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Originally Posted by Doctordick
No I do not mean any such thing. That is why I put it the way I did! How these measures are to be established is of utterly no consequence so long as the the procedure used is not confused by either party; that they will agree that the procedure being used is the “correct” procedure as per their explanation of reality (their “physics”). My presentation is much more open to alternate possibilities than is your statement.
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So all that is necessary to insure that measurements in one frame will agree when transformed to a new frame with the measurements made in the new frame is that the same procedure is used in both frames to arrive at their units of measure. It doesn’t matter how the units used are defined as long as they are made in the same way since in order for a flaw-free explanation to exist in both frames their laws of physics (their explanations) must agree when their measurements are transformed to a single frame.
Now in the case in which the measurements that the observers make do not follow the Lorenz transformation, the only possibility is that one or both of the observers are using a flawed explanation.
I’m somewhat puzzled though by exactly what the scale invariance is, it seems that it is stating that no matter how you define distance and time that the same explanation will be a valid explanation and as long as you use the same units it doesn’t matter what they are. Or in other words it doesn’t matter how we define length along any axis as along as it is consistent with the explanation. I’m wondering if this is the case because it seems that the scale invariance vanishes when we define a system of units.
Quote:
Originally Posted by Doctordick
That sentence just doesn't make any sense to me. The flaw-free explanation is scale invariant when the entire universe is included. If you have a solution (an explanation) and that explanation includes a “scale” obtained by some procedure (internal to that universe) and you change the scale of the entire universe, the scale used in that explanation changes in exactly the same way. That is scale invariance. The problem arises when the two observers are leaving out different pieces of the universe (which is exactly what they are doing when they each propose their frame of reference is inertially “at rest”): i.e., they are presuming that the motion of the far away portions of the universe are of no significance to their physics (their explanation). The consequence of that fact is that, to quote you, “the observers will not agree on what they see” if their personal universes are scale invariant. The obvious answer is that they can not be scale invariant. Their “Physics” must establish a mechanism which “explains” the transformation required.
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So since both observers are leaving out different parts of the universe when they define the units of there explanations they will not agree on there explanations (that is the units defined using one explanation will not be consistent with the other) but in order for both explanations to be flaw-free they must differ by nothing more then the scale (this corresponds to the scale of objects in their explanation) and in order for them to see the same event and agree on what happened in any particular frame that scale must be the same as what is defined by the Lorenz transformation.
Now the actual scaling of the fundamental equation is just a consequence of the transformation used to change the explanation in one frame to a new frame while still keeping the fundamental equation valid.
Quote:
Originally Posted by Doctordick
I think you have the horse on entirely the wrong side of the cart here. You should have said, “This does not however prove that the explanation obeys the Lorenz transformation; only that, if it does not, the explanation is flawed in that “the rest of the universe can not be omitted”. It is entirely possible that the proper “physics” (the flaw-free explanation requires information about the rest of the universe).
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But isn’t the issue of if any flaw-free explanations can obey the Lorenz transformation still open or is the fact that if they do, observers in different frames will agree on the measurements when transformed to the same reference frame enough to insure that two different flaw-free explanations will obey the Lorenz transformation. Basically I’m asking how do we know that the measurements in one frame can be transformed to any other frame even if both explanations are flaw-free. It seems that this may be equivalent to asking if all flaw-free explanations differ only by a scale.
Quote:
Originally Posted by Doctordick
The question then becomes the problem of examining such an object from two different frames. There is no problem of moving such an object: movement from one inertial frame to another occurs all the time in Newtonian mechanics.
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This still seems to leave open the question can an object in one frame be moved to any other frame. That is are there frames that an object in one frame can’t be moved into from some other frame. Or can an object in any frame be moved to any other frame.
Quote:
Originally Posted by Doctordick
Yes, but the solution is only flaw-free in the original inertial frame: i.e., these are your expectations if you take the position that the moving frame is “wrong”.
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Isn’t it still an open issue though that is if we can call the moving frame wrong or not it may be that there are no wrong frames only incomplete explanations or it may be as you seem to be suggesting that there is in fact a unique frame that is the only frame in which the fundamental equation is valid in.
