Paper CQG-102165 on Quaternion Gravity Rejected
In the Spring of 2015, I developed a new approach to gravity. It was my responsibility to give the peer-review system a try with the paper "Quaternion Space-Times-Time Invariance as Gravity". This effort was doomed because I am not a peer of a Ph.D. level physicist. I cannot walk their walk, cannot talk their talk. And of course the idea could be wrong. I submitted the paper to the Journal Classical and Quantum Gravity. I have never been able to read and understand an abstract in that journal because it was too dense with jargon. The title of the jorunal did sound relevant. Here was the abstract I submitted:
The square of a quaternion luckily has the Lorentz invariant interval of special relativity as its first term. The other three space-times-time terms are commonly ignored. Ways to vary a quaternion with a continuous function that leave the interval in the square invariant are discussed. One method uses exponentials, leading to the hyperbolic functions found useful in special relativity. Using the same approach to keep the space-times-time invariant leads to a dynamic interval term. By preserving the space-times-time terms using an exponential function and the geometric source mass, an interval term is found that is similar but experimentally distinct from the Schwarzschild metric applied to space-time 4-vectors. Space-times-time invariance is not a field theory, so gravitons are not necessary and quantization is moot.
The paper was given to one reviewer who provided this one line critique:
The scientific level of the paper is much below standards adopted in the Classical and Quantum Gravity Journal.
As this is one line, there is not much one can learn from the limited time and effort the reviewer devoted to the paper. The paper was so much below standards that nothing specific needed to be pointed out.
We will never know what was the reason for the one line reject. Here are a few possibilities:
I used a home address, not one from a University. This says to the reviewer that we are not peers, I live in a much lower level cave. In my experience, most such works are not worthy of comment. I have had one exception from an engineer in Mexico city about quaternion triple products and gamma matrices.
"Quaternions" were in the title, abstract, and paper. In my experience, about half of very technical folks don't know what a quaternion is. If the reviewer had no working knowledge of quaternion, the paper would be dead on the first word in the title. A good third of the folks who do know about quaternions hold them in disdain, a leftover from Lord Kelvin's contempt. "Space-times-time" is a made up word. Guilty, but what was I supposed to do?
Not a field theory? No. N. O. Newton's theory of gravity is a scalar field theory. Einstein's general relativity is a metric field theory. All sensible proposal for gravity to date have been field theories. Climb on board.
Gravitons are not necessary? The name of the journal is "Classical and Quantum Gravity". People get jobs in quantum gravity. You cannot have a field theory without a particle to mediate it (true by the way, but quaternion gravity is like special relativity, math rules for all calculations and thus not a field).
The reviewer read the entire article, looked at the references, and concluded the scientific level was well below the standard adopted by "Classical and Quantum Gravity".
Reviewers are not paid. They are busy. One or a combination of these could explain the one-liner.
I learned of a nice way to be more formal in the description of this work. I had to pay 50 reputation points at math.stackexchange.com, but it was well worth it.
The proposal depends on a math idea known as equivalence classes. An equivalence class in an operation on a structure that preserves that structure while having the properties of being reflexive, symmetric, and transitive.
In order to think about intervals in space-time using quaternion requires two preliminary steps. First one must look at the difference between events. What this does is eliminate any role for the origin where an observer happens to be. Imagine one had three observers lined up in a row each one meter apart looking at a pair of events. Each would have different values for the spatial terms for the individual events, but the dq (delta quaternion) could be the same. The next requirement concerns the choice of coordinates. This is a subject where my lack of education costs me. I know how to make what I call a distance function (call it D) in Euclidean coordinates. Here you do nothing. Unlike what people expect, the distance function has four parts to it because changing math structure is evil in my book. I know how to create a distance function in cylindrical (t, r, theta, z) and spherical coordinates (t, r, theta, phi). I would also assert but be unable to prove that no matter what choice one makes for coordinate systems in space-time, there must exist a distance function that can be created with quaternions such that the first term of the square of D(dq) is identical to a 4-vector metric contraction. This whole discussion needs to be couched in differential geometry language which I don't speak. Too bad for my team.
The bottom line is that I am studying equivalence classes of the square of distance functions on delta quaternions of events in space-time. Imagine two observers looking at the same pair of events in space-time. Due to difference between the observers, the two delta quaternions are not the same: dq != dq'. As a consequence, neither the distance function, nor the square of the distance function of the delta quaternions are not equal either. Why are they not equal? In the first case, the primed observer is moving at a steady velocity relative to the other observer. Special relativity can be interpreted as this equivalence class:
Let me read this one off. The distance functions on a delta quaternion are both quaternions. We say the two are equivalent if the real part (the funny looking R) of the square of the distance function on the delta quaternions are the same. I claim that is a different way to describe special relativity. The focus is on what is invariant instead of on group theory or transformation properties, both of which are valid approaches to special relativity. The imaginary part will necessarily be different. Those differences could be used to determine precisely how the primed observer is moving relative to the unprimed observer. This is a good additional feature to have.
In the second case, the two observers are not moving relative to each other. Instead they are at different distances from a gravitational source. The quaternion gravity proposal is that this approximate symmetry in the standard approach is actually exact:
This time they are equivalent if the imaginary parts are equal. This means that the real part is different.
Emotional Response to the Rejection
Nature doesn't care if we understand gravity. I don't care if the physics community does either. The review was what I expected. I cannot change my affiliation (none) which makes the odds of acceptance under 2%. I need quaternions everywhere, lower that by 50%, then the quqaternion cynics are a third of that. A made up word like "space-times-time" takes another 50% cut. The starting odds are under 0.2%. The odds are greater that 80% that the reviewer has written a technical paper on quantum gravity and 100% that the reviewer has peers who have written such papers. Admitting the entire research effort into quantum gravity is wrong - and that is interesting - is not part of high scientific level supported by journals.
I did spend a few moment wondering about life if the paper had been accepted. It would be interesting, but the stress level would be absurd.
This paper was a form of intellectual insurance. If the core idea here is wrong, this blog and CQG-102165 do not matter. If the core idea is right, it is the tradition of science that correct ideas eventually get recognized and obliterate much of the work in vogue. Such a shift requires a social nucleus with technical credibility.