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Mike_Fontenot
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I think this "elephant-in-the-room" issue is important enough to deserve its own thread. I believe it is at the root of many of the disagreements that repeatedly occur on this forum. So I copied my last posting over from the "The case for True Length = Rest Length" thread. Here is that posting:
Here's another way to describe that "elephant-in-the-room" issue:
The standard time dilation result of special relativity answers the following question:
"What does an inertial observer conclude about the rate of ticking of some particular distant clock, which is moving at a constant speed relative to the inertial observer?".
The standard answer is:
"The inertial observer will conclude that the distant clock is ticking gamma times slower than his own watch."
But what exactly IS "an inertial observer"? Is it someone who is TEMPORARILY not being accelerated, but who may have accelerated in the past, or who may choose to accelerate in the future? Or is it someone who is PERPETUALLY unaccelerated? If it's the latter, does that mean that each tiny bit of matter making up the observer's body has never accelerated before? Could ANY person meet THAT test?
And, in order to determine the clock rate of the distant clock, does the inertial observer need to know the distance to that clock?
The Dolby& Gull simultaneity, and the Minguizzi simultaneity, answer the above two questions very differently than does my CADO simultaneity.
My CADO simultaneity says that an observer is inertial during any segment of his life in which he is unaccelerated, regardless of the duration of that segment. And my CADO simultaneity says that the tick rate of the distant moving clock does NOT depend on how far away that clock is.
If the observer is NOT perpetually unaccelerated, then both Dolby&Gull and Minguizzi DO require that the distance to the moving clock be specified, before they can determine its tick rate. So anyone who subscribes to either the Dolby&Gull simultaneity, or to the Minguizzi simultaneity (or to ANY simultaneity other than my CADO simultaneity), needs to be clear about the answers to the above two questions, before they can say anything about the tick rate of the distant moving clock. And what they say about that tick rate will often NOT be what the standard time dilation result says.
Mike Fontenot
Mike_Fontenot said:[...]
The issue that you (JesseM and GrayGhost) are both "dancing around" (the elephant in the room, really), is this: Whenever a person is NOT accelerating for some segment of his life, WHEN in that segment can he legitimately be considered to be an inertial observer?
[...]
Here's another way to describe that "elephant-in-the-room" issue:
The standard time dilation result of special relativity answers the following question:
"What does an inertial observer conclude about the rate of ticking of some particular distant clock, which is moving at a constant speed relative to the inertial observer?".
The standard answer is:
"The inertial observer will conclude that the distant clock is ticking gamma times slower than his own watch."
But what exactly IS "an inertial observer"? Is it someone who is TEMPORARILY not being accelerated, but who may have accelerated in the past, or who may choose to accelerate in the future? Or is it someone who is PERPETUALLY unaccelerated? If it's the latter, does that mean that each tiny bit of matter making up the observer's body has never accelerated before? Could ANY person meet THAT test?
And, in order to determine the clock rate of the distant clock, does the inertial observer need to know the distance to that clock?
The Dolby& Gull simultaneity, and the Minguizzi simultaneity, answer the above two questions very differently than does my CADO simultaneity.
My CADO simultaneity says that an observer is inertial during any segment of his life in which he is unaccelerated, regardless of the duration of that segment. And my CADO simultaneity says that the tick rate of the distant moving clock does NOT depend on how far away that clock is.
If the observer is NOT perpetually unaccelerated, then both Dolby&Gull and Minguizzi DO require that the distance to the moving clock be specified, before they can determine its tick rate. So anyone who subscribes to either the Dolby&Gull simultaneity, or to the Minguizzi simultaneity (or to ANY simultaneity other than my CADO simultaneity), needs to be clear about the answers to the above two questions, before they can say anything about the tick rate of the distant moving clock. And what they say about that tick rate will often NOT be what the standard time dilation result says.
Mike Fontenot
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