98.245.112.8: Added section which compares some alternative frames.

2011-08-23T16:03:14Z

Added section which compares some alternative frames.

← Older revision		Revision as of 16:03, 23 August 2011
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	So, for any given point on his world line, we can immediately draw his line of simultaneity through that point. And we can then directly see where that line of simultaneity intersects the horizontal axis. Since the horizontal axis is the world line of the home-twin, that point of intersection directly gives us her current age, according to the traveler. That result, obtained graphically, is exactly what we can get (more quickly and easily) from the CADO equation.		So, for any given point on his world line, we can immediately draw his line of simultaneity through that point. And we can then directly see where that line of simultaneity intersects the horizontal axis. Since the horizontal axis is the world line of the home-twin, that point of intersection directly gives us her current age, according to the traveler. That result, obtained graphically, is exactly what we can get (more quickly and easily) from the CADO equation.

			==Comparison of the CADO Frame with Some Other Frames==

			Other reference frames have been defined for the traveling twin (or for any observer who sometimes accelerates), which do not involve the equivalence principle, and which do not involve any gravitational fields. Any such reference frame ''must'' be consistent with the indisputable fact that the two twins (in the standard twin paradox scenario) will agree about which of them is younger, when they are again reunited; the twin who accelerated while they were apart will always be the younger.

			There is currently no consensus about which of these different reference frames is the most appropriate. Two such alternatives (in addition to the CADO frame) are the "Radar" frame,<ref>Dolby, Carl E. and Gull, Stephen F, "On Radar Time and the Twin 'Paradox' ", ''Am.J.Phys.'', 69 (2001) pp. 1257-1261</ref> and the "Minguzzi" frame.<ref>Minguzzi, E., "Differential Aging from Acceleration, an Explicit Formula", ''Am.J.Phys.'' 73 (2005) pp. 876-880</ref>

			The above alternatives give different answers (different than the answers that the CADO frame gives, and different from each other) to the following two important questions.

			The first question is, "If an observer accelerates during some segment of his life, can he be considered to be an inertial observer during the other segments of his life in which he is ''not'' accelerating?". Specifically, ''when'', during unaccelerated segments of his life, is he entitled to use the Lorentz equations to determine simultaneity and position at a distance, just as a perpetually-inertial observer is always entitled to do? And, similarly, ''when'', during those unaccelerated segments, is he entitled to use the well-known time-dilation result?

			The CADO frame says that for an unaccelerated segment of the observer's life, of any length whatsoever (no matter how short), the observer is a ''full-fledged'' inertial observer during that ''entire'' segment, regardless of how he has accelerated ''before'' that segment, or how he may choose to accelerate ''after'' that segment. (Taylor's and Wheeler's Example 49 is consistent with that answer).

			The Radar frame says that for some finite time ''before'' his acceleration begins, and for some finite time ''after'' his acceleration has ended, the observer is ''not'' an inertial observer. The Radar frame is thus ''non-causal'', in the sense that the observer's conclusions about simultaneity, during an unaccelerated segment of his life, depend on whether or not he will ''choose'' to accelerate ''in the future''.

			The Minguzzi frame says that the observer is an inertial observer at any time ''before'' the acceleration begins (provided that he has undergone no recent previous segment of acceleration), but that he is ''not'' an inertial observer for some finite time ''after'' his acceleration ends. So the Minguzzi frame (like the CADO frame), is causal.

			For both the Radar and the Minguzzi frames, the ''duration'' of those unaccelerated, but non-inertial, portions of the observer's life depends upon how far away the perpetually-inertial object or person is. For perpetually-inertial objects or persons that are sufficiently far away, there will be ''no'' portions of the unaccelerated segments of the observer's life in which he entitled to be considered to be an inertial observer. During such unaccelerated, yet non-inertial, segments of his life, the traveler may be co-located with perpetually-inertial observers for many years of his life, but he will not be allowed (by the Radar and Minguzzi frames) to agree with them, during all those years, about the current age of distant objects or persons.

			The second important question (for which the different alternative frames give different answers) is, "How does the current age, of some given distant perpetually-inertial object or person, ''change'' during periods of acceleration by the observer?". The CADO frame says that the current age of the distant perpetually-inertial person (the "home-twin") can change extremely rapidly (either positively or negatively) during rapid velocity changes by the observer. In fact, in the idealized, limiting case of the traveler's instantaneous turnaround in the standard twin paradox, the CADO frame says that the home-twin's age will instantaneously increase during that instantaneous turnaround. (Again, Taylor's and Wheeler's Example 49 is consistent with that answer). Neither the Radar nor the Minguzzi frames ever give such abrupt age changes of the distant perpetually-inertial person, and her age changes are never negative.

			The answers to the two questions are not independent. ''Any'' frame for the traveling twin, which gives no abrupt age change for the home-twin, during the traveler's abrupt turnaround, ''cannot'' say that the traveler is entitled to use the time-dilation result during the entirety of the unaccelerated segments of the traveler's trip. Otherwise, the two twins would not agree, about the correspondence between their ages, when they are reunited.

	==The CADO Frame When the Distant Person Is Also Accelerating==		==The CADO Frame When the Distant Person Is Also Accelerating==

98.245.112.8: Added complete reference. The later short-form references aren't helpful, without the initial complete reference.

2011-08-17T14:56:57Z

Added complete reference. The later short-form references aren't helpful, without the initial complete reference.

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			The CADO reference frame<ref>Fontenot, Michael L., "Accelerated Observers in Special Relativity", ''Physics Essays'', December 1999, pp. 629-648</ref> is defined for an observer who accelerates in any manner whatsoever. Specifically, the observer's acceleration ''a(t)'', where ''t'' is any instant in the observer's life, can be whatever the accelerating observer wants it to be, without restriction.

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wikademia>Eme at 06:39, 13 August 2011

2011-08-13T06:39:41Z

← Older revision		Revision as of 06:39, 13 August 2011
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	~~<poem>~~
	~~{{pad\|4em}}~~
	~~</poem>~~
	The CADO reference frame<ref>Fontenot, Michael L., "Accelerated Observers in Special Relativity", ''Physics Essays'', December 1999, pp. 629-648</ref> is defined for an observer who accelerates in any manner whatsoever. Specifically, the observer's acceleration ''a(t)'', where ''t'' is any instant in the observer's life, can be whatever the accelerating observer wants it to be, without restriction.

	~~<poem>~~
	~~{{pad\|4em}}~~
	~~</poem>~~

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wikademia>Eme: Created page with " {{pad|4em}} The CADO reference frameFontenot, Michael L., "Accelerated Observers in Special Relativity", ''Physics Essays'', December 1999, pp. 629-648..."

2011-08-13T06:38:48Z

Created page with "<poem> {{pad|4em}} </poem> The CADO reference frame<ref>Fontenot, Michael L., "Accelerated Observers in Special Relativity", ''Physics Essays'', December 1999, pp. 629-648</ref>..."

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The CADO Reference Frame for an Accelerating Observer - Revision history

98.245.112.8: Added section which compares some alternative frames.

98.245.112.8: Added complete reference. The later short-form references aren't helpful, without the initial complete reference.

wikademia>Eme at 06:39, 13 August 2011

wikademia>Eme: Created page with " {{pad|4em}} The CADO reference frameFontenot, Michael L., "Accelerated Observers in Special Relativity", ''Physics Essays'', December 1999, pp. 629-648..."