Physics Implications of a New 1st Order PDE
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This book is on a generally covariant generalization of the Dirac equation found by substituting general covariance (in the form of a point source diagonalized Ökmn) into the standard Dirac equation:
Sm(Ökmmgm¶y/¶xm)- wy=0 with koo=1/krr=1-rH/r (1.9) with koo= 1-2e^2/(rm_e(c^2)) º1-r_H/r. This equation requires only ONE postulate of a geometrical point to prove (ch.1) and deals with one particle, the electron. We solve this equation in three domains:
r>r_H, r»r_H, r
This new equation explicitly includes curved space (i.e., rH not zero), thus includes force, thus naturally explains all the forces with direct, straightforward derivation. For example at r>rH the third term in the expansion of the energy term (in this new pde) gives the Lamb shift without the higher order diagrams, doesn’t require the standard pathology of adding and subtracting infinities to get the QED high precision (section 17.4, ch.18). Even if the mistake is made of setting rH=0 we still explain why the infinities are then needed to get this high precision if the gauges are then added (see Chapter 6, they lucked out here). Thus even the QED high precision results are understood here from first principles, eq.1.9.
Also at r»rH it gives a bound state 2P3/2 trifolium, thus charge e spends 1/3 of its time in each lobe (fractionally charged lobes), there are 6 P states (6 flavors), the lobes can’t leave (asymptotic freedom), P wave scattering (jets), explaining all the major properties of quarks (ch.3), giving us the strong interaction without any new assumptions!
(e.g., deuteron bond J=1 (section 19.6) and hyperon mass eigenvalues terminating the divergent Frobenius series solutions to equation 1.9 at r»rH are found in ch.19)
The standard Dirac equation on the other hand applies to flat space (rH=0 there), which is a mistake to use (except for in flat space) since indeed there are forces. So what do people do to try to get the experimental results after making such an egregious error? They add in gauge after gauge, Lagrangian term after Lagrangian term, free parameter after free parameter: when their model doesn’t explain new experimental results they just fudge in a new term, resulting in a big mess of a theory that confuses, stops the progress of theoretical physics dead in its tracks. Why they can prove anything this way!
In any case Dirac thought there was something missing from his equation as well, given all these pathologies resulting from trying to correct its mistakes. He advised physicists to fix his equation, which is what has been done here. “People work with a Hamiltonian which, used in a direct way, would give the wrong results, and then they supplement it with these rules of subtracting infinities. I feel that, under those conditions, you do not really have a correct mathematical theory at all. You have a set of working rules. So the quantum mechanics that most physicists are using nowadays is just a set of working rules, and not a complete dynamical theory at all.
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About the Book
A New Look at Our Universe!
This will revolutionize the way we think, the way we work, and the way we live.
This is a game-changer for science.
More than 80 years ago, the flat space (Minkowski metric) Dirac equation was derived. But we know space is not flat; indeed there are forces! To compensate for such a fundamental mistake of dropping force (i.e.,the curved space metric term) many gauges, free parameters and renormalization must be fudge factored in.Theoretical physics has thereby become confusing and permanently off track. In this book we correct this mistake by NOT arbitrarily dropping this term. We thereby include the general covariance in the Dirac equation and so naturally introduce force. Here the general covariance is provided by a new spherically symmetric nonMinkowski metric kij (with koo=1-r_H/r, with r_H=2e^2/(m_e(c^2)).
This corrects the original math mistake and so puts theoretical physics back on track resulting in breakthrough physics propulsion, breakthrough energy ideas and a much deeper, clearer understanding of our physical universe.
Dirac himself in the last paragraph of his last published paper urged physicists to fix his equation. They wouldn’t do it, the gauges and free parameters remain, and so theoretical physics is at a dead end; fundamental science, our future, is at a dead end. In this book, you will see the math mistake, undo it, and begin to solve riddles in science that have plagued mankind for more than 80 years.
About the Author
David Maker received his physics PhD on a NASA fellowship and won a technology award while working there. He taught college physics for 12 years, worked in the field for many years and has presented this topic at many APS meetings.