Lacking the papers to prove I am a theoretical physicist, I have built something working class: a lunchbox

The box contains Yoplait Yogurt, Del Monte 100 Calorie Mixed Fruit, and White Cheddar Cheese Smart Food Pop Corn (note: all product placements are unpaid). The apple included indicates I work on gravity.

[The video is a reading of the content contained herein, so click or skip]

Near the handle is the name I use to encompass this work, GEM, for Gravity and EM.
The acronym has already been taken by gravitomagnetism. English is full of words with multiple meanings, so I hope people will tolerate my use of GEM for a unified standard model using quaternions and hypercomplex numbers. GEM sounds of more valuable than GSM.

One of the main panels features the following quote:
How can physics live up to its true greatness except by a new revolution in outlook which dwarfs all its past revolutions? And when it comes, will we not say to each other: “Oh how beautiful and simple it all is! How could we have missed it for so long?

- John Archibald Wheeler
Along with Misner and Thorne, Wheeler wrote the telephone book “Gravitation”. This is an unexpected vision coming from someone with so much depth on the subject.

What is my beautiful and simple idea? Newton’s math required he claim that space and time are absolutes, separate from each other. In 1905, Einstein showed how time could rotate into space for travelers with constant velocity. A decade later using math that remains arduous, time and space are free to combine. We lack the math chops to work on anything except the simplest cases. I propose that time and space must always be together without dimensions so that events in spacetime can be added, subtracted, multiplied, and divided however the physical situation warrants. Time has no choice but to play with space in ways that will boggle the eye and mind.

“Gray Albert” and “Turquoise Einstein” are a pair of oil paintings I did that hang in my living room. Einstein’s hair was not bright yellow, nor did he have a silver or gold front tooth. The paintings bring me joy, so I am glad to carry a reminder on the box.

Here is the featured equation:

$J_q-J_m=\square^2 A$
The Maxwell equations in the Lorenz gauge are here. For a period of several years, I thought gravity could be accounted for with the other current density. It cannot. The lunchbox is wrong, at least at the field theory level. I like making as specific a proposal as possible to then learn from the errors.

One problem is with the eight degrees of freedom on the left that are not reflected on the right. When the fully relativistic Maxwell equations are quantized, I remain skeptical about the non-physical scalar and longitudinal modes of emission found. Like others before, I thought there was a chance to do something with those modes.

Alas, the real killer turns out to be subtle. The current coupling term in the Lagrange density, JA, hides a flaw. How could two letters cause an issue?  Feynman shows in chapter 3 of “Lecture Notes on Gravitation” how the phase of that term requires a spin 1 angular momentum projection operator, and thus has like charges repel. Perfect for EM, deadly for any efforts at a vector theory for gravity. I have interacted with two experts in these arts who were instantly dismissive because they knew this flaw. I did come to accept the critique, as is the way of the ultra-conservative fringe. My drive around the road block moved me from quaternions - which are unpopular - to hypercomplex numbers - which are freak-show rare.

What I would put it place of the source Maxwell equations in the Lorenz gauge is the vacuum Maxwell equations in the Lorenz gauge minus the terms of the Lorenz gauge. If one unifies gravity with EM, there can be no charge density that both attracts and repels its same charge. Having a Lagrangian that is invariant under a gauge transformation is a lovely thing. Might as well have that property for the field equations as well. Change the gauge for Maxwell or GR, and the field equations morph. The GEM equations don’t budge a bit. See the snarky puzzle at the end if you want to do a little math.

The other large panel is a way to view the underlying approach to gravity:

use a 4-potential OR use a dynamic metric OR some combination of both. For light bending around the Sun, Newton’s scalar potential theory gets half the answer right. Why not use a dynamic metric to contribute the missing bending of space? Why not use a 4-potential which has the freedom to cover the space bending? The reason was given above: all vector theories must have like charges repel. I agree that a current coupling with spin 1 is a hypothesis killer so long as you use the standard tensor contraction rules which are the same as working with a scalar of a quaternion product. Nature uses multiple ways to multiply to avoid this roadblock.

The two side panels have the calculation for the precession of the perihelion of Mercury, 24 steps in all. At the 7th Eastern Gravity Meeting at Bowdoin College in Maine, I presented the exponential metric as an alternative to the Schwarzschild metric of general relativity. In the llterature, it is called the Rosen metric, but I prefer a descriptive name. If you know the Taylor series expansion of the Schwarzschild metric, you can write out the exponential metric like so:

$g_{\mu \nu}=\begin{bmatrix}exp(-2 G M/c^2 R)&0 \\ 0 & -exp(2 G M/c^2 R) \end{bmatrix}$

The exponential metric does not solve the Einstein field equations. It is manifestly prettier than the Schwarzschild metric in isotropic coordinates, the first step away from the Minkowski metric in flat isotrophic spacetime. The metric is butt ugly one finds them presented as a question at the end of chapter 31 of “Gravitation”, page 840:

$g_{\mu \nu}=\begin{bmatrix}\frac{(1 - G M/2 c^2 R)^2}{(1 + G M/2 c^2 R)^2} & 0 \\ 0 & -(1 + G M/2 c^2 R)^4 \end{bmatrix}$

In physics, pretty wins. Defend the Schwarzschild coordinates if you must, but that looks like lipstick on a pig to me. A static, non-rotating, uncharged, spherically symmetric gravity source should use a pair of exponentials because exponentials show up so many fundamental equations in physics. When the exponent is zero, there is Minkowski. Take a small step away, harmonic motion will be seen. The Earth is still doing the year-long tango with the Sun four billion years after their birth.

For light bending around the Sun, the exponential metric predicts exactly the same amount of bending as general relativity, 1.75 arcseconds, twice the prediction of Newton’s theory. The initial data from 1919 was a bit sketchy, but subsequent work, particularly with radio astronomy, has confirmed the first order parameterized post-Newtonian (PPN) predictions. At second order PPN accuracy, the exponential metric predicts all of 12% more bending than GR, 11.5 microacrseconds versus 10.8. While measurements have improved by a factor of 10,000 since 1919, two more orders of magnitude improvement are needed to distinguish that subtle a difference.

At the end of the presentation, one professor from a university in Florida asked: had I shown the precession of the perihelion calculation worked with the exponential metric? I answered the two were the same to first order PPN accuracy, so there should be no difference at all. I agreed that someday I should do the calculation.

That someday would take three years.
It was not a high priority, since a review of the calculations showed they did so using only the first terms in the Taylor series.The derivations always presumed only a bright graduate student would be reading these sections who knew how to fill in the blanks. I kept looking for a derivation that was simple enough for me to follow. I think it was finally a combination of Sean Carroll’s lecture notes with another GR book that together let me write down the answer. After step 4 on the box, there is no difference between the exponential metric and Schwarzschild. The print is too small for me to read, but I can carry the answer with me.

How many such lunchboxes exist on the planet? I bought 10 from lunchboxshop.com, all shiny and blank. I gave away 5 to the groomsmen at my wedding:
I am the guy in the black zoot suit with red stripes. The best man Dean is in red zoot suit with black stripes. Symmetry, plus some chaos for the others.

I thought just saying I had a hypothesis that was testable and different from GR would get professionals interested. The data suggests that is not the case. On Science Friday a few years ago, I heard Lee Smolin and Brian Greene go at it over the value of work on strings which is not a theory. Both agreed on how vitally important experimental tests were. So I decided to test both of them by sending each professor one of these lunchboxes with a technical paper inside, discussing my testable hypothesis. Brian Greene was a null result. I say nothing about null results, good symmetry that way.

Lee Smolin came to Boston to give two talks. The first lecture was on the value of work on strings. That got a big crowd because people find conflict interesting. Fight! The second talk on loop quantum gravity was much smaller, held in a typical classroom, with the typical donuts and coffee beforehand.

As a member of the ultra-conservative fringe, if I plan on approaching someone at their talk, I try to send an email ahead of time to warn the person, sorry, introduce myself and my proposal. I told Smolin that I was the lunchbox guy with a testable hypothesis for gravity. When I saw him with his coffee, he said he got my email, but did not understand the lunchbox reference. Although I had mailed it six months before, with his job at the Perimeter Institute, the travel, the wife, and most importantly, his new child, he had not seen it. He apologized, which struck me as unnecessary, but does indicate he is a nice guy. It shows that important physicists are too busy to even fart, certainly too busy to closely examine a non-trivial variation on Maxwell.

The other three lunchboxes? One was a draft box, done with shellac, so has that yellow, done-in-shop-class look. The one I use every day is a bit banged up but still works.

One remains in pristine shape. That lunchbox is on sale until Dec. 31, 2012, for \$995k, a markup of 10,000 on the cost of production. I expect to keep it in my possession. According to blogs I have read here on Science 2.0, by the end of 2012, the LHC will determine if there is a Higgs boson and have a great shot at seeing the first supersymmetric particles. If they report that the Higgs is 123 GeV (+/-50), some folks will be excited, but my GEM efforts will have to be retired. If the Higgs is excluded, then real theoretical physicists might out of desperation do a Google search to find a theory that predicts no Higgs. It shouldn’t be that hard to find my GEM technical work.

What price would people pay for a lunchbox Albert Einstein made in 1914 that had his best effort at a gravity field equation on the side (missing the -g_uv R/2 term needed to conserve energy)? If there is a global announcement that there is no Higgs or supersymmetric particles as has been the way of all colliders before, I will climb into the LHC and go into hiding. They didn’t find the Higgs, they won’t find me either. I prefer playing privately with gorgeous math.

Good luck in your studies,
Doug
sweetser@alum.mit.edu

Snarky puzzle
This is Gauss’s Law:
$\rho = - \vec{\nabla} \cdot \frac{\partial \vec{A}}{\partial t} - \nabla^2 \phi$
These are two gauges:
1. The Coulomb gauge
$\vec{\nabla} \cdot \vec{A}=0$
2. The Lorenz gauge
$\vec{\nabla} \cdot \vec{A} + \frac{\partial \phi}{\partial t}= 0$
Apply these gauges to Gauss’s law. Prove that the resulting equations are not the same. Do not try and impress your friends with this obvious result.
The is the GEM version of Gauss’s Law:
$0 = \frac{G \hbar}{c^3}\nabla^2 \phi$
Apply the gauges from above if you can.
“Toto, I have a feeling we're not in [Normandy] any more” Dorothy, misquoted to reference Pierre-Simone Laplace’s home state.
“Only bad witches are ugly” Good looking Good Witch of the North

Note to any reader getting this far: it is my goal to create a blog once a week, late on Monday, including the video.