Very precise pulsar measurements

A neutron star is made of neutrons, right? Astrophysicists ponder this question and forge theory after theory, but the only thing they conclude with certainty is that a neutron star by any other name would still be made of the densest form of matter know to exist in our Universe. Under certain conditions a star which has exhausted all of its fuel and is sufficiently massive will not be able to support its own weight with pressure support (as in a regular star) or with electron degeneracy support (as in a white dwarf) such that electrons and protons merge to form neutrons because it is a more energetically favorable arrangement of the matter. A neutron star is a sort of massive atomic nucleus, but without charge. The actual composition and detailed properties of neutron star are still theoretically uncertain.
New measurements of the pulsating neutron star and helium-oxygen-carbon white dwarf binary system J1614-2230 reported in a Nature letter are the highest precision determinations of a neutron star's mass to date. The data comes from the massive Green Bank Telescope using the new Green Bank Ultimate Pulsar Processing instrument which accurately records the time of arrival of each radio pulse sent out by the rapidly rotating neutron star (which is a pulsar). The quality of this instrument, having over a tera op of computing power, and the size of the telescope, 100 meters, made this measurement possible. For a quick rundown of this result you can watch these quick movies on the scientific implications and the technology behind the discovery which were created by the NRAO.

The analysis uses a general relativistic effect involving the time delay of light known as the Shapiro delay effect. When a light ray passes a massive object it follows a curved path. General relativity says that curvature of light rays can only take place when the velocity of the propagation of the light rays also varies with position. The Shapiro delay increases the light travel time through the curved space-time near a massive body. The equation to determine the time delay effect is delightfully simple.

The delay depends on the mass, M, of the time delaying body between the source and the observer, the gravitational constant G, the speed of light, c, and the geometry of the system. The geometry is that light has to be passing near the gravitating body before it gets to the observer for the effect to occur at all so the vector that points from the observer to the source, R, and the vector that points from the observer to the gravitating mass are vital. Pulsar J1614-2230 is a nearly edge on, 89 degrees, system meaning that when the white dwarf passes in front of the pulsar during the binary orbit the Shapiro effect will be very strong. I ran a quick calculation of the time delay and found it to be exactly on the order of a few microseconds. The first figure in the paper shows the geometry and the measured effect.

With this data in hand the standard Keplerian orbital parameters are calculated for this clean binary system and the masses of the objects are calculated. The mass of the neutron star was found to be 1.97 +/- 0.04 solar masses which is the most precise measurement of neutron star mass to date. Unfortunately this measurement technique does not provide any information about the radius of the neutron star, but because the mass was so high it already set a limit on the equation of state of the neutron star matter. This means that we can begin to answer what a neutron star is really made of. Different kinds of matter have a different behavior as you add more mass to them which is intuitive if you thought how discrepant with respect to size a planet made out of cotton candy versus rock would be. This result indicates that exotic models of hadronic matter including hyperons, kaon condensates are ruled out. Condensed quark matter is not ruled out, but highly constrained with this data. This is a big deal for particle physicists because this kind of system is an experiment that could never be carried out in a lab, but is necessary to probe fundamental physics.

This cool result on neutron stars glosses over another application of precise pulsar measurements that the authors of this Nature paper regarded as noise. The plot above is very neat and clean, but before the data looks like that a timing analysis must take into account the time delays associated with many more mundane effects. Effects that change the time of arrival of the pulsar include the variations in the Euclidean distance between the Earth and the pulsar resulting from Earth’s orbital motion, the proper motion of the pulsar, and its binary motion, dispersive delays in the interstellar medium, and time dilation of clocks in the observatory and pulsar frames and along the propagation path. The Earth's orbital motion about the solar system barycenter (known as the Roemer delay) is up to 500 seconds and so must be removed from the data. The powerful thing is that the Earth's orbital motion tells us about the mass and orbits of all the bodies in our solar system. A paper published in the Astrophysical Journal states that with ten years of careful observation of 20 pulsars the masses and orbits of solar system bodies could be determined better than with any other method and even undiscovered trans-Neptunian objects could be found.

Precise pulsar measurements are powerful. The first extrasolar planet ever discovered was actually made with pulsar measurements. Pulsars can tell us about the nature of neutron stars, the properties of own solar system, oh and even gravitational waves. If only astronomers had the money to build a pulsar timing array...

References

Demorest PB, Pennucci T, Ransom SM, Roberts MS, & Hessels JW (2010). A two-solar-mass neutron star measured using Shapiro delay. Nature, 467 (7319), 1081-3 PMID: 20981094

D. J. Champion, G. B. Hobbs, R. N. Manchester, R. T. Edwards, D. C. Backer, M. Bailes, N. D. R. Bhat, S. Burke-Spolaor, W. Coles, P. B. Demorest, R. D. Ferdman, W. M. Folkner, A. W. Hotan, M. Kramer, A. N. Lommen, D. J. Nice, M. B. Purver, J. M. Sarkissian, I. H. Stairs, W. van Straten, J. P. W. Verbiest, & D. R. B. Yardley (2010). Measuring the mass of solar system planets using pulsar timing ApJ arXiv: 1008.3607v1

White Cosmonaut, Red Cosmonaut

Check out this lovely art by Jeremy Geddes. He is a Melbourne artist who works with mostly oil paints. His paintings have glowing colors and he has this recurrent cosmonaut theme that vaguely makes them seem relevant. Below are three of my favorite images that I have seen: The White Cosmonaut, The Red Cosmonaut, and Heat Death. Of his cosmonaut series he himself is vague,

I wanted to construct my own reality through my paintings, a quiet melancholic space that operates by it’s own set of underlying rules and runs it’s own oblique narrative. With each successive painting, I try to build the world and uncover it’s form. The cosmonaut paintings are the first step in this.

And on his piece Heat Death he again lets your mind linger on meaning and reasoning,

Hopefully, I communicate everything I want to say through the painting itself. I’m not interested in giving it a didactic final meaning. I just want to spark questions in the viewer.

Artists have the luxury of letting their art speak so that they don't have to. Scientists don't have this luxury and generally must have a didactic (although, not intending to imply moral) explanation of nature; an explanation which may or may not be close to the truth. Science ultimately doesn't self explain its emphases on truth seeking. Truth is like art, sought for its own sake. Oh and please, if someone wants to buy me the Red/White Cosmonaut diptych print feel free.

The Goldilocks Planet

Once upon a time there was a planet named Earth. It orbited exactly one astronomical unity away from a G2V type star. Billions of years went by and Earth found that it lived right in the habitable zone where liquid water was maintained on it surface and life spontaneously arose. Pretty soon life on Earth became restless, questioned its own existence, and looked for life on Gliese 581. Earthlings found many planets and exclaimed, 'Gliese 581 b is too hot, Gilese 581 c is slightly too hot, Gliese 581 d is slightly too cold, Gliese 581 e is way too hot, Gliese 581 f is too cold, but Gliese 581 g is just right!' so the story goes.

Gliese 581 is an unassuming star: it is relativity close at 20 light years away (the 87^th closest cataloged star to earth), it is only a third the mass of the sun, and it is relativity quiet in terms of stellar activity (which is beneficial for life because flares scorch planets). It is the sixth planet from Gliese 581 denoted merely as g that harbors so much potential. It is not to hot, not too cold, it is just right. It is the Goldilocks planet. Vogt et al. 2010 recently reported on the discovery of this planet which is a 3.1 Earth mass (or larger) planet orbiting in the habitable zone of the M3V type star Gliese 581. The problem is that this planet may not exist.

The Media

I did not immediately discuss Gliese 581 here at The Astronomist because I wanted to read the paper before weighing in. However the authors were compelled to issue a press release about their findings before making their peer reviewed paper available. After I finally looked at the paper I was somewhat disappointed. The whole thing was a science journalism media circus. A selection of some of my favorite excerpts:

• “Found: An Earth like Planet, at Last” Time magazine
• “The chances of life on this planet are 100 percent,” Steven Vogt
• “Could contain more gold than we could ever imagine” PR Fire
• "Are the Gliesans going to Hell?" Huffington Post
• "An Alderaan Moment: Earth-Like planet disappears" Death+Taxes

Media coverage is a double edged sword for science. Scientists strive to come up with compelling results that often fall flat when presented to the media or public, but other stories make waves disproportionately large relative to their scientific impact. Arguably the discovery of an earth like planet should have been accompanied by a much larger amount of media attention. The misinformation spread about Gliese 581 g is a symptom of the real problem which is the science. This is not a confirmed planet detection, there is no evidence this planet has a hospitable atmosphere anything like Earth, and there is certainly no evidence of life. This wont stop the media from speculating or spreading dangerous misinformation (like the idea we could travel there if we trash Earth). The quote from Steven Vogt is an example of poor journalism where he prefaced the statement by saying, 'my own personal feeling is that the chances of life on this planet are 100 percent,' but the crucial context was thrown away for headlines.

The Science

All the planets around Gliese 581 were discovered using the radial velocity technique. In any gravitationally bound system the bodies orbit their common center of mass. It is a subtle effect in a star-planet system where the central star dominates the mass. The central star will move at a characteristic speed depending on the orbits of the planets around it. The movement of the star is measured through the Doppler shift of the light emitted by the star. Modern instruments are super sensitive to even the smallest movements of stars down to as little as 1 m/s. Observations of the radial velocity of the star over a period of time (usually several years) is analyzed using Fourier analysis. The Fourier analysis identifies periodic signals in the data corresponding to the orbital period of the planet or planets.

The researchers used two data sets spanning almost two decades. Most of the data came from the researcher's own instrument HIRES, and additional data came from a Swiss group with the HARPS instrument. The HIRES data spans a larger time range, but the HARPS data is more precise. This combined data set is how the researchers identified two new planets f and g.

The Problems

A little after this new Goldilocks planet was announced the Swiss group announced that they could find no evidence of Gliese 581 g in their data. Does this mean it doesn't exist? Well this is tricky. A planetary researcher in my department, Rory Barnes, spoke to the New York times before the Swiss group had spoke up and said that the planet looked like the 'real deal'. After the announcement was made I spoke to Barnes again and he said that he would have to hold off further judgment until more information was available.

The onus of proof in science is upon those who make extraordinary claims. Vogt et al. were only able to find this planet by combing the available data sets; they actually state in their paper that they did not detect the planet in either of the data sets independently, only in combination. The damning part of the Swiss groups statement is that they say they have much more data available at this point that Vogt et al. did no have access to during their analysis. When the Swiss team forces planet g to fit their complete data they actually get a negative fit indicating that planet g really isn't there. The thing about this paper that I am least happy with is the quoted false alarm probability. The false alarm probability appears to be 1% based on the figures in the paper (see figure 3 specifically), but in the text it is quoted as ~10^-5. I don't know what is going on.

Then there is their error analysis (warning this is about to get technical feel free to skip this paragraph). Vogt et al. used the peaks in the power spectrum to identify the planets in the system then subtracted off the highest power modes corresponding to the planets they had found. The power spectrum for each planet carried with it a false alarm probability, but once the planet had been subtracted out of the power spectrum its false alarm probability was washed away (you can see this happening in figure 3). They compound their errors after the 1st, 2nd, 3rd, 4th, and 5th planets which have varying false alarm rates. The proper way to do this is a joint fit model to all planets in the system using Bayesian analysis.

The strangest thing about all this is that when this paper was first submitted to The Astrophysical Journal the Swiss group was reviewing the paper and it was rejected. This Vogt paper meta chronicles its own history and discusses why it was retracted previously over concern of systematics. Unfortunatly the quality of the paper may not have improved. The Swiss group has actually leveled one specific concern, Vogt used perfectly circular orbits to find planet g, but the evidence shows the orbits are probably slightly elliptical. In fact in 2009 Vogt used elliptical orbits, but in this new paper circular orbits have been adopted. The image above illustrates this and makes a pictorial argument as to how circular vs elliptical orbits could introduce errors.

The discovery of an Earth-like planet seems imminent. I do not know if this is it.  I will hold off further judgment until more information was available.

References:

Steven S. Vogt, R. Paul Butler, Eugenio J. Rivera, Nader Haghighipour, Gregory W. Henry, & Michael H. Williamson (2010). The Lick-Carnegie Exoplanet Survey: A 3.1 M_Earth Planet in the
Habitable Zone of the Nearby M3V Star Gliese 581 ApJ accepted : arXiv: 1009.5733v1

Also thanks to Amit and Rory for discussion and figures.

ATLAS Mural

ATALAS commissioned an impressive mural of their detector that has just been completed. Artist Josef Kristofoletti created the massive mural of the Large Hadron Collider's ATLAS detector on the outside wall of loop point 01. The mural was commissioned by the ATALAS experiment after Kristofoletti first painted a similar, though much smaller, mural on the side of the Redux Contemporary Art Center in Charleston, South Carolina. Kristofoletti found inspiration for the art by merging his enjoyment of classic Italian Renaissance murals and his life long fascination with science. He says that the humongous size of ATALAS and the tiny particles it finds make the Large Hadron Collider fascinating, like an unprecedented modern cathedral of science. The event depicted in the mural shows an actual event recorded by ATALAS of a Z boson decay into two muons.

There are more concept pictures here or finished pictures from CERN here.

Skeptical: Philosophical Umpire

Making good decisions is complicated. Game theory applies logic and mathematics to determine the optimal course of action for individuals when acting in the presence of other participants. Now, individual actions must take into account logic, morals, and personal preference, but there are general rules or situations in which the optimal course of action is clear. This comic (or infographic?) by SMBC illustrates the application of game theory to a classic problem, the prisoners dilemma, and by extension morality.

The prisoners dilemma is a great way to find your moral compass. We can apply a similar decision matrix as used above to many different kinds of situations, like Pascal's wager, where one attempts to bet on the existence of God. The logic of pascal's wager concludes that one should believe, or at least act as if one believes in God (this result is unsatisfactory to many, but wait I have a response). I was recently considering applying a decision matrix to answer the question, 'Should you believe in science?' There are other ways to phrase the question, like 'Should you be a skeptic?' or 'Should you follow logic?' Decision theory gets tricky here. In order to answer the question I recalled an analogy a professor used in a philosophy class I took long ago. My professor wanted us to consider a philosophical umpire calling a game. The umpire could either state that she was very vigilant such that she, 'calls em as I see em' (admitting fallibility), or the umpire could say that, 'I call them as they are' (denial of fallibility).  In the situation before replays I could almost see the umpire taking either stance with reason because they are the final arbiter on the field. In this modern age it is completely untenable for an umpire to state that she calls everything'as they are because replays are available. In life any experience that can be repeated is like a game with replays; an experiment is a game with replays. We all must be like the philosophical umpire and we can reason out how to behave using these ideas.

Below I have made a logic table. On the left vertical axis is the true outcome of an event with respect to how you perceived it and on the top horizontal axis is how you see yourself judging the event. The conclusion of the table is that application of the scientific method is really powerful. Admitting that you make errors in judgement means that you always allow potential for improvements in the future outcomes, but insistence on being right leads you to a false world view. I think that scientists, skeptics, and atheist have essentially the same goal and are all standing in the top right corner there jumping up and down trying to get people to choose to be skeptical.

	'calls em as I see em' (skeptic)	'calls em as they are'
right	positive result, skeptic world view, positive future results positive result, superficially correct world view, positive future results negative result, skeptic world view, potential for improved future results negative result, false world view, negative future results
wrong

It almost seem to be a tautology that logic says you should use logic to understand the world. This decision matrix casts doubt on the result of all other decision matrices like Pascal's wager such that we can escape being certain that belief in God is best, but simultaneously this result casts doubt on itself. Paradoxically what this really seems to say is that you should be skeptical about being skeptical.

Magnetic Fields in Cosmology

The existence of magnetic fields on cosmologically large scales is an unsolved problem in astrophysics. Theory favors a universe that did not begin with any magnetic fields present and classical magnetohydrodynamics restricts the spontaneous emergence of a magnetic state under the influence of ideal forces. In a paper entitled Twisting Space-Time: Relativistic Origin of Seed Magnetic Field and Vorticity appearing Physical Review letters Swadesh Mahajan and Zensho Yoshida propose a universal magnetic field generating effect using ideal special relativistic fluid dynamics. Mahajan and Yoshida's insight was that in describing magnetic fields, which are mathematically equivalent to a vorticity, a careful application of ideal dynamics in the framework of distortions caused by special relativity may result in the spontaneous emergence of a magnetic state in contrast to the previous theoretical result.

Magnetic fields are found to be important in every scale hierarchy of the universe. Most notably detailed images of galaxies paradoxically display regions of chaotic turbulence and beautiful grand coherent designs at once. Thus it is clear that turbulent motion on scales below hundreds of parsecs does not necessarily destroy coherent optical or magnetic features over scales of kiloparsecs. Indeed, magnetic fields are indirectly observed at optical and radio wavelengths by detecting the polarization of the electromagnetic field through the Faraday effect and also by the Zeeman splitting effect. The Faraday effect is the rotation of the linear polarization vector of light which occurs when polarized radiation passes through a magnetized and ionized medium. Radio observations are the most powerful technique and by measuring both the dispersion and polarization rotation the mean of the magnetic field along the line of sight can be measured. Such observations indicate a wide range of magnetic field are present in astrophysics. The image at right below shows the magnetic fields present in M51 which are likely similar in structure and strength to that of the Milky Way.

The total radio continuum emission from the "whirlpool" galaxy M51 (distance estimates range between 13 and 30 million light years) is strongest at the inner edges of the optical spiral arms, probably due to the compression of magnetic fields by density waves. The vectors give the orientations of the regular magnetic fields as derived from the polarized emission. The field lines follow nicely the optical spiral arms. Unexpectedly, strong polarized emission is observed also between the optical arms which indicates the action of a dynamo. This image was observed with the VLA in its most compact configuration at 6cm radio wavelength (broadband continuum). As the VLA cannot detect the diffuse, large-scale radio emission, data from the Effelsberg 100-m telescope in Germany at the same wavelength was added. Investigator(s):  Rainer Beck (MPIfR Bonn, Germany), Cathy Horellou (Onsala Space Observatory). Image courtesy of NRAO/AUI

Microguass fields are present in galaxies at scales of a few kiloparsecs and on the much larger scales of megaparsecs ordered fields of perhaps a few orders of magnitude less are present in galaxy clusters. Magnetic fields in astronomy are controlled by induction of partially ionized gas. A common model for creating these magnetic fields is the dynamo effect wherein an electrically conductive fluid accelerated by some kinetic force generates convective motions in the fluid; it is plausible that a turbulent hydromagnetic dynamo of some kind coupled to an inverse cascade of magnetic energy wold give rise to regular galactic magnetic fields. Following the basic dynamo theory magnetic field lines can be simulated for galaxies which are consistent with observations. The dynamo theory is actually a mechanism for maintaining or growing fields rather than creating them, but it is expected that minuscule primordial magnetic field seeds in the early universe of cosmological origin drive the magnetic fields observed today.

The magnetic dynamo and the primordial magnetic seed theories are both unsatisfactory. The model wherein the the large scale magnetic field in galaxies is the result of the twisting of a cosmological magnetic fields by galactic differential rotation is not satisfactory because a primordial field wound up by differential rotation ultimately decays in an effect known as flux expulsion. The primordial seed theory must explain the presence of large magnetic fields in higher redshift objects when the universe was much younger when the fields should not have had sufficient time to grow. Researchers disagree over what initial primordial field strength is necessary to create the magnetic fields seen today; estimates vary from as large as 10^-9 gauss [1] to 10^-30 gauss [2], but either way an alternative model would be welcome.

Mahajan and Yoshida's work was motivated by the search for a universal mechanism for magnetic field generation. They key to creating a magnetic field is the vorticity of an ionized material which is analyzed in this paper with topological constraints. In mathematical terms fundamental cosmology requires a topological constraint on the vorticity of the universe (consider that you wouldn't expect the universe to have a preferred rotation), however this constraint can be broken by the application of special relativity. The problem of magnetic fields lies in the fact that vorticity must vanish for every ideal force such as the entropy conserving thermodynamic forces (this can be proven though the governing Hamiltonian dynamics of an ideal fluid where ultimately Kelvin's circulation theorem shows that if the initial state has no circulation the later sate will also be vorticity-free). Introduction of the Lorentz factor γ=(1-(v/c)²)^-1/2 from special relativity destroys the exactness of the ideal thermodynamic force and allows spontaneous vorticity.

The authors find a new term that provides a magnetic field growing mechanism as long as the kinetic energy is inhomogeneous. The authors mechanism can provide a finite seed for even mildly relativistic flows. They provide an example for very standard parameters (electron density n=10¹⁰ cm³, temperature T= 20 eV and velocity, v, compared to c of v/c=10^-2) and find their relativistic drive mechanism remains dominate over other effects until magnetic fields of 1 gauss or so which is much larger than most magnetic fields ever observed, thus the relativistic drive is the only dominant effect. The relativistic drive mechanism will likely help us understand, among other things, the origin of magnetic fields in astrophysical and cosmic settings.

References:

[1] Beck, R., Brandenburg, A., Moss, D., Shukurov, A., & Sokoloff, D. (1996). GALACTIC MAGNETISM: Recent Developments and Perspectives Annual Review of Astronomy and Astrophysics, 34 (1), 155-206 DOI: 10.1146/annurev.astro.34.1.155

[2] Davis, A., Lilley, M., & Törnkvist, O. (1999). Relaxing the bounds on primordial magnetic seed fields Physical Review D, 60 (2) DOI: 10.1103/PhysRevD.60.021301

[3] Mahajan, S., & Yoshida, Z. (2010). Twisting Space-Time: Relativistic Origin of Seed Magnetic Field and Vorticity Physical Review Letters, 105 (9) DOI: 10.1103/PhysRevLett.105.095005

The Future History of the Universe

Current observations of our universe indicate that the universe is expanding at an accelerating rate. The expansion of the universe will eventually place all galaxies which are not gravitationally bound to the Milky Way beyond our observable horizon (yet I caution that the notion of a horizon is a subtle point and a source of expanding confusion). Galaxies will cease to be brilliant. The passing of time will see stars exhaust all of their fuel. Stars will cease to shine. Black holes will evaporate due to Hawking radiation dispersing a bath of dull photons into the universe. Black holes will cease to exist. The universe will cool as it expands to a uniformly frigid temperature. Entropy will be maximized. The universe will be cold, dark, and lonely.

The future history of the universe described above is an implicit result of the standard cosmology accepted today. It is an extrapolation of accepted theory into the distant future. There is good reason to be skeptical of extraordinary predictions which is why the big bang and the past expansion history of the universe is the major focus of cosmology and not predicting the future of the universe. We need to know exactly what happened in the past to understand the reasons for the accelerating expansion (what is dark energy?). The current observations and the 'standard cosmology' I speak of are part of what is known in physics as the concordance model of cosmology. Every peer reviewed research paper that discusses the universe has this one sentence in it that goes something like this (taken from generic research paper on cosmology and extragalactic astrophysics):

Throughout this paper we assume a Friedmann-Lemaître-Robertson-Walker metric with a standard cosmology with Ω_M=.3, Ω _Λ=.7, H₀=70 km s^-1 Mpc^-1.

Lets break down this generic statement and see what it implies. The Friedmann-Lemaître-Robertson-Walker metric implies we are assuming a universe which is consistent with a homogeneous isotropic expanding universe, the Ω values are dimensionless energy density parameters which quantify the energy contribution from matter (mostly dark matter, denoted M) and dark energy (denoted Λ), and finally the H₀ value is the Hubble parameter in units of kilometers per second per megaparsec which describes how fast, v, an object at a given distance, d, is moving away from us such that H₀=d/v. The statement effectively means that the universe is flat (it is conceivably possible that you could travel a very long way in one direction and end up where you started, like what happens if you travel around the earth, but observations indicate that this is not the case so we conclude the universe has no curvature) and the universe is expanding in such a way that the universe will not collapse back down on itself. Thus our best guess is that the universe will keep expanding forever. The consequence of this, and this is the crux here, is that as time moves forward entropy inexorably increases (this is the second law of thermodynamics) to the point that all ordered processes, complex systems, life and semblance of thought is impossible.

If you lived forever it would be hard to avoid the situation where eventually you and your fellow space travelers were huddled around a few dieing stars in a bland galaxy in an exhausted void. There are small stars which are burning today and will be burning in 100 billion years and more stars will form for a while. But eventually, stars really will shut down and cool. You could try to travel to another galaxy, but that would take a long time (if the distance to our neighbor galaxy Andromeda was held constant it would take about 2.5 million years to travel there at the speed of light), and even then there would be few stars and most problematically most other galaxies would have receded beyond our horizon. Where would you want to head in this barren universe? Recent studies of the entropy of the universe indicate that the majority of the entropy in the universe is actually contributed by super massive black holes. Interestingly gravity is rather unlike most systems in thermodynamics. Generally entropy is increased by say smashing something into many pieces, but for gravity when energy is uniformly distributed gravity is quite low compared to the state where matter has collapsed into stars or to the extreme state of a black hole. There is one more step in producing more entropy which occurs as black holes slowly emit radiation in the form of Hawking radiation. A black hole the mass of the sun would emit Hawking radiation for 2 × 10⁶⁷ years which is much longer than the current age of the universe at 13.7 × 10⁹ years. A super massive black hole of 100 billion solar masses, about the mass of our entire Milky Way galaxy, would emit Hawking radiation for 2 × 10¹⁰⁰   years. You could hang out near one of these black holes for a while as a source of energy because the black hole would still be producing entropy. Finally, all the black holes would also evaporate and the universe would consist of a diffuse gas of photons and leptons. Any activity in the universe would be very limited at this point and what did occur would take truly epic time scales.

The concordance cosmology, the theoretical models, and the measured parameters implicitly assume that the end of the universe is cold, dark, and lonely. The universe ending as cold void in which life can no longer be sustained is sometimes known as the Big Chill. At this point there is only speculation, perhaps it is philosophical. The universe may expand again in a secondary inflationary epoch or the vacuum may decay into an even lower energy state. Actually, there are other possible scenarios such as the Big Rip in which dark energy pulls apart the fabric of space through some exponentially increasing expansion. Revisionist history is the best kind of history, so when talking about the future history revisions are always welcome. There may already be information about universe which has been erased that would change our expectations. One example of the universe erasing information is if the radius of curvature of the universe is much greater than the horizon distance then observing this curvature would be like trying perceive the curvature of the earth just by looking at the horizon so as the universe, or earth, expanded observing curvature could more difficult. Paradoxically, conceding that there is information about the universe which has been erased which would indicate an ultimate fate other than the one outlined here also supports the argument that the ultimate fate of the universe is an extremely high entropy state.

Conceding that the universe may not be infinite or that the end is simply cold and lonely is very difficult for some. This theme was explored in Issac Asimov's story The Last Question in my previous post. In this story man ponders how the heat death of the universe can be avoided. Man asks the greatest computer created how the second law of thermodynamics can be reversed. [spoiler alert] After hundreds of billions of years the computer still cannot answer the humans. Ultimately all of humanities mental facilities from the trillions of humans spread throughout the universe merge their minds with this ultimate computer to from a singular unified mental process. The question is asked again and there is still no answer. Time goes on until space and time cease to exist, however the ultimate mind continues to ponder the question in hyperspace and eventually finds an answer. There is no one or no thing left to report the answer to so the mind decides to show the answer by demonstrating the reversal of entropy. The mind spends another eternity determining how to do this and writing a careful program to execute. Upon execution of the program the mind reverses entropy and thus creates the universe anew.

The Last Question

The last question was asked for the first time, half in jest, on May 21, 2061, at a time when humanity first stepped into the light. The question came about as a result of a five dollar bet over highballs, and it happened this way:

Alexander Adell and Bertram Lupov were two of the faithful attendants of Multivac. As well as any human beings could, they knew what lay behind the cold, clicking, flashing face -- miles and miles of face -- of that giant computer. They had at least a vague notion of the general plan of relays and circuits that had long since grown past the point where any single human could possibly have a firm grasp of the whole.

Continue reading The Last Question by Isaac Asimov or hear it spoken below.

It is interesting to note that different versions of this story I have encountered state the the sun will burn for ten billion years or 20 billion years. The written story above says twenty while the spoken story says ten. I don't know what the original version said (does anyone out there?). Perhaps this reflects our changing understanding of our sun which suggests that ten billion years is more appropriate.