Space-time is a construct, entirely dependent for its existence on Einstein's particular (and entirely optional) method of clock synchronization. The best one can do with a space-time argument in the context of the twin paradox is to note that one party, when changing inertial frames, will observe a jump in the reading of the clock time of the other party, using the 'lattice of clocks' method dictated by Einstein's particular clock synchronization.

But since no such jump on anyone's clock (or identically in anyone's aging) actually occurs, it is a false jump in the reading of the clock time of the other party.

In contrast with the space-time argument: When the two parties check the status of each other's clock with the regular sending of radio pulses, they note an incrementally increasing time differential, first noted at the turn-around point. That real-world experiment reveals the real incremental increase of time differential.

[William Geraint Vaughan Rosser (1991). Introductory Special
Relativity, Taylor & Francis Inc. USA, pp. 67-68.]

[Luebeck, R. (2008). Relativity Trail, L B Writ
Publishing. Mpls, pp. 12-14]

[Luebeck, R. (2008, Sept 1). Relativity Trail.
http://relativitytrail.com/relativitytrail.pdf pp. 12-14]

In short:

Space-time is a construct, dependent on an optional clock synchronization method, and generates a false jump in time reading.

Space itself is not a construct, nor is time-keeping. And a real-world experiment reveals a real-world incremental increase in the time differential.

It is precisely ones motion with respect to the universe that dictates the actual clock rate, resulting in the actual time differential upon reuniting with the other party. As the time contraction equation is not linear, it is always the party that changes inertial frames that will age the least, based on the combination of his speed relative to light speed and his distance covered in absolute terms.

It has been known for 111 years that relativity developed in absolute terms is consistent with Einstein's purely relative treatment, yet the public remains largely misinformed.

John A. Wheeler, in his book "Spacetime Physics", states that there is no physical experiment which can distinguish Einstein's purely relative approach from an absolute approach. [Wheeler, J., Taylor, E. (1992). Spacetime Physics, second edition. W. H. Freeman: New York, p. 88.]

Einstein's treatment of Special Relativity is limited to assigning measures that parties of different inertial frames must make of each other's properties, for the satisfaction of Einstein's postulates of measures. Einstein's treatment does not in any way address the question of where the missing time has gone in the twin paradox. Einstein himself regarded the time differential as "peculiar" and never attempted to explain it. Identically and necessarily, space-time cannot address it. The jump in the time reading upon changing inertial frames is simply built into Einstein's clock synchronization.

All the results of Einstein's special relativity can be derived independent of Einstein's clock synchronization. Einstein's entire treatment of special relativity - most notably his clock synchronization method - can easily be diagrammed against a system at rest with respect to the totality of the universe. This includes the diagramming of how parties in different inertial frames assess each other's properties in a symmetrical manner, such as each other's clock rate and length.

One is then left with no clock paradox. In such a treatment, it is seen with clarity that the time differential occurs due to actual differing clock rates.

Although the universe is expanding, special relativity easily holds true at any conceivable scale of distance at which we might test the theory.

As mentioned, space-time arguments regarding the twin paradox generate a jump in the reading of the time on the Earth clock, even though no such jump in the Earth clock time actually occurs.

Furthermore, space-time diagrams are constrained by Einstein's hopelessly circular definition of inertial frame.

Thus, not surprisingly:

In Spacetime & Electromagnetism, Lucas and Hodgson, using the space-time paradigm, wrestle with the twin paradox for fifteen pages, and claim no resolution.

In a footnote on page 73, they write: "Is it fair to give the Earth-bound twin the vertical world line? Does not that beg the question in his favour? Why not draw another diagram with his world line set at an angle to the vertical, and his lines of simultaneity correspondingly inclined (but at a contrary angle) to the horizontal?" [J.R. Lucas & P.E. Hodgson, Spacetime & Electromagnetism, p 70-84.]

That alternative diagramming of the situation is identical to the consideration that one might just as well consider that it is the Earth, along with the entire cosmos, that changes inertial frames. That, in fact, is something we hear often from commentators on the twin paradox. Of course, that simply makes the twin paradox unresolvable, as either party can then lay equal claim to being the party that ages the least. This is demonstration that one must consider the entirety of the cosmos, the imparter of inertial properties, to be the judge of the matter regarding actual motion.

Space-time is a convenient method for making calculations in relativity, but it obscures the underlying reality.

Although the absolute approach to Einstein's relativity is 111 years old, it remained essentially undeveloped in any sound manner until Relativity Trail appeared in 2008.

In Relativity Trail:

1. A natural and instinctive basis is provided for two
postulates which parallel Einstein's postulates.
2. Clock functioning is defined in conjunction with
the first postulate.
3. The process of measuring across inertial frames is diagrammed.
This includes the diagramming of the measuring of the clock rate,
length and speed of the object in the other inertial frame.
4. Einstein's clock synchronization is diagrammed in absolute terms.

None of those four things was done in Einstein's, Poincare's, Lorentz's, or anyone else's treatment.

Poincare and Lorentz, the most famous of the "absolutists", had merely argued from a "bottom line" mathematical premise. They had both postulated "actual clock slowing" without any basis, and they had both postulated "actual length contraction" without any basis. They did not define clock functioning, and they didn't diagram anything.

Nor did Einstein define clock functioning. Einstein also provided no basis for his postulates other than to say they were necessary in order to conform to the results of recently conducted experiments. Einstein merely assigned measures to the parties of each inertial frame so as to satisfy his postulates of measure. Einstein could provide no diagramming of the measuring process, due to his purely relative approach.

A few details from Relativity Trail:
Symmetry of Measuring. Diagrams and equations
demonstrating the symmetry of clock rate and length
measures across inertial frames.
Twin Paradox Analysis. Diagrams and equations
demonstrating the symmetry of measures and time
differential regarding case 1 and case 2.

For a comprehensive and concise overview of the situation, click:

Relativity Trail is a complete mathematical treatment of Einstein's special theory in absolute terms. In addition to being consistent with Einstein's treatment - it subsumes Einstein's treatment. It reveals precisely what is transpiring behind the scenes of Einstein's treatment. It incorporates an (experimentally indiscernible) frame of reference at rest with the sum total of the cosmos. The machian principle of the universe as the imparter of inertial properties is appealed to -- the very principle Einstein embraced in an on and off again manner.

Relativity Trail has 192 pages, with 65 diagrams, covering every aspect of Special Relativity.

The animations:

The animations below illustrate two basic
possibilities for completing a round trip between
two parties. They produce identical time
differentials, demonstrating the
impossibility of anyone determining their true
motion status relative to the universe.

For maximum clarity, the trips themselves involve
just a light second or two in distance, and all
parties make use of photon clocks which are a
whopping 1/2 light second in width. The photon
clocks tell the story of time contraction.

The horizontal white lines represent the travelers. They each carry a photon clock. There are three clock start/stop events - A, B, and C. Again, the fact that time differential is identical in both scenarios (twin paradox animation 1 and twin paradox animation 2) confirms that one cannot experimentally detect ones true motion status with respect to the universe.

i.e. - none of the parties involved can assume anything about their actual state of motion; thus they cannot know whether they are participating in scenario 1 or scenario 2. The blue circle in the opening diagram represents nothing but a point in space where a clock start/stop event occurs.

Scenario 1:

In the twin paradox animation below, an astronaut
and a space station occupant start their clocks as
the astronaut passes by. A second, incoming,
astronaut starts his clock as he passes by the
first astronaut. The incoming astronaut and the
space station occupant stop their clocks as the
incoming astronaut passes by the space station.

If the video has ended, and you want to replay it,
click on the replay button at the bottom center
of the video box.

Scenario 2:

In the twin paradox animation below, an astronaut
and a space station occupant start their clocks as
the astronaut passes by. A second, also outbound,
astronaut starts his clock as he passes by the
space station. This second astronaut chases down
the first astronaut. As the first astronaut is
caught, both astronauts stop their clocks.

The time contraction equation is easily obtained
from the above diagrams. For instance, in the first
diagram (animation), the clock at rest with the
universe ticks off one cycle while the traveling
clock ticks off .8 of a cycle. A simple application
of the Phythagorean Theorem yields:

t' = t * sqr rt of ( 1 - V^2 )

where t' is the time recorded by the traveler,
t is universal time (full clock rate, since at rest
with the universe), and v is the speed of the
traveler.

Keep in mind that the traveler, moving at .6 light
second per second of universal time, went a
distance, in absolute terms, of .6 light second.

A photon went the same distance in the station's
clock as it did in the traveler's clock, namely,
1 light second.

Thus, 0.8 = 1 * sqr rt of ( 1 - .6^2)

= 1 * sqr rt of ( 1 - 0.36)

= 1 * sqr rt of ( 0.64 )

= 0.8

(There is no need to use c (light speed) in the
equation, since we are using units of light seconds.
Light travels one light second in one second.)

See the book Relativity Trail for more details, including
an analysis of how all parties involved assess
each other's clock speed and lengths in mutually
symmetrical fashion, as well as detailed derivations
of length contraction, the Lorentz transformations
and e = mc^2.

Other documents which are recommended
reading before reading the book:

Relativity in Absolute Terms. My most comprehensive online document. A concise overview of why special relativity must be diagrammed in absolute terms.

Relativity Trail, free pdf format, with 192 pages, 65 diagrams
and 75 illustrations, will provide you with complete detailed
algebraic derivations of all the kinematical effects of special
relativity. Everything is charted out in absolute terms against
a system at rest with respect to the totality 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.