Prof. Barak Shoshany's Website 
Hi! My name is Barak Shoshany (ħe/ħim) and I am a theoretical, mathematical, and computational physicist. I work as an Assistant Professor of Physics at Brock University, where I recently won the FMS Award for Excellence in Teaching. I am also a Sessional Lecturer of Computational Science at McMaster University. My research focuses on the nature of time and causality in general relativity and quantum mechanics, as well as symbolic and highperformance scientific computing. In my spare time I am also a multiinstrumentalist and composer. You can find my CV here. 
Table of contents 
Course websites and lecture notes ^PHYS 3P94: Mathematical Methods in Physics ASTR 1P01/02: Introduction to Astronomy I/II PHYS 4P51: Quantum Mechanics CSE 701: Foundations of Modern Scientific Programming ASTR 2P42: Astrophysics & Cosmology PHYS 1P22/92: Introductory Physics II PHYS 1P21/91: Introductory Physics I PHY 256: Introduction to Quantum Physics FasterThanLight Travel and Time Travel Lie Groups and Algebras Quantum Theory 
Employment ^

Education ^

Teaching and course development ^Undergraduate and graduate courses taught as course instructor:
Minicourses taught at various programs for highschool, undergraduate, or graduate students at Perimeter Institute:
Teaching assistant for graduate courses:

Research interests ^I am a theoretical, mathematical, and computational physicist. During my graduate studies, my research focused primarily on quantum gravity. For my MSc thesis, I explored the concept of relative locality in string theory under the supervision of Laurent Freidel. For my PhD thesis, I provided proof of a fundamental relationship between continuous and discrete spacetime geometries in loop quantum gravity, supervised by Laurent Freidel and done in collaboration with Florian Girelli. This research was published in three papers, two in Physical Review D (1, 2) and a third in Classical and Quantum Gravity. Working on quantum gravity has allowed me to develop a broad expertise in general relativity, quantum mechanics, quantum field theory, and related areas of mathematics. After I received my PhD, I decided to focus on classical and semiclassical general relativity. I am particularly interested in the nature of time and causality, especially the possibility and consequences of causality violations. My other major research interest is scientific computing and computational physics, focusing on both symbolic and numerical computations. Time and causalityMotivationTime and causality are two of the most fundamental concepts in physics, and yet they remain poorly understood. In my research I use general relativity and quantum mechanics, two cornerstone theories of physics with great theoretical and experimental success, to investigate one of the most exciting and thoughtprovoking questions about time and causality: whether causality can be violated. The two most commonly known manifestations of causality violation are fasterthanlight (FTL) travel and time travel. In time travel, the traveler directly violates causality by traveling to their own past. In FTL travel, the traveler merely travels so fast that they can causally influence events they could not have otherwise  but as it turns out, if FTL travel is possible, then it could hypothetically be used to facilitate time travel. Can these concepts be transformed from science fiction into real science, even just in principle? The answer to this question is currently unknown, and this indicates a major deficiency in our understanding of the universe. A positive answer would revolutionize physics and require substantial rewriting of our existing theories. A negative answer would provide valuable insights into the inner workings of our theories, by figuring out the mechanisms by which our universe protects causality, as first conjectured by Stephen Hawking. The ultimate goals of this research are to enhance our understanding of how time and causality work in our universe, expand and improve our fundamental theories of nature, and lay the foundations for future technological and scientific advancements. Time travel paradoxesGeneral relativity admits solutions to the Einstein equations containing closed timelike curves (CTCs), which can hypothetically be used to travel to the past and violate causality. It is currently unknown whether such spacetime geometries are permissible in our universe. However, if they are, and time travel is possible, this would lead to time travel paradoxes, which must be resolved. Two main types of time travel paradoxes frequently appear in the theoretical physics literature. The first type is consistency paradoxes, where time travel to the past creates a chain of events that ends up preventing the journey through time from happening in the first place. For example, if Alice puts a bomb inside the time machine and sends it a few minutes to the past, then when the bomb arrives, it will kill Alice, or even destroy the time machine itself; but in that case, Alice will not be able to send the bomb through the time machine after all. This chain of events is inconsistent, and hence paradoxical. The second type of time travel paradoxes is bootstrap paradoxes, where an event causes itself  or more precisely, the chain of events is a closed loop, with no cause outside the loop. For example, consider the scenario where Bob is working on a new book, but struggling with writer's block. He builds a time machine, opens it, and finds the finished book inside. Bob publishes the book, and becomes a bestselling author. A few years later, he sends the book to his past self using the time machine. In this case, everything is perfectly consistent, so we do not have a consistency paradox; and yet, the entire chain of events has no external cause, and the book appears to have been created out of nothing. Proposed resolutionsOne proposed way to resolve time travel paradoxes, known as the Novikov selfconsistency conjecture, suggests that one can simply never make any changes to the past. Any attempts to change the past will necessarily fail, or even bring about the very future they tried to prevent. If the past cannot be changed, then there is also no possibility of paradoxes. In more technical terms, Novikov's conjecture proposes that local solutions to the equations of motion must also be globally selfconsistent. In other words, any attempt to create an inconsistency, despite seemingly being possible according to all local laws of physics, will not work because it will violate global consistency. This means that the probability of any event that would cause a consistency paradox must be exactly zero, and only initial conditions leading to selfconsistent evolutions are allowed. In the consistency paradox described above, where Alice tries to kill her past self by sending a bomb back in time, the selfconsistency conjecture implies that this goal cannot possibly be achieved. Perhaps the bomb fails to explode, or perhaps it does explode, but pastAlice survives. The bootstrap paradox, however, cannot be resolved by the selfconsistency conjecture, as it contains no inconsistencies and is therefore fully compatible with it. Another possible resolution of time travel paradoxes discussed in the literature is parallel timelines, also known as multiple histories. In this scenario, time travel necessarily results in creating a new timeline, or equivalently, splitting one timeline into two. Consistency paradoxes are then resolved because changes to the past can only influence events in the new timeline, and thus cannot prevent time travel from being initiated in the original timeline. Bootstrap paradoxes are also resolved, because the chain of events is no longer a closed loop, and any event which seemingly has no cause in the new timeline can have its cause in the original timeline. Let us consider how the consistency paradox is resolved in the parallel timelines approach. Alice is alive in timeline 0, and therefore she is able to send a bomb back in time. The bomb arrives in a separate timeline, timeline 1, where it kills Alice. However, the fact that Alice is dead in timeline 1 does not create an inconsistency, as the bomb was sent by Alice of timeline 0, who is alive and well. The bootstrap paradox can also easily be resolved using parallel timelines. In timeline 0, Bob works hard and eventually finishes writing his book. He then sends the book back in time. The book arrives in a separate timeline, timeline 1, where Bob benefits from it without having to do the work. However, the book was clearly not created from nothing; it was created by Bob of timeline 0. My contributionsMy first contribution in the field of causality and its violations was an uptodate, comprehensive, and selfcontained review of FTL travel and time travel based on our current understanding of general relativity and quantum field theory, covering everything from basic concepts to recent developments. This review was published in SciPost Physics Lecture Notes. My most significant contribution so far is my work on time travel paradoxes. In a series of three papers, the first published in Physical Review D, the second in General Relativity and Gravitation, and the third currently under review, I proposed several arguments against the validity of the selfconsistency conjecture. Most importantly, I showed that there are some concrete time travel paradox models that simply cannot be made selfconsistent, as they generate an inconsistency with probability 1 for any initial condition. I provided a rigorous mathematical proof that these paradoxes can nonetheless be resolved using parallel timelines. In my third paper, I proposed a new mechanism for resolving paradoxes with parallel timelines, within the framework of the Everett or "manyworlds" interpretation of quantum mechanics. In my model, called "entangled timelines" or ECTCs, the timelines are created by quantum entanglement between the time machine and the environment. As the entanglement gradually spreads out to additional systems, the timelines spread out as well, providing a local and welldefined alternative to the naive "branching timelines" picture often presented in the literature. My model differs from Deutsch's familiar DCTC model, and improves upon it by using only pure states and providing a concrete definition of the timelines using entanglement. Aside from time travel paradoxes, I am also interested in the possibility of FTL travel. In particular, I am very interested in warp drives, which are a class of spacetime metrics that appear to allow FTL travel by exploiting a loophole in general relativity: while one cannot move FTL within space, it is possible for space itself to move at arbitrary speeds. However, warp drives violate the energy conditions, which means they require impossibly large amounts of matter with negative energy density. It has often been suggested in the literature that FTL travel can be used to facilitate time travel, particularly in the context of warp drives. In a paper currently under review, I constructed a spacetime geometry with two warp drives, which explicitly contains closed timelike geodesics; to my knowledge, this has never been explicitly done before. To achieve this goal, I created a warp drive that can "land", that is, finish its journey at rest in a different reference frame  a subtle but important issue that has so far never been discussed in the literature. Ongoing researchOne of my current research goals is to find a concrete definition of what it means for a spacetime metric to support FTL travel. There are several such definitions in the literature, but they are not consistent with each other; perhaps there can be a definition that encompasses all of them, or perhaps some definitions could be disregarded due to being too strong or too weak. Another one of my ongoing projects explores the creation of wormholes. All currently established wormhole metrics are eternal  there is no known way to actively create a wormhole where it did not exist before. Interestingly, almost no work has been done to solve this problem so far, despite the fact that it is extremely important for "practical" applications (given sufficiently advanced technology). As a first step toward solving this problem, I am currently trying to find a metric describing a traversable wormhole that only exists for a finite amount of time; so far, all attempts to write down such a metric resulted in a naked singularity, and hence a nontraversable wormhole. Finally, I have recently been working on a new model for FTL travel called "hyperspace". In this model, our universe is a 3+1D brane inside a higherdimensional "bulk", as in some brane cosmology models; the extra dimension is referred to as "hyperspace". The metric is designed such that one can leave the brane, travel through hyperspace, and then return to the brane, having traveled along a timelike geodesic throughout the journey, but along an effective spacelike geodesic from the point of view of the brane itself. Scientific computingMy other main research interest is scientific computing, especially in the form of writing software for scientific use, for both symbolic and numerical computations. One of my main goals is making scientific computing more userfriendly and accessible to both novice students and established researchers. For this purpose, I write software packages and libraries with special focus on producing clear, lightweight, thoroughlydocumented, and easytouse code, which is made freely and publicly available on my GitHub page. In symbolic computation, I am interested in implementing advanced concepts in mathematics and physics using computer algebra systems. I am the author of OGRe, an objectoriented general relativity package for Mathematica, intended to streamline and simplify symbolic calculations in general relativity and differential geometry. I am also currently working on porting this package to Python. This package has been published in the Journal of Open Source Software, and has a modest but steadily increasing number of citations and GitHub stars. In numerical computation, I am interested in writing highperformance software for scientific research using optimized algorithms, multithreading, cluster computing, GPU programming, and other modern techniques. My C++ thread pool class, which provides a robust, compact, and selfcontained interface for enabling multithreading in highperformance scientific software, is one of my most popular opensource projects on GitHub, with over 1,600 stars and 200 forks, and a very active community; the companion paper (currently under review) is my most cited scientific computing paper. 
Research students ^If you are interested in doing research under my supervision at Brock University, either at the undergraduate or graduate level, please feel free to contact me! Alessandro Pisana Alessandro received his BSc and MSc in physics from the University of Padua in Italy, and was an Erasmus student at AixMarseille University in France. For his master's thesis, he worked on the interface of quantum gravity and tensor networks. He started his PhD in my group at Brock University in September 2022. Gabriela Valencia Gabriela, an undergraduate student at the University of Valle, did a research project under my supervision, as part of the Mitacs Globalink Research Internship, from June to August 2023. In her project, Gabriela expanded the entangled timelines model previously developed with my student Zipora Stober to account for more general and/or sophisticated paradox scenarios. Gabriela presented her project in the 2023 Brock Undergraduate Research Symposium. Mark Sun Mark, a grade 12 student at Sir Winston Churchill Secondary School in St. Catharines, did a research project under my supervision, as part of the Faculty of Mathematics and Science Mentorship Program, from September 2022 to February 2023. In his project, Mark analyzed popular depictions of time travel in science fiction, how they resolve time travel paradoxes, and whether they are compatible with known physics. Mark presented his project at the 2023 FMS Mentorship Program Symposium. Ben Dobozy Ben, an undergraduate student at the University of Toronto, did a research project under my supervision, funded by the NSERC USRA award, from September to December 2022. In his project, Ben worked on developing a concrete mathematical definition of fasterthanlight travel in general relativity, which is a necessary step toward understanding its feasibility and consequences. Ben presented his project at the 2023 Canadian Undergraduate Mathematics Conference (CUMC). A video of his talk is available on YouTube. Ben Snodgrass Ben, an undergraduate student at Durham University, did a research project under my supervision, as part of the Mitacs Globalink Research Internship, from June to September 2022. He is currently a graduate student at Cambridge University. In his project, Ben worked on creating a generalized model for warp drives that can "land", i.e., finish their journey at rest in a different reference frame, and used them to construct an explicit model demonstrating that fasterthanlight travel can lead to time travel. The results were published in our paper "Warp Drives, Rest Frame Transitions, and Closed Timelike Curves". Zipora Stober Zipora, an undergraduate student at the University of Aberdeen, did a research project under my supervision, as part of the Mitacs Globalink Research Internship, from May to August 2022. She is currently pursuing a PhD in astrophysics at the University of North Carolina at Chapel Hill. In her project, Zipora worked on developing a new model for resolving time travel paradoxes by generating new timelines using quantum superposition and entanglement. The results were published in our paper "Time Travel Paradoxes and Entangled Timelines". Jared Wogan Jared did a summer research project under my supervision, funded by the Brock Match of Minds Award, from May to August 2021. He then continued to do a research project under my supervision towards an undergraduate thesis, from September 2021 to April 2022. He is currently pursuing a PhD in quantum gravity at the University of Western Ontario. In his first project, Jared worked on making the model previously published with my student Jacob Hauser more realistic, in order to strengthen our argument that time travel necessarily leads to multiple histories. The results were published in our paper "Wormhole Time Machines and Multiple Histories". In his second project, Jared worked on developing a Python port of OGRe, my objectoriented general relativity package for Mathematica. The new Python package, OGRePy, will be released soon. Alicia Savelli Alicia did a research project under my supervision towards an undergraduate thesis, from January to December 2021. At the time she was an undergraduate student at Brock University. She is currently pursuing a PhD in astrophysics at the University of Toronto. In her project, Alicia worked on showing that if a warp drive is defined in 5 spacetime dimensions, rather than the usual 4, then the negative energy requirements can be reduced to an arbitrarily small amount. The results will be published soon. Michael Astwood Michael did a summer research project under my supervision, funded by the BUAF Explore Grant, from May to August 2021. At the time he was an undergraduate student at the University of Waterloo. He is currently pursuing an MSc in mathematics at Wilfrid Laurier University. In his project, Michael worked on developing and analyzing a variety of different approaches towards formulating a concrete mathematical model of spacetimes with multiple histories, using both analytical and computational techniques. Katie Curvelo Katie, an undergraduate student at McMaster University, did a summer research project under my supervision, funded by the BUAF Explore Grant, from May to August 2021. In her project, Katie worked on deriving the exact conditions under which fasterthanlight travel can lead to time travel, for both tachyons and warp drives, with either constant velocity or constant acceleration. The results are posted on GitHub. Jacob Hauser Jacob did a summer research project under my supervision, as part of the Perimeter Institute undergraduate summer program, from June to August 2019. At the time he was an undergraduate student at Pomona College. Later, he was an MSc student in the Perimeter Scholars International program. He is currently pursuing a PhD in physics at UCSB. In his project, Jacob worked on proving that if time travel is possible, then multiple histories must also be possible, using a model of a time travel paradox that cannot be resolved by assuming Novikov selfconsistency. The results were published in our paper "Time Travel Paradoxes and Multiple Histories". Mir Jalal Jalal did a summer research project under my supervision, as part of the Perimeter Institute undergraduate summer program, from June to August 2019. At the time he was an undergraduate student at Forman Christian College in Pakistan. The project was cosupervised with Daniel C. Guariento of Perimeter Institute. In his project, Jalal explored various modifications to the warp drive metric, to see if they might reduce the amount of negative energy required. He also attempted to find a specific classical or quantum field that could be used as a hypothetical source of exotic matter. 
Publications ^The following is a comprehensive list of my scientific publications. Students under my supervision are indicated in red. Authors are always ordered alphabetically by last name, not by level of contribution. All of my publications are, and will always be, freely accessible to everyone. The openaccess arXiv preprints have the same content as the published versions, and often also include postpublication fixes and updates that are missing from the journal versions. Therefore the arXiv version should always be preferred over the journal version, especially in cases where a paper was published in a nonopenaccess journal.
See also: arXiv  INSPIRE  ORCID  Google Scholar 
Scientific computing projects ^Programming and markup languages I am highly proficient with include:
My past and present scientific computing projects include:
Source code for all of my projects is and always will be freely and publicly available on my GitHub profile. 
Grants and awards ^

Talks and conferences ^

Media interviews ^
See also this YouTube playlist which includes all of the interviews that were made available on YouTube. 
Outreach activities ^

Service and organization ^Award committee memberships:
Professional memberships:
Organizing committee memberships:
Supervisory committee memberships:Hooman Nanchian
Mahdieh Gol Bashmani Moghadam
Jaskaran Maan
Comprehensive examination committee memberships:Samin Tajik

Music compositions ^I like to compose music in a wide variety of genres, including classical, progressive rock, metal, and electronic. Some of my older compositions (songs in Hebrew, not featured here) were even broadcast on Israeli radio and TV. My first album, "Travel Music About Time", contains the following 5 tracks. Please see my SoundCloud page, or click on the links below, to listen to the tracks for free.
The album is also available on many music streaming services, including Spotify, YouTube Music, Amazon Music, Deezer, Apple Music, and more! 
Other hobbies ^I love playing board games and tabletop roleplaying games. I ran my own original Dungeons & Dragons campaign from May 2016 to December 2018, as well as other campaigns using the Dungeons & Dragons, Numenera, and Mutants & Masterminds game systems. My other hobbies include computer games, science fiction and fantasy, and standup comedy. 
Photo gallery ^Please click on the photos for higher resolution. 
"There is a theory which states that if ever anyone discovers exactly how to quantize gravity, the universe will instantly disappear and be replaced by a universe in which quantizing gravity is even harder. There is another theory which states that this has already happened."  Paraphrased from "The Restaurant at the End of the Universe" by Douglas Adams 