Talk:Equivalence principle

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.

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)

Articles for deletion/Equivalence principle (geometric)
Deletion of Equivalence principle (geometric), an article closely related to this one, is being discussed. Please consider joining the discussion. ~Kvng (talk) 18:29, 28 December 2023 (UTC)

Kepler's ratio
The current article says $$\frac{D_\text{Moon}}{D_\text{Earth}} = \frac{M_\text{Earth}}{M_\text{Moon}}$$

According to Moon the Moon's diameter is 1/4 of Earth and its mass is 1/81 of Earth. So we have $$\frac{(1/4) D_\text{Earth}}{D_\text{Earth}} = \frac{M_\text{Earth}}{(1/81)M_\text{Earth}}$$ or $$1/4 = 81 ??$$

Even if we pick different values for relation between Moon and Earth, I can't see any Kepler would make such a claim even 400 years ago. What am I doing wrong here? @Net'em 0n

In any case I think we should delete these sentences as WP:OR Johnjbarton (talk) 01:25, 24 February 2024 (UTC)

The D's are the distances moon and Earth would travel towards each other, not diameters. It's my fault for not making that clear. The 1/54th instead of 1/81 is because Kepler had to assume (and admitted in the quote it was an assumption) that Earth and moon have the same density. The moon is less dense which is why it's actually 1/81. That error isn't important because the point is to show his math shows he assumed the equivalence principle which is probably why Newton made the same assumption, being an expert in Kepler's writings.

To make the math explicit, Kepler's mental model (there was no algebra) was doing the same as us plugging a = F/m into the D equation, and knowing F on Earth and moon in this situation are the same F, and recognizing t to collision is the same for both. This gives us:

D_moon = 1/2 * F / M_moon * t^2

D_earth = 1/2 * F / M_earth * t^2

D_moon / D_earth = M_earth / M_moon

So the question is, what was Kepler's mental model to get the correct answer if he didn't know F=ma and assume the equivalence principle before Newton? More to the point for this article, is there a reference that discusses this so that we can include it? Ywaz (talk) 21:20, 24 February 2024 (UTC)


 * I removed the entire paragraph. A similar one would make sense in the context of an article about Kepler, the history of the Mass of the Moon, or even gravity. But here the paragraph is too long and not on topic. And we don't agree about what it should say. So let's move on. Johnjbarton (talk) 01:50, 24 February 2024 (UTC)
 * I am amused how one swiftly jumps on the conclusion about removal of what one doesn't understand. No offence is planned, but the world will be a better place if people won't touch anything they don't understand completely; and if something is written, it is to be read thoroughly at first.  Let me explain.
 * = The value of the ratio =
 * The last bit of the citation from the Kepler's "Astronomia Nova" says that he assumes the Earth and Moon densities to be the same: "... the substance of both is of the same density". Of course, at his time this was completely unknown what is the mean density of the Moon, so this is the sound assumption.
 * This means that we (after Kepler: we're describing/following his train of thought) should base solely on the radii: they were known with sufficient precision even then. R_Earth/R_Moon \approx 6731/1757 \approx 3.88 (by today's data).  Mass ratio is cube of it (for equal mean densities), so it is \approx 58.2.  Looking at the Kepler's original work, https://ia800204.us.archive.org/5/items/Astronomianovaa00Kepl/Astronomianovaa00Kepl.pdf: Introduction, page 5 (25 in the PDF file) says
 * "Si Luna&Terra non retinerentur vi animali, aut alia aliqua aequipollenti, quaelibet in fuo
 * circuitu; Terra afcenderet ad Lunam quinquagefimaquarta parte intervalli, Luna defcenderet
 * ad Terram quinquaginta tribus circiter partibus intervalli:ibique jungerentur:pofito tamen,
 * quod fubftantia utriusq; fit unius & ejusdem denfitatis".
 * "quinquagefimaquarta parte" is "54th part" and "qiunquaginta tribus" is 53. Of course, values of 6731 and 1757 (kilometers) taken above for the ratio are modern ones: for Kepler's time, I assume, the value of 53 is a tremendous achievement: it is just 10% off.
 * And distance ratio is (1/54)/(53/54) = 1/53. Thus, I hope, it is clear, that
 * - the original English citation from "Astronomia Nova" is correct and just follows the original;
 * - the real ratio *from Kepler's work* is 1/53.
 * = Your question about "1/4 = 81" =
 * Spherical volume is proportional (with 4\pi/3 as the coefficient, but that's not relevant here) to the third power of radius. When mean densities are assumed to be the same, the mass ratio, M_Earth/M_Moon is (R_Earth/R_Moon)^3.  This is the reason for my estimate of 58.2 above.
 * The current article says about D_Moon/D_Earth ratio, but that's not the ratio of their diameters. This is the ratio of their travel path lenghts, provided they will be placed to the empty space with no initial velocities and will be attracted to each other via gravitational forces.
 * That's just what Kepler said (and you had deleted it from the page we're talking about):
 * "If two stones were placed in any part of the world near each other, and beyond the sphere of influence of a third cognate body, these stones, like two magnetic needles, would come together in the intermediate point, each approaching the other by a space proportional to the comparative mass of the other. If the moon and earth were not retained in their orbits by their animal force or some other equivalent, the earth would mount to the moon by a fifty-fourth part of their distance, and the moon fall towards the earth through the other fifty-three parts, and they would there meet, assuming, however, that the substance of both is of the same density."
 * And this has a direct relation to the principle of equivalence: travel distance of the body in the uniform field (with no initial velocity) is D = a*t^2/2, with a being the acceleration. In the case of Earth/Moon system, this acceleration is due to the gravitational force.  But, in F = m*a, m (the mass) is the inert mass -- proportionality constant in the Lagrangian kinetic term (or, per Newton's train of thought, the proportionality coefficient between total force vector and acceleration vector).  When Moon or Earth falls in the field of it's partner (Earth or Moon, that is), we can try to view it as the equivalent of the Moon/Earth free fall in the given force field.  This gives F = 2*m*D/t^2 where m is the object mass and D is the travel distance at the time t from the beginning of movement with zero initial speed.  Forces exerted by Moon at Earth and by Earth at Moon are just the opposite to each other, but we're talking about their moduli, so when they will come to an intermediate collision point, the time t will be the same for both.  Thus, m*D is constant for both bodies.
 * This gives M_Earth * D_Earth = M_Moon * D_Moon. You can substitute D_Earth -> L_Earth and D_Moon -> L_Moon (L is, perhaps, slightly more common notion for travel path -- "length" it is; though, D is for "distance").
 * = Why your deletion of the whole paragraph is absolutely wrong =
 * Kepler more than 400 years ago managed to use these arguments (and this is just a perfect example of physical thinking and calculations: we take numerical values we have, we make assumptions about unknowns, we use equivalent processes to find relations between various variables) and to, in modern terms, use the equivalence principle to produce travel distance ratios.
 * So, your "A similar one would make sense in the context of an article about Kepler, the history of the Mass of the Moon, or even gravity. But here the paragraph is too long and not on topic" is the opposite of the reality: the paragraph is spot on money, but it had two errors, one numerical: 1/54 -> 1/53, one in formulae: the ratio of masses (or travel distances -- choose one) was reversed. Moreover, it is the perfect illustration of the physics involved (in equivalence principle).
 * An approach of "And we don't agree about what it should say. So let's move on" is just unacceptable.
 * Please, don't delete anything you don't understand: it harms. Please, back out your last edit.
 * Thank you. Net&#39;em 0n (talk) 08:30, 24 February 2024 (UTC)
 * Thank you for the detailed explanation!
 * You say that Kepler used these arguments "... to, in modern terms, use the equivalence principle to produce travel distance ratios." This is an analysis on your part. The quote is referenced, but any connection to the article topic was something you added based on your logic and understanding. Wikipedia is committed to presenting information backed by sources, not by logic or expertise.
 * I disagree with your logic and understanding. In Kepler's time the concept of weight and mass were not separate and thus their equivalence was not a mystery or issue. Of course we can go back and re-analyze discussions about gravity in terms of the equivalence principle, but that does not make those discussions relevant to the principle.
 * I suggested moving on because I don't think you will find a reference and "The burden to demonstrate verifiability lies with the editor who adds or restores material.".
 * If you do find a reference we can restore the content, but even then I do not believe it should be included. The paragraph is too long for the scale of the history section and it distracts from the "main event" in the article. Instead I think there are other articles where this content would be greatly enhance the article. I would help you to find such a spot.
 * Otherwise, Wikipedia has a mechanism to resolve disputes between editors. I suggest the relevant group of editors to consult would be in the  Physics project. Johnjbarton (talk) 15:54, 24 February 2024 (UTC)
 * In my opinionated view, you won't recognize the physical idea or even some relation even if it will bite you: you need (lengthy) explanations.
 * That being said, I see you want to go in a formal route ("Wikipedia is committed to presenting..."). Fine, let's go analyze the parts of the whole article.
 * First, you don't deny that the Kepler's quote (KQ below) is referenced. You just see it as having no connection to the article topic.
 * - The first paragraph of the current article says "The weak form, known for centuries..." referencing equivalence principle.
 * - Galileo and his experimental treatise of the falling bodies (albeit he was talking about velocities /"...veduto, dico, questo cascai in opinione che se si levasse totalmente la resistenza del mezzo tutte le sostanze descenderebbero con eguali velocità"/) is the recognized principle of free fall universality (https://doi.org/10.1119/1.4798583, https://indico.cern.ch/event/600191/contributions/2520383/attachments/1430105/2196622/2017_GG_Pisani_CERN.pdf) It is the weak equivalence principle in action.
 * - The 1/53 ratio from Kepler's work (that is by far more mathematical in nature then even the Galileo's one: http://www.ousia.it/SitoOusia/SitoOusia/TestiDiFilosofia/TestiPDF/Galilei/DimostrazioniMatematiche.pdf or https://en.wikisource.org/wiki/Dialogues_Concerning_Two_New_Sciences) is taken from the part of "Astronomia Nova" that talks about axioms of gravity (see page 55 /book numbering/ from ISBN: 0-521-30131-9 or directly page 25 /in PDF speak/ from https://ia800204.us.archive.org/5/items/Astronomianovaa00Kepl/Astronomianovaa00Kepl.pdf, starting from "Vera igitur doctrina de gravitate his innititur axionmatibus...") KQ is the continuation of the paragraph "If two stones were set near one another in some place in the world outside the sphere of influence of a third kindred body, these stones, like two magnetic bodies, would come together in an intermediate place, each approaching the other by an interval proportional to the bulk [moles] of the other", together they comprise the universal principle (applicable both to stones and Earth/Moon system).  Axioms are foundations, Kepler took them not completely out of the blue.  And the calculation was presented along with KQ to show the route on how it could be obtained using things known at that time.
 * You, in your response,
 * say "that's all fine and dandy, but I disagree with your logic and understanding". The thing is that you have _no understanding_ at all: you're not able to deduce the simple proportion from the given equations; you were using modern mass ratios for Earth/Moon in your reply about 1/4 and 81.  You gave yourself no time to understand that D is the path, not the diameter.
 * Next, you say "In Kepler's time the concept of weight and mass were not separate and thus their equivalence was not a mystery or issue": this is a non-argument, we're talking about Kepler's (possible) way of thinking, not about his time. He is the creator of theories, not the man who follows some general ways of thinking of his time.
 * And, just the next phrase, "Of course we can go back and re-analyze discussions about gravity in terms of the equivalence principle, but that does not make those discussions relevant to the principle" is a simple word trick: I read it as "even if I am wrong about Kepler's time, discussions aren't relevant to the principle". I'd dismiss it as the non-argument, but, strangely, the opposite is true: /strong/ equivalence principle is a rather hard-to-find base from which, as you might know, the modern theory of gravitation was born.  So, even the understanding on how people 400 years ago might produce the (weaker) form of it and use for axiom-based reasoning, can shed some light onto the current affairs and the next steps (in gravity theory).
 * I can see the answer: "go, produce your original research on the topic of Kepler's possible ways to obtain his ratio relation and connection to the equivalence principle, publish it (going via the process of refereeing; or not? Just an ISBN will be enough?), do anything your like, but <>".
 * The too-long-for, <> argument of yours: again, this is an opinionated view. It might be yours, it might be Wikipedia rule's -- whatever: I don't mind writing anything lengthy if it will shed even a smallest additional bit of light onto the thing being discussed, written about, etc.  Anyone who is distracted can just train their brains: for the mankind's good, presumably.
 * On the BURDEN (https://en.wikipedia.org/wiki/Wikipedia:Verifiability#Responsibility_for_providing_citations): the BURDEN section talks about _citations_. The citation is verifiable, it has reference to the Bethune's book.  The verifiability of the equations and deductions from the lies in the realm of algebra, Wikipedia rules say something about it?  The connection from Kepler's citation to the equations/algebra in question (aka "why this length stuff is relevant for the <> section"): I sincerely hope it just won't be lost in the removal noise; the connection of (possible) ideas.
 * That's about it for your arguments supporting the removal.
 * Let's move to your comments and the style of their presentation: you require me to feel the burden of verifiability? Fine: I can try to demonstrate that you aren't following you own requirements /put on others, of course/.
 * You say in your non-argument (I had said above that Kepler is the original thinker, this is the source of the "non-argument" tag) "In Kepler's time the concept of weight and mass were not separate and thus their equivalence was not a mystery or issue"? Oh, and did you provide a reference for that?  No.  May be you're a time traveller from that past or Kepler's contemporary who also happen to talk to him in person?  I doubt.  And were I talking about equivalence of weight/mass in any of my comments or, may be, some of my edits referenced that?  No.  The best you'll tell me that I am equating the "free fall" (of Moon in the Earth's field or the Earth in the Moon's field) acceleration to, what?.., to the force/mass ratio (as in the Newton's second law)?  That's a definition for the "free fall" acceleration for the given distance r between the gravitating body (it's center, if we take it to be spherical or material point) and the second body; g = k*M/r^2, that is.  At best.  For a given body that's just a matter of moving the difference between gravitational and inert mass into the constant "k".  *The crux* of Galilleo experiments (and Eötvös work a tad later, some 200-300 years after) is to demonstrate that this constant "k" is the same for all bodies (examined in their experiments, that is).  That's why it is called universal gravitation constant: universality matters.
 * Next, "If you do find a reference we can restore the content, but even then I do not believe it should be included". I can read it as "resistance is futile".  Moreover, just after it you're giving me a great offer of help: "Instead I think there are other articles where this content would be greatly enhance the article.  I would help you to find such a spot".  Thank you so much, but I have my own brain in my head, I don't need any help at all; from people who I don't view as capable of supporting the proper level of discourse -- especially.
 * Couldn't help to address some personal things.
 * I don't need any Physics projects, disputes, etc: you're just wasting my time in attempts to force your erroneous understanding of the topic that you don't understand at all and have no time (at least) to research on. And I am not an editor: Vi is the editor, Emacs also (though, it is more of an operating system), Notepad as well.  Nor you're.  I am researcher.  Who're you, I wonder.
 * The supplementary (just supplementary: I'd do it in the complete void around me anyways) idea of my answers here is to demonstrate to the others reading this (some of my students, some of my children are doing it, I assume) on how to politely say "Fuck off!" in the context of the "scientific discussion". But, I won't refrain from doing this impolitely: "One may suck my principle of equivalence: it won't be disturbed by this action in any (even non-inertial) frame, light cone it lives because".
 * I'll just wait for a couple of days, see what will be done with the article and restore the contents I see fit. Not because I want to, but because it will preserve the knowledge in the place it belongs to.  And then anyone can call for a dispute, commission, Kepler's spirit et al.
 * Dixi. Net&#39;em 0n (talk) 09:01, 25 February 2024 (UTC)
 * A bit of history (for the page itself: no /Git-like/ blame functionality, doing it by hand): the errorneous proportion was introduced at https://en.wikipedia.org/w/index.php?title=Equivalence_principle&diff=prev&oldid=1195565324 by @CactiStaccingCrane more-or-less recently, January 2024.
 * "1/54" problem is due to @Ywaz https://en.wikipedia.org/w/index.php?title=Equivalence_principle&diff=prev&oldid=686516911, October 2015. Net&#39;em 0n (talk) 17:12, 24 February 2024 (UTC)
 * At the top right of the article page click "View History" then at the top of the history External tools: Find addition/removal (alternate) has two links for Blame tools. Johnjbarton (talk) 17:17, 24 February 2024 (UTC)
 * I appreciate others noticing and keeping up the fight for what I tried to include in the article 9 years ago. I suspect Kepler is mistreated in the history of gravity because he was German while Newton was English, and the bias continues to show itself in this article. English historians, backed by a dominance in economics and technology around 1800, would claim kepler thought gravity WAS magnetism instead of "like". Or they would claim his references to things like "animal spirits" and the Earth "breathing" were literal. Some claim he thought every planet had a different "gravitational constant" and thereby say Newton discovered "Universal" gravity because it was too hard to deny how well Kepler understood gravity. It's ironic he's criticized for being "flaky" but at the same recognized as the one who brought observation (almost the opposite of flakiness) to the forefront of physics. Kepler seemed to surpass Galileo in terms of understanding gravity. Galileo rejected Kepler's claim that tides were a gravitational effect due to the moon. Having a tide when the moon is on the opposite side of the Earth may have prevented this from being obvious. But Wikipedia principles are explicitly against teaching and saying what's true if it's not done elsewhere. I admit I'm the first one I know of that pointed out Kepler's apparent direct knowledge of equivalence. Ywaz (talk) 19:05, 24 February 2024 (UTC)
 * Thank you for this explanation and confirmation that this material should be removed. Johnjbarton (talk) 19:07, 24 February 2024 (UTC)
 * "Confirmation" in whose view? Yours?  I don't see @Ywaz saying: "you have my confirmation that this bit is to be removed" or anything directly equivalent.
 * Please, don't use the word mangling and rhetorics: as we say here, in the non-democratic Russia, "I was the instructor in the place you was a student of".
 * You want to go via the formal dispute? Go for it: waste your time, prepare the appeal and support it.
 * You want to excercise your ability to edit/talk? I'll excercise mine. Net&#39;em 0n (talk) 09:10, 25 February 2024 (UTC)
 * I took the final two sentences of the reply as agreement with my claim that this content is against the Wikipedia policy of WP:OR.
 * "But Wikipedia principles are explicitly against teaching and saying what's true if it's not done elsewhere. I admit I'm the first one I know of that pointed out Kepler's apparent direct knowledge of equivalence."
 * I'm sorry if my tone offended, I was just trying to be direct. Johnjbarton (talk) 16:10, 25 February 2024 (UTC)
 * I took the final two sentences of the reply as agreement with my claim that this content is against the Wikipedia policy of WP:OR.
 * "But Wikipedia principles are explicitly against teaching and saying what's true if it's not done elsewhere. I admit I'm the first one I know of that pointed out Kepler's apparent direct knowledge of equivalence."
 * I'm sorry if my tone offended, I was just trying to be direct. Johnjbarton (talk) 16:10, 25 February 2024 (UTC)