|A. Einstein's relativity double-integrated zero-differential acceleration front-end-to-back of a near-lightspeeding train and accumulated nonzero-differential distance, but this does not work in mathematics, And even worse, his original event-interferometry-clock was trippy, paradoxic, acausal (*), and regularly breaking (modernly remedied) while accelerating...|
[See also ppt-videos "the Einstein-Minkowski Acausality Paradox (trailer)" (*) and "Correcting Einstein: The Other End Is Running Late (trailer)" (*)]
* (the Ultra Paradox of acausality, versus, its solution by correctly developing the spacetime coordination transform in an accelerated frame: its self-forward-length-contraction -v/c term exactly canceling 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)
[See also angular stellar aberration, harmonic magnetism, and The Faraday-Maxwell Tease (trailer) incomplete by a centuries-old transformer equivalence]
FOREWORD: (April 20th 2017 as I expect to be referring to this in class this week I'll post it here this minute)
Einstein's original(?) diagram showing 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 (possibly the original cause somebody cranked that Einstein was a "D-student in math"): 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 my work-in-progress, Linear Stellar Aberration, for the proper analysis of acceleration)....
(Further problems with his diagram included its asymmetry of forward-vs-backward travel implicating not just temporal dilation but distortion of dwell-time, which I used for a moment in my screenplay "StarTrails Game" 2000, as to whether fast interplanetary speed might electrochemically alter among familiar flavors of food...)
P.S. Later that day we looked at Einstein's claimed '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 start late, so the front appears nearer and the rear appears farther, and so time-synchronized photons from the front and rear in the train's own frame will not-meet at the center... i.e. there is, a preferred, frame reference.... Early analysis had allowed for natural-shrinkage of atomic distances and whence objects' lengths compensating where time-is-distance, but if the speed of light were fixed in the accelerated, frame, it could no-longer be symmetric by its compounded shrinkage retained even when it resumes 'inertial mode'....
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... the mathematical difference accounts for Einstein's 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...
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, (he won a Nobel Prize for the photoelectric effect 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 checked his arithmetic (else would he have seen the time-space coordinational distortion we'll examine momentarily, 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 the grandiose-unification theory, leaving their dust under the 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...
Let us answer the questions--
OBJECTIVE vs. SUBJECTIVE ACAUSALITY (There is no Frame Relativity)--
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 lightspeed measurement experiments--a few seconds...
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' which is the hallmark of mathematics getting every step correct from the beginning rather than wading through heaps of smelly approximations)...
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...)
N.B. By such Clock-tripping, Tgrid (real) = T(real) * γ² , Special Relativity has two timing considerations, Tgrid (fast) and Tgear (slow) , so now--
(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')...
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: (Solution to the Acausality Paradox, and 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')...
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)
EXAM QUESTIONS: (relatively fun)
[under construction, and this whole article is being rewritten for direct-reading]
MORE, IMPORTANT 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... 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... (tbd)
Space-Time-Light-Relativity (a conceptual experiment) 
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→
Conservation of space-time-mass-moments (It is notable what many moments are conserved) 
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...
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; The review and correction herein is nontrivial.
* [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 unto itself]
A premise discovery under the title,