Essay Abstract

I propose to ask mathematics itself for the possible behaviour of nature, with the focus on starting with a most simple realistic model, employing a philosophy of investigation rather than invention when looking for a unified theory of physics. Doing a 'mathematical experiment' of putting a least set of conditions on a general time-dependent manifold results in mathematics itself inducing a not too complex 4-dimensional object similar to our physical spacetime, with candidates for gravitational and electromagnetic fields emerging on the tangent bundle. This suggests that the same physics might govern spacetime not only on a macroscopic scale, but also on the microscopic scale of elementary particles, with possible junctions to quantum mechanics.

Author Bio

The author, born in 1964, having a background of electronics, software engineering and general problem solving, is currently a student of physics at the University of Tübingen, Germany.

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Dear Carsten,

Your essay is magnificent, and most of your conclusions are probably true. You began with math as our language to describe logical behavior. I believe that logic is a key feature of physical reality and that physical reality supports AND and NOT logic at every level of structure, and thus math applies at every level.

Your approach based on two axioms and the assumption of holomorphism leads to 'quaternionic space-time' which leads immediately to the Minkowski metric and emergence of special relativity. [By the way you might wish to check out Gary Simpson's current essay, which is focused on quaternions and Alexander Soiguine's essay on geometric algebra.] Both of these imply the electromagnetic Faraday tensor.

I will not review your conclusions, but they are eminently reasonable, and the fact that they apparently do not lead to event horizons, black holes, or gravitational waves bothers me not at all.

You ask "where are the weak and strong nuclear forces?" I would suggest that you left these out when you decided to rule out vortex fields. I have presented a suggestion of how this might work in The Chromodynamics War. If you had started with an even simpler axiom, I believe you would have found the quantum of action emerging, as well as Bohm-like 'pilot waves' induced. I've touched on both of these in my previous essays. I also invite you to read and comment on my current essay, The Nature of Bell's Hidden Constraints, which I believe to be compatible with your views.

I am in full agreement with you that, rather than concluding that particles and fields evaporate in a space-time view, instead "this space-time should rather be something." Einstein noted "there is no space absent of field." It is the physical field that is the substantial reality, and the logical structures possible flow from this field. Your knowledge of math and your physical intuition allow you to reconstruct physics in the beautiful way you have done. If you, or anyone else, began simply with math, you would never reach reality.

My best regards,

Edwin Eugene Klingman

Sir,

Thanks so much for your essay. I did appreciate the presentation and at a deeper level the paragraph concerning the quaternions.

I agree with the idea that quaternions (and probably octonions) play a central role in the "fabrication" of a given geometry because they can be directly related to the gravitational term appearing in the Lorentz-Einstein law.

Perhaps my own approach (which is only one made by an amateur) can be helpfull for your own research:

The Differential of the Triad and the Extended Lie Products

Like you, I have presented an essay here.

Thierry PERIAT

5 days later

Hi Carsten,

As a student of physics you are supposed to be very open minded. You ask questions and you are not attached to the existing paradigms. You propose: "...we know in advance that this will effectively come out as a (3+1) spacetime." You are looking for axioms in physics. There were many attempts to formulate axioms in physics (D. Hilbert, J. von Neumann, L. Nordheim, H. Weyl, E. Schrödinger, P. Dirac, E. P. Wigner and others). All these efforts failed . That is a pity however a deductive system can consist of axioms or other, already established theorems. As far theorems were reserved exclusively for mathematics. That means that we can use theorems only if we accept that the reality is isomorphic to mathematical structures. (Not necessarily vice versa). I think you agree to that point.

My proposal is to use the geometrization conjecture, proved by Perelman (so it is a theorem). We have the set of 8 Thurston geometries. We can treat them as a space-like, totally geodesic submanifolds of a 3+1 dimensional spacetime... and get all interactions and matter.

If you are interested you can find details in my essay

http://fqxi.org/community/forum/topic/2452

I would appreciate your fresh view and comments. Thank you.

Jacek

a month later

Dear Carsten,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher