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American Journal of Physics

Paradox of the Twins

Royal M. Frye, Virginia M. Brigham

Published Nov 1, 1957• 5 citations
Publisher

Abstract

There is no ambiguity about the relationship between time and motion, either in terms of experiments with rapidly moving mesons or canal rays, or in terms of general relativity theory. But contradictory results are obtained when it is attempted to make computations using only the special relativity theory. A number of opinions to the contrary have recently found their way into print.

DOI
10.1119/1.1934547

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There is no ambiguity about the relationship between time and motion, either in terms of experiments with rapidly moving mesons or canal rays, or in terms of general relativity theory. But contradictory results are obtained when it is attempted to make computations using only the special relativity theory. A number of opinions to the contrary have recently found their way into print.
Quantum paradoxes The next few chapters are devoted to resolving a number of quantum paradoxes in the sense of giving a reasonable explanation of a seemingly paradoxical result in terms of the principles of quantum theory discussed earlier in this book. None of these paradoxes indicates a defect in quantum theory. Instead, when they have been properly understood, they show us that the quantum world is rather different from the world of our everyday experience and of classical physics, in a way somewhat analogous to that in which relativity theory has shown us that the laws appropriate for describing the behavior of objects moving at high speed differ in significant ways from those of pre-relativistic physics. An inadequate theory of quantum measurements is at the root of several quantum paradoxes. In particular, the notion that wave function collapse is a physical effect produced by a measurement, rather than a method of calculation, see Sec. 18.2, has given rise to a certain amount of confusion. Smuggling rules for classical reasoning into the quantum domain where they do not belong and where they give rise to logical inconsistencies is another common source of confusion. In particular, many paradoxes involve mixing the results from incompatible quantum frameworks. Certain quantum paradoxes have given rise to the idea that the quantum world is permeated by mysterious influences that propagate faster than the speed of light, in conflict with the theory of relativity. They are mysterious in that they cannot be used to transmit signals, which means that they are, at least in any direct sense, experimentally unobservable.
As Quine wrote in 1961, what strikes us in a paradox is its initial air of absurdity, which develops into a sort of psychological discomfort when we compare the conclusions of the reasoning with the apparently irrefutable arguments on which it is based. However, as he went on to observe, ‘More than once in history the discovery of paradox has been the occasion for major reconstruction at the foundations of thought’. Catastrophe may therefore lurk even in the most innocent-seeming of paradoxes and force us to recognize the arbitrary nature ‘of a buried premise or of some preconception previously reckoned as central to physical theory, to mathematics or to the thinking process’. More recently, ideas of this kind have been used to assert in general that the role of paradox in the growth of knowledge is to generate category switches and to construct new universes of discourse. It could also be argued that paradoxes constitute elements of the logic of discovery capable of amplifying and thus making intelligible the still obscure phases accompanying paradigm shifts. Paradoxes would thus represent points of accumulation for the tension created between a given system of conceptual representation and a theory or empirical discovery that violates it. Historians of science have tried different interpretative approaches in their attempts to unravel the thought process that was to lead Einstein in 1905 to the formulation of special relativity and the simultaneous demolition of the classical conception of space and time.
ABSTRACT An experiment is suggested to settle the question whether two clocks which are synchronized and subsequently separated must necessarily show identical readings on being brought together again. Charged π-mesons play the role of a clock travelling with a velocity comparable with c, this clock being read by passing the mesons through a scintillation counter or counters. It is pointed out that the experiment can be designed in a way which makes it technically feasible for a laboratory possessing an accelerating machine capable of producing mesons in the 100 Me V. energy range. Some considerations suggested by the proposed experiment are examined, and it is concluded that only the orthodox result—that in general the two clocks will record the passage of different time intervals between successive coincidences—is consistent with the result of an experiment which has already been made, or with the special theory of relativity.
This chapter shows the math used in modern physics. It examines first relativity and then quantum mechanics. The discussion of special relativity opens with the Michelson-Morley experiment that disproved the existence of the ether. There is then a discussion of space-time and the idea of non-positive-definite metrics. Hyperbolic functions are examined and employed. Discussion of the space-time point of view leads to the twin paradox and its resolution. Examination of energy leads to E = mc 2 which rounds out special relativity. General relativity begins with examination of gravity which led Einstein to learn differential geometry and use it to describe motion in space-time with gravity. We then shift to quantum mechanics. We begin with particle-wave duality and from them follow Schrodinger's approach to generate his quantum wave equation. We then explore the meaning of solutions to Schrodinger's equation in terms of the probability distributions that they give rise to. We move on to Heisenberg's algebraic approach to quantum mechanics, including his uncertainty principle. We end with a discussion of quantum field theory and the question of what math will be needed to help unify modern physics.