|A. Einstein's relativity double-integrated zero-differential acceleration front-end-to-back of a lightspeed-capable train and accumulated nonzero-differential distance, but this does not work in mathematics; and even worse, his original event-interferometry-clock was trippy, acausal, paradoxic breaking continually while accelerating, modernly ignored...|
[See also ppt-videos the Einstein-Minkowski Acausality Paradox (trailer) and Correcting Einstein: The Other End Is Running Late (trailer), and, linear stellar aberration, and angular stellar aberration]
[See also, harmonic magnetism, and The Faraday-Maxwell Tease (trailer) centuries-old transformer equivalence 'extras']
FOREWORD: [April 20th 2017 plus]
Einstein's original(?) diagram of a photon clock consisting of a pair of photons emitted perpendicularly and returning at the same instant (because the remeeting-event occurrence exists in both frames), is-or-was incorrect arithmetic: in particular the outrigger distance is-or-was incorrectly measured only-forward, whereas the in-line distance is-or-was measured correcting for the asymmetry of moving-measures... the remedy is to use the proportion from the in-line distance-and-length by applying it also to the outrigger distance (not a length of anything)... The result is still-again an approximation instead of a true mathematical analysis (SEE Linear Stellar Aberration, for the proper analysis of acceleration)...
Further problems with Einstein's diagram included its asymmetry of forward-vs-backward travel implicating not just temporal dilation but distortion of dwell-time (which I used for a screenplay moment in my “StarTrails Game” 2000, as to whether fast interplanetary speed might electrochemically alter familiar food flavors)... Furthermore, his ‘passing station clocks’ grid-time-bias resulted in grid-distance-bias two-gammas (γ2) shorter, contraction—so his "contraction" was actually expansion, from double-contraction...
Also, Einstein proclaimed 'no-preferred-reference-frame' where Newtonian analysis (had Newton analyzed it) reveals that if an observer were at the middle of a train, then, when the train starts, the other ends appear to start late, so the front appears nearer and the rear farther e.g. time-synchronized photons from the front and rear in the train's-own frame will-not-meet at the center, plus its differences grow while the train continues to accelerate, and the compounded shrinkage is retained even when it resumes 'inertial mode' (no-longer accelerating)... Early analysis had allowed for natural-shrinkage of atomic distances and whence objects' lengths compensated where time-is-distance, but if the speed of light were fixed in the accelerated, frame, it could no-longer/never-again be symmetric... i.e. there is, a preferred, frame reference....
On page 26 of RELATIVITY, 1962 USA-only edition, Einstein presumes his train can get up to near-light-speed without its adverse effects on his measurement theory. But if we consider a train starting from standstill, from a point midway ordered Go, and follow that progress, we find a disabused result: the back end sees the front end start late by a tiny fraction of a second, because of the distance the view-light photons must take from front to back, and, conversely, the front sees the back start late by the same. The same difference also appears in the velocity: each end sees the other end starting and remaining late in its velocity profile: each is seeing the other move more slowly, while acceleration remains, continually, unterminating, and the differential velocity accumulates: the front sees the back recede and-yet the back sees itself gain on the front... and the roundtrip averages account for even-order time dilation when we apply the same ersatz reasoning to each atomic electron i.e. everything seems late in forward and rearward views as photon-bouncing clocks run more slowly... even the other ends of straightedge rulers measuring the frame....
Facts in-favor of Einsteinian relativity were also facts-against: that, motion-perpendicular photon aberration must occur on the speeding experiment frame viewed in the reference frame, suggesting non-aether equations of motion, But, it could never get there by acceleration, because crossing photons would slip out the back end, or, if an Einstein clock were closed-up by extending the mirrors, crossing photons would eventually strike the rear mirror and orthogonality would be lost—by both that practical-conversion and, by angles the crossing photon would only partially lean forward shy by lightspeed effects, (Modern college physics textbooks install a low-duty-cycle-pulse-repeater to avoid 'thinking' about the adversity of integrating the cross-photon-slippage-or-loss-of-orthogonality)... Another Einsteinian presumption was his equational absence of the spatial-aether as-if charge-space-time existed substantially self-extant in absolute-perfect-vacuousness (nonextancy) with its nothingness having absolute-perfect-mathematical-measurability (a standardness of something-else-ness), and, as the only substance of those properties, that they should charge-space-time-interact so as to itinerate all developments while themselves inextricably fixed to his vacuously-extant-mathematical-measure-nowhere-explained... and then it got even stranger when he claimed its nothingness could expand and contract on its mathematical basis or conversely its mathematical basis expand and contract leaving its vacuum in-situ (sic 'doublespeak') for-which it had no establishable fixity, connection, registration...
(Things got even-stranger when he worked-up his General Relativity without reasonable knowledge of where, mass-and-energy are, although he was known to have stated that 'particles are extended in space' he placed no mass-energy there, or anywhere, and generations of his students would never know whether a mass-hole aka 'black hole' had all its mass inside, or not, or, in-other-words, gravity wasn't, strictly, 1/r2, yet none of his subsequent teachers-of-next-generation-students ever relayed what that envelope-function was, meanwhile 4th-graders knew that Einstein's singularity was-not mass-energy-conservative, and even outside his singularities, potential energy if-located-in-test-particle-situ would've totaled infinite for any mass at all...)
How could this have come-to-pass in physics:—simply, physics is experimental art and otherwise presumptuous using mathematics to calculate its 'landings' but-not-how-to-get-there... Einstein was searching for energy, when he did his original light-beam postulations, (cf his prominent photoelectric effect theory i.e. atomic energy quantization), but inertial equivalence, guessed-at by Galileo et al, was never proved nor proven except at zero-velocity and 'immeasurably' small at Newtonian subsonic indeed-'sub-pony-express' velocities (and he reputedly never traveled, not that he should have seen it), and neither he nor his adherents for the next four centuries ever developed his arithmetic (else would all have found the time-space coordinational distortion we'll examine later, and risked a renewal of holy-Inquisitions, upon himself and posthumously Galileo)... Minkowski the mathematician merely extrapolated-back from Einstein's results to something like Maxwell's results (Lorentz contractions) and all cheered their grandiose-unification theories tossing-away-infinities and leaving the dust under a trippy carpet—for us...
Let us presume rather the ab-sense of Einstein's theory of absolute-vacuum-mensurability, Let us carry forward his ersatz Gedanken [mind-thought] experiments from a more mathematically concise expectation, and finish what Einstein merely started and dabbled-in and got-taken-over by wooden-stick-theoretical relativity...
EINSTEIN: OBJECTIVE vs. SUBJECTIVE CAUSALITY--
Assume a place in the universe where the speed of light is a constant in all directions--which seems ordinary enough because the universe seems stable and somewhere should be large enough to run kilometer lightspeed measurement experiments a few microseconds...
Assume an experiment consisting of three pieces aligned on a perpendicular grid with its system-motion so that one piece sends and receives photons to the other two; At standstill the length and width are equal, L = W, and photons take the same time to return... in practical experiment this would be an event-interferometer 'clock' of photon-exact identical length and width (*)...
* (But not necessarily the Michelson-Morley setup as assumed very-long photon-trains of end-to-end-coherence from a thermal source, constant train-loading from a thermal source, only-later an ultrafine-tuned CW laser source, dispersional-phase coherence of parallel-photons-not-entirely-a-wavefront, constant beam-splitting-balance-and-wavefront-refill-without-angular-dispersion for switched-out-missing-photons, and, no load-switching nor mirror-repolarization at beam-splitters, no nonlinear-interferometric auto-modulation at the silvered mirror, no natural-'re-lasing' by glass-mediums, no evanescent waves nor overlap-standing-wave-frequency-lockup, no perpendicular-velocity-swamping by cosmic-relative motion, no explanation that it was ever pre-compensated for mirror-in-motion-tilting as would affect spatial patterns, not temporal,--nor in government documents,--etc.... Spatial phase coherence produces a grid-pattern of nulls at 0.71-wavelength on the silver surface by the interference of source and returned beams that in-canceling prevent polarization-phase-inversion and results in closely-spaced auto-modulation flipping photons even 'randomlike' between nulled-standing-peaks and incident-nulls; and even creates perpendicular grid-bridge-photons ... It is usually depicted with a slit lacking vertical coherency, rather than a point source... It was not, a properly imagined experiment.... Note, there should be further question of electromagnetic phase rotation at the mirror surface in motion--not unlike the phase-flip-or-not depending on silvering-conductance... Note too that 'perpendicular-velocity-swamping by cosmic-relative motion' is twice a concern to their experiment, because, that was the very 'thing' they were trying to determine by measure but then assumed the only detectable motion was inline with either 2D-experiment leg, --which seems innocuous to assume and underestimated-to-boot when contrarily it was quite-expectably-certain that our Earth, Solar System, Local Group, galaxy, galactic cluster, cosmic-attractor-region is, traveling a significant portion of even 'half' the speed of light from the nominal 'center' of the cosmos, and, a small sine portion is all that's needed to 'swamp' the vector-addition into a perpendicular,-sum... They and-successors could even have missed it by not checking all the possible 3D, sky, in particular the polar regions detectable from the equator were neglected or not broadly reported... Or, they dropped singular 'momentary' positive detections as nonrecurring 'glitches' within the region they did,-test, as the Earth turned...)
And we assume the experiment packages accelerate uniformly, all pieces, so that no reshaping occurs in any frame 'real' or 'relative'—objects remain everywhere 'normal'—that may be an awful lot to ask, but Einstein assumed-so, apparently, by his own published original depiction, and we're going to find the correction to his assumptions, that illumines, inspires, and reassures, the correct process and results, and even explains and makes-room-for his results... (rather than start from 'scratch' getting every step correct from the beginning which is the hallmark of mathematics rather than wading through heaps of smelly approximations)...
FOREWORD: We are not-firstly concerned with the higher order terms in the ½mv2 energy formula of Newtonian motion vs. Einsteinian relativity, but rather with Newtonian analysis of Einstein’s gedanken, (also note that we skip Galileo who supposed relativity and a finite speed of light but without proof):
ABSTRACT: Einstein’s Theory of Relativity has troubled students more than a century, Scholars repute only three people in the world understood it, (‘punchline: Who’s third’)… We can find, the trouble, We can fix, the trouble, Or, we can start afresh, correctly, from Newton’s mathematical principle-set…
TEASER: Suppose Einstein detects a 10 m lance traveling at 60% lightspeed as it arrives at ground zero and his second detector marks its other end as 8 m, but,—just then his first detector jumps into the lance inertial frame and measures its full 10 m length but the second detector 6.4 m behind: Did the other end get marked or-not-yet… maybe ‘relativistic effects’ are traveler-local with far-distances remaining far ‘til their distance and time contractions and biasing effects arrive, roundtrip, at the speed of light; Einstein’s gedanken-clock effects calculated only after, photons, had gone, roundtrip, so maybe his theory doesn’t even apply, ‘til they do—(even isotropically, round, even incrementally a roundtrip-equivalent, especially for accelerated-re-arrangers ever-‘refreshing’ their roundtrips; A similar test can be done with two lances of different lengths and speeds)….
►The speed of light is finite,
►(Galileo and others had supposed so; Newton and Einstein knew so by measured values):
►Newton recognized Rømer’s estimate we know as ⅔ c in timing the orbits of Jupiter’s moons,
►Einstein had Foucault’s 10 ppm estimate by the deflection of photons off a spinning mirror
►(n.b. Michelson’s estimate was 20-50× coarser than Foucault’s);
►The speed of light is singular and constant,
►Newton saw the speed of light was one-and-the-same for all colors visible—
►his new reflector telescope corrected Galileo’s prismatic glass refractor color ‘rainbowing’
►and showed no white-smear nor edge-color aberration on the bright heads of passing comets
►(cf 10−4 c magnified by his scope factor of 40× is 14 arcmin. ≈ 14× common ocular acuity),
►But he did-not know whether it was fixed by the speed of emission, or the speed of space itself,
►Modern experiments confirm the speed is the same for all electromagnetic waves ELF to γ-rays—
►and that it’s by their speed in space itself, (and for particles too, protons, electrons, neutrinos),
►Einstein had Michelson-Morley’s interferometry-null for white-light-speed in a traveling frame,
►(n.b. the Michelson-Morley experiment is unknown for directions within 34° of Earth’s axis),
►(n.b.#2. the Michelson-Morley experiment has since been refined by 108×, e.g. Schiller et al);
►We too have all-this so we can ‘boldly’ upgrade Newton’s Principia on his behalf—
►Q. Is the speed of light the same constant in all directions,
►If faster in some direction, atoms and waves should be elongated-so
►and measurement rulers should thus be—equally—elongated so,
►and the speed of light should therefor be perceived-as isotropic, so—
►Light-time is light-distance;
►Q. Is the speed of light the same constant in all directions for travelers,
►Or is there a preferred direction such as inline traversal or quadrature transversal (perpendicular),
►‘Well’ firstly, to get to any, speed, you accelerate,—and this is where Einstein and Newton differed:
►Einstein skipped his acceleration step and assumed multiple ‘inertial’ frames without first accelerating
►(Einstein did-not-compute the A-student analytical mathematical sense that made Newton famous),
►So, Newton’s mathematical principled ‘walking path’ may sleuth for us where Einstein did-go, or-not,
►Or…maybe-not-at-all if atoms and waves are elongated-so in all, roundtrip-faster-directions, of travel,
►(experiments constructed of distorted-atoms might-be equally-distorted, cf Lorentz Contraction);
►Einstein’s preference was for an analytical physics sense that photons have a width-structure
►that is—(as must be)—preserved when photons appear carried-along sideways-relative,
►beginning earlier at the rear and propagating forward across the wavefront, to be later-moving
►to avoid a Huygens’ contradiction (that a photon wave travels perpendicular to its wavefront);
►Thus Einstein, who believed photons were wave-spaces, pre-expected a loss-of-simultaneity
►(for anything with self-entangled structure such as, an energy-wave-like-particle ‘wavicle’),
►but this meant photon-spaces would be deformed, shingled stacks, in the traveler’s ‘inertial’ frame,
►(and under acceleration photons would become individually ‘chirped’, bent, dispersive-angled),
►Yet, photons do-have long cohesive wavepacket envelope structure, else they’d violate deBroglie,
►(So maybe photons instead have circular ‘footprints’ of equilateral transversal-wave structure);
ANALYSIS: getting a ‘contained photon’ up to speed:
►There are two ways to observe events: Remotely-far-and-synchronized, and, Up-close-and-immediate,
►(the third way is the way Einstein did it—conjecturally relative anywhere by-single-observer);
►Plus, for Newton there exists a Reference Frame, fully-self-synchronized for comparison sake,
►non-moving and never accelerated—a ‘preferred’ frame, (a test frame is accelerated, moving, etc.),
►We will watch how-and-where acceleration affects the mover vs (not) the remainer—
►Under acceleration that is constant, transversal photons ‘fall back’ to the rear, inline, mirror,
►and rebound somewhat forward—reaching unto as far forward as their points of origin again,
►Orthogonality (and orthonormality)—is lost, and,
►some transversal photons cross faster than others (fastest mid-orthogonal, slower ‘zigzag’ steeply),
►so the traveler’s clock is messed-up,
►And, the traveler knows it,
►And when acceleration quits to coast, all-but-one transversal photons reach the front mirror,
►faster or slower depending on where they were at that instant of regime-transition-to-coast,
►The traveler’s photon clock orthogonality remains lost, totally messed-up, permanently ‘broken’
►(meanwhile the preferred, unaccelerated frame remains unaffected, never breaking its clocks),
►Furthermore, velocity-and-position-changes, even if returned to zero, cumulate an average ‘wear’
►retaining a traveler-clock-mess ‘cryptic summary’ of the position-velocity-acceleration histories,
►n.b. all things in the accelerated frame are affected, messed-up, particles, waves, photon-generators,
►but then, wavicle cohesiveness, nonlinearity, quantumscale interference, diffuse, the traveler’s mess
►(cf electron colliders ‘see’ infinitesimal points of finite energy intrinsically stable under messing);
►But, by that acceleration, transversal photons do-not-return to their full, original forward position,
►because—the same photons are also partially chasing-forward their traveler-clock-system velocity,
►and so near-orthogonal photons lose ‘ground’ aft the original position, the faster the clock travels,
►and yet, the traveler might-not-notice this shortage if its atomic-structure-length contracts equally,
►and…this is Einstein’s frame-contraction, but, only by half, as it occurs only, during, acceleration,
►and the unaccelerated preferred, frame ‘half’ never has this shrinkage by others merely looking-on:
►for, if it did, or if its photons were seen to bend over, they’d be ‘falling’ toward their, clock-rear…
►(Note that transversal photons act as having rest mass under acceleration—bouncing against the rear mirror but not the forward, and increasing overall Doppler shift, yet being pure energy, might ‘fry’ the system by ‘internal-light-barrier’—an exception that does-not-occur with ordinary gravity,
►but, more-massive atoms have more-massive electrons in lower-orbitals absorbing the energy fry,
►and, photons traveling forward, when acceleration occurs, are deenergized rather than energized
►but, on-the-average more photons are chasing forward than rearward, so average mass increases
►but, also, photon momentum-energies are ‘double-deposited’ upon bouncing against each mirror
►and that momentum-force, would spread the mirrors apart, but for their mechanical attachments,
►Such details complicate the photon-energy-equations by more component diffusion—tbd…);
►(Subnote that Einstein’s photon clock was a system with external secular motion independent of all internal photon motions; its effective-speed-of-light-within ceff therefor reduced by ceff2+v2 = c2 where the ordinary-speed-of-light c is the usual limit ergo ceff = c√(1−vc2) which implicates time dilation or length contraction and may have inspired such theories of Larmor, Lorentz, FitzGerald, Poincaré.)
►So, there is, no, inertial-frame-equivalence (unless coefficient-adjustments ‘throw-a-rug-over-it’),
►whereas not-only-Galileo had long-supposed motion was relative, as was ‘obvious’ at low, speeds,
►There is, no, ‘Special’ Einstein solution to relativity (without that ‘inertial frame equivalence’)—
►You can’t get there from here, without, acceleration, and acceleration breaks it,
►Unless there’s a correction-process to recover it, or some sub-solution, there is, no, ‘inertial frame’,
►Nevertheless, Einstein, assumed, ‘Fuzz—it all goes inertial, again—all, by itself…’
►Meanwhile, Newton’s mathematical principled-steps do-not-support such fuzzy fuzzied assumptions,
►Newton ‘walks unhurried’ where Einstein ‘rode like a madmouse’ (hard-acceleration rollercoaster);
►(N.B. Modern physics—textbooks—assume each clock-photon is disposable ‘use-once-and-discard’ without tracking displacement—a ‘fresh’ clock-photon is emitted replacing it,—but we find the entire clocking system and all its component photons and atomic-orbital E-M waves remain ‘whacked-out’);
ANALYSIS: the traversal ‘frictionless cart’ photon:
►A traveling photon clock adjusts photon wavelengths, inline shorter forward and longer rearward:
►At velocity vc (relative to light speed c=1) inline-traversal-photons bounce against the rear mirror
►compressing wavelength 1/(1+vc) by its approach against the photons, (note, −vc decompresses),
►and deexpanding wavelength (1−vc) as it recedes while chasing the photons, (note, −vc expands),
►for total compression (1−vc)/(1+vc) retained for forward-travel time duration extended by 1/(1−vc),
►and, bounce-back against the front, with total decompression—inversely, (1+vc)/(1−vc) (as c=−1),
►and that retained for rearward-travel time duration foreshortened, by 1/(1+vc), roundtrip 2/(1−vc2),
►for roundtrip-compounded compression-decompression resuming its initial value =1 per photon,
►and, photon momentum which-is-energy and-force, imparted on both mirrors, is balanced equal,
►(the same photons each bounce each end mirror equally—deemed elastically—while coasting),
►(bouncewise (1)(1+vc) ⩲ ((1+vc)/(1−vc))·(1−vc) = ((1+vc)/(1−vc))·(1−vc) ⩲ (1)(1+vc) = 2(1+vc)),
►(but even then reflectance-field electrons should be expected to have a slight-impedance delay);
►(Note thus traversal photons too exhibit mass reactance and energy gain by acceleration),
►(Note photon-wavetrain-length is also part of the calculation of ‘total light’ duration, and
►Inline-photon-travel-time ‘total light’ duration-ratio (1+vc)/(1−vc) is a ‘headlight effect’);
ANALYSIS: ‘special’ inertial speed:
►Einstein’s photon clock quadrature-photon travel length was incorrectly set up or calculated:
►inline-photon travel between emitter (aft) and forward mirror (fore) was measured roundtrip,
►(forward-and-backward, the average is the inline ‘mechanical’ length),
►quadrature-photon travel between emitter and outrigger mirror was also, measured roundtrip,
►(outward-and-inward, the average is the quadrature, mechanical, width)
►but the quadrature-photon travel vector viewed relatively, has also a component of inline length:
►that is, length, not-frame-travel distance, but actual, photon-motion, to-be-measured-roundtrip,
►but was instead measured twice,-forward, without, consideration for its backward,-return-path
►(in calculating the average-hypotenuse-length of photon travel by Pythagorean components),
►The length of objects and in-particular-here photon travel, is-not an objective-frame-velocity distance,
►Inline, length, is measured as the roundtrip, average, of here-to-there-forward, and-there-back-to-here,
►His outrigger mirror travel to meet its quadrature photon was measured distance but he needed length,
►(this may be fixed simply by ratiocinating with its inline-photon proportion shorter by 1/(1+vc)),
►(else we could measure it by a separate emitter and mirror, even at a separate time and place),
►(but maybe-not because photon travel is-not free-speed-relative with perpendicular components);
ANALYSIS: ‘effective’ time and distance:
►Relativity does-not change the time passing by any window, though every clock outside turns slowly,
►therefor outside grid-time is biased tbias = vc dgrid/c compensating for its slow-turning clock gear-times:
►this time-bias is added relative to the fully-self-synchronized-grid-frame time right-outside a window,
►observed length-contraction d = dgrid/γ, time-dilation t = γtgear and therefor its clock-tripping t = tgrid/γ,
►(n.b. by clock-tripping Special Relativity has two timing-externalities: faster tgrid and slower tgear),
►(consistent with Einstein’s full reciprocity v = d/t = (dgrid/γ)/(tgrid/γ) = dgrid/tgrid = vgrid = vlookingback),
►(relative velocity, horizontally oncoming, passing, offgoing, common vertical ‘up’ but no gravity),
►(cf his 3-point “Twins [non]Paradox” grid-time and-distance contracted equally, for the traveler),
►and, as tgrid = γt = γ2 tgear needs compensation, tbias = tgrid−tgear = (tgrid= dgrid/v)·(1−γ−2= v2/c2) = vc dgrid/c,
►therefor, in the traveler’s vantage, oncoming clocks will be relatively closer, by dbias = v tbias = dgrid vc2,
►so that in traveler-view equations, deff = dgrid−dbias = dgrid/γ2 = d/γ (super contracted), tbias = γ2 vc deff/c,
►(that’s reciprocal for the meaning of ‘effective velocity’ veff = deff/teff = (dgrid/γ2)/((dgrid/v)−tbias) = v);
►(N.B. acceleration was no part of Einstein’s calculations, as soon as ‘inertial frames’ took-over),
►(Sidebar: there is no FTL time-travel as oncoming clocks would advance while turning backward
►from their time-bias even greater—BUT—with dbias>dgrid FTL-clocks should arrive from behind);
►(Note that photons are deemed gridless, bearing only the timestamp ‘image’ of their interactions),
►(also note photon γ = ∞ so its finite length must be infinite in its own frame if it has a real frame),
►(subnote the sublime impossibility, Einstein couldn’t ride a zero-energy photon of infinite length),
►(sub-subnote that a photon of any length would see the universe zero-length but containing, itself),
►(sub-sub-subnote that physicists correct this as geodesic-acceleration-distortion-per-perspective),
►(but, sub-sub-sub-subnote that, per-perspective-acceleration is asymmetric, local-first-then-away);
►So Einstein’s calculable, effective, contracted, relative distance is shorter than his measured, observed,
►maybe-ill-defined-contracted remediable by γ-expansion, distance γ2-contracted by distance-time-bias,
►so that in traveler view equations, d = γ(deff=dgrid−dbias) = dgrid/γ (same Einstein contraction equation),
►(n.b. it would appear that Einstein simply skipped identification of foreshortening, as contraction),
►(We’re still expecting ultimately to consider Newtonian one-sided acceleration contraction effects);
►(Note that holding Einstein’s time-bias constant, clock gear-time is continuous, slower and linear),
►(yet updating time-bias by his inertial triangle-ratiocination is relative to grid-time and so equal);
ANALYSIS: ‘insider’ clock-time:
►Photons (inline only) in the grid-frame, arrive one-way at the clock-mirror Lgrid fore or aft at Lgrid/c,
►meanwhile his traveler observes tbias = ±vc Lgrid/c, Leff = Lgrid/γ2, arriving, t = L/(c±v) = Lgrid/γc(1±vc),
►meanwhile likewise, his traveler observes effective, arriving, teff = Leff/c(1±vc) = Lgrid/γ2c(1±vc) = t/γ;
EINSTEIN’S ROUND DELAY PARADOX vs ‘Newton’s bucket’—
►Photons travel equally-around a wheel, forward and rearward, and meet again at their starting point,
►But also equally for an observer for whom the wheel is spinning, to meet again at that starting point,
►But, that common starting point has moved and yet all photon meeting events must be the same one,
►while cumulatively discounting wheel rotation one photon revolution, returning to its original angle,
►Moreover for consecutive slow rim clocks time bias must continually climb and thus be multivalued,
►but yet again Einstein would have the far side of its wheel at opposite velocity subtracting-back bias,
►and Mach’s preferred rotation frame may not help this time if both observers are rotating oppositely;
►(note of course atomic structures in the grid frame have such time bias by incremental summation);
ANALYSIS: ‘third-party’ racer, velocity:
►Any object racing inline at velocity v3:grid travels d3:grid arriving at t3:grid = d3:grid/v3:grid in the grid frame,
►but Einstein’s traveler observes tbias:3 = vc(dgrid:3= d3:grid−vtgrid:3)/c, and solves it as = t3:grid − tgrid:3 for t3,
►solving... vc(v3:grid t3:grid−vtgrid:3)/c = t3:grid − tgrid:3 ⇒ tgrid:3 = γ2 t3:grid(1−vcv3:grid:c) = γt3, where γd3 = dgrid:3, ►so v3 = d3/t3, Einstein’s compound relativistic velocity formula, v3:c = (v3:grid:c−vgrid:c)/(1−v3:grid:c·vgrid:c),
ANALYSIS: Einstein’s ‘four-point acausality’ paradox:
►Assuming the traveler’s own frame can be fully-self-synchronized—
►(Apart from the asymmetry of directional length, allowing Einstein’s roundtrip length, symmetric)),
►(Einstein’s other assumptions such as v=vlookingback are still unproven, so this analysis is ‘curious’):
THE ACAUSALITY PARADOX: (aka the Predating Paradox, student version)
In the Event-Interferometry Clock: the same event occurs in two ways a pulse of light from its T=0 event, mirrored both inline a T=L/c event to be returned for a T=2 L/c event, and mirrored outline a T=L/c event, to return at the same T=2 L/c event, the two ways being commensurate: even as viewed by a 'passing relative' who agrees that events are 'events' (hence an event is a logical tensor invariant), but in either case it was roundtrip and we should confirm each 'leg'--
* (which resolves the "Twins Paradox" usually resolved as the relative-twin's shorter time for the real-twin's shorted distance; Note this solution does not require acceleration in its equation: 1. a longer run is proportioned to distance, time, velocity not to acceleration, 2. the twins synchronize clocks in passing at the T=0 event, and the traveling relative drops-off information at the destination, rather than decelerate and turn around...)
(Which seems specious that velocity advances and retards the time-now in any passing inertial frame ahead or behind as though it controlled its future and past but no locally real clock jumps its own reality... yet consider too the 'Zeno' Paradox for light: Tbias (light) = ±L /c , c → 0 between ±c as photons pass, and, light travels rearward into its past...)
But, now the trouble, the Ultra Paradox--
Or alternatively, the same ultra paradox--
So: as the T1 relative event is acausal, there is no Special Relativity at all..., Or, not by the present construction...! It was overlooked, possibly because ΔT²-ΔS² let T,S range together: easily missed in cases of equal alternates... It was overlooked, possibly because Michelson-Morley interferometry is not repeated in all 3D directions... (This is not like a co-moving-frames problem: this has no accelerations) Einstein's SR theory needs repair...!
We may reconsider co-moving width pinch of Bernoulli-Venturi 'inertial' flow In the vacuum-aether of space... we may try Cosmic Expansion where light-speed-constancy is only local, (Ultra-acceleration needs testing...), And lastly, I'd think to revisit the notion of time as quantum-entropy; But, 'til then' before next semester, "You just can't get there from here" (Equations don't dispute equations)... It's all part, of the calculation...
The Student can also find the relativistic lead's own L1' T'grid is way-behind on its time than its T'0 observer by the T'bias applied the other way the real observing the relative (and flipping the order of past and future relative events), so, in the farther future at their correct-sometime in each frame, the event occurs, but, each frame can certifiably state, that it has happened-or-not at a different moment than when announced by the other... no relative can 'tell the truth' to another, and if anyone changes velocity, their 'truth' changes... (*)
* (Consider a marking-test on the relativistic lead-L1' after, the Tgrid time the T'0 observer declares fait accompli but before it reaches the real-event L1... Does, it mark the lead-L1' because it was before, it reached--as stated,--Or does it miss, and mark the T'0 observer instead: because the lead-L1' was already past L1 per the Minkowski-relativistic, claim?!)
So, the Rocket-twin's inability to 'tell the truth' to the Earth-twin, and likewise the Earth-twin's inability to 'tell the truth' back, attributed to Time-advance/bias (cf the long-pole-in-the-short-barn-paradox) where such an advance means seeing the future of distant galaxies by a leader in the Rocket-frame, but for another to declare it in the same 'synchronized' frame is a simultaneity-mismatch in the other, frame, and there is no easy fix by including the other's velocity (for that can change later): so Einstein-Minkowski Special Relativity makes the 'god of physics true but every physicist a liar'... and better for all to shut-up 'til the event occurs and then compare notes... (not nice for mathematicians who 'sing for their supper')...
PART II: Gravity:
GRAVITATIONAL MASS-ENERGY EQUATIONS:
►A test particle (e.g. electron) falling into a singularity gains infinite energy by reaching bottom,
►Conservation of mass-energy dictates a gravity envelope-function,
►Where is the potential energy,
►If in situ its outer-space integral is infinite,
►(the spherical integral is constant for all radii),
►Potential energy is mass,
►Kinetic energy is deBroglie waves,
►Newton purportedly did only force and motion, acceleration and velocity, not energy—
►so we’re extending his:
►LIGO shows “black holes” are hollow:
►Each radiates 4.6% of its mass-energy, in coalescence,
►cumulatively radiating (1−4.6%)^n by n coalescence-pairings,
►(holing probably retains some of a neutrons star’s initial interior mass inside, but leaves most outside),
►Mass-energy is sucked out as potential energy in a collapsing neutron star,
►Potential gravitational mass-energy is distributed throughout the gravitational stress-field,
►recoverable at light speed, around,
►Gravity is the effect of mass-presence slowing light,
►Light bends by its nearward side slowing,
►Particles are like gyroscopes of light-in-place,
►Slowing of light captures photon momentum,
►Whence mass-field has angular momentum,
►Whence Mach’s Principle Effect,
►Gravity compresses ahead of moving objects,
►Massive stars drag the gravitational field,
►(similarly to the Big Bang dragging space to expand),
►simulating ‘dark matter’ because stars must move faster to ‘stay aloft’,
►Early cosmic expansion increased the atomic mass-energy,
►which decreased the deBroglie wave-size of atoms which decreased the total mass necessary for SN-1a,
►which results in dimmer SN-1a now and thus seeming to accelerate cosmic expansion “as dark energy”
►so the cosmos could-be the big-bang of energy sucked-out by an outer-cosmic quark-star collapsing— to ‘armageddon’
►interior structure the same for all mass-holes ergo small holes are hollow to extremely low percentage
►there is no singularity, except holes are singular not plural
►(calculate the spreading-movement of hole-outer-gravitational-stress-space as two merge)
NUMEROUS MORE DIFFERENCES:
►Einstein radial-gravity was the same as linear-acceleration—But, linear-gravity would be constant over distance,
►An electron passing through a double-slit interferes with itself—But, does a double-slit passing-through cause an electron interference pattern,
►Speed-contracted circles are ellipses with two foci,
►The derivative of acceleration is scalar ‘pump’, vector ‘swing’, (compare to Earth rotation)—But, Jerk’ is higher, (compare ‘squeeze the trigger, don’t jerk it’ implicates increasing force but little speed, whereas pump implicates increasing force for more speed, but, still-again, ‘pump the swing, don’t jerk it’),
►((look also at separation by parts of momentum-energy-transfer))
►Are there ‘two science-world views’—
►(Perhaps Einstein never really cared whether Newtonian analysis might come up similar),
CONSTRUCTION FRAGMENTS PILE: (non sequential, non series)
►The other obvious approach to Relativity (but counter-Einsteinian) was to assume time is, motion:
►thus tgrid = vc Lgrid/c similar-to-the-above but photon motion is, its time-at-a-distance
►(n.b. particles though perpetual-like are cycles continually affected by accelerations and fields),
►Example—a traveler sees photons from ahead at the place-and-time along their-own star’s frame
►with star and photons both advanced on the traveler-imposed time-bias, and same-speed of light:
►Coming from distance Dgrid ahead starlight will meet the traveler at time Deff/(c+v) = Dgrid(1−vc)/c,
►(the star at Dgrid is observed advanced tbias, dbias nearer and the rest closes converging at c+v),
►so = (Dgrid/γc)·(1−vc)γ = Dgrid(1−vc)/c by the star chasing its-own photons in the traveler’s frame,
►(the traveler’s observed contracted-distance, shortened by the star chasing it, uncontracted);
►and this has been suggested by some scholars as the real, impetus, for a special-relativity,
►and so they formulated ‘relativistic-doppler’ the same consideration, as special-relativity,
►(Einstein assumed single common velocity while Newton has linear stellar aberration),
►(maybe we’ll find an algebraic topological lift function between Einstein and Newton)
►(a sidebar observation here: cosmic expansion should be enlarging all orbitals);
►(similarly by motion of a traveling observer ‘here’ the universe ‘suddenly looks contracted’),
►(whereas by simple optical arguments objects ahead must appear as focusing farther ahead);
►a problem for stars moving ‘toward-or-away’ in far-distant galaxies, being nearer than their galaxy itself by their relative motion to the observer… not concerning cosmic space expansion nor galactic space drag, just doubly-extreme distances,
►the distance-ahead must be distance-re-biased or the cosmos has yet-another re-expansion-velocity,
►Also, if the traveler quickly-accelerates to relativistic speed, a photon is still its-distance-away in its-own photon-frame, yet its origin-star is closer by γ,
►Marking Test #2: A train shortened by relativistic speed leaves a station and at the next a painter slaps its engine with paint, but the observer on the caboose says the distance between the stations was the shorter and the painter slapped late and splashed the caboose… so, which, got painted…—
►(e.g. time-bias on a 5.76 millisecond pulsar at 510 l-yr thereby cycles ±28 years each rotation),
►(e.g. a star crossing a far galaxy at 0.4% c inline with an observer here jumps out of its galaxy),
►(to Einstein, gear time and grid time were real but bias was parallactic, or maybe none were real)
►Galileo used the term “inertia” differently from Kepler on Copernicus,
►‘fortune cookie—Clock with backward hands striking behind may be tachyon clock from ahead...’
© -2017 Mr. Raymond Kenneth Petry
A LONGER EXAMPLE PARADOX:
For γ ≈ 360, V ≡ c (1-½γ-2), taking 1 yr ≈ 360 dy (an old-3600-day-decade year),
Let L ≈ 1 l-yr so that the fast-relative takes 1 yr + 2 min and it measures L' ≈ 1 l-dy,
So, T1' ≡ L' / (c+V) ≈ 0.5 dy, And so, L1' ≈ 0.5 l-dy, And so, Tbias ≈ 0.5 yr, And so,
Tgrid:0(T1') ≈ 0.5 yr and is halfway at L / 2 ≈ 0.5 l-yr - 1 l-min, As so it was said…
But now let's also add a beacon from the L-mirror, also sent at Tgrid = 0,
So, the lead-L1' is already just seeing the beacon at (T0'≡T0=0) + Tbias ≈ 0.5 yr,
which L0' announces at T0' ≈ 0 ('pre-dicting' as usual for its lead-L1'), continuing…
So at 0.5 yr reaching 0.5 l-yr where its lead-L1' is γ-contracted just 2 l-min ahead,
So, the L-mirror-beacon meets the lead-L1' where both, are, on the real grid—
So at this event the Tgrid is seeing the lead-L1' when, it is supposed-to…
So, the question becomes: "When, did, the mirror-beacon light up--?
The L-mirror itself must be almost there too-- (Tgrid ≈ 1 min. behind)
as it was traveling only ½γ-2 shy of light-speed... so, Where, is it...really...?!
ANSWER: The L-mirror-beacon lit-up one,-year,-prior: one light-year-relative-time...!
There is no gamma-time-dilation on Time-Bias ≡ Relative-Time!
THERE ARE TWO CLASSES OF SOLUTION one-or-more to be found:
1. Set Tbias = 0 in the real frame and let the 'olde' relativistic equation be revised,
2. Minkowski, misunderstood, Einstein, and we should revise the 'olde' Minkowski,
2.a. Einstein meant relative-at-one-point-only like a baby is born-relative-once,
2.b. Minkowski thought a wooden ruler, made relatives within an inertial frame...whence his arithmetic fit a long pole in a short woodshed, But, Einstein, were he thinking on his original thought, would've had the woodshed frontdoor observer measuring relativistic shortening of the pole-not-entirely-in meanwhile the reardoor observer a shorter pole but already-sticking-out...the long pole,-not,-fitting... Einstein meant shortening-per-observer, cf a concave lens shortening length for each observer viewing through one side each... Einstein meant length calculated-as 'velocity-times-time'-per-relative-observer...
2.c. (But note also, this acausality paradox also exists for Einstein's alone, but, does not involve a 'thing' in the relative frame--It is certifiable arithmetic, only.)
2.d. (Note also: If the fast-relative twin could abruptly stop within the real twin's next few subfractions of time, the certified relative future vanishes...into...the...future...!)
2.e. (Sidebar-note there's no gamma-time-dilation on Time-Bias ≡ Relative-Time; Einstein's Special-Relativity one-year-ago-real equals one-year-ago-relative! Minkowski's proper-time, spacetime-dilated-time-calculations are sometimes convenient but meanwhile time-itself still exists--in its primitive, real, form for other, times; Spacetime observation times are merely offset so that a 'caboose' is not on its 'engine' time...)
So, We remove the Minkowski assumption, and review the Einstein-experiment original: (We may also find a Minkowski-like matrix for geometry and such...)
We'll take L' = (L-Lgrid) / γ for any-and-every relativistic view of the experiment 'real' frame, for each-and-every grid-position: There is no longer contraction of the real in the relativistic frame, but per-observer... The paradox still exists because even to the relativistic single-observer, though there is no relativistic co-observer, the T1 and T1' events still occur and get reported--the photon still bounces on-time at the mirror, and the mirror-observer there still promptly sends a report of the event, as in the Minkowski depiction, of the past century, but it's only the real-observer by designation who was indeed already there in the real experiment: there is no relativistic-observer ('thing') leaping ahead of co-reality: there is no certifiable 'stooge' in the Einstein picture...just his imagination, and his arithmetic, as before...and those are measurably the same-relativistic dilations and correlativistic contractions in the single-observer's view...
But if we wish further, we can press this problem to certifiably-not,-certifiable (other meaning), by setting Tbias = 0 in the real frame, and reconsidering Co-Moving constancy that had been assumed but that's not true for electric charges (motion generating magnetic forces) and should it be so true for inertial mass...cf gravitational mass to electric charges 1042 stronger but when neutralized leave the residual gravition, so inertial-mass-motion should be weaker pinch effect by 10-42 less than charge-motion pinch-or-repulsion magnetic effects...
As we've shown, SR is the translation-back to "what-actually-happens-now", SR is the 'advanced field' for the very-shrunken accelerated frame.
Other possible investigations include, like for gravity, that fields-ahead are shrunken and fields-behind are stretched-out...moving the center-of-field-weight ahead of a moving object pointwise-definition...this is almost redundant to the present accelerated-frame derivation but meaning rather in terms of objective, evidential, 'here-it-is' proof...(cf just for examples, trying to explain where-the-energy-is in a particle at a velocity does it increase its mass-energy or rest-mass or gravitational mass, or like trying to explain where-the-magnetic-field-is in electron-flow while moving the wire-mass itself of proton-counterflow)...
The inline photon roundtrip time is T2-T0 = (2LC/C²-V²), and the perpendicular, assuming aberration, is T2'-T0 = (2W/√ C²-V²) ... Obviously -mathematically- not equal....
At this point in the discussion the 'Einsteinian' theory declares that as this is not what is observed, that objects in-fact remain self-synchronously intact, thus T2'=T2 ... but gives no reason for Lorentz-Fitzgerald -object- contraction: It is not Frame contraction:--
It is not, Frame, Relativity-- but virtually declares an absolute-aether-causation to 'Einsteinian', relativity....
BUT LET'S ALSO TRY THIS THE 'FORMALISM' WAY:
Assume a flat space, --meaning outward-bound objects if they return come back the way they went except-for plus angular moment which is conserved,-- And two rockets each in its own galaxy separated 10Glyr (The gedanken experiment is the same at 1lyr, or less impressive) and fueling-up, and-- at our-same-instant both leave station and accelerate as-it-happens exactly the same direction, same acceleration, same time, same velocity, same distance...
Does, the distance between them shrink as-if they were a particle-pair, Does either jump out of its galaxy to make up the shrink loss--? despite, the fact that neither can have moved faster than the speed of light, and the fact that Einstein never suggested that the rules of acceleration should change....
Apply the Special-Relativistic formalism: There are two (2) Events, though they appear the same instant in the galaxy frame, they are nevertheless, together, two-- separated by the great distance, And within each frame we allow that SR holds: the rockets shrink and time dilates -in our, observation, of them,- But we allow also that they don't jump lightyears toward each other in our galaxy observer frame... because there was no difference, to be, Albeit, SR wants there to be, simply because it imagines them to be within 'its' frame.
What happens then, is, They each observe each other at the split-instant before the launch event, and then again after they've reached lightspeed, assuming this to be fast process, and the forward rocket observes the rear to have shrunk the distance between them, having started earlier on the timeline, And likewise the rearward rocket observes the forward to have started late and so shrunk the distance between them... This is in their-view having split the launch event: We see neither rocket leave its galaxy, nor either galaxy shrink. But they, see each other shrink-with and-dilate for being observed in the galactic frame: for being another, a second, event, observed therein-- else the 'lead' should observe the the 'lag' slip behind its very launch station as the cosmos shrinks forward between them: Exactly contrary to the claim of SR for what-shrinks and what-dilates and what-doesn't.
Liken this to two muons created in the high atmosphere: Each dilates time,and shrinks, but neither jumps ahead in our Earth-spacetime-frame, And each sees the other doing likewise.
A clear contradiction to SR, unless there is, no flat space, or, there is no simultaneity: Hubble observed the apparent loss of simultaneity: Objects at great distance appear to be time-disproportionately delayed to the reference time, and moving away at great speed ... (though in reality, it's just speed proportionate to its directional distance).
NOTE TO THE READER: IT IS TIME [20110803-11]
The author is preparing a short booklet of a few pages and diagrams to explain the first order correction to Einstein's Special Theory of Relativity: The final result, when published, will make plain all the funny stuff about neutrino mass and velocity (by neutrino shaping per electron shaping and high-energy longevity), and quantum-entanglement faster-than-light, and show a most-amusing result that the Special Theory, for all its accuracy, is but an Almagest of bizarre equations, that, for all their accuracy, must imply that 'we' are probably one-level away from understanding the exact coincidence of mathematical metric theory and astrophysical spacetime theory: which hitherto was only ever an approximation, (cf the Thompson theory of the smoke-ring-atom we discovered one-level away from understanding what electrons, are).
[The following is being prepared as a powerpoint-presentation]
High Energy Astrophysics
Mr. Raymond Kenneth Petry (Senior Visitor)
Extracurricular - Presentation
Nov. 6, 2011 (preliminary draft)
FIRST ORDER CORRECTION TO SPECIAL RELATIVITY
Special Relativity theory, published a century ago, was a lemma to a conjecture that the speed of light en vacuo was constant in all directions: Doctor-Candidate Albert Einstein assumed it so, and published his consequences; The Michelson-Morley tabletop interferometry experiment had shown the speed of light equal in a few pairs of directions, Lorentz-Fitzgerald answered it with Length-contraction, Time-dilation; Others raced to up, theory and practice: Minkowski introduced his Invariant, for computing this new space-time with mathematical, conventionality; Hilbert almost beat-out Einstein publishing his equations of General Relativity....
But--nobody so-much-as checked Einstein's arithmetic: the bounds of functions: Albert never checked that his work was complete, meanwhile decrying quantum-entanglement for bucking his concept of Locality, And earned some chiding that he must've done poorly as a boy in mathematics, But neither did Hilbert, check...
Withstanding, quantum-entanglement faster-than-light, we herein redress this mathematical grievance, and CHECK Einstein's bounds→
(A COLORING BOOK FOR HIGH ENERGY ASTROPHYSICISTS,
DOCTORAL CANDIDATES, AND PROFESSORS EMERITUS)
SIMULTANEITY: Solved. (Physicists had misassumed it to be possible.)
SPATIAL RELATIVITY: Solved. (It came from a hundred light-years away.)
THE RELATIVISTIC TWINS [CLOCK] PARADOX: Solved. (Non simultaneity.)
SPOOKY ACTION AT A DISTANCE: Solved. (An open-jaws experiment).
HELICITY FASTER-THAN-LIGHT: Solved. (An open-jaws experiment).
DARK-ENERGY ACCELERATED-EXPANSION OF THE COSMOS: Solved. (The equivalence of spherical cosmic radius and linearly expanding motion.)
THE AGE OF THE COSMOS: Solved. (The universe is as old as it is big.)
DARK MATTER: Notes. (Still a linear combination of MACHOs and WIMPs.)
THE TRUE SPEED OF LIGHT: Half. (Half the distance recorded at halftime.)
THE NEAR FUTURE DISCOVERY: (When the Almagest equals the Reality.)
PRIMER: SPACETIME RELATIVITY, ONE FRAME - PARALLAX: (classic)
Suppose an Observer Frame, far from gravitational influential effects, and, every event occurring in this Frame: This is the way science has been done thousands of years on Earth: despite Earth's solar orbit and gravity-well... But the notion is, calculable for objects and events passing in gedanken (thinkabout) experiments:
Suppose on the far side of our Frame an interstellar beacon flashes as it passes exactly-aligned-center, a marker there, the light travels 500 seconds to reach us, while the object continues-on 15000 kilometers, gliding 30km/sec. Slowish but→ Its light appears in a direction advanced 10-4 radians, forward of its new position, relative to us, due to Stellar Aberration: whether it, moved, or we moved... But→
This shows the difference between Observation, and Measurement: We know by observing-devices and estimate by calculation where the object is at the moment of its beacon flash: Physicists usually try to observe the measurements of events confirming their calculations, but astrophysicists usually try to observe the events and deduce, the measurements, But, this is not always possible or convenient...
PRIMER: SPACETIME RELATIVITY: TWO FRAMES, ONE EVENT: (basic)
We assume, per Einstein's Special Relativity, physics events will result the same when repeated anywhere within Euclidean flat space, And we assume the speed of light is constant, 299792.458 km/s; Then, we derive and CHECK, calculations.
Now: Suppose we measure a system of photons bouncing among mirrors in one frame, from a second frame moving past at high speed: Because the speed of light is constant according to spatiotemporal measurement in the second frame as well, photon motions must be correlated -convolved- with the selected frame measuring the system: Artifacts must be measurably-and-computably-real not merely measured as apparent-parallax....
Special Relativity for velocities, notices that perpendicular paths of lengths equal in the Rocket Frame were very unequal, both length and transit time, in our Observer Frame: Mensurability required that the other-Frame be time-dilated and length-contracted, and their transformation equations would advance the lag-direction time over the lead time: All might have been thought good-enough-for-government-work, but length contraction seemed to violate the speed of light and acceleration at great distances in the cosmos, and time advancement would necessarily jam the Frame edge on causality alone.
(There seemed to be a merger of measurement-and-observation where parallax would become the Special Relativity standard, measurement and calculation....)
Case 1. The Clock by perpendicular light beam: The onboard beam travels side-to-side W = CT, but that in the exterior Frame is a longer, triangular-hypotenuse path of length
L' = CT' = √(W2 + (VT')2), for width W, time T, relative velocity V, lightspeed constant C,
resolving to CT' = CT / √(1-(V2/C2)), or T' = T / γ, the usual-famous Relativistic equation with its gamma-curve Contraction-factor γ = √(1-(V2/C2)) (sometimes-as the reciprocal);
(γ, represents the simplest, constant substitution: 1/γ occurs as readily as γ.)
Case 2. The Clock by collinear light beam: The onboard beam travels end-to-end front-and-back L = CT, that in the exterior Frame is a pair of unequal, longer, paths of length
L'1 + L'2 = (CT'1 = L' + VT'1) + (CT'2 = L' - VT'2) in total, for length L, path lengths L'1, L'2,
resolving to L' = (C-V) T'1 = (C+V) T'2, or T'1 = T'2 (γ*2/γ2) and L' = ...
resolving to L'1 + L'2 = (Lγ / (1-(V/C))) + (Lγ / (1+(V/C))), or L'avg. = CT'avg. = CT / γ.
These relations were then superseded by Lorentz Transformations and their Minkowski spacetime Invariants: X' = (X+VT)/γ, T' = (T+(VX/C2))/γ, (Ct, x; y, z) = Ct + xi + yj + zk.
(We should also expect 'Bernoulli-Venturi' Contraction on the perpendicular, but the shrinkage would be common-- and, so, Observable only at great distances.)
Altogether, the only valid sense of single-event is when the object is self-connected: not Frame-Relative per sé though that was the special case in the original experimentation: Mirrors running parallel remained parallel but collinear mirrors needed reinforcement....
But is also seems obvious that a moving Frame is always uptodate....
Clock Simultaneity Paradox
Suppose two Stellar triplets have synchronized their clock-time (to the average between them). The Rocket triplet goes the distance-- But finding that distance contracted, arrives sooner (All time-dilated the same) and cumulates less time;
But then paradoxically, as v → c and the Rocket's distance → 0, its rider reads both Stellar clock times → 0, when contrarily those clocks read of the long wait all-those-years for the Rocket to get light-years from one to the other...! BUT→
Spatial Simultaneity Delay
Since there is no-way, by no-means of Rockets passing, for either Earth-sync'ed
clock to jump into the future before its own present, the clocks at a distance must
have instead been 'late' to begin-with, and the Rocket passing revised its view of
'weird' static-time-offset: Only Present-here is Now, while all others, proportional to
their distances, are late, younger, behind the present-here-and-now...! BUT→
consider a broadside
wave-pulse from the train not-only radiates from the initial place, it should travel
backwards and suck-around the end of the train like windflow compressing over a wing
as the train moves forward: except the charge-balance in a photon keeps it intact as a
wavicle...wagging the other way on the negative-return-half-wave... or so went
the longitudinal theory of photons... yet corotating stars suggested not...
EXAM QUESTIONS: (relatively fun)
MORE PARADOXES TO RESOLVE: [2014/12/06]
If we set up an experiment like the original interferometer 'clock' but use a sublightspeed particle, it seems a priori that the particle has its own frame and moves differently relative to its original Earth-frame: E.g. for a particle moving at v, perpendicular, and the fast-relative-(frame) at v, parallel, the two are moving relative to each other on their 45° angle with co-relative velocity very shy of that needed to keep the particle on its perpendicular track: (2v√½/1+½v²)), shy of needed v, parallel.
And a Newtonian-relativity paradox that needs-be-solvable doesn't appear any easier in Einstein-Minkowski SR: TO WIT: By symmetry, a test-particle in the frame of a Z-particle decaying to an anti-pair of relativistic electrons β± viewed from the frame of one of the two escaping, should gravitate toward the original barycenter (of the Z system), but the mass-energy of the kinetic velocity, when viewed offside like this, seems to belong-to-the-other and therefor the test-particle would be drawn to the other the relative-faster... We need identify what-and-where is the mass-energy of kinetic velocity—is it internal, like mass, or external, like magnetic-field... If we assume it is lightlike rather than restmasslike, the misdirection is more pronounced... unless a particle in its own frame has a standing deBroglie wavelength...
If an electric wire carrying current is moving at exactly the opposite velocity of its 'drifting' electrons, then its magnetic field must be emanating from the excess protons... but nominally-all the protons are in-excess, so from-whence does the magnetic field emanate, or is it pointwise-slightly different from the magnetic field of the fewer, more-individual-like, conduction-electrons... magnetism is a collective far-field and, transporting energy, must have a deBroglie momentum wavelength—but, is that shorter, by 'collective entanglement', (See also The Faraday-Maxwell Tease (trailer) centuries-old transformer equivalence 'extras' Maxwell's Equations skipped)...
A CONCEPTUAL EXPERIMENT: 
SO—REVISING SPECIAL RELATIVITY:
We start by removing Einstein's professor Minkowski's fluky-flunky arithmetic to give-back Einstein his infamously-purported "D in Math..." Einstein, perhaps interested more in realism, than in mathematic'ism, meant relative-at-one-point-only, like a baby is relative-from-birth... Minkowski, on other-handedness, thought a wooden stick, made relatives within an inertial frame...and thence Minkowski arithmetic fit a long pole in a short woodshed, But, Einstein, were he thinking his original thought, would've had the woodshed front-door observer measure relativistic shortening of the pole-not-entirely-in, meanwhile the rear-door observer the shortened pole-already-sticking-out...the long-pole-not-fitting... Einstein meant shortening-per-observer, cf a concave lens shortening length for each observer viewing through one side... Einstein meant length not as material but as 'velocity-times-time'-per-relative-observer: an arithmetic property having the same unit of length but not a 'thing', (physicists drop too many units too often, to be understood in any one statement)... Einstein was allowing for certifiable arithmetic, not certifiable observers, but Minkowski by meso-matics thought any equation could be applied to things, because 'things' were the objective thoughts of physicists who were not mathematicians by intents-and-purposes...
THE OTHER END IS RUNNING LATE: (causality, and the correction to Special Relativity so-thorough it obviates it)
So simple it's like Newton fixed for finite light-speed (had he known)--
A quick summary of the ppt-video: An object everywhere-equally accelerating-forward in the Earth frame does not change length as the double-integral of zero-differential-acceleration does not produce a change in relative position, (at least not noticeable below relativistic speeds, say 0.1 c where γ = 0.005), However, in the accelerated frame itself each component sees the other components starting and running late—proportionally to distance, observing at the speed of light—and so there is a velocity difference in this accelerated frame...and, importantly...this difference is in the coordination, and peculiar: the front appears to close-in and the rear appears to recede... But 'perhaps strangely' the change in distance is proportional to the velocity, whatever the acceleration (easiest explained if the acceleration is constant), and the distance...and...exactly compensates the time-bias acausality of Einstein's SR...so that there is, no, acausality...but importantly also there is no inertial "equivalence principle" and, this means SR must be reconsidered on this proof-by-(mathematical)-truth and, SR is still necessary to get the answer of where-the-other-components 'right now' see themselves--because the other-component observers, though seeing them mere-instants-away, are instants seen measured no longer in velocity but in portions-of-the-speed-of-light...this is simply the 'reality' of finite light speed and spacetime...and...the next important result should-be that the constancy and isotropy of the speed-of-light is also, a result of 'pure' mathematics on spacetime (but not all perfectly 'clean')...
(Its self-forward-length-contraction -v/c term exactly cancels its self-forward-time-bias +v/c , and contra-similarly its aft-length-extension and aft-time-bias, and thus proving the falsity of the supposition of an inertial "equivalence principle" yet keeping a second-order-but-not-more-SR-like-γ-correction for translating to 'what-actually-happens-now' in the unaccelerated frame... it may ultimately make-simple-or-prove-why lightspeed appears constant isotropically at all speeds)
The example (indicating its mathematical simplicity) from the ppt-video is:
Note the fine point: This numerical analysis example is a one-digit approximation to an exponentially-diminishing slope, e-0.1 ~ 1 - 0.1 + 0.005 ≈ 0.905, with an average forward-closing-velocity and-time-slip ≳95% an order-of-magnitude-larger ≈20× than SR γ which is only its ≲5% approximation-difference...
THE INTEGRAL SOLUTION:
Acceleration exhibits three main phases: (for a simple case of constant acceleration)
* [I'd found immediately, unexpectedly, in learning Einstein's Special Theory of Relativity, in college, the assumptions seemed purely calculatory and wrong, (co-moving widths without Bernoulli-Venturi pinch effects), and reference-less, (the rear contracted toward the front, and the front toward the rear--of the 28-Glyr-wide cosmos), and the meaning detached (mass-energy coordinated purely vacuously to its mathematical number field space) and the discussion jumped from simple notions of 'time' dilation and 'length' contraction directly to advanced calculation of spacetime transforms--without calculating how to ever get there... leaving students grasping its confusion of what time means having two components, clock-tripping grid time minus gear-time with its slow-turning hands, to calculate the necessary time bias everywhere × everyspeed now; meanwhile time is not really dimensional but a quantum-entropy-æther-property-transfer rate; And, the learner should have received an explanation of why only some, of these physics properties, had been included in the theory: why, inertial, mass was simplified to nothing, but gravitational, mass was given a whole new theory....
(N.B. College professors usually wait 'til General Relativity, before declaring that there are not, two, kinds of time, But here we derive the two and further point out that in the current theory, raw time, is not entirely absent from SR equations: For the relative to calculate when, the future was at Tgrid = 0, 'he' must refer back to 'his' past exactly the same, undilated, Tbias...which may help in fixing SR.)
(N.B.#2. The Twins Paradox does-not require acceleration: the passing relative merely synchronizes 'his' clock at T0, and desposits 'his' information at the destination point: without slowing...)
Recalling that 'Einsteinian' physicists presume the time-dilation and length-contraction is in the 'observer's frame itself, we must ask the obviating questions e.g. how would a train ten light-years long shrink two light-years while accelerating at about an Earth-gee to very near the speed of light in a year's time: part of it would have traveled backwards, or part of it forwards faster than light, contradicting the entire theory and practice, but not calculations... (A similar discrepancy in corotating stars was noted in his century-ago early era of Special Theory).
I've concluded a disproof of the original Theory of Special Relativity though I'd studiously expected a development or extension such as the lightspeed-expanding event-horizon around every event (bound under the Schwarzschild radius in cases of extreme mass): There's no Einstein-Minkowski inertial-frame-co-relativity as such...
For reproof, so next semester may be taught, the first approach to the resolution is to let contradictions become constraints replacing assumptions, e.g. the comoving width is a leading candidate.... It's still interesting that the cosmic æther is mathematically simple....
FROM HERE: We'll see that the calculation of T1 is correct in both frames and for all four observers, the Earth and its L-mirror, the fast relative and the lead observer, and realize that the only faulty claim is that of the fast relative's immediacy obtruded on knowing that the relative frame is presynchronized: which is equally true for the Earth frame observers presynchronizing Earth clocks... the concept of here and now becomes stranger than the General Relativity which was once said to be understood by three physicists.
ALTERNATIVELY: It may be said that a 'problem' crept into SR, that is the inability of any 'physicist', to tell-the-truth about what's happening within 'his'-own-self-synchronized frame: Because of time-biasing, each 'observer' must calculate-in each-other's velocity in order to 'tell the truth' to each other, but when-and-where is ambiguous, and changes if either changes velocity. Solve for a common when and where.
A NOTE TO STUDENTS: The concept of causality begins with the setup of an experiment followed consequently by its results, So, experiments in school, work according to the procedures, but, SR claimed that results could be observed sooner by a fast-relative but when in fact the real-observer knows, can ascertain and verify, the relative's lead L1 has not yet arrived hence the relative claim of certifiable early-sight is acausal not causal: only seeming causal by faulty predating, an assumption plying on the setup reliability...
* [We note also that the Biblical Book of Daniel by several storied analogies discusses the perceptual relations of space, counting steps on two horizontal dimensions and weighing on the vertical third, and of time, dividing the past and future and as the divisor of rates of travel and travail, and, as exposed by perfect fire aka light on three-dimensional objects, 'hats and hosen', revealing the timely fourth like another dimension, ruling over all]
P.S. In the college textbook, Spacetime Physics, Taylor and Wheeler, 1969, it was understood that Special Relativity had been tested as many-times-or-more than Euclidean-Newtonian theory; But the review and correction herein is nontrivial—the true test was probably never done before....
A premise discovery under the title,