Thanks for the comments Alex,
Yes--I used E=mc^2 as it is the more common form of the equation and we are also addressing a lay audience, but the results are the same! Mass is equivalent to energy because the fourth dimension is expanidng relative to the three spatial dimensions: dx4/dt = ic. The more formal approach is included in longer treatments of Moving Dimensions Theory, along with treatments of proper time, which jive perfectly with MDT. There's a 5,000 word limit on the current essay, so I had to drop a lot.
Moving Dimensions Theory fully supports Feynman diagrams and it actually provides a *physical* stage underlying Feynman's many-paths interpretations and Huygens' Principle in all realms.
"Consider the emission of a photon in free space," could apply to a photon being emitted from an atom or entity into an unobstructed area. Now I know one could argue there are no such things as a truly unobstructed area and that space is naturally abuzz with a quantum soup, but there again, we see that the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, so there is indeed a lot going on at every point throughout "free" space!
However, we can picture a photon emitted into this which propagates without crashing into anything, and that was how I was using the notion of a photon being emiited in free space. Perhaps I could have written "picture a photon being emitted from an atom or other entity into relatively free space where it does not crash into anything," but I feel most people get the drift of the shorter sentence, and there's a word limit. Perhaps the longer description will appear in future papers, so thanks!
Thanks for noting the dropped constant "ic" in the third step on page 7--I saw that and corrected it a couple weeks back. It got dropped in the transcibing, and it comes back in the next step and is there at the end; but perhaps I'll upload the corrected version. However, the conclusion remains the same: dx4/dt = ic --> the fourth dimension is expanding relative to the three spatial dimensions.
Have you ever thought about Feyman's "many paths" interpretations of quantum mechanics and why it is that a particle somehow "feels" out every path en route to its destination? Well, moving dimensions theory accounts for this.
How can a single point become a spherically-symmetric expanding wavefront?
It happens all the time in QED and nature, and it happens all the "time" in teh expansion of the fourth dimension.
Please see Huygens Principle, as clues are to be found in the Huygens-Freznel Principle:
http://en.wikipedia.org/wiki/Huygens'_principle : "The Huygens-Fresnel principle (named for Dutch physicist Christiaan Huygens, and French physicist Augustin-Jean Fresnel) is a method of analysis applied to problems of wave propagation (both in the far field limit and in near field diffraction). It recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. This view of wave propagation helps better understand a variety of wave phenomena, such as diffraction."
MDT states that the expansion of the fourth dimension appears as a spherically-symmetric wavefront expanding through the three spatial dimensions.
Just like Huygens' Principle, which pervades all levels of nature, MDT recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed. The fourth dimension is expanding, manifesting itself as an expanding 3D sphere in our world, and each point on its surfcae obeys Huygens' principle, underlying Huygens' principle in all realms.
And thus MDT explains double-slit diffraction.
Wikipedia writes,
Huygens' principle follows formally from the fundamental postulate of quantum electrodynamics - that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. It is then the result of interference (addition) of all path integrals that defines the amplitude and phase of the wavefunction of the object at this given point, and thus defines the probability of finding the object (say, a photon) at this point. Not only light quanta (photons), but electrons, neutrons, protons, atoms, molecules, and all other objects obey this simple principle.
And so it is seen that MDT underlies Feynman's many-paths treatments and the fundamental postulate of quantum electrodynamics - that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point. All paths have a probability of being followed because of the fundamental nature of a fourth dimension that is expanding relative to the three spatial dimensions. The probability distribution of the photon expands at the rate of c. After a photon is emitted, the spherical wavefront that defines its probability for being found at any point has a radius of 186,000 miles. This is the net result of billions and billions of quantum expansions of the fourth dimension, and during each expansion, the photon had an equal chance of being found anywhere on the surface of the net sphere, which is the sum total of billions upon billions of smaller spheres.
These diagrams illustrate the basis of Huygens' Principle, which pervades all of nature, providing clues for a fundamental reality from which Huygens' principle arises:
http://support.svi.nl/wikiimg/hugensPrinciple_2.png
http://cache.eb.com/eb/image?id=5704&rendTypeId=4
http://www.lems.brown.edu/vision/researchAreas/Shocks3D/Figs/fig4.jpg
MDT describes the fundamental motion of the unviverse, from which time and entropy arise--both which characterize the constnat motion of dx4/dt = ic.
From the simple postulate: "The fourth dimension is expanding relative to the three spatial dimensions," captured in the simple equation d(x4)/dt=ic, the following emerges:
Huygens' Principle: The fundamental postulate of quantum electrodynamics - that wavefunctions of every object propagate over any and all allowed (unobstructed) paths from the source to the given point
Time
Entropy
Action at a Distance
Entnaglement
Double slit interference
Relativity
Length contraction
Time dilation
The equivalence of mass and energy: E=mc^2: Energy is but matter (momenergy) caught upon the fourth expanding dimension.
Time's radiative arrow
Time's thermodynamic arrow
Time's qunantum Arrow
And finally, the goal of physics is ultimately to describe physical reality. We live in a universe whose physical reality is that the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic, from which relativity may be derived and which provides a physical model underlying entropy, entanglement, Hugens' principle time's arrows, and father time himself.
