Thanks for the paper!
You write, "(Mere verbal reasoning about time is paradox-prone since it simultaneously uses the notion of time already in the tense-structure of language.)"
Well, using math does not necessarily allow us to escape the tautological, circular definitions of time.
You write, "Briefly, Maxwell’s equations admit two types of solutions: retarded and advanced, corresponding to the
well-known retarded and advanced Lienard-Wiechert potentials. Retarded electromagnetic waves have been likened to the ripples that spread out when a stone is dropped into a pond. Advanced waves correspond to the time reversed situation and propagate into the past: in the pond analogy, seen in the forward direction in time, ripples would seem to converge onto the centre of the pond, and throw the stone out. This is not normally observed."
This alone should be enough to scream that the math is not quite grasping something fundamental about our physical reality, as we have never seen advanced waves. This is because the fourth dimension is *physically* expanding relative to the three spatial dimensions, and thus radiation, which is but matter caught upon the fourth expanding dimension, appears as expanding spherical wavefronts and never shrinking spherical wavefronts.
The simple physical model of Moving Dimensions Theory comes with a physical postualte and equation: "the fourth dimension is expanding relative to the three spatial dimensions at c."
MDT provides all of time's arrows and assymetries across all realms, while also providing a foundational model for entropy, and quantum mechanical entanglement and nonlocality. All of relativity is derived from MDT's postulate in my paper.
MDT provides time's tilt.
Your note the problem with the tautological definition of time that Einstein also noted--a seemingly paradoxical, circular definition (c is defined by t and t is defined by c) which MDT resolves by postulating that dx4/dt = ic is a fundamamental universal invariant--the fourth dimension is expanding relative to the three spatial dimensions, and t, or dt, is an emergent parameter that we measure on our watches and clocks, as timeless, ageless photons surf the fourth expanding dimension, giving rise to the oscillating change in our clock's cicuitry, which we tune to mark the propagation of time in seconds.
However, time is not the fourth dimension, nor did Einstein ever state it was. Instead, Einstein wrote x4=ict. And t and ict are very different things. If God had wanted the fourth dimension to be t, He would have commanded Einstein to write x4=t. But He did not.
Please see MDT in the context of simple, tautological light clocks in the attached figure.
Our definititions of time are based on measurement, which is based on the propagatin of energy, which propagates at c, which is defined in units of m/s (distance/time)! So it is that the time measured on our quartz crystal watches and on our computers, which depends on the emission and propagation of photons, which propogate at c, which is measure in m/s or distance/time, is tautologically defined!
The great thing about MDT is that it also accounts for this tautology, with a deeper fundamental invariant--the fourth dimension is expanding at c--which sets the velocity of light to c, the maximum and minimum and only velocity through spacetime to c, while also weaving into the fabric of spacetime the fundamental rate of change--c. MDT postulates that the fourth dimension is expanding relative to the three spatial dimensions at c.
“My solution was really for the very concept of time, that is, that time is not absolutely defined but there is an inseparable connection between time and the signal [light] velocity.” –Einstein
So it is that time rests upon the velocity of light, which of course is defined by units of m/s or distance/time, and this tautological definition and paradox is nothing new.
MDT takes the paradox head on and blows the tautological fog away, exposing a new fundamental universal invariant which weaves change into the fabric of spacetime for the first time in all of history, liberating us from frozen time and the block universe, while providing a physical mechanism for entropy and quantum entanglement and nonlocality--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c: dx4/dt=ic.
You would enjoy my essay, where the source of this tautological, circular definition of time is finally apprehended by the relaization of a new physical invariant--the fourth dimension is expanding relative to the three spatial dimensions at c:
"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."
I would be quite wary of jettisoning words and logic and reason, while exalting blind math.
Do not take my word for it, but heed the Greats:
Just found this quote from Plato:
"I have hardly ever known a mathematician who was capable of reasoning."
It is hanging in the Boston Museum of Science, and it seems to agree with Albert Einstein, Galileo, and Max Born:
"I personally like to regard a probability wave as a real thing, certainly as more than a tool for mathematical calculations. ... how could we rely on probability predictions if we do not refer to something real and objective? (Max Born on Quantum Theory)"
Max Born wrote, "All great discoveries in experimental physics have been made due to the intuition of men who made free use of models which for them were not products of the imagination but representations of real things."
"Gradually the conviction gained recognition that all knowledge about things is exclusively a working-over of the raw material furnished by the senses. ... Galileo and Hume first upheld this principle with full clarity and decisiveness." --(Albert Einstein, Ideas and Opinions)
To reject *physical* intuition and replace it with the nonsensical block universe MDT does away with seems to go exactly against the spirit by which physics has ever advanced, according to Galileo, Einstein, and other noble physicists.
It seems a preposterous conclusion that quantum mechanics, which works so very well, must be thrown out and reformulated for something which MDT shows there is no need for--the block universe.
"In the long run my observations have convinced me that some men, reasoning preposterously, first establish some conclusion in their minds which, either because of its being their own or because of their having received it from some person who has their entire confidence, impresses them so deeply that one finds it impossible ever to get it out of their heads. Such arguments in support of their fixed idea ... gain their instant acceptance and applause. On the other hand whatever is brought forward against it, however ingenious and conclusive, they receive with disdain or with hot rage - if indeed it does not make them ill. Beside themselves with passion, some of them would not be backward even about scheming to suppress and silence their adversaries. I have had some experience of this myself. ... No good can come of dealing with such people, especially to the extent that their company may be not only unpleasant but dangerous."--(Galileo Galilei)
"my dear Kepler, what do you think of the foremost philosophers of this University? In spite of my oft-repeated efforts and invitations, they have refused, with the obstinacy of a glutted adder, to look at the planets or Moon or my telescope." --Galileo Galilei
We must forver keep physical reality in the front and center, along with logic and reason and *physical* intuition--otherwise progress in physics will grind to a halt, as it has for the past thirty years.
"But before mankind could be ripe for a science which takes in the whole of reality, a second fundamental truth was needed, which only became common property among philosophers with the advent of Kepler and Galileo. Pure logical thinking cannot yield us any knowledge of the empirical world; all knowledge of reality starts form experience and ends in it. Propositions arrived at by purely logical means are completely empty as regards reality. Because Galileo saw this, and particularly because he drummed it into the scientific world, he is the father of modern physics -- indeed, of modern science altogether." --Albert Einstein, Ideas and Opinions
Math can be very pretty, but Einstein reminds us that physicists ought pursue *physics,* founded in a physical reality--“Mathematics are well and good but nature keeps dragging us around by the nose.”"
"It is anomalous to replace the four-dimensional continuum by a five-dimensional one and then subsequently to tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself." –Einstein to Paul Ehrenfest. Just think what Einstein would have said about entire parallel universes we cannot see!
With an heroic spirit, MDT takes us back to origin of modern physics--to the original papers on relativity and QM, and it humbles itself upon that mountaintop. And when it comes on down, off the shoulders of relativity and QM's giants, MDT presents us with a fundamental view of reality that conforms to all experimental evidence, while not only resolving the paradoxes of the non-locality of the EPR effect and seemingly frozen time in Godel’s block universe, but also unifying the resolution of both physical curiosities within a simple physical postulate--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic. In a sense, this is the first theory to predict QM's nonlocality and entanglement, by postulating that the fourth dimension is inherently nonlocal via its expansion--an empirical fact that the timeless, ageless, nonlocal photon agrees with, as the photon surfs the fourth expanding dimension. And not only does MDT predict this, but it also provides a *physical* model for entropy and time and all its arrows and assymetries throughout all realms. And finally, all of relativity may be derived from MDT's simple postulate, as it is in my paper--the fourth dimension is expanding relative to the three spatial dimensions--dx4/dt = ic. A postulate and an equation representing a novel *physical* feature of our universe--a fourth expanding dimension--and the natural, subsequent prediction of all of relativity, qm's nonlocality, entropy, time's arrows and assymetries in all realms, and quantum entanglement.
I don't believe in mathematics. --Einstein, Quoted in Carl Seelig.
Do not worry about your difficulties in mathematics, I assure you that mine are greater. --Einstein
Geometry is not true, it is advantageous. --Jules H. Poincare
Dr. E (The Real McCoy)
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