Thanks for the paper!
I also greatly enjoyed your book: THE END OF TIME.
Loved your quote: "As Ernst Mach said (1883) : It is utterly beyond our power to measure the changes of things by time ... time is an abstraction at which we arrive by means of the changes of things; made because we are not restricted to any one de¯nite measure, all being interconnected. Einstein, an admirer, quoted this passage in his obituary of Mach, calling it a gem. Oddly, Einstein never directly attempted a Machian theory of time, but in fact such a theory of `time without time' sits hidden within the mathematics of his general theory of relativity , the foundation of modern classical physics."
Mach uses that word "change" twice, and yet it does not seem that change was ever woven into Einstein's and Minkowski's spacetime, until now.
Finally we have been liberated from frozen time and the block universe, with a simple postulate and equation--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, or dx4/dt=ic.
This naturally implies x4 = ict, and thus all of relativity may naturally be derived from this postualte and equation of Moving Dimensions Theory.
Give me a 4D universe where
And all of relativity will naturally arise--all because of a fundamental invariant--dx4/dt=ic--the fourth dimension is expanding relative to the three spatial dimensions.
Now a great thing about this hitherto unsung universal invariant--the expansion of the fourth dimension--is that as an invariant, it can also easily account for the slowing of light and time by gravity, as well as the gravitational redshift, as is done in the attached paper.
For the first time in the history of relativity, change has been woven into the fundamental fabric of spacetime with dx4/dt=ic.
Loved the Shakespeare quote too (from one of his sonnets), which tells us that change does indeed need to be woven into the fundamental fabric of spacetime, which is exactly what Moving Dimensions Theory does:
When forty winters shall besiege thy brow,
And dig deep trenches in thy beauty's ¯eld,
Thy youth's proud livery, so gazed on now,
Will be a tattered weed of small worth held.
Wheeler oft quoted Shakespeare. Modern physicists could benefit infinitely from a more classical liberal arts education--there's something about that heroic spirit, which underlies the advancement of art and science, that our academies are failing to teach these days.
I think you will enjoy my paper: Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken :
"In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth dimension, but rather he wrote x4 = ict. The fourth dimension is not time, but ict. Despite this, prominent physicists have oft equated time and the fourth dimension, leading to un-resolvable paradoxes and confusion regarding time's physical nature, as physicists mistakenly projected properties of the three spatial dimensions onto a time dimension, resulting in curious concepts including frozen time and block universes in which the past and future are omni-present, thusly denying free will, while implying the possibility of time travel into the past, which visitors from the future have yet to verify. Beginning with the postulate that time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c, diverse phenomena from relativity, quantum mechanics, and statistical mechanics are accounted for. Time dilation, the equivalence of mass and energy, nonlocality, wave-particle duality, and entropy are shown to arise from a common, deeper physical reality expressed with dx4/dt=ic. This postulate and equation, from which Einstein's relativity is derived, presents a fundamental model accounting for the emergence of time, the constant velocity of light, the fact that the maximum velocity is c, and the fact that c is independent of the velocity of the source, as photons are but matter surfing a fourth expanding dimension. In general relativity, Einstein showed that the dimensions themselves could bend, curve, and move. The present theory extends this principle, postulating that the fourth dimension is moving independently of the three spatial dimensions, distributing locality and fathering time. This physical model underlies and accounts for time in quantum mechanics, relativity, and statistical mechanics, as well as entropy, the universe's expansion, and time's arrows."
Thanks for the paper & all the best,
Dr. E (The Real McCoy)Attachment #1: 12_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf