [the following outline] was the substance, in short form, of a publication here in Pennsylvania recently. And it has everything to do with our transformation and growth in the Christian faith. The article, mainly in outline form is entitled "Why We Are Voting for John Kerry" by Mike and Shirley Winship.

LEADERSHIP - U.S. Senate experience. Honorable, dedicated military officer.

ENVIRONMENT - Environmentalists and Sierra Club support him.

STEM CELL RESEARCH - He supports it for its immense potential for healings and medical possibilities for so many.

VETERANS - Against the sneaky Bush back-door draft and for keeping our VA Centers open and funded.

MILITARY - Decorated combat experience; for strong military and improved homeland defense.

INTERNATIONAL AFFAIRS - Would restore the lost respect and trust of old allies by respecting and working with them.

HEALTH CARE - Access to adequate health care for all.

EDUCATION - Would give priority to elevating student opportunities and teacher excellence and compensation.

PRESCRIPTION DRUGS - Make them accessible to all at prices comparable to what people in other countries pay.

PERSONAL HUMILITY & INTEGRITY - contrast with Bush arrogance and lies.

DEMOCRATIC PARTY - this is the party of and by and for the people. We are followers of Christ, and He and the Bible describe the work of the Kingdom of God as helping the poor, the oppressed, weak, sick, hungry, hurting (Isaiah 58, 61; Luke 4), and forgiving and peace-making. We are former Republicans (until year 2000), and our Christian faith finally demanded our rejection of the party of the rich and powerful and arrogant, and our alignment with the party of the hard working people all around us. It was, for us, like coming from darkness into the light. It was a gradual and thoughtful process of change, and George Bush proved us right.

Dick, I know how you have wrestled yourself with issues the Presbyterian church has been contended with, and I would seriously ask you consider some of our positives mentioned above. Compare the conventions this summer and look at the difference you will see in the faces of the people there at each. Think of the OT prophets and the sins of Israel/Judah and how God rebuked them for looking away from those oppressed and for their love of ease and self-enrichment. Look at the real sin of Sodom as mentioned in Ezekiel 16:47-50. Then compare the two major parties of America, and see where your heart is.

See, Dick, they call me retired, but I am still the pastor and counselor. One lesson God has taught me in recent years, for which I am so grateful and liberated, is to listen for His voice in all kinds of people, Christian and non-... For me, since Stony Brook, change and the power to change my mind and direction, is the essence of transformation, which the Apostle Paul said was crucial (Romans 12:1-2). Jesus, a true and pure liberal, said the repentance and move into the "Kingdom of God" was so radical that it required nothing less than being"born again." When one is an active pastor, he is rarely free enough to actually go that far. The "Pharisees", or today's conservative equivalents, will crucify you, or at least kick you out of the church. By the way, Jesus was indeed a liberal (free, liberated a la Galatians 5:1). What conservative would say "You have heard it said ... (i.e. the law), but I say unto you ...."?

Just some thoughts, Dick.

Spoken in Spirit and love. Mike

Stephen Hawking's Black Hole 2004

Back from vacation and eager to see/hear informed comments on Hawking's Dublin presentation of his conclusion that black hole formation and evaporation does not involve a loss of information.

John Baez (math: U C Riverside) for provides a transcript of Hawking's talk, as well as comments about the technical details of Hawking's calculation. ( a link to Baez's discussion appears on the General Relativity 17 conference home page ).

John Preskill (physics: Cal Tech) comments on Hawking's talk and the link to a pdf file containing the text of a Preskill seminar at Cal Tech dealing the the black hole information paradox.

Sean Carroll (physics: U. of Chicago) discusses Hawking's talk on Chicago Public Radio (with Juan Maldacena of the Institute of Advanced Study at Princeton) where both give a discussion in lay terms of the significance of Hawking's talk and the problem in general. The talk appears on the Odyssey program for July 22, 2004.

Sean Carroll is one of the few first rank physics researchers who cares enough about public outreach (this of course is my characterization!!) to write a regular blog, which covers many interesting topics.

Hawking's results are derived (the details remain to be published) using an approach to quantum gravity in ordinary four dimensional spacetime (three spatial plus one time dimension) which uses the "Euclidean" version of the Feynman path integral (t -> it), with the approximate final answer analytically continued back to the "real world" via the inverse Wick rotation (it -> t ) . The exact answer requires integrating over all 4D geometries possible in the Euclidean space (which has four spatial dimensions). As Baez discusses (see above) , no one knows how to sum this Feynman path integral (FPI) formulation in four dimensions over all possible geometries.

Baez discusses how Hawking uses a "semi-classical" approximation which involves including only contributions from geometries "close to some solution of the classical equations of general relativity." Hawking includes the FPI contributions from only two such classical solutions.

Jacques Distler (U. Texas physics ) , a noted string theorist, notes that Hawking has to include an extra term, "a small negative cosmological constant", in the Lagrangian to keep the expression well defined at low energies. Distler notes that Hawking doesn't really deal with how that mathematical device allows a description finally in terms of the observed universe.

Distler also considers the black hole information paradox as "solved" in principle by string theorists for a multi-dimension version of the universe possessing "AdS/CFT" . In his Dublin talk , Hawking says:

"Finally, it was claimed that the issue was settled in favour of conservation of information, by ADS, CFT. ADS, CFT, is a conjectured duality between supergravity in anti de Sitter space, and a conformal field theory on the boundary of anti de Sitter space, at infinity. Since the conformal field theory is manifestly unitary, the argument is that supergravity must be information preserving. Any information that falls in a black hole in anti de Sitter space, must come out again. But it still wasn't clear, how information could get out of a black hole. It is this question, I will address. "

Hawking is trying to understand this problem in ordinary 4D spacetime.

An interesting approach to the black hole information paradox is contained in a recent preprint: "Black holes Conserve Information in Curved-Space Quantum Field Theory", by Christoph Adami and Greg L. Ver Steeg. The abstract is:

" We show that black hole formation and evaporation in curved-space quantum field theory is unitary if stimulated (as well as spontaneous) emission at the event horizon is taken into account. In particular, we show that the entropy accreted by a black hole when particles cross the event horizon is exactly balanced by a commensurate entropy increase of the rest of the universe, owing to the quantum entanglement between the black hole, Hawking radiation, and scattered radiation (including stimulated emission). As a consequence, the emitted radiation is non-thermal, and information can be retrieved using standard error corrections methods for noisy quantum channels."

The authors analyse the problem using quantum information theory instead of thermodynamics. In their conclusion, they state:

"In conclusion, we found that a consistent treatment of black hole dynamics requires the presence of emitted radiation outside the event horizon beyond the usual Hawking radiation. The radiation field in this region is non-thermal, while accretion and evaporation described by the Hamiltonian Htot = H + Hs is unitary. This guarantees that any change in the entropy of the inside region is exactly balanced by a commensurate change in the outside, so that the total entropy of the universe is constant under this dynamics. The information dynamics of black holes surprisingly turns out to be that of a
very standard quantum channel that is used to transmit classical information, where Hawking radiation provides the noise source. We further note that this solution to the black hole information paradox does not require to go beyond curved-space quantum field theory."