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Volume 12: Pages 629-648, 1999
Accelerated Observers in Special Relativity
Michael L. Fontenot
1755 Gillaspie, Boulder, Colorado 80305 U.S.A.
The Lorentz equations of special relativity unambiguously specify the current age of a distant object (CADO) according to an inertial observer. This paper demonstrates the following points. 1. For an accelerating observer, consistency with special relativity requires that the CADO be defined in one and only one way. 2. There exists an equation for the CADO, derivable from the Lorentz equations, which explicitly shows how sudden changes in the relative velocity of the observer affect the CADO. Sudden velocity changes can cause the CADO, expressed in years, to vary over a range numerically equal to twice the (object‐measured) separation, expressed in light‐years, between the observer and the object. The equation is well suited for handling arbitrary acceleration profiles and piecewise‐constant accelerations. 3. The CADO thus defined behaves in a very bizarre manner for an accelerating observer. Specifically, the CADO can decrease as the age of the observer increases, even when the observer's acceleration is limited to 1g. The CADO is also, to a large extent, controllable by the observer. 4. According to an accelerating observer, for a 1g acceleration occurring when the separation is sufficiently great, the object's maximum (in magnitude) rate of aging is greater than the accelerating observer's rate of aging by a factor approximately equal to their separation, as measured in the object's frame, in light‐years. If the observer is accelerating toward the object, the object will be getting older at that rate. If the observer is accelerating away from the object, the object will be getting younger at that rate. 5. If an observer undergoes a constant acceleration forever, the object's age will approach a finite limit, according to the observer. If their initial separation has a certain critical value, the object's age will never change at all, according to the observer. 6. An inertial observer can compute the CADO from first principles, using only his own (appropriately synchronized) clocks and measuring sticks. 7. Under a specific definition of “meaningfulness” and “reality,” the bizarre behavior of the CADO, for an accelerating observer, must be regarded as being fully meaningful and real.
Keywords: simultaneity, time dilation, Lorentz equations, twin paradox
Received: December 2, 1998; Published online: December 15, 2008