Talk:Equivalence principle

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Questionable statement

"a free-floating (weightless) inertial body will simply follow those curved geodesics into an elliptical orbit. An accelerometer on-board would never record any acceleration." I'm quite certain that an object approaching from a distance, in a hyperbolic trajectory, cannot enter into an orbit without experiencing acceleration (actually, deceleration). So-called "ballistic capture" of spacecraft by other bodies always involves at least some maneuvering, or else the involvement of a moving third body to temporarily alter the shape of the geodesic.

References

Article issues and classification

The article is tagged "citation needed" since 2011, weasel-worded phrases (November 2018), and failed verification (June 2018). There is also a great deal of unsourced content including equations. The B-class criteria #1 states; The article is suitably referenced, with inline citations. It has reliable sources, and any important or controversial material which is likely to be challenged is cited. Reassess to C-class. — Preceding unsigned comment added by Otr500 (talk • contribs)

Desperately seeking clarity

This paragraph:

"Newton, just 50 years after Galileo, developed the idea that gravitational and inertial mass were different concepts and compared the periods of pendulums composed of different materials to verify that these masses are the same. This form of the equivalence principle became known as 'weak equivalence'."

refers to "this form of the equivalence principle", but never states clearly what "this form" refers to.

I hope someone knowledgeable about this subject can rewrite this paragraph much more clearly. — Preceding unsigned comment added by 2601:204:f181:9410:11b1:2ee1:b5d3:78da (talk)

For some reason the content above does not have a Reply button.

I changed the paragraph, please check. Johnjbarton (talk) 22:15, 8 October 2024 (UTC)[reply]

Prior to noticing this discussion, I did a light copyedit on the new text that @Johnjbarton provided. My main goal related to the minor issue which I documented in my edit comment. Thanks all. 24.19.113.134 (talk) 00:40, 11 October 2024 (UTC)[reply]

P.S., the word “deemed” is intended to allow Newton the good faith assumption that he would understand that any conclusions are inherently constrained by the even best available experimentation technology of the era. 24.19.113.134 (talk) 00:54, 11 October 2024 (UTC)[reply]

Sorry, one more: @Johnjbarton It looks like the original complaint of this Talk section remains unaddressed, as the referent of “This form...” is still unclear towards the purpose of introducing what(ever) “weak equivalence” is. Is it a name for the idea that gravitational and inertial mass are exactly and absolutely the same thing in every possible and conceivable way? 24.19.113.134 (talk) 01:06, 11 October 2024 (UTC)[reply]

I wouldn't quite use those extra words "exactly and absolutely the same thing". The words should be "gravitational and inertial mass are the same thing". Here is how the article states it:

"The equivalence principle is the hypothesis that this numerical equality of inertial and gravitational mass is a consequence of their fundamental identity."

The weak vs strong form are related to the scope of the test. A local lab test like Newton's can only test the weak form because all of the objects involved are immersed in Earth's gravity.

I think the current text omits a logic step. I would write:

He compared the periods of pendulums composed of different materials and found them to be identical. He concluded that gravitational and inertial mass are the same thing. This lab-based form of the equivalence principle later became known as "weak equivalence".

Johnjbarton (talk) 01:46, 11 October 2024 (UTC)[reply]

Thanks so much @Johnjbarton, with your permission and excellent advice I can craft the appropriate repair within a few hours from now, unless you prefer to do so by posting an edit yourself, in which case I will stand down. BtW I especially love how your turn of phrase touches on “the numerical equality...”. I think that’s an important part of the crux here.. 24.19.113.134 (talk) 04:17, 11 October 2024 (UTC)[reply]

Sorry again, one more question about your suggested, “This 'lab-based' form...” That is, “lab-based” as opposed to.. what?

And in turn, is your answer to this, then, also one-and-the-same with a definition of the “strong” version of the equivalence principle?

24.19.113.134 (talk) 04:22, 11 October 2024 (UTC)[reply]

ok, I might have sufficiently figured it all out (and learned stuff!). Feel free to check and modify my edit. Thanks.. 24.19.113.134 (talk) 05:03, 11 October 2024 (UTC)[reply]

"a uniform gravitational field"

The definition of the weak equivalence principle includes the phrase "a uniform gravitational field". Real gravitational fields produced by (or associated with) an actual mass m0 (such as the Earth) have a force and a direction (f,d) at every point in space, and there are no two different points in space, p1 and p2, having (f1,d1) and (f2,d2) respectively, where (f1,d1) = (f2,d2), where f1 and f2 are the gravitational attraction on p1 and p2 exerted by m0. So it appears that the weak equivalence principle is not entirely well-related to the real world.

 How much this is important within the Equivalence Principle, I do not know.  But in the supposed equivalence between a closed room sitting on the surface of the Earth (situation 1), and a closed room being accelerated in deep space with a constant acceleration g (situation 2), a person with sufficiently accurate scales could tell which situation he was in as follows.  
 Suspend two one-pound-mass objects and two scales from the ceiling with string as follows:

FLOOR M1---S1---M2---S2---CEILING We suppose the mass of the string and scales is negligible. We suppose that M1 and M2 are each exactly one pound-mass. In both situations, we read the scales after the setup has reached equilibrium and none of the items is moving relative to the others.

 If we buy our scales at the local hardware store, scale S1 will read 1 pound, and scale S2 will read 2 pounds in both situations 1 and 2.  But if we have very sensitive scales, one of the scales in situation 1 will read differently than in situation 2.
 We consider situation 2 first.  The only significant forces acting on M1 consists entirely of the tug of the string attaching it to scale S1, that tug being exactly 1 pound.  The only significant forces acting on M2 are the tug of the string attaching it to scale S1, which is exactly 1 pound, and the tug of the string attaching it to scale s2, which is exactly 2 pounds.  So scale S1 reads exactly 1 pound, and scale S2 reads exactly 2 pounds.
 But when we consider situation 1, we find things more complicated.  Gravity tugs independently on both M1 and M2, and the tugs are not the same because M1 and M2 are at slightly different altitudes.  If we arrange to hang M1 exactly at sea level, then the force of Earth's gravity on M1 will be exactly 1 pound.  But M2 is slightly higher than sea level, so Earth's gravity tugs on it a tiny bit less than 1 pound.  So scale S1 will read exactly 1 pound, but scale S2 will read slightly less than 2 pounds. 
 This slight difference will enable a person with a sufficiently sensitive scale to determine whether he is in situation 1 or situation 2. 69.243.124.241 (talk) 17:53, 29 March 2025 (UTC)[reply]