Tag Archives: Einstein’s theory of general relativity

A mathematical sculptor, a live webcast (May 6, 2020) with theoretical cosmologist and author Katie Mack, & uniting quantum theory with Einstein’s Theory of General Relativity in a drawing

I’ve bookended information about the talk with physicist Katie Mack at Canada’s Perimeter Institute on May 6, 2020 with two items on visual art and mathematics and the sciences.

Mathematical sculpting

Robert Fathauer’s Three-Fold Hyperbolic Form exhibits negative curvature, a concept in geometry and topology that describes a surface curving in two directions at every point. Hemp crochet by Marla Peterson. Image courtesy of Robert Fathauer. [downloaded from https://www.pnas.org/content/114/26/6643.full]

You’ll find this image and a few more in a fascinating 2017 paper (see link and citation below) about mathematical sculpture,

Ferguson [Helaman Ferguson], who holds a doctorate in mathematics, never chose between art and science: now nearly 77 years old, he’s a mathematical sculptor. Working in stone and bronze, Ferguson creates sculptures, often placed on college campuses, that turn deep mathematical ideas into solid objects that anyone—seasoned professors, curious children, wayward mathophobes—can experience for themselves.

Mathematics has an intrinsic aesthetic—proofs are often described as “beautiful” or “elegant”—that can be difficult for mathematicians to communicate to outsiders, says Ferguson. “It isn’t something you can tell somebody about on the street,” he says. “But if I hand them a sculpture, they’re immediately relating to it.” Sculpture, he says, can tell a story about math in an accessible language.

Here’s a link to and a citation for the paper,

Science and Culture: Armed with a knack for patterns and symmetry, mathematical sculptors create compelling forms by Stephen Ornes. PNAS [Proceedings of the National Academy of Sciences] June 27, 2017 114 (26) 6643-6645; https://doi.org/10.1073/pnas.1706987114

This paper appears to be open access.

Live webcast: theoretical cosmologist & science communicator Katie Mack

The live webcast will take place at 4 pm PT (1600 hours) on Wednesday, May 6, 2020. Here’s more about Katie Mack and the webcast from the event webpage (click through to the event page to get to the webcast) on the Perimeter Institute of Theoretical Physics (PI) website,

In a special live webcast on May 6 [2020] at 7 pm ET [4 pm PT], theoretical cosmologist and science communicator Katie Mack — known to her many Twitter followers as @astrokatie — will answer questions about her favourite subject: the end of the universe.

Mack, who holds a Simons Emmy Noether Visiting Fellowship at Perimeter, will give viewers a sneak peek at her upcoming book, The End of Everything (Astrophysically Speaking). She will then participate in a live “ask me anything” session, answering questions submitted via social media using the hashtag #piLIVE.

Mack is an Assistant Professor at North Carolina State University whose research investigates dark matter, vacuum decay, and the epoch of reionization. Mack is a popular science communicator on social media, and has contributed to Scientific American, Slate, Sky & Telescope, Time, and Cosmos.

PI is located in Waterloo, Ontario, Canada.

Uniting quantum theory with Einstein’s Theory of General Relativity with a drawing about light

The article by Stephon Alexander was originally published March 16, 2017 for Nautilus. My excerpts are from a getpocket.com selection,

LIGHT IN THE GARDEN: This drawing by the Oakes brothers, Irwin Gardens at the Getty in Winter, inspired the author to think anew about quantum mechanics and general relativity. The meticulous drawing, done on curved paper, allows viewers to reflect on the act of perception. Credit: Ryan and Trevor Oakes [downloaded from http://nautil.us/issue/46/balance/what-this-drawing-taught-me-about-four_dimensional-spacetime]

My aim as a theoretical physicist is to unite quantum theory with Einstein’s Theory of General Relativity. While there are a few proposals for this unification, such as string theory and loop quantum gravity, many roadblocks to a complete unification remain.

Einstein’s theory tells us the gravitational force is a direct manifestation of space and time bending. The sun bends the fabric of space, much like a sleeping person bends a mattress. Planetary orbits, including Earth’s, are motion along the contours of the bent space created by the sun. This theory provides some critical insights into the nature of light.

… one summer, I had the most unexpected breakthrough. Beth Jacobs, a member of the New York Academy of Sciences’ Board of Governors, invited me and some friends to her New York City apartment to meet the Oakes twins, artists who have gained attention in recent years for their drawings as well as the innovative technique and inventions they deploy to create them. An Oakes work, Irwin Gardens at the Getty in Winter (2011), an intricate drawing of the famous gardens designed by Robert Irwin at The Getty Museum in Los Angeles, was displayed on the balcony of Jacobs’ apartment overlooking Central Park, with the backdrop of the New York City skyline lit with a warm orange sky moments before sunset.

As I gazed at the drawing, I could feel the artists challenging me to reconsider the nature of light. I began to realize I should consider not only the physics of light, but also how light information is perceived by observers, when theorizing and conceiving new principles to unify quantum mechanics and general relativity. …

Ryan and Trevor Oakes, 35, have been exploring the impact and intersection of visual perception and the physics of light since they were kids. After attending The Cooper Union for the Advancement of Science and Art in New York City, and years of experimentation and inventing new techniques, the twins exploited the notion that light information is better described when originating from a spherical surface.

Fascinating stuff. BTW, you can find the original article here on Nautilus.

Time traveling at the University of British Columbia

Anyone who dreams of timetraveling is going to have to wait a bit longer as this form of timetraveling is theoretical. From an April 27, 2017 news item on ScienceDaily,

After some serious number crunching, a UBC [University of British Columbia] researcher has come up with a mathematical model for a viable time machine.

Ben Tippett, a mathematics and physics instructor at UBC’s Okanagan campus, recently published a study about the feasibility of time travel. Tippett, whose field of expertise is Einstein’s theory of general relativity, studies black holes and science fiction when he’s not teaching. Using math and physics, he has created a formula that describes a method for time travel.

An April 27, 2017 UBC at Okanagan news release (also on EurekAlert), which originated the news item, elaborates on the work.

“People think of time travel as something fictional,” says Tippett. “And we tend to think it’s not possible because we don’t actually do it. But, mathematically, it is possible.”

Ever since H.G. Wells published his book Time Machine in 1885, people have been curious about time travel—and scientists have worked to solve or disprove the theory. In 1915 Albert Einstein announced his theory of general relativity, stating that gravitational fields are caused by distortions in the fabric of space and time. More than 100 years later, the LIGO Scientific Collaboration—an international team of physics institutes and research groups—announced the detection of gravitational waves generated by colliding black holes billions of light years away, confirming Einstein’s theory.

The division of space into three dimensions, with time in a separate dimension by itself, is incorrect, says Tippett. The four dimensions should be imagined simultaneously, where different directions are connected, as a space-time continuum. Using Einstein’s theory, Tippett explains that the curvature of space-time accounts for the curved orbits of the planets.

In “flat” or uncurved space-time, planets and stars would move in straight lines. In the vicinity of a massive star, space-time geometry becomes curved and the straight trajectories of nearby planets will follow the curvature and bend around the star.

“The time direction of the space-time surface also shows curvature. There is evidence showing the closer to a black hole we get, time moves slower,” says Tippett. “My model of a time machine uses the curved space-time—to bend time into a circle for the passengers, not in a straight line. That circle takes us back in time.”

While it is possible to describe this type of time travel using a mathematical equation, Tippett doubts that anyone will ever build a machine to make it work.

“H.G. Wells popularized the term ‘time machine’ and he left people with the thought that an explorer would need a ‘machine or special box’ to actually accomplish time travel,” Tippett says. “While is it mathematically feasible, it is not yet possible to build a space-time machine because we need materials—which we call exotic matter—to bend space-time in these impossible ways, but they have yet to be discovered.”

For his research, Tippett created a mathematical model of a Traversable Acausal Retrograde Domain in Space-time (TARDIS). He describes it as a bubble of space-time geometry which carries its contents backward and forward through space and time as it tours a large circular path. The bubble moves through space-time at speeds greater than the speed of light at times, allowing it to move backward in time.

“Studying space-time is both fascinating and problematic. And it’s also a fun way to use math and physics,” says Tippett. “Experts in my field have been exploring the possibility of mathematical time machines since 1949. And my research presents a new method for doing it.”

Here’s a link to and a citation for the paper,

Traversable acausal retrograde domains in spacetime by Benjamin K Tippett and David Tsang. Classical and Quantum Gravity, Volume 34, Number 9 DOI: https://doi.org/10.1088/1361-6382/aa6549 Published 31 March 2017

© 2017 IOP Publishing Ltd

This paper is behind a paywall.