Quote:
Originally Posted by Bombadil
So the requirement that the Lorenz transformation is part of our explanation is a consequence of being able to construct an object in our explanation where we have defined an object to be a collection of elements that maintain their orientation over changes in t. Would this be equivalent to saying that an observer at rest with an object will always use the same explanation even after they both have accelerated?
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Your use of the word “orientation” here bothers me! An object was defined to be a collection of elements which could be considered an entity unto itself for sufficient time to examine or use that fact. The only orientation of interest is its momentum direction in the four dimensional space being used here. No “orientation” is being maintained; the only thing being maintained is the fact that the elements making up that object have to remain in the vicinity of one another. Since they are all moving at the same speed (v
?) that fact has important logical consequences.
Quote:
Originally Posted by Bombadil
... he will still consider the object to have the same measurements.
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Well, of course, that is exactly the phenomena under examination.
Quote:
Originally Posted by Bombadil
... but for the time being is considered a useful approximation as it shows that the Lorenz transformation is a consequence of being able to explain things with the use of objects.
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Ok.
Quote:
Originally Posted by Bombadil
But in considering possible explanations of such objects, what will happen to the expanding sphere?
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Somehow I don't think you are following the deduction at all. If you followed what I was doing, you wouldn't ask such a question.
Quote:
Originally Posted by Bombadil
I know that the fundamental equation is still the equation of an expanding wave, we just can‘t say that it is expanding at a constant speed because we can‘t define the distance that it has expanded or how long it has expanded for.
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Why don't we just drop these issues for the time being as they have nothing to do with the problem presented in this thread.
Quote:
Originally Posted by Bombadil
But isn’t the only thing that is important is that there is some way that we can map the behavior of the elements in however we are explaining them into a solution to the fundamental equation? How we are explaining them and what we are explaining is of no importance as long as such a mapping exists.
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Ok.
Quote:
Originally Posted by Bombadil
Is there a way though, to define a coordinate system without the use of objects that we can use to define distance?
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Again, I don't think this has anything to do with what this thread is talking about. You are trying to discuss things far beyond the issues presently being argued here.
