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Twin Paradox Resolved in Relativity, in Absolute Terms

    That two reunited clocks show a disparity in their recorded time
    is proof that the two clocks experienced actual differing clock
    rates while in differing states of uniform linear motion. If the
    disparity one can see at the same place moment is a reality, then
    so too is the notion of actual differing clock rates a reality.
    Those two realities are inseparable. They are one and the same reality.

Probably ninety nine percent of commentators on relativity will simply state, without qualification, that there is no absolute frame of reference.

What they are referring to, is our inability to determine whether any particular inertial frame might be at rest with respect to an absolute frame of reference, such as the universe itself.

Relativity, developed in absolute terms, is not only completely compatible with Einstein's special relativity, but in fact subsumes it.

There are more solid common sense reasons to believe in the underlying reality than one can shake a stick at. Conversely, without such concept of an absolute frame of reference, one is left with confounding "explanations" of both the twin paradox and the symmetrically mutual assessments across inertial frames as we know them in relativity.

    One should never suggest (as they so often do) that there was
    some sort of "jump in time" involved with the change of inertial
    frame (meaning at the turn-around point). The simple act of
    starting a clock as an inbound astronaut passes an outbound
    astronaut cannot possibly create a "jump in time". (Remember,
    the outbound astronaut hands off his clock reading to the
    inbound astronaut.)

    One should do a search on Einstein's clock synchronization,
    and its bearing on spacetime diagrams. He or she will find
    that the notorious "jump in time" is built into that clock
    synchronization, because it gets instantly replaced with a
    different synchronization when a new inertial frame is adopted.

Since there is no jump in time on the earth clock (or a jump in aging for the earth-bound twin), the suddenly returning astronaut's perception (identically "calculation") of a "jump in time" for the earth clock is in fact a misperception (identically a "miscalculation") forced by Einstein's convention for synchronizing clocks.

All the measuring results as we know them in relativity can be derived independent of Einstein's clock synchronization. In fact, Einstein's clock synchronization can easily be diagrammed, and thus seen for what it is, against the absolute frame of reference.

It is because clocks do actually slow down and aging does actually slow down, that two reunited clocks show an actual disparity in their readings and two reunited twins do show an actual disparity in their aging.

The time contraction formula [t' = t * sqr rt of (1 - v^2)] is not linear. That is why the party who changes frames to bring the two parties back together will register the least amount of time on his clock with the symmetry of the situation preserved.

The actual distances relative to the universe and actual speeds relative to light speed will vary depending on which party changes frames, but the parties involved cannot possibly detect that. That is in keeping with the postulates and deductions of special relativity.

Time-keeping, distance and speed are interminably bound in one equation. Therefore, actual differences in clock rates implies actual length contraction dependent on actual speed relative to light speed. Actual length contraction works in combination with actual time-keeping contraction to preserve the symmetry of measures across inertial frames.

There is clock functioning at every level, dependent on actual light speed, at even the atomic level. Our observations and measuring paradigms of every nature are constrained by the speed of light, as is our "synchronizing" of clocks.

Special relativity can be charted out in actual terms (absolute terms), where light speed is constant in an actual sense. All the results of special relativity, including the consistent measured speed of light, fall naturally into place when charting these actualities against the rest state of the universe.

Actual time-keeping and length contraction arise naturally from the fact that all phenomena are dependent on the speed of light, which is itself invariant in actuality, being massless.

Consider that A.P. French writes on page 150 of Special Relativity: "Note, though, that we are appealing to the reality of A's acceleration, and to the observability of the inertial forces associated with it. Would such effects as the twin paradox exist if the framework of fixed stars and distant galaxies were not there? Most physicists would say no. Our ultimate definition of an inertial frame may indeed be that it is a frame having zero acceleration with respect to the matter of the universe at large."

In Mach's Principle, an object is affected by a change in motion relative to the matter of the universe at large. But such effect cannot occur unless the object is in a relationship with the matter of the universe at large regarding its state of unaccelerated motion to begin with.

Remember, an effect due to a change in motion is not simply an "either or" effect, rather it is an effect of degree based on "degree of change". No effect of degree stemming from a degree of change can occur unless there is an effect based both on initial state of motion and final state of motion. Put another way, a change in motion in the context of the universe is not meaningful without motion itself in the context of the universe.

Mach himself regarded the matter of the universe at large to be an actuality, and the effect on the object to be actual. We can't have it both ways. If the matter of the universe at large is a reality which has an actual relationship with an object concerning a change in motion, then so too is it a reality which has an actual relationship with an object concerning motion itself. (And again, our observations (measures) are something fundamentally different from the underlying reality, a reality which generates our observations (measures), which can occur only at light speed.)

    In SR, Einstein was able to make an absolute frame of reference
    superfluous by postulating only the constant measured speed of light.
    In GR, he made Mach's Principle superfluous by again holding to only a
    postulated measured speed of light.

One can relocate oneself relative to ones house can one not, by traveling from the living room to the kitchen? Can one not relocate oneself relative to the universe by traveling through it?

A spatial seperation between two objects can actually be achieved, rather than merely seem to be achieved.

Thus, there actually is relative motion.

My house actually exists, even though it is not perfectly rigid. I can actually move relative to my house, despite the fact that all the elements of which my house is comprised are moving about relative to the overall structure of my house. I can actually travel from one end of my house to the other end. And in so doing, I affect the motion, relative to my house, of each individual element of my house.

The universe does actually exist, rather than merely seems to exist.

Thus, there actually is motion relative to the universe.

After all, how can you agree that there is actually relative motion, agree that there actually is a universe, but not agree that there is motion relative to the universe.

All the elements of the universe are moving about relative to the overall universe.

Also, one obviously does not need to be at the barycenter of the universe to be at rest with the sum total of the universe. You don't need to be at the center of your house to be at rest with your house, do you?

Light, being massless, has a constant and maximum speed as it moves through the universe, and all objects move at some fraction of that speed, the speed by which all other speeds must be defined. If the speed of light is real in a real universe, then the speeds of objects are real in a real universe.

I have other documents online which expand on this topic:

Twinparadox.pdf includes a table of an analysis of the incrementally building time differential of the Twins Paradox.

Relativitytrail_abstract.pdf discusses the absolute version of Einstein's postulates.

A Twin Paradox animation. Light rays and traveling twins are diagrammed in absolute terms against the (experimentally undetectable) rest state of the universe.

Twins Paradox Explained

Relativity Trail, with 210 pages, 65 diagrams and 75 illustrations, will provide you with complete detailed arithmetical derivations of all the kinematical effects of special relativity. Everything is charted out in absolute terms against the rest state of the universe for perfect clarity as well as soundness of theoretical basis. It is the totality of the universe that imparts the inertial properties of clock rates and lengths which generate the effects of relativity. This is explained in detail in Relativity Trail.

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