2017-11-20 17:46:52 UTC
David Morin, Introduction to Classical Mechanics With Problems and Solutions, Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [...] For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older." http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
The student does some search and finds that the "enough strangeness" is actually a homogeneous gravitational field introduced by Einstein in 1918. This field, generated during the turning-around acceleration of the traveling twin, somehow reaches the distant stationary twin and converts him into an old man:
Albert Einstein 1918: "A homogeneous gravitational field appears, that is directed towards the positive x-axis. Clock U1 is accelerated in the direction of the positive x-axis until it has reached the velocity v, then the gravitational field disappears again. An external force, acting upon U2 in the negative direction of the x-axis prevents U2 from being set in motion by the gravitational field. [...] According to the general theory of relativity, a clock will go faster the higher the gravitational potential of the location where it is located, and during partial process 3 U2 happens to be located at a higher gravitational potential than U1. The calculation shows that this speeding ahead constitutes exactly twice as much as the lagging behind during the partial processes 2 and 4." http://sciliterature.50webs.com/Dialog.htm
"When the twin in the spaceship turns around to make his journey home, the shift in his frame of reference causes his perception of his brother's age to change rapidly: he sees his brother getting suddenly older. This means that when the twins are finally reunited, the stay-at-home twin is the older of the two." https://hubpages.com/education/Twin-Paradox
The student is in a difficult situation, isn't he/she?
Peter Hayes, The Ideology of Relativity: The Case of the Clock Paradox: "In the interwar period there was a significant school of thought that repudiated Einstein's theory of relativity on the grounds that it contained elementary inconsistencies. Some of these critics held extreme right-wing and anti-Semitic views, and this has tended to discredit their technical objections to relativity as being scientifically shallow. This paper investigates an alternative possibility: that the critics were right and that the success of Einstein's theory in overcoming them was due to its strengths as an ideology rather than as a science. The clock paradox illustrates how relativity theory does indeed contain inconsistencies that make it scientifically problematic. These same inconsistencies, however, make the theory ideologically powerful.[...] The prediction that clocks will move at different rates is particularly well known, and the problem of explaining how this can be so without violating the principle of relativity is particularly obvious. The clock paradox, however, is only one of a number of simple objections that have been raised to different aspects of Einstein's theory of relativity. (Much of this criticism is quite apart from and often predates the apparent contradiction between relativity theory and quantum mechanics.) It is rare to find any attempt at a detailed rebuttal of these criticisms by professional physicists. However, physicists do sometimes give a general response to criticisms that relativity theory is syncretic by asserting that Einstein is logically consistent, but that to explain why is so difficult that critics lack the capacity to understand the argument. In this way, the handy claim that there are unspecified, highly complex resolutions of simple apparent inconsistencies in the theory can be linked to the charge that antirelativists have only a shallow understanding of the matter, probably gleaned from misleading popular accounts of the theory. [...] The defence of complexity implies that the novice wishing to enter the profession of theoretical physics must accept relativity on faith. It implicitly concedes that, without an understanding of relativity theory's higher complexities, it appears illogical, which means that popular "explanations" of relativity are necessarily misleading. But given Einstein's fame, physicists do not approach the theory for the first time once they have developed their expertise. Rather, they are exposed to and probably examined on popular explanations of relativity in their early training. How are youngsters new to the discipline meant to respond to these accounts? Are they misled by false explanations and only later inculcated with true ones? What happens to those who are not misled? Are they supposed to accept relativity merely on the grounds of authority? The argument of complexity suggests that to pass the first steps necessary to join the physics profession, students must either be willing to suspend disbelief and go along with a theory that appears illogical; or fail to notice the apparent inconsistencies in the theory; or notice the inconsistencies and maintain a guilty silence in the belief that this merely shows that they are unable to understand the theory. The gatekeepers of professional physics in the universities and research institutes are disinclined to support or employ anyone who raises problems over the elementary inconsistencies of relativity. A winnowing out process has made it very difficult for critics of Einstein to achieve or maintain professional status. Relativists are then able to use the argument of authority to discredit these critics. Were relativists to admit that Einstein may have made a series of elementary logical errors, they would be faced with the embarrassing question of why this had not been noticed earlier. Under these circumstances the marginalisation of antirelativists, unjustified on scientific grounds, is eminently justifiable on grounds of realpolitik. Supporters of relativity theory have protected both the theory and their own reputations by shutting their opponents out of professional discourse. [...] According to the view proposed here, this only indicates how special and general theories function together as an ideology, as when one side of the theory is called into question, the other can be called upon to rescue it. The triumph of relativity theory represents the triumph of ideology not only in the profession of physics bur also in the philosophy of science. These conclusions are of considerable interest to both theoretical physics and to social epistemology. It would, however, be naive to think that theoretical physicists will take the slightest notice of them." http://www.tandfonline.com/doi/abs/10.1080/02691720902741399