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TrickyDicky
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In another thread, it's considered a generally accepted fact that the WEP is not valid anymore the way it was initially postulated:
So it is argued by the previous quoted posters that the WEP is only valid at the limit of vanishing mass test particles. But this seems to make useless the WEP given the fact that the principle is precisely about the equivalence of inertial mass and gravitational mass no matter how big or small is that mass, how can it be valid only at the limit of negligible mass,that would simply make the principle null. Which is probably what the above quoted poster hint at when they cite authors that assert that the WEP is simply false for GR.
Here is Einstein's presentation of the principle:
"A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is:
(Inertial mass)times (Acceleration) = (Intensity of the gravitational field)times (Gravitational mass).
It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body. "
A more modern definition: "The world line of a freely falling test body is independent of its composition or structure"
Is it really the consensus current view that the WEP is only valid at the limit of negligible mass and therefore it does not apply to physical bodies such as binary pulsars?
Wouldn't this amount to saying the WEP as it was originally stated by Einstein is no longer valid? In this case I believe this very important fact is not sufficiently stressed in GR textbooks.
PAllen said:WEP was a motivating principle for the theory. It is not an axiom. Some respected authors (e.g. J. L. Synge strongly argue that it shouldn't even be taught anymore because, mathematically speaking, it is simply false for GR. The more consensus view is that it is valid heuristically, and can be made true in the limit, though there are numerous papers (Bcrowell has provided links) that show it is basically impossible to formulate fully precise, mathematically true, formulation of it).
I find this surprising, because such a change in the principles of the theory should be more stressed in introductory GR textbooks, and kind of disturbing because precisely the WEP is considered to be a necessary condition for any theory about gravity, if only because the notion of gravitational redshift rests on it.bcrowell said:The equivalence principle is a statement about the limiting case where the mass of the test object is small
So it is argued by the previous quoted posters that the WEP is only valid at the limit of vanishing mass test particles. But this seems to make useless the WEP given the fact that the principle is precisely about the equivalence of inertial mass and gravitational mass no matter how big or small is that mass, how can it be valid only at the limit of negligible mass,that would simply make the principle null. Which is probably what the above quoted poster hint at when they cite authors that assert that the WEP is simply false for GR.
Here is Einstein's presentation of the principle:
"A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is:
(Inertial mass)times (Acceleration) = (Intensity of the gravitational field)times (Gravitational mass).
It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body. "
A more modern definition: "The world line of a freely falling test body is independent of its composition or structure"
Is it really the consensus current view that the WEP is only valid at the limit of negligible mass and therefore it does not apply to physical bodies such as binary pulsars?
Wouldn't this amount to saying the WEP as it was originally stated by Einstein is no longer valid? In this case I believe this very important fact is not sufficiently stressed in GR textbooks.