Mathematical Methods for Quantum Mechanics and General Relativity
Colloquium Series

The fifty-sixth meeting will be held Tuesday, November 28, 2017 in room L-213 at 4:00 PM. Trevor Gamble will speak.

Trevor proposed two talk titles: Journey Into The Demilitarized Zone: What Einstein's Equations Say About Black Holes And Other phenomena or, alternatively, A Very Small Grinch in Einstein's Theories ...

His description: "I'd like to start with what GR (and Physics as a whole) says about black holes, then see where that discussion takes us."


Ultimately, our goal for the year is to understand the nature of Gravity Waves and how calculations---such as the mass determinations of the LIGO events---can be carried out.

Most of the talks on Tuesday this year should be in aid of this project, so if you are thinking of speaking please bear that in mind.

On the math side this involves Differential Geometry and attendant disciplines such as Topology. On the Physics side this involves GR and Cosmology in general, but also understanding the extreme conditions near a precipitating event as well as the nature of spacetime over gigantic distances.

This room is also available on Thursday, and if you wish to share other topics we can set that up and announce it to the division for that day. (Just ask Larry Susanka to get that scheduled.)


Officially, talks start at 4:00 pm sharp, but the room (and coffee, tea and pastries) will be available to us for general (fairly random) arguments and discussions from 3:30 to 4:00. Sometimes these can be as entertaining as the talk itself.

Note to speakers: try very hard to make all your points by 5:00 pm, or save them for the next meeting in the 3:30-4 pre-meeting period.


Link to the Direct Progenitor Series, Hilbert Space for Quantum Mechanics, 87 Meetings from January 2013 to December 2015

Link to the Older Mathematics and Physics Colloquium Series, 45 meetings from January 2003 to May 2006


Here is Part I of some notes on Differential Geometry dealing with first derivative issues: tangent and cotangent spaces, differentials, solutions of DEs on a manifold and so on. This part is close to complete. Last modified on 02/26/17 at 13:34.

Here is Part II of these notes on Differential Geometry. This part is just started. Last modified on 08/15/16 at 21:24.

Here are some notes on tensors with every construction I can think of that doesn't involve derivatives. In these notes I focus on a single vector space V and two bases a and b. It is essentially linear algebra pushed a step or two farther. Last modified on 03/19/17 at 12:50.

Riemann's Lecture to the Göttingen Faculty, 1854 (taken from Spivak's "Comprehensive Introduction to Differential Geometry Vol II") Although only living to age 40 (1826-1886) the incredible richness and creativity of his accomplishments in pure mathematics and mathematical physics cannot be overstated. In addition to his eponymous integral he made fundamental contributions to Complex variables, Riemann surfaces, methods of series solutions to differential equations still in use, special functions, number theory, algebraic geometry and the beginning of manifold theory in higher dimensions. This last led to Felix Klein's Erlangen program and eventually to Einstein's General Relativity.

Here is a Wikepedia article on the metric tensor in GR, which might be interesting.

Physical Review Letters    Observation of Gravitational Waves from a Black Hole Merger  Abbot et al.    Last modified on 02/11/16 at 11:52.

Physics Today LIGO Detects Gravitational Waves April 2016 Issue   Observation of Gravitational Waves from a Black Hole Merger  Sung Chang    Last modified on 04/14/16 at 18:31.


Our first meeting of this new series was held Thursday, January 14th, 2016. Larry Susanka recapped part of the discussion of differentiable manifolds, a key structure in many areas of mathematical physics including the relativity theories, Lie theory and the Noether Theorems on the relationship between conserved quantities and symmetry of physical law. Our second meeting of the current series was held Thursday, January 21th, 2016. Larry Susanka continued the discussion of differentiable manifolds. Our third meeting of the current series was held Thursday, January 28th, 2016. Larry Susanka continued the discussion of tangent vectors and differentials on manifolds.
Our fourth meeting of the current series was held Thursday, February 4th, 2016. Robert Hobbs discussed the development and uses of the E-CLASS survey as an assessment of desirable attributes of a laboratory course in physics. Some discussion of the development, research context, and validation of the survey got us started. Some results from BC courses, national upper and lower division courses and typical outcomes will be presented on future dates. The discussin can then take several turns. Preliminary results for approaches to address detected deficiencies, other PER projects involving E-CLASS, examination of E-CLASS items (copies will be provided) are some of the possibilities. Our fifth meeting of the current series was held Thursday, February 18th, 2016. Robert Hobbs continued his discussion of the development and uses of the E-CLASS survey. Our sixth meeting of the current series was held Thursday, February 25th, 2016. Robert Hobbs finished his outline of the development and uses of the E-CLASS survey, though I am sure he will have more to say about this over time. After this initial discussion he talked about the recent Nobel-worthy advent of gravitational astronomy. "First light" was recorded at the gravity telescope at Hanford, the LIGO facility there.
Our seventh meeting was held Thursday, March 3, 2016. Larry Susanka discussed the tangent bundle of open subsets of the paradigm manifolds, Euclidean space. Our eighth meeting was held Thursday, March 10, 2016. Larry Susanka continued the discussion of the tangent and cotangent bundle of open subsets of the paradigm manifolds, Euclidean space. Our ninth meeting was held Thursday, March 17, 2016. Susanka continued to discuss the tangent and cotangent bundle of open subsets of Euclidean space.
Our tenth meeting was held Thursday, April 14. Larry Susanka continued to talk about manifolds. Here are some notes on open submanifolds of Euclidean space. Our eleventh meeting was held Thursday, April 21. Larry Susanka continued to talk about manifolds and this time we made it to the definition of the cotangent space. Our twelfth meeting was held Thursday, April 28, 2016. Larry Susanka talked about various convenient representations of tangent and cotangent vectors.
Our thirteenth meeting was held Thursday, May 5, 2016. Victor Polinger talked about phenomena associated with "wave-function collapse." Our fourteenth meeting was held Thursday, May 12, 2016. Kevin Wheelock began talking about relativistic issues; special first, general soon. Our fifteenth meeting was held Thursday, May 19, 2016. Sheila Dwyer [dwyer_s@ligo-wa.caltech.edu] a physicist from LIGO talked about things related to the recent first-observation of Gravity waves. This was followed by a public talk at 7 PM in Room N-201 where she discussed the discovery, and gravitational astronomy in general. The colloquium at 4:30 PM in Room B-251 focused on some techniques Dr. Dwyer created and used to "cheat" the uncertainty principle to reveal more information in the LIGO context than it would otherwise allow.
Our sixteenth meeting was held Thursday, May 26, 2016. Kevin Wheelock continued talking about relativistic issues; special first, general soon. Our seventeenth meeting was held Thursday, June 2, 2016 in room L-120. Larry Susanka talked about three representations of vector fields on a manifold. Our eighteenth meeting was held Thursday, June 9, 2016. Kevin Wheelock spoke on "Experimental observation of quantum entanglement of photons".
Our nineteenth meeting, the first of this academic year, was held Tuesday, September 27, 2016. Susanka talked about the Geometrization of Physics, the history of this gradual reformulation and why Differential Geometry is the toolbox we need to get the job done. Our twentieth meeting, was held Tuesday, October 4, 2016. Susanka continued to talk about the history of the Geometrization of Physics. Our twenty-first meeting, was held Tuesday, October 11, 2016. Susanka continued to talk about the history of the Geometrization of Physics.
Our twenty-second meeting was held Tuesday, October 25, 2016. Susanka continued to talk about the history of the Geometrization of Physics. Here are the final slides from the October 25 meeting. (October 25 was also the day future-nobelist Rainer Weiss gave his talk "Gravitational Wave: The Frontiers of Physics" at the UW Public Lecture Series at Keynes Hall.) Our twenty-third meeting was held Tuesday, November 1, 2016. Kevin Wheelock talked about the Heisenberg Uncertainty Principle. Our twenty-fourth meeting was held Tuesday, November 8, 2016. Kevin Wheelock spoke about an expanded table-top Bell-type experiment that he participated in at Whitman College.
Our twenty-fifth meeting was held Tuesday, November 15, 2016. Susanka and Polinger talked about the work of 2016 Nobel Physics Prize winners David Thouless, Duncan Haldane and Michael Kosterlitz. Our twenty-sixth meeting was held Tuesday, November 22, 2016. Kevin Wheelock talked about a Bell-type entanglement experiment. The twenty-seventh meeting was held Tuesday, November 29, 2016. Kevin Wheelock continued to discuss a Bell-type entanglement experiment. These results can be found in the very interesting book by Mark Beck (Whitman College in Walla Walla Washington) "Quantum Mechanics Theory and Experiment." This is a very interesting and well-written book aimed at upper division physics majors and is focussed on assembling the tools, starting from the basics, needed to understand entanglement issues.

Kevin spent time at Whitman and actually performed and/or observed the experiments described in his talk.

The twenty-eighth meeting was held Tuesday, January 10, 2017. Larry Susanka discussed a few of the issues needed to make sense of the symbols deployed in Einstein's field equation. The twenty-ninth meeting was held Tuesday, January 17, 2017. Larry Susanka discussed notation from Linear Algebra, needed to make sense of the symbols deployed in Einstein's field equation.

In addition, this week on Thursday there was also a special-session second talk on a subject of interest throughout the experimental sciences given by Robert Hobbs and which is quite important to our function as science educators. The topic was modeling of experimental data and the question of "outliers". This is woefully neglected in many science classes and Robert presented an interesting analysis of Snell's Law with student-acquired data and several interpretations of supposed "outliers."

The thirtieth meeting was held Tuesday, January 24, 2017. Larry Susanka discussed alternative coordinate-change notations. Here are some notes on Linear Algebra basics.
The thirty-first meeting was held Tuesday, January 31, 2017. Larry Susanka continued discussion of issues related to linear algebra and the symbols deployed in Einstein's field equation. The thirty-second meeting was held Tuesday, February 14, 2017. Larry Susanka continued saying good things about tensors. Attendees seemed partially convinced. The thirty-third meeting was held Tuesday, February 21, 2017. Larry Susanka finished the outline of tensor operatiions. Here are some slides with some of the information about these matters:
This is a moving target. Check here for the latest version. Last modified on 02/12/17 at 15:10.
The thirty-fourth meeting was held Tuesday, February 28, 2017. As you can see in the Wikipedia article General Relativity corresponds to facts (and their interpretation) about the metric tensor on the space-time manifold. Larry Susanka tried to carry on in that general direction. The thirty-fifth meeting was held Tuesday, March 14, 2017. Susanka talked about integration on singular n-cubes. The thirty-sixth meeting was held Tuesday, March 21, 2017. Susanka continued to talk about integration on manifolds.
The thirty-seventh meeting was held Tuesday, April 11, 2017. Integration on manifolds was still the topic. The thirty-eighth meeting was held Tuesday, April 18, 2017. We got side-tracked onto the unconventional convergence of divergent series, a topic of interest to Quantum Field Magicians .... Here are some notes. Last modified on 05/1/17 at 07:24. The thirty-ninth meeting was held Tuesday, April 25, 2017. Susanka continued with two separate topics: Unconventional Convergence and Integration on Manifolds.
The fortieth meeting was held Tuesday, May 2, 2017. Victor Polinger talked about convergence at the boundary of convergence of power series The forty-first meeting was held Tuesday, May 9, 2017. Steven Ziskind spoke about Fejer's Theorem on convergence of Fourier Series. This was Steven's inaugural talk at our seminar. The forty-second meeting was held Tuesday, May 16, 2017. Steven Ziskind continue to speak about Fejer's Theorem on convergence of Fourier Series and some consequences. Here are his notes.
The forty-third meeting was held Tuesday, May 23, 2017. Steven Ziskind continued to speak on various topics with a relation to Fourier Series. Here are his notes on the Gibbs Phenomenon. The forty-fourth meeting was held Tuesday, May 30, 2017. Steven Ziskind continued to speak on various topics with a relation to Fourier Series and the Gibbs Phenomenon. He then brought it home with some facts about prime numbers. The forty-fifth meeting was held Tuesday, May 30, 2017. Trevor Gamble talked about some recent developments in Cosmology. The Title: "Recent Measurements Stir Disagreement Among Top Big Bang Theorists ." This was Trevor's inaugural talk at our seminar.
The forty-sixth meeting was held Tuesday, June 6, 2017. Trevor Gamble continued to speak on recent ideas in Cosmology. The forty-seventh meeting was held Tuesday, September 26, 2017. Larry Susanka will spoke on the mathematics side of the history of the geometrization of Physics, from ancient to modern times. Here are the slides for this talk. The forty-eighth meeting was held Tuesday, October 3, 2017 in room L-213. Trevor Gamble spoke on the Physics-side of symmetry and geometrization. Title: "Development of Space-time: From Ether to Poincaré, Lorentz, Minkowski and Einstein."
The forty-ninth meeting washeld Tuesday, October 10, 2017.

Gwynne Crowder spoke: Searching for a background of gravitational waves with Advanced LIGO's first observing run

Over the course of Advanced LIGO's first observing run, many interesting insights have been gained from the first direct detection of gravitational waves. These include growing evidence for a population of coalescing massive black holes, which has been further bolstered by the recent joint detection with Advanced LIGO and Advanced Virgo. The detections of binary black hole mergers represent just one of the many kinds of science that can be achieved with these detectors. A potential source of gravitational waves is the stochastic gravitational-wave background, a background predicted from the combination of unresolved astrophysical and cosmological sources. This background offers a rich source of study through its potential to probe a wide variety of scenarios. In this talk, we discuss the search for the stochastic background in the first observing run and examine implications for the background from black hole mergers.

The fiftieth meeting was held Tuesday, October 17, 2017. Larry Susanka gave a compact introduction to the basic ideas of Group Theory. The examples of most interest to us are the Galilean group, the Poincaré group and its subgroup, the Lorentz group. These groups describe crucial symmetries associated with Newtonian and Special-Relativistic Mechanics in Euclidean and Minkowski space. This is the reason we need to understand the vocabulary and basic ideas of group theory. The actual Galilean group, the Poincaré groups will be discussed starting next week. The fifty-first meeting was held Tuesday, October 24, 2017. Larry Susanka talked about various matrix groups and the Quaternions and the Pauli spin group.

Here are slides with new material, but also including the slides from last week. (Last modified on 10/24/17 at 19:39.)

Here is a Maple worksheet to implement rotation with Quaternions.

Here is Rodrigues' formula which explains how to use a known-to-be-rotation matrix to easily find axis and rotation angle.

Finally (!!!) Here are my full quaternion notes with proofs of all the comments and formulae.

The fifty-second meeting was held Tuesday, October 31, 2017.

Kevin Wheelock discussed "Questions on Transforming Maxwell's Equations to a Moving Reference Frame."

The fifty-third meeting was held Tuesday, November 7, 2017. Larry Susanka talked about the philosophical underpinnings of Newtonian Mechanics and Special Relativity/Minkowski Geometry: how they are similar, and how they differ, with historical references. The fifty-fourth meeting was held Tuesday, November 14, 2017. Larry Susanka spoke. In order to understand the Relativity Principle in relativistic mechanics it helps to see how an equivalent concept plays out in a more familiar setting, the universe of Newton's Laws together with Galileo's admonitions concerning who should be trying to create simple physical law. In this talk we discussed Galilean-admissible observers and Newton's Laws.
The fifty-fifth meeting was held Tuesday, November 21, 2017. Larry Susanka spoke.

In order to understand the Relativity Principle in relativistic mechanics it helps to see how an equivalent concept plays out in a more familiar setting, the universe of Newton's Laws together with Galileo's admonitions concerning who should be trying to create simple physical law.

In this talk we finished our discussion of Galilean-admissible observers and Newton's Laws with some examples (conservation of momentum and energy) and paved the way to talk about the Lorentz transformations and analogous ideas from the world of Special Relativity.

Here are the slides from the last few talks.

If you wish to contact someone about these seminars send email to Larry Susanka at lsusanka@bellevuecollege.edu or call (425) 564-2484.

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