Paradox in physics can be defined as an incompatibility between an interpretation of a physical phenomenon and its everyday experience. Ever since Einstein recognized that light has properties commonly associated with both waves and particles (the nature of waves and particles had previously been perceived and thought mutually exclusive), paradox has been increasingly accepted and even expected in theoretical physics. Einstein felt that the light paradox would someday, somehow be resolved, but with the advent of quantum theory, the strange and seemingly unnatural behavior of subatomic particles made acceptance of paradox a scientific norm.
It is in consequence no longer possible to dismiss a physical hypothesis because it seems unnatural or incompatible with accepted theory. And such tolerance is not necessarily a good development. Gravitation theory is an excellent example: Gravity is treated as both a geometric warping of spacetime in the presence of mass and as a force, with little or no concern for the incompatibility of the two models; thus the tolerance of paradox has been extended to a tolerance of discrepancies between theories. Another example: "Dark energy" and "dark matter", although unobserved and perhaps unobservable, are favored explanations for cosmological phenomena, despite a long-established scientific principle that ranks questioning theoretical models above accepting seemingly unnatural entities.
The so-called "twin paradox" suffers from the same sort of theoretical malaise. It arose from an implication of relativity theory, that acceleration will produce discrepancies between clocks -- not relative differences as with uniform motion, but real differences that could result in a twin going to and from a distant star system and returning home significantly younger than the stay-at-home twin. This is not really a "paradox" if clock-speed is accepted as an attribute of each body's state in spacetime, rather than a universal constant, and it has been confirmed by experiment. But there has been an enduring problem with explaining how arbitrary periods of time spent by the traveling twin in uniform motion would be resolved upon the twins' reunion: When in uniform motion, each twin will regard the other's clock to be moving with an identical relative discrepancy, but upon their reunion they will have to agree that those observations were only relative, and the buildup of the mutual effect must somehow vanish.
Not only has the conundrum (not a paradox) involved with the twins' experience of a disappearing mutual discrepancy been tolerated, a proposed resolution has evoked almost no curiosity, and has even provoked outright dismissal. Only The European Journal of Science (EJS), an intrepid but relatively remote publication, has shown an interest in and appreciation for a resolution of the twin "paradox" (conundrum), and has published it in their January 2016 issue.
So do physicists love their paradoxes, discrepancies, and conundrums too much?
The article follows, and can also be found here:
EJS Vol 12 No 3 (2016)
The "Twin Paradox" Resolved
James R Arnold
The so-called "Twin Paradox", in which a relativistic effect is hypothesized to produce verifiably different clock rates between bodies, has not been resolved to the satisfaction of many theorists, and it is disbelieved entirely by others. Experiments have confirmed the relativistic effect of acceleration, but there has been an abiding difficulty with clarifying how arbitrary periods of uniform motion between accelerations, when each twin will observe the other's clock to move more slowly, can be resolved at their reunion. Spacetime diagrams are used to demonstrate visually and conceptually that there is a non-paradoxical explanation for the effect of periods of uniform motion that has not been previously proposed.