Saturday, November 26, 2016

Stellar Collapse and Time Travel?

This post summarizes work done in collaboration with Prof. Jayashree Balakrishna (Harris Stowe State U.) and Dr. Christine Corbett Moran (Caltech). Our paper just appeared in the cosmology section of the Frontiers Journal.
Supernova explosion (artist: Mehau Kulyk)
Stellar Collapse. In the simplest stellar collapse model of classical General Relativity (Oppenheimer & Snyder 1939), the collapsing star is idealized as a uniform ball of dust that contracts under the pull of gravity. The dust particles that make up the star are assumed to be classical and thus infinitely small, infinitely light, and interact only gravitationally with other matter. Infinitesimally small particles would be then infinitely large in size, and could never be localized within the stellar horizon.  The smaller the mass of the constituent particles, the more significant the quantum mechanical effects become, breaking down the classical approximation.

Quantum Effects
When we include quantum effects,  a particle on the surface of the star is no longer localized, but is instead represented by its wavefunction. Every particle now has a finite probability of escaping the gravitational pull of the star. This allows for the possibility that some configurations will not collapse to black holes, but will instead disperse or even form stable new configurations. 

Why should we care about black holes?
Supermassive black hole. Artist conception.
In order to understand the universe, we have to understand black holes. They are the most permanent objects in our universe. All life revolves around them. Every galaxy has a black hole at its center. In the early universe, black holes acted as the seeds around which material collected, and eventually galaxies as complex as our own formed.  Black holes are also believed to be the only objects that will be left in the very far future as our universe continues to expand growing cold and empty. They do evaporate, but the evaporation of black holes that are stellar mass or higher happens on timescales longer than the age of the universe and thus is not observable. To truly understand black holes we have to understand their quantum nature, which is not only important in understanding the final stages of stellar collapse, but also in understanding whether they will form at all.

Classical paths with all initial velocities
We model stellar collapse using a path integral formulation In the special case of the dust ball collapse the paths can be computed analytically for all initial velocities (towards and away from the center of the star).  We derive analytic solutions to all classical paths (space-like, time-like, and light-like) in Schwarzschild (Table I and II in our paper) and Kruskal coordinates (see Table V and VI).

The evolution of the wavefunction
In Schwarzschild coordinates, we can only study the collapse outside r=2M. The motion of the particle on the surface of the star is analogous to the vertical motion of a ball moving under gravity, which can go (1) from an initial point to a final point directly, (2) reach its highest and fall back down or (3) escape. Thus some particles that initially move away from the star can return and contribute to the collapse. Each of these paths is unique taking a different amount of time to complete.

In Kruskal coordinates,  we can model the behavior of a particle on the surface of the collapsing star up to the physical singularity at r=0.  We find that classical time-like paths are unique. A path between an initial and final point can be either direct or indirect (turns back in space).  Space-like paths can turn back in time, but cannot turn back in space. They are also no longer unique when the final point lies inside r=2M. Classically, no information can exit the black hole. However, by integrating around the classical paths one might be able to extract information from inside the horizon. We only compute the paths in the Kruskal case, and leave the computation of the wavefunction and full exploration of the quantum collapse to future work.

Back in Time?
 In the dust-collapse model, the classical paths that turn back in time are space-like. This means that they are outside the light-cone, i.e., not in the realm of paths considered possible. Further understanding of these low probability paths that are traditionally ignored might lead to new physics. We conjecture the classical space-like paths and paths around them play an important role in the quantum mechanical collapse in the same way passing through the potential barrier is important in tunneling. Classically, it can never happen, and yet the tunneling probability cannot be ignored in quantum mechanics. It may be that time travel could be achieved by some kind of tunneling from time-like paths to the space-like paths that turn back in time.

Why include the space-like paths There is no theory of quantum gravity that works, but the theories that do exist and are accepted in the literature are causal. In our case, the propagator does not vanish outside the light-cone, and so we include all paths in our integration. The propagation on and around the space-like paths is acausal, i.e., backwards in time in some Lorentz frames. Whether or not this proves to be admissible in the ultimate theory of quantum gravity is beyond the purpose of this exploration since no such theory exists today.
 We assume that the radius is the only spatial degree of freedom that is not frozen. Such restrictive approximations make the problem tractable analytically.

The wavefunction of a particle on the surface of the collapsing star

WKB & Schrödinger comparison
t=5 M, multiple masses
The initial wavefunction is taken to be a Gaussian centered far away from r=2M.  In Schwarzschild coordinates, we compute closed form solutions to the propagator in (1) the WKB approximation where an expansion is performed around the classical paths and (2) in the Schrödinger approximation. We compare the resulting wavefunctions and find that the two solutions converge towards each other at intermediate times. They are out of step at early and late times with the Schrödinger solution being more exact at early times, and the WKB approximation being more accurate at late times. For lower particle mass, the star resists collapse longer and the probability that it disperses increases. Further work is needed (including the addition of higher order corrections to the Schrödinger solution) to determine the mass limit at which stellar configurations no longer collapse.
M=0, dotted (WKB), solid (Schrödinger)

In the limit when the mass of the star is zero, the WKB approximation converges to the Schrödinger solution at all times. This checks that the WKB approximation is accurate. The Wheeler-DeWitt equation converges to Schrödinger equation in this limit making the Schrödinger solution the exact solution of the free particle problem (Redmount and Suen 1992). Note that Redmount and Suen did not find a good agreement between their WKB approximation and the exact Schrödinger solution due to numerical issues, while our approximation converged. Space-like classical paths give the dominant contribution in the construction of the WKB approximation outside the light-cone.
Black holes or boson stars?
Even with LIGO's detection, it is still unclear whether black holes exist or not. We have no proof of a singularity. Theories suggest that black holes can be mimicked by boson stars or that the black hole itself could be a collection of Bose-Einstein condensates (e.g., Dvali and Gomez).  However, to obtain black holes as massive as the ones just seen by LIGO, the scalar particles would have to be very light. Quantum effects would be important in this situation, and the gravitational waves might look different due both the size and nature of the star.

Classical boson stars are believed to form from dark matter particles (fundamental spin zero particles) that Bose-condense creating a macroscopic quantum object. The size of this object depends on the wavelength of the constituent particle and can either fit in your pocket or be larger than a galaxy. Since no fundamental spin zero particles have been discovered other than the perhaps the Higgs boson, it is difficult to know if boson stars exist. Supermassive boson stars could lie in the centers of galaxies. Upcoming instruments sensitive to light may detect supermassive boson stars through lensing (e.g., see Boson stars as Gravitational lenses and Method for detecting a boson star at Sgr A* through gravitational lensing). If such stars exist in the mass-range that LIGO sees,  we might soon see a pair of co-orbiting boson stars. Additionally, detectors beyond LISA may see gravitational waves from perturbed supermassive boson stars.

Feeding on dark matter?
Macroscopic dark matter particles?
Dark matter particles come close to the attributes of classical dust. Unlike virialized dust halos or stars, the super-fluid dark matter particles would have negligible momentum and thus accrete easily. If somehow black holes can feed on dark matter particles,  the paucity of super-massive black holes immediately above a certain mass M (e.g., we don't see intermediate mass black holes) could be linked to the presence of ultra-light particle halos that black holes heavier than M can feed on. Black holes lighter than M would be unable to capture such dark matter particles in the same way mini black holes produced at the LHC cannot be grown on atomic matter and pose no danger to the Earth. As soon as a black hole reaches mass M, it starts feeding on dark matter and grows rapidly, perhaps swallowing the entire halo. 

This is the first article I have written where all the authors are women. It is also coincidentally my most technical article to date. Note that my co-authors and I do not discriminate against men and believe in equal rights for everyone. Our collaboration just happens to be 100% female.

Saturday, November 19, 2016

Science: the land of unpaid maternity leave

My contract ended on September 30, and my son, James, was born on the 10th of November. My first son is six years old. This is my second child, and my second unpaid maternity leave. It is also the first leave where there is no contract afterwards. I am not complaining. I can afford to take time off and be with my children. This is simply a post that summarizes my experience, while trying not to impose judgement.

Dreams and science
I have been working in science for the past 15 years, and felt on the top of the world since. I started research in 2001, two months before the September 11 disaster. My first research project was in grid computing, and our dream was that "the grid", which was made up of remote computers connected through the internet, would be accessible to everyone. In the years that passed, the grid became the cloud, and the dream was achieved. My second research project from that period involved modeling gravitational wave emission from boson stars (compact objects that can mimic black holes and are made up of dark matter-like particles) numerically. The dream there was that gravitational waves would be found, and that models like the one we made up could be constrained. LIGO found its first waves in 2015, and work on constraining various models with real data is underway. So, from a scientific perspective, I am in the unique position of saying that some of what I dreamed of happened. Of course, there were other projects I started later, which still have to reach this dream-like outcome, e.g., we still don't know what dark matter is, and if it is made-up of luke-warm ultralight particles or not, and we don't know much more about neutron stars than we did when I started my PhD thesis. We also don't wear atomic clocks on our wrists and while we have them in space, they don't yet go around in trucks and planes to monitor density changes underground.

The academic environment
In all this time, the academic environment has been surprisingly static. Proposals are written the same way, and the process is even more complicated and time consuming than in the past with fewer positive outcomes. Grants do not, generally, come with money for maternity or paternity leave even in countries where these kind of leaves are the norm. In Europe, countries provide for their own citizens, but most scientists work in countries that are not their own and cannot take advantage of these programs.

There are some very few specific awards on which there is support, but, on average, postdoc and PhD advisors are still in the position where they have no money to provide their staff with if they get pregnant. They also do not know how to handle these situations because there are so few women and no rules and no help. If they are stuck in the position of having a pregnant employee under a contract that cannot be broken, a good advisor mostly allows the person to show up and do what they can when they are able to once they have their baby.  This attitude is a choice and not something supported by the university or grant office. At the faculty level, some provisions have been made for women professors, where they teach less or not at all for some time after having a baby. It helps to be in a university with money and staff to spare.

The reaction at work
I did not mention my pregnancy until it was obvious. So, everyone at the University of Zurich noticed I was pregnant only after I came back from the US in the beginning of September. This was during the LISA meeting. My colleagues congratulated me, and asked how far along I was.

I had an informal discussion during coffee with Karsten Danzmann from the AEI Hannover over a potential position. He also asked me when the due date was and congratulated me over the pregnancy. He jokingly asked if I am one of those crazy people who are back at work a day or two after having the baby. I smiled and stared blankly. He then patted my back and said I should, of course, take as much time off as I needed. My AEI visit was already scheduled for late September. He proceeded to explain why it makes sense that I come visit AEI in person even though neither him nor the other group leader would be there at that time - I would be meeting the rest of the group and their opinion was decisive as well. By then I was more than 34 weeks along, and insurance does not cover travel beyond the 34th week.  I booked my ticket and tried to come.  I am tall and my pregnancy did not show very much, and so I thought the airline might not notice how far along I was. However, Wizz Air refused boarding. I wonder if, in their opinion, it is better to drive or take the train. I did contemplate these options between the moment I was denied boarding, and the moment I canceled the trip. Even though I lost the money for the tickets, it was easier this way. Edward had started school and refused to do homework with anyone but me. It would have been unreasonable to leave him alone and angry yet again. While Karsten wrote me a week after our coffee-break chat that I did not fit in his group, the AEI is still keen in having me visit, and believe I am more suited for an independent grant (i.e., they would give me a desk and a support letter if I brought my own money) than for a regular postdoctoral position.

Fancy, lovely dinner
My postdoc advisor, Philippe Jetzer, honestly said he would not have been able to provide leave if I had been under contract because neither my fellowship nor his grant come with such money. Luckily, my contract was over before I gave birth. The sad part is that he is correct. There is no money for maternity leave on most science grants even in Switzerland. Like in the US, there are one or two very specific awards that come with maternity leave, but the majority of grants do not come with such provisions. I would like to stress that Philippe and our group at the UZH are outstandingly nice people as is Karsten and his group at the AEI. This is simply a statement of the general situation. Furthermore, the day care facility on the UZH campus is so small, it is not available unless one registers on their waiting list soon after getting pregnant or even before that. It is, however, quite prominent on campus and with a beautiful see-through glass window through which one can see the handful of children they care for.

Before I left, my group took me to dinner, and we had a wonderful time. I am still affiliated with the UZH for any research I do for the next 2 or 3 years. This means I can access computers, journals, the library, publish. I can also use the software, etc. While it involves working for free, all this is tremendously helpful. I also have computer accounts at NCSA, which come with a similar kind of affiliation. The AEI in Hannover still say they would be happy to have me visit, which I cannot do easily with a 7 day old baby, but there is always next year with its spring and summer.

Why I will NOT be applying for grants aimed at parents returning to science
I looked at these type of applications with my brother when he was considering re-entering the academic world. We were looking at the Marie Curie action with its CAR program, and we were told that the probability of getting funded in STEM in such a program is less than through a regular program. Basically, like with the UZH day care, they make such programs visible, but the money is so little and the chances of getting funded are so low that it is not worth the time to write the 15+ pages of application. To restrict the applicant pool, they add conditions that enforce no work is published for the period of the leave, which is not something that would fit me. Mihai did apply that year and did not get funded, but I am not up to another such involved application with a baby and two other children to raise. My time is too valuable to write grant applications of tens of pages that have a probability of success of a few percent.

So what next?
Science-wise, I would like to finish the projects I started, and perhaps work one or two more things. It would be nice to be paid for some of this, but I do not wish to be at work from morning till night again while James is small, and Edward and David still need me so much. Even if day care was available, I do not want James to be away from me for most of the hours of the day.

Edward is in second grade even though he is only 6, and David is in 5th grade at 9. They have lots of homework, and catching up to do, which I have to help with.  With Edward, I add multiple digits numbers, solve equations, and next semester we'll learn to multiply. With David, we do powers, systems of equations, and series of thousands of terms. This is the math, but there are also the other subjects that are mostly in a poorly translated German that have to be made sense of + Romanian with its grammar, poets, and writers. 

I have a chicken army: we adopted 15 chickens from the factory farm in October under the assumption that half of them will die. So far they are all thriving. They now have feathers and spend most of their time outside. They come and eat from Edward's hand and we get about 2 eggs a day (total). We also have tortoises, 3 more chickens, terrapins, and a dog. The dog eats eggs, and so we have to make sure we get them before he does. 

There is also other property to manage and lots of people to help and other things to do.

Why do I try to do so many things? Most pressure is self-imposed. I have always felt I have to prove that I am worthwhile and that I am leaving something behind. That something takes the form of an article, a book, a house, a happier child, a happier chicken, a new child, etc. It partly also comes from never receiving unconditional support from anyone other than my mother (and my grandmother when she was alive). For the rest of the world, I keep having to prove that I have non-zero value and I am so tired of these endless proofs.

I try to invest some fraction of what I earn in what I think would grow and/or last. I have done this since I started working. It helped to be living in the privileged side of the world while keeping a relatively simple life-style. I have used cars (16+ years old) with small engines, and never had a taste for eating out, alcohol, cigars or fancy clothes. I do travel. I started taking vacations after having children because they need to see the world to understand it, and because we enjoy it. We will continue to travel some of the time.

Thursday, November 17, 2016

My name is Bond, James Bond..arescu

On November 10, I gave birth to my second son. He is seven days old now, and smiles and laughs in his sleep. I know it is just testing reflexes at this age, but Edward and David enjoy watching him smile. He also tries to grab the tortoises when placed next to him, and made a sound like a ‘ja’ when asked whether he liked them or not.  He showed no interest in chickens, Terrapins or in the dog as of yet, but the children are convinced that this is only because it’s cold and we spend most time indoors. 

A serious James
James is the first child of the family to be born in Lugoj, Romania. Andy says that the has two sons: one born in Pennsylvania and one in Transylvania. James and I were assisted by one of my mother’s former students who leads the hospital here. She and her staff were amazing. The hospital was warm and clean, and they allowed the birth to go like I wanted. I went for as natural as possible without medication, and they respected that. Once I entered the hospital, they put me on the table and started the delivery process. I did not have to fill out forms while in pain. I did that after I gave birth. The baby came sideways, which caused back pain and a slightly slower delivery.  He had a good heart beat all the way through, and we were allowed to come home a day later. More than six years have passed since Edward was born.  I had forgotten how painful it is to have a baby, and how challenging breastfeeding is in the beginning, but James and I are slowly getting over all obstacles. 

Before coming into the world: last few months of pregnancy
I had a safe pregnancy with James. I could travel and work. The lease for my apartment in Zurich ended on June 30. So, before that the furniture and most of our things left for Romania and we sub-leased a furnished two-room apartment (in Oerlikon) from some students.  Then school was over in mid July and my mother, Edward and David (not yet 6 and 9) moved to Romania, while I continued to travel back and forth.

In August I went to the US. I figured it was my last opportunity for work-only travel. I gave seminars, and drove between Cornell and Penn State. I also spent some time working with my collaborator, Prof. Jayashree Balakrishna, in St Louis, and took the bus to NCSA, where I saw Linda Lorenz again, and Cornel and Doina Costescu, their daughter, and grand-daughter. They were all as kind and amazing as I remember them if a little older. Linda and Ed Seidel had been my advisors as an undergraduate. Without her I would have never been able to graduate from UIUC's engineering program in one year and half (out of which I was a full time student for only one semester).  I, of course, also saw Ed Seidel and Gabrielle Allen,  gave a seminar on atomic clocks and started a new project with former collaborators on boson stars. I came back to Zurich for the LISA meeting in the beginning of September, which we were organizing.

 I officially moved to Romania on September 30. I could have kept things simple, and stayed in Timisoara, but instead I started renovating two houses that have not been lived in for the past 16+ years: one in Lugoj and one in Chizatau (a village that is 18 km away). Andy jokes that it only matters that they are both in Transylvania and that the children and I shared them with bats when we first moved in.

With Mihai in the school yard
We first moved to Chizatau. It took some time to get water into the house through pipes that did not leak and the power is still in a partial short-circuit, but it works. It was lovely because the summer was extremely warm and the house is on the Bega river. So, the children played a lot on the river bank and in our huge yard. They found praying mantises (green and brown; the first one landed on Edward’s neck), crickets, and some green bugs that look like thorns.

In Lugoj, we hired a neighbor to help clean the house. My grandparents had had the house painted by artists with hand-made colors. He painted some of the walls in a sloppy white, left some unpainted, and added some plugs with some thicker wire, which he did not connect to the main circuit.

my Zurich farewell dinner 
Edward and David started school in mid-September. As the rains started, it became pointless to drive from Chizatau every morning and afternoon instead of living close enough to walk to school. Also, there was no heating system, and it was cold at night and in the morning. So, we moved to Lugoj while the wood floors were being worked on. They had been damaged years ago when the next-door neighbor had a plumbing problem that had badly leaked over. There was lots of noise and dust. On our first overnight stay in Lugoj, the power blew out due to a severe short circuit. The plumbing was clogged. My mother fixed it by removing the sand and rocks from it by hand. Hot water and a central heating system were non-existent, but we had wood-stoves.

I hired an array of people. Some have been expensive and extremely unreliable (and partly toothless), while others were kind and trustworthy like Traian,  the electrician, and Ioji, who still solves most problems that come up. Edward and David enjoy following them around and asking lots of questions.

By the time I gave birth, we had electricity, heat, water, plumbing, and clean, slightly shinny wood floors. The central heating system has been flaky, and so we light an additional fire now and then and/or supplement electrically. We have finally learned how to clean a furnace, and I now think we’ll manage well enough after it will get cold.

James’ birthday and family history

James almost shares a birthday with my PhD advisor, Prof. Ira Wasserman. We missed by a day. Instead, he has the same birthday as my great-grandmother, Ana. I hope he will grow to be as smart as Ira, and live as long as Ana or more. She entered this world 138 years ago, and lived through two world wars, and the Holocaust period.  Yet my mother says she had been the most cheerful person she had ever known. She lived to 95 and kept her good humor up to her last day, when she assured everyone she felt fine, but asked if somebody could stay up with her at night because she was passing away.

Ana had one of the most beautiful voices in the county. So, when the head of the Romanian church came to visit, they'd asked her to sing for him with a boy, called Aurel Curuti, as the male-lead. She fell hopelessly in-love with him when they were both 18. While he acknowledged both fondness and attraction, Aurel refused to marry her. With the impetuosity of youth, he explained that she was too simple for him, her blood was not blue enough and her family was inferior to his. 

Ana and Teodor at their wedding in 1897.
The next year, in 1897, she married my great-grandfather, Teodor, instead.  He had piercing blue eyes and a breath-taking smile. He was also not musical and poor, but had mind-blowing intelligence and enthusiasm about most things and people around him. In school, he tutored a friend who later became one of Hungary’s ministers.  Yet throughout her life, Ana retained a fondness for Aurel. When her first babies were born (twin daughters), she named one of them Aurora. Unfortunately just like her romance, these babies did not live.

Some 15 years later,  Teodor and Ana moved to Murava (or Semlacul Mare), a remote village in Transylvania that lays close to the Serbian border. By 1918, he openly supported Transylvania’s union with Romania, and this turned him into a wanted man. When the authorities came to arrest him, he hid into a secret loft over the kitchen. So, they arrested Ana instead. Their youngest daughter, Octavia, remembered how she ran after the soldiers that were taking her mother away. One pointed a gun at her. She was four years old. She grew scared and stumbled into the mud. The village women told her that if she had cried louder, and begged more, maybe they would not have arrested her mother. It was her first time failing to stop unreasonable events. 

In prison, Ana was not physically tortured, but to persuade her to give her husband's hiding place away they started killing a person she knew in front of her every day. She would retell the dialogue:
Officer: “Tell us where he is!”
Ana: “How should I know? He never tells me where he goes. I am a simple woman.”
Then they brought in and shot Almajan, and his blood soon started flowing at my feet.

Back in Murava, one of her sons came home in vacation, and found his mother gone. His four year old sister was in the attic of a neighbor with her hair full of hay and feathers. She told him what happened. He immediately called his uncle Adrian, an officer in the Austro-Hungarian army who had studied in Paris with Charles de Gaulle. Adrian demanded Ana’s immediate release or else he'd come with his battalion of soldiers and demand justification for the arrest of an innocent woman from an army that should have a moral code above this. They took her home the next day in a beautiful carriage and apologized for her arrest and any inconvenience caused. Her release was more efficient than her arrest had been at convincing Teodor to surrender. He did not want other people to suffer because of his beliefs or choices.

Teodor and his children in 1922
While Transylvania's union with Romania happened soon after, Teodor’s guilty verdict did not change. For two years after he surrendered, he was imprisoned on a ship. There he developed tuberculosis. He returned home ill. Under treatment he lived for another 8 years. He used to say he wished to live to see his youngest child, Octavia, in highschool. He died in 1928 when Octavia turned 14.

Ana and Teodor on the livingroom wall
 When Ana and her now grown children returned to the Lugoj/Caransebes area, they met the next generation of Curuti. One of them offered to marry Ana’s daughter, Octavia. She refused. Octavia did not like the idea of being married to somebody called “Curuti” (the name translates to small butt; and people referred to his musical performances as “curu-ti canta” or your butt is singing).  

my pipes in the basement
When I returned to Romania this year, I was 8 months pregnant with James. In Lugoj, I moved into the house where Ana had spent the last part of her life. It had been my grandparents home after their retirement, and Ana was living with them. Out of the array of people I hired, the plumber turned out to be a Curuti. Interestingly enough, he inherited the musical talent of his ancestors and offered to sing at James’ baptism. I do not believe Ana's story was passed on to him. He did do the plumbing and the water pipes for my second bathroom. The cold water pipe is bow-shaped and tied with a wire, and the warm water pipe leaked. The latter was installed by a friend he recommended.

I am not having a baptism for James and I am not paying for musicians. I consider such events come with too many people and viruses for a small baby.  I would, however, like to have a functional second bathroom soon, and will try to make this happen.

I do worry over the future with Brexit and the US election results. I hope my children will be safe, and not have to live through the kind of experiences that Ana and her children had.