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Originally Posted by Luna2uno
Thanks papageno for your response. My purpose for entering this hypothetical question on the Equivalence Principle here (rather than Against the Mainstream, per Lunatik & Jerry) is not to argue for a variable G, which would be speculative, but to consider how such a (hypothetical future) discovery would affect our measure of mass in kilograms. Which kilograms would we use, and how would they be affected? Your response addresses how kilograms work at 1 G, which is known, but how would this change if we found a variable G, at 10G for example? Or would it not change at all, and still preserve equivalence?
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Equivalence principle and the value of
G are independent from each other.
Do not confound mass and weight.
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Originally Posted by Luna2uno
To my thinking (and I must admit I really do not know the answer to this hypothetical question on measuring mass under a variable G scenario), the kilograms we developed in our 1G universe are in part a function of gravity, mainly Earth's gravity, so we can weigh things in kilograms. The Equivalence is that this same kilograms applies to F = Ma, as you pointed out, so we can measure inertial mass with the same unit. I believe it was Einstein who thus resolved that gravity and inertial mass are linked, which we know as the Equivalence Principle. So the question remains, in a hypothetical variable G, would the kilogram units remain the same, or forced to change?
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It would be the same.
The Equivalence principle is based on experimental results. Einstein decided to elevate to the status of postulate.
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Originally Posted by Luna2uno
I would think this is a valid astronomy-physics question, in anticipation of some point in the future that our distant space probes, or other observations, yield a variable G. To date, this has not been observed, to my knowledge.
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I explained it to
Lunatik.
If
G depended on positions, the mass of an object would not be affected, but the gravitational
force would be.
A different force would give a different acceleration, because the inertial mass has not changed.
But this problem is no more exotic than a variable dielectric constant in electromagnetism (which gives us refraction, and lenses).
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Originally Posted by Luna2uno
Perhaps this question of measurement in kilograms (at this point a merely philosophical question since we have not confirmed any change in Newton's G from its universal constant) should be explored in the event we find the universal G is something else. We must allow for nature to be a tricky place, so she might throw us a surprise. Would we know what to do with our units of measure of mass at that point if she did? :-?
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Yes, because the experiments used for the units would not change their outcome if we found something new.