A Brief Definition of Spacetime
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Doing Physics with
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doug <sweetser@alum.mit.edu>
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The Book

A one page summary of my unified field model for gravity and EM is available here: pdf
A technically detailed Mathematica notebook starts from the Lagrange density for unifying gravity and EM, and gets to two experimental tests that can confirm or reject the proposal (available as html, pdf, or .nb)
Talk entitled "Realizing Einstein's Dreams: Unifying Gravity and Light, and Why Quantum Mechanics is Weird" for the Spring NE Section of the APS/AAPT (html or pdf)
Talk entitled "Why a Rank 1 Unified Field Theory is Compelling and Its Background Mathematical Structure" for the 8th Eastern Gravity Meeting (html or pdf)
Talk entitled "Unifying Gravity and EM by Generalizing EM" for the 7th Eastern Gravity Meeting (html or pdf)
Poster for Brookhaven National Lab meeting, "Unifying Gravity and EM by analogies to EM" (pdf).
A more formal presentation of the unified field model is available here: pdf (v1.4, 18 pages).

MIT IAP course: "Unifying gravity and EM by analogies with EM"
Slides available.
Day 1: Lagrange Densities (html or pdf)
Day 2: Fields and Quantum Mechanics (html or pdf)
Day 3: Forces, Metrics, and New Physics (html or pdf)

The Cosmological Consequences of the Chain Rule (pdf), slides for a 15 minute talk at joint APS/AAPT meeting, March., 2004. A Universe with zero dark matter is good :-)

4-potential Equations for Gravity and Electromagnetism (pdf), slides for a 15 minute talk at a joint APS/AAPT meeting, Oct., 2003.

Dynamic graphs, a way to visualize complex numbers and quaternions using animations. Uses gif, so all can see for the first time the cosine of a quaternion! This is hugely fun, honest.
Figuring out stuff takes time (money) and money. If I can raise $0.3 K, that will cover a local meeting, $2 K would mean I could buy Mathematica (used a student version for a decade), $5.2k would go for a Mac with Final Cut Pro (making "Stand-Up Physicist" teaching videos) and $30 K would mean a year devoted to math and physics. This stuff may be important enough for me to ask so directly for funding.
Intro, Mathematics, Classical, SR, EM, QM, G, Conclusions
An overview
A brief history of quaternions
Mathematics (.pdf)
Multiplying quaternions the easy way
Inner and outer products
Scalars, vectors, tensors and all that
Quaternion analysis (.pdf)
Where quaternions fit in math, adapted from Max Tegmark, 1998.
Tools for algebra, trig, logs... and a Quaternion calculator (in Java)
An open source project QEMation to develop Quaternion Equation driven aniMation. The first result of this effort, Visualizing Constant Inertia , is more interesting from a math/physics perspective than one might guess.

F = m a: Classical Mechanics (.pdf)
F = m a, in an inertial frame, in polar coordinates, and in a rotating reference frame
The simple harmonic oscillator and wave equation
4 tests for a conservative force

E = m c squared: Special Relativity (.pdf)
Doing the work of the Lorentz group with rotations and dilations
An alternative algebra for boosts

Problem set questions and solutions from MIT's 8.033, Classical and Relativistic Mechanics
Index and links to solved problems
PS 1: Kinematic effects of relativity
PS 2: More kinematic effects
PS 3: The Lorentz transformation and the addition of velocities
PS 4: The Doppler effect, 4- vector invariants, and the twin paradox
PS 5: Energy, Mass and Momentum
PS 6: The Compton effect and threshold collision problems

Curl B = 0: Electromagnetism (.pdf)
Classical electrodynamics
Electromagnetic field gauges
The Maxwell equations in the light gauge: QED?
The Lorentz force
The stress-energy-momentum 2-tensor of the electromagnetic field

bra phi cket psi Quantum Mechanics (.pdf)
Bracket notation & quaternions: quaternions as a complete inner product space
Multiplying polar representations (without Campbell-Hausdorff!)
Commutators and the uncertainty principle
Unifying the representations of spin and angular momentum
The Schrödinger equation
The Klein-Gordon equation
Time reversal

F = G M m/r squared: Gravity (.pdf)

Einstein's vision
Einstein spent the last forty years of his life trying to unify gravity and electromagnetism in a way that also lead to a new subtle understand of quantum mechanics. Just like for special relativity and general relativity, he was looking for a new logical foundation that would not change any experimental tests much at all. For a general audience, there is a slide presentation for ways of thinking about events using quaternions.

A draft paper ( pdf, v1.4) and notes for a talk (pdf) on unifying gravity and electromagnetism in a way that can be quantized are available. This method contains no quaternions, but the algebra is based on that earlier effort.

To a degree that has really surprised me, the pair of papers (last updated September 2001) is a work in progress towards that goal:

A paper was submitted to a peer review journal on the content of the second paper, with all references to quaternions deleted :-) You may read a summary of that process, along with a call for papers , the submission , and comments from the first referee , second referee , and editor. I learned, so it was good.
Strings and Relativistic Quantum Gravity
A slide presentation of string ideas, small movies, little math
Answering prima facie questions in quantum gravity using quaternions (post to s.p.r)
The length of a quaternion in curved spacetime: a close relative of the affine parameter of general relativity
General metrics
Gravitational redshift experiments

A summary of physics equations written as quaternions

Stuff to get

A few good papers:
  1. Sudbery's first paper (memo, 1977, 44 pages) on why quaternion analysis is no good.
  2. Sudbery's second paper (1979, 28 pages) on the topic. Please look to my work above on quaternion analysis for a much better alternative!.
  3. C. A. Deavours paper, "The Quaternion Calculus". My critique is that using his definition of a quaternion derivative, if a function like f=q is analytic in q, f^2 is not. That indicates a better definition must be found before quaternion analysis can really begin.
  4. Salamin's paper (1979, 9 pages) on rotations.
  5. Howell and Lafon's paper (1975, 13 pages) on the efficiency of quaternion multiplication.
  6. Silberstein's paper (1912, 20 pages) on using biquaternions for quaternion special relativity. Biquaternions are NOT an algebraic field, and are not used in any operations on this web site.

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Doug's background in physics
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Intro, Mathematics, Classical, SR, EM, QM, G, Conclusions

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