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A Brief Discussion of New Physics

ABSTRACT: Readily comprehensible mathematical concepts are presented that provide a foundation to the solution of quantum gravity. The complete discussion inclusive of Parts 2 and 3 also introduces new ideas related to anticipated new developments in the practical exploitation of nuclear physics.

AUDIENCE: This discussion is appropriate for all professional physicists. It is also appropriate for anyone familiar with the fundamentals of physics, starting with advanced undergraduates in physics and other physical sciences (e.g., chemistry). It is particularly relevant to quantum mechanics and nuclear physics.

TIME: 10 minutes – Part 1 is a brief rapid introduction to essential new concepts.

REFERENCE: The short url QGRAV.org conveniently redirects to this discussion.

Part 1 – New ideas about energy in physics

The following is one of the most fundamental textbook equations in mathematical physics.

Because energy is an observable, we are inclined to model this equation as follows.
(It is natural to assume that all of the terms are produced by squaring real numbers.)

Noether’s theorem relates symmetry transformations to conserved quantities. Accordingly, rest mass is invarient with respect to a Lorentz boost. (Regardless of relative speed, the intrinsic rest mass of a particle does not change.) On the other hand, momentum is clearly covarient. Consequentially, while the above model may appear mathematically correct, it is physically incorrect as it naïvely sums (“mixes”) Lorentz invarient and covarient terms, producing the following Pythagorean formula in the real numbers.

It should be immediately clear that the following equation is identical to the first (i ² = -1).

Momentum is not energy per se. When we represent momentum as its energy equivalent, it is apparent from this fundamental equation that an imaginary coefficient is required. — We again rearrange the terms with the notion that real and imaginary terms do not “mix” improperly as previously discussed.

We apply the identity (-i ² = +1) yet preserve the imaginary value of “momentum energy” (ipc).

The preceding naïve “energy triangle” is transformed into a robust model in the complex plane.

It becomes readily apparent that relativistic energy E, which has a measurable real-valued magnitude
|E| = mc², is fundamentally a complex number. This mathematical fact arises from first principles.

It should be clear that “momentum energy” is necessarily imaginary in the context of relativistic physics. —
The worldline of a photon is at 45-degrees in the complex space-time (momentum-energy) plane. Therefore its momentum is real-valued while its energy is imaginary-valued. While the magnitudes of these two energy quantities are equal (|E| = |pc|), it is necessary to multiply the real-valued momentum by i (aligning the vectors) in order to represent momentum as its energy equivalent (E = ipc).

E and p are the two distinct components of the 4-vector momentum p^μ.

The argument of the relativistic energy phasor is clearly the arcsine of relativistic beta. —

As the phasor term in the above equation is required according to first principles, the ubiquitous form of the conventional mass-energy equivalence equation is incorrect. However, what Einstein actually stated in his epochal 1905 paper is, of course, correct and consistent with the above: “If a body gives off the energy L in the form of radiation, its mass diminishes by L/c².”

There are empirical implications to the phasor form of the energy equation that are not implied by the conventional form of the equation, which are subject to experimental verification. The false equality of the conventional form of “Einstein’s equation” effectively concealed important physical phenomena.

As was true for the transition from the classical notion of energy to the relativistic notion of energy, this improvement in the mathematical model of energy has profound practical consequences. In addition, we now easily make the distinction between the total extractable energy and the complete energy budget. Assuming the potential energy to be zero, conventional “total energy” is simply the mass energy. However, E, which incorporates the relativistic kinetic energy K, is clearly only a subset of the complete energy, which is the linear sum of the magnitudes of the rest energy and the momentum energy.

Energy conservation implies a significant energy F (represeted by the yellow bar) in excess of E.
F is the remaining momentum energy that does not manifest in the form of relativisitic kinetic energy.
F can represent only one thing; it is the energy required to produce the gravitational field.

In hindsight, this is all very simple and obvious while solving many prior confusing problems.
Quark momentum (quantified by the Heisenberg uncertainty principle) is the primary source of F.

Part 2 – Quantum gravity in a nutshell