Talk:Equivalence principle/Archive 3

Archive 1

Archive 2

Archive 3

Unclear

I found the article extremely unclear and barely helpful at all. The article should begin with a straightforward definition but doesn't. Then, we must wade through long text trying to distinguish between different kinds of equivalence, when the article lacked any introductory outline. As it is, this article will only help those who already know something about this subject. It starts with its application and history, instead of starting with a concise definition.

I agree with the above comment. This is a very poor article - and not just because it's badly written. The content is also messed up. It appears to have been written by people who have no idea what the Equivalence Principle really is. Maybe I'll take a stab at posting a revision.130.76.32.23 19:37, 27 September 2007 (UTC)

The nature of mass as a vortex of space-time

I found also the article a little bit confusing, excessively technique, so i introduced a better philosophical beginning to explain people what truly equivalence means: that we cannot distinguish gravitational forces and masses from acceleration. Thus the universe according to einstein is in perpetual acceleration, as forces and masses become under the 'strong' principle of equivalence (which Einstein favored in his seminal works and letters) accelerated flows of lineal and cyclical movement. I believe the beginning is not clear about the essence of this principle, which is as all Relativity Principles, simple in its appareance but with deep philosophical implications that change our vision of the Universe: an eternally accelerating Universe, seems today proved by the observation that space accelerates between galaxies and black holes. Where black holes are the most massive vortex, accelerating at c-speed.

Though the introduction was reverted and i wont place it again, i believe it is not clear at all the essence of the principle which is the fact that force and acceleration are homologous concepts. I left your original introduction, though i think the equivalence between acceleration and gravitational force should be the first sentence and now is not clear. What i reposted and please do not erase it, as it is new material that doesnt replace anything but is essential to our modern understanding of relativity and mass, is a concept which has been around for a century among relativists, albeit poorly formalized: the nature of mass as an accelerated vortex, that is the equivalence between cyclical acceleration and mass. Mass as a vortex of space-time is the relativist alternative to the concept of mass sponsored by quantum physicists as produced by a quantum particle. Since Einstein the concept of mass as a vortex of space-time that curves the acceleration of gravity into a cyclical movement ('time curves space') must be included in any serious encyclopedia that deals with all the aspects of relativity. In my view, perhaps because there ae 10 quantum physicists (more jobs) for each relativist, the articles on relativity need some further reworking and extension. Please do not erase the mass part. If you want to change it, let us discuss how to include the concept of mass as a vortex of space-time, i will include quotes and citations when i have sometime to go to the library and get them. Thanks —Preceding unsigned comment added by Homocion (talk • contribs) 17:58, 13 January 2008 (UTC)

I've heard a lot of relativists talk about gravitation, but I've not heard this 'vortex' business once. Vortex implies rotation, whereas in general relativity both rotating and non-rotating bodies gravitate. The Schwarzschild solution, the paradigm of a curved gravitating spacetime, does not rotate. Where is the need for a 'vortex'? what is the meaning of 'cyclical movement' for a static body in a static spacetime? - and more to the point, where are your citations? --Tdent (talk) 22:53, 22 January 2008 (UTC)

Also, not to insult you, but your English isn't really up to technical/academic standards, at least not in that section. You're also missing technical information - I assume from your comment here that you removed previously existing technical information? If you're going to make an article simpler to read for laymen (which is admirable) you should still leave the technical information for experts wishing to read it. Specifically, you might think about explaining why exactly mass is equivalent to a rotating vortex of space time, what the math is for arriving at this idea, and how it might be tested for falsified. Also, cite your sources! I've never heard of this work; where was it done and what papers were published? Until you can at least add that, the section appears to be fanciful at best. Dbutler1986 (talk) 10:03, 27 January 2008 (UTC)

I have deleted the section on "The Principle of equivalence and the meaning of Mass". It looks like gibberish to me (or, being kind, is perhaps original research) and is completely unsourced. Timb66 (talk) 12:13, 29 January 2008 (UTC)

well always such arrogance ts, ts, i was adressing exactly waht above someone says: this is totally impossible to understand for anyone who is not a physicst i propose to repost and ad this introduction as a normal reader wants. let us stop being so pedantic is easy to cut and paste from a specialist source, this is nto what ecnclcipedias are about htough:

The Principle of Equivalence between force and acceleration is the fundamental principle of dynamics and motion. It is also a philosophical principle of the utmost importance in the understanding of what the Universe is. In its clearest philosophical meaning (Newton, Einstein, Mach), it positions acceleration rather than motion, equivalent to force (F=Ma in Newtonian Physics) or mass (Einsteinian Physics), as the fundamental 'substance' of space-time. If men first considered the world made of fixed substances (Greek philosophers), Galileo proved that all was in constant motion and made of speed, v=s/t the first fundamental equation of science. Yet Newton first and Einstein latter affirmed that all exist under forces and weights which are accelerations: f=mxa. The full meaning of that expression implies though a world of infinite speeds rather than fixed particles, motions derived from acelerations, through Laplacian double derivatives, the first of which would be steady motion and the second fixed, constant form. Thus from accelerations (rotational or lineal), actions are created with a constant speed (temperatures, h constants), which derive into quiet space, and those 3 dimensions of time=change, form, movement and acceleration, become the 3 essential searches of physics in all systems and laws. As the Principle of Relativity had two ages of classic physics (Galilean Relativity) and Einsteinian physics, so happens to the Equivalence Principle. We can consider the classic age of Newtonian Equivalence, defined by the equation F=Mxa, in which the mathematical model preferred is that of a newtonian fluid accelerating in a vortex or orbital motion, and the modern age of Einsteinian Physics, defined by the equivalence between acceleration and mass/weight. This second age changes the mathematical model to XIX c. Riemannian geometries but the essence of the principle remains the same: There is a substance (called ether in newtonian physics, light-space/time in Relativity), which shapes a background space-time subject to motions. Those motions of forces constantly accelerate with a speed proportional to a constant of curvature/acceleration, called G.

As Newtonian Equivalence is normally studied as a different subject, we shall here concentrate in the description of a world made of accelerations and decelerations, no longer of fixed substances but of motions. —Preceding unsigned comment added by 76.89.246.73 (talk) 18:14, 14 March 2008 (UTC)

Einstein's Mistakes

In the new book Einstein's Mistakes Dr. Hans Ohanian states that Einstein's Principle of Equivalence is actually vacuous and easily disproved, and he gives a number of examples where the supposed principle quickly breaks down and is easily shown to be false. 72.186.213.96 (talk) 14:12, 17 September 2008 (UTC)

Equivalence principle misinterpretation

The effect of the force F acting on mass M causes the same acceleration, whether it's origin is gravitation or other (electrostatic,...). Of course - if the force and mass is the same, acceleration will be the same. Equivalence principle after Galileo is misinterpretation of the law a = F / M. We only know, that gravity acts on mass and mass causes gravity - gravity and mass are interacting. Explicit constant G, the experimental number of theory, introduces the quantity of the gravitational influence generated by mass M. The real physics behind the so called Equivalence principle is the fact, that gravity causes same acceleration of two different masses in the same gravitational field (introduced by Galileo). This physical fact manifests the physical interaction between the mass and the gravitational field. That means, the gravitational interaction is proprtional to the mass of interacting object - therefore acceleration is the same. In electrostatics, interaction is also proportional to the charge of interacting object. Today no theory realy explains gravitational interaction, that means - what is mass and what is gravity. In electrostatics we don't know what is charge and what is electrostatic field - situation is the same - we know them by their proprties. Tell me - what is charge ? The fundamental difference between the charge and mass is, that the charge is conserved but mass is not. How can someone explain what is gravity, if he cannot explain what is mass ? Every such explanations are invalid. We just know how gravity works on macroscopic scale - macroscopic properties of gravity. We don't know what is the cause of gravity and what is the cause of mass. If gravity is the effect of mass, mass is the cause of gravity. If we don't know what is mass, we don't know what is cause of gravity. If we say, the cause of gravity is geometry, that means we say the mass is geometry. If we say mass is not conserved, than we say geometry is not conserved. If someone says, that he knows what is cause of gravity, he must say what is mass, or what is cause off mass. Softvision (talk) 22:18, 29 June 2009 (UTC)

New version ready

I have been working on this article again, trying to get it better organized and to remove some of what I have come to see as my own warping of it. The result is in User:Ems57fcva/sandbox/Equivalence_principle. There really is not that much in the way of changes this time. Most of it is text having been moved around to redirect the emphasis of the article, combined with some rewordings to make it more coherent. It is easy enough to see what I did by viewing the history and comparing the initial and current versions.

Any comments? If not, I will move this update over in a day or two. --EMS | Talk 29 June 2005 22:25 (UTC)

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I like it. I made a minor change (to remove the abbreviation of GR). I've been doing some historical reading, and added a couple Dicke references, so take care not to overwrite them when you make the switch. –Joke137 30 June 2005 19:56 (UTC)

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Thanks. I will be careful about your references. --EMS | Talk 04:45, 1 July 2005 (UTC)

gravitational mass ≠ inertial mass

the article states that the equivalence principle explains why gravitational mass is equal to inertial mass. however the equivalence principle (The trajectory of a falling test particle depends only on its initial position and velocity, and is independent of its composition) is compatible with the formula F₁₂=M_i1 * M_g2/r² where F₁₂ is the force upon mass1 due to the gravity of mass2 and r is the distance between them. i=inertial and g=gravitational. this formula does not require gravitational mass to be equal to NOR PROPORTIONAL TO inertial mass just-emery (talk) 06:13, 13 May 2009 (UTC)

In other words, the gravitational field produced by mass2 depends, by definition, only on its gravitational mass while the amount of force that any given gravitational field exerts upon mass1 depends only on the strength of the given gravitational field at the point where mass1 is located and mass1's inertial mass. 69.226.243.111 (talk) 01:14, 4 August 2009 (UTC)

I deleted the sentences

" While this picture works very well for most calculations, the inertial mass in Newton's second law, $F=ma$, mysteriously equals the gravitational mass in Newton's law of universal gravitation. Under the equivalence principle, this mystery is solved because gravity is an acceleration from inertial motion caused by the mechanical resistance of the Earth's surface."

from the first section, as they are incorrect and misleading: there is nothing mysterious about the equality of the gravitational and inertial mass as they are equal by definition due to the choice of the gravitational constant. The equivalence principle only relates to the proportionality of the two, and that is the only thing that experiments can determine. The assertion that both are equal is indeed only a postulate made by GR, which in fact is observationally irrelevant (note that the gravitational constant is a free parameter in Einstein's field equations, so it is in any case an empirical quantity).

Thomas —Preceding unsigned comment added by 81.103.110.25 (talk) 15:06, 24 May 2009 (UTC)

Wot is inertial motion equivalent to in the equivalence principle?

Is the principle of equivalence that inertial motion is equivalent to (i) uniformly accelerated motion at a rate of 9.81 m/s2, or to (ii) uniformly accelerated motion at any rate whatever, or to (iii) gravitational free-fall, which is of course not a uniformly accelerated motion and whose acceleration depends upon distance from the gravitational centre, or to (iv) any form of accelerated motion whatever ?

The article currently seems unclear about this issue, as in the following text:

"The equivalence principle proper was introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1g (g = 9.81 m/s2 being a standard reference of gravitational acceleration at the Earth's surface) is equivalent to the acceleration of an inertially moving body that would be observed on a rocket in free space being accelerated at a rate of 1g. Einstein stated it thus:

"we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system." (Einstein 1907)

So I propose to flag it for clarification please.

--Logicus (talk) 18:03, 23 July 2009 (UTC)

No. Einstein is not being imprecise at all. He's talking about an accelerated reference frame.- (User) Wolfkeeper (Talk) 18:21, 23 July 2009 (UTC)

You clearly do not understand the question. 'AN accelerated reference frame' is about as imprecise as it gets. What kind of acceleration, Uniformly accelerfates, or as in free fall as per Newton ? --Logicus (talk) 18:27, 23 July 2009 (UTC)

Well, I don't know. Do you think I'm sticking my neck out to suggest that that Einstein meant that it must be the right kind of accelerated frame so as to give the same effect as gravity?- (User) Wolfkeeper (Talk) 19:00, 23 July 2009 (UTC)

I would suggest to you you need to understand accelerated reference frames better before claiming that this is ambiguous.- (User) Wolfkeeper (Talk) 19:00, 23 July 2009 (UTC)

Logicus to Wolfkeeper: Better than speculatively sticking your neck out, can we not nail down what kind of acceleration Einstein meant ?

As he is quoted

"we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system." (Einstein 1907)

but the corresponding acceleration in a gravitational field is an exponentially increasing acceleration in Newtonian classical mechanics, and whose kinematical distance-times law to replace Galileo's radically mistaken scholastic mechanics law s = gtt/2, was given by Newton in Proposition 32 of Book 1 of Principia.

But this would contradict the article's claim that

"The equivalence principle proper was introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1g (g = 9.81 m/s2 being a standard reference of gravitational acceleration at the Earth's surface) is equivalent to the acceleration of an inertially moving body that would be observed on a rocket in free space being accelerated at a rate of 1g."

As for the Wikipedia accelerated reference frames article you quote, these are said to be frames with a constant acceleration. So this apparently contradicts the most plausible interpretation of Einstein's statement, since acceleration in a natural gravitational field is not constant according to classical mechanics, but variable. So in the classic example of Einstein's lift/elevator in gravitational free-fall, that motion must be an exponentially increasingly accelerated motion.

Meanwhile I restore the Einstein clarification flag you humorously deleted, because of course it does not have to be Einstein who clarifies what he meant. Surely somebody knows what he meant ?

But what on earth is the above passage on the equivalence principle saying ? That a uniform acceleration of bodies towards the centre of the Earth at a rate of 1g, which could of course therefore not be gravitational free-fall according to classical mechanics, but rather must involve some retarding resistance to prevent an exponentially increasing acceleration that would be induced by unfettered gravity alone, is equivalent to the acceleration of a rocket in free space being accelerated at a rate of 1g ? So what ? It this just asserting the tautology that all uniformly accelerated motion is uniformly accelerated motion ?

And what on earth does "the acceleration of an inertially moving body that would be observed on a rocket in free space being accelerated at a rate of 1g" mean ? Does "inertially moving body" mean 'a body in uniform motion' ? Or does it mean a body in gravitational free-fall ? And is that body observed on a rocket (i.e. observed to be inside a rocket), or from a rocket (i.e. observed to be outside the rocket by an observer looking out a rocket window) ?

So is there any significant difference of physics between the following text and the current passage ?:

"The equivalence principle proper was introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1g (g = 9.81 m/s2 being a standard measure of gravitational acceleration at the Earth's surface) is equivalent to the acceleration of a rocket in free space being accelerated at a rate of 1g."

In comparison the current passage seems to be gobbledegook.

Einstein's theoretical transition post-1905 from SR to GR in 1915 is of course intellectually fascinating. But the question of whether he reduced gravity to (Minkowskian) space-time curvature, as traditionally claimed in university level physics pedagogy, remains outstanding. And if inertial motion in GR is uniformly accelerated motion, then surely he did not ?

Perhaps a more appropriate flag for the passage in question is 'not in citation given', since the Einstein quotation does not confirm it, because it does not say the acceleration must be uniform, and nor even more particularly at a rate of 9.81 m/s2

--Logicus (talk) 14:19, 25 July 2009 (UTC)

The non-Einstein paragraph that Logicus cites is badly garbled. Presumably it intends to say that freefall is equivalent to inertial motion and/or that being at rest with respect to the earth (at sea level) is equivalent to a 1 g acceleration in free space. The latter could be expressed more generally: Being “at rest” in a gravitation field is equivalent to being accelerated in free space at the rate a body would freefall in the gravitational field. —teb728 t c 06:41, 1 August 2009 (UTC)

Galileo did not refute Aristotle

In the Development of gravitation theory section, the article curreklty claims "Something like the equivalence principle emerged in the late 16th and early 17th centuries, when Galileo expressed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated, thereby refuting Aristotle."

But Galileo did not refute Aristotle, because Aristotle predicted all bodies would fall with the same infinite speed in gravitational free-fall. He did not predict bodies fall with different speeds proportional to their weight in gravitational free-fall. I therefore delete this mistaken claim. --Logicus (talk) 14:56, 2 August 2009 (UTC)

Problems with the first 3 entries in the weak equivalence principle table

The historical table in the Weak Equivalence Principle section conflates two historically different issues, for the prediction that unequal weights would fall with the same speed in a void is conflated with that of the gravity or weight of a body being proportional to its inertial mass. The difference between these in such as Galileo, for example, is that whilst in his final mechanics in his 1638 Discorsi he predicted that in a void all unequal weights would fall with the same speed, on the other hand unlike such as Kepler and Newton he had no concept of inertial resistant mass, and so could not possibly assert the proportionality or equivalence of gravitational and inertial mass. In fact nobody in this list before Newton had any concept of inertial mass.

The list also conflates theoretical claims with experimental demonstrations. But there is no evidence that Philoponus or Galileo ever did any such experiments, and it seems likely that nobody before Newton in this list did any relevant or acceptable experiments to verify unequal weights free-fall with equal speed.

And Galileo never claimed to have verified unequal weights would free-fall with equal speeds by rolling balls down the inclined plane. His only use of the inclined plane in his publications was to try and demonstrate his radically mistaken theory that gravitational free-fall throughout the universe, especially that of the planets towards the Sun, would be a uniformly accelerated motion. But not that it would also have the same rate of acceleration universally, and thus the same time of fall for any given distance, irrespective of differences of weight.

And Philoponus held that speed of free-fall is proportional to density, so that only bodies of same density fell with equal speeds, but even bodies of the same weight would fall with unequal speeds if of unequal densities, and as also Galileo held in his 1590 Pisan (Philoponan) dynamics. As for Stevin, dropping lead balls means balls of same density, but this does not establish different densities also fall with same speed.

For the moment I flag each of these three claims for clarification in the light of these errors, but think they will all have to go.

A basic decision to be made here is whether the table should be just of experiments, or also include purely theoretical predictions of equal speeds for unequal weights in the void, or of the proportionality of gravity to inertia.

I suggest they could be replaced by a brief history of equal speeds for unequal weights in free-fall, as follows:

Fifth century BC: Aristotle predicts equal speeds of unequal weights in gravitational fall in a void, but regarded it as an absurdiity that refuted the void.

13th century: Aquinas posits all bodies universally have inherent inertial resistance to motion proportional to their mass, and sublunar bodies also have inherent gravity/weight proportional to their mass, thus implicitly positing the mutual proportionality of gravitational and inertial mass for sublunar bodies. But celestial bodies do not have gravity.

Early 15th century: Paul of Venice draws the conclusion that since the ratio between the weight and inertial resistance to motion is a constant, then unequal weights would free-fall with same speeds in accordance with Aristotle’s law of motion as follows: v @ F/R = W/m = W/W = 1, thus v = k for all weights. So not an absurdity. ('@' = 'is proportional to')

But first experimental confirmation of this prediction is unclear. Is it Newton in Principia ?

However, the brief history of proportionality of gravitational mass and inertial mass is different, being

Aquinas Paul of Venice Kepler Newton

--Logicus (talk) 18:24, 3 August 2009 (UTC)

Further clarifications: Actually the question of when the proportionality of gravitational and inertial mass universally was first asserted is obscure. Whilst Aquinas has it implicitly for sublunar bodies, it was not possible for superlunary bodies until they were attributed with a universal gravity. Burt the celestial spheres did not have gravity, and it was Averroes who first gave them inertia. After the dissolution of the spheres it was Kepler who first attributed inertia to the planets and coined the very term inertia for a non-gravitational inherent resistance to motion in all bodies universally. But he did not give the planets gravity towards the sun. It seems that was Borelli. But question is who has proportionality of gravity and inertia before Newton ? It does seem to have been in the 17th century, albeit after Aquinas had first distinguished them in the same sublunar bodies.

Also the question of who first demonstrated equal speed of all unequal weights in free-fall is also obscure. Was it by a pendulum experiment, maybe Newton’s in Bk 3 Prop 6 Principia ? Or could planetary free-fall in a virtual vacuum somehow be taken as a demo ?

Does anybody have any clues here ?--Logicus (talk) 18:02, 4 August 2009 (UTC)

active, passive, and inertial masses

by definition of active and passive gravitational mass, the force on mass₁ due to the gravitational field of mass₀ is:

$F_{1}={\frac {Mass_{0}^{act}*Mass_{1}^{pass}}{r^{2}}}$

likewise the force on a second object of arbitrary mass₂ due to the gravitational field of mass₀ is:

$F_{2}={\frac {Mass_{0}^{act}*Mass_{2}^{pass}}{r^{2}}}$

By definition of inertial mass:

$F=mass^{inertial}*acc$

if mass₁ and mass₂ are the same distance r from mass₀ then by the experimentally proven Weak equivalence principle they fall at the same rate (their accelerations are the same)

$acc_{1}={\frac {F_{1}}{mass_{1}^{inertial}}}=acc_{2}={\frac {F_{2}}{mass_{2}^{inertial}}}$

hence:

${\frac {Mass_{0}^{act}*Mass_{1}^{pass}}{r^{2}*mass_{1}^{inertial}}}={\frac {Mass_{0}^{act}*Mass_{2}^{pass}}{r^{2}*mass_{2}^{inertial}}}$

therefore:

${\frac {Mass_{1}^{pass}}{mass_{1}^{inertial}}}={\frac {Mass_{2}^{pass}}{mass_{2}^{inertial}}}$

in other words, passive gravitational mass must be proportional to inertial mass for all objects.

Further by Newtons third law of motion:

$F_{1}={\frac {Mass_{0}^{act}*Mass_{1}^{pass}}{r^{2}}}$ must be equal and opposite to

$F_{0}={\frac {Mass_{1}^{act}*Mass_{0}^{pass}}{r^{2}}}$

it follows that:

${\frac {Mass_{0}^{act}}{Mass_{0}^{pass}}}={\frac {Mass_{1}^{act}}{Mass_{1}^{pass}}}$

in other words, passive gravitational masses must be proportional to active gravitational mass for all objects. Lemmiwinks2 (talk) 01:24, 27 September 2009 (UTC)

I have created a list of known places where the above comment appears. Brian Jason Drake 11:40, 29 September 2009 (UTC)

Lemmiwinks2 deleted the section on their talk page containing that list. Revision 318510298 was the list revision containing that list. A cleaned-up version of the above comment now appears in the article. Brian Jason Drake 07:41, 28 October 2009 (UTC)

Important details

"The equivalence principle proper was introduced by Albert Einstein in 1907, when he observed that the acceleration of bodies towards the center of the Earth at a rate of 1g"

This statement is only true if the test masses used are lifted from the earth, so that the total mass of the system does not change. External test masses will always accelerate at more than one g, depending on their mass.

The equivalence principal does not refer to the relative acceleration of a mass and the earth. It refers to the acceleration of a mass relative their mutual center of gravity. When a heavier body is used, the center of mass shifts, and the *relative* acceleration increases. Only the acceleration of the body relative to the mutual barycenter is unchanged.

"g" is not the acceleration of a body relative to the earth. It is the acceleration of a body relative to their common center of gravity.

Acceleration is often mentioned without providing a reference frame. "Gravitational acceleration" is ambiguous. Acceleration can be relative to the two bodies, or relative to their common center of mass, or relative to an arbitary reference frame, or relative to an encompassing barycenter (such as the solar system barycenter, geocenter, etc).

Newton's second law describes acceleration relative to a local instantaneously unaccelerated frame. g*m/r^2 is acceleration relative to the mutual center of mass of two bodies. g*(m1+m2)/r^2 is the relative acceleration of the two masses.

Uniform gravitational fields do not exist in reality. This should be stressed early in the article to avoid confusion.

This is why modern treatments of the equivalence princpal rely on the concept of a limit. Nearly all of the "principals" mentioned are true only in the limit of some infinitesimal. For example, the weak equivalence principle is true only in the limit of an infinitesimaly small object with infinite rigidity and an infinitely small mass separated by an infinitesmally small distance during an infinesimally small time inverval.

These restrictions must also be applyied to Newton's law of universal gravitation before it can be applied to physical systems. However, they are implicit in Newton's law due to the non-physical assumption of "point masses". The same technique should be applied here.

Norbeck (talk) 02:00, 30 December 2009 (UTC)

Section "The weak equivalence principle"

The mention of capillarity appears to be complete nonsense, and much of the section on Eötvös and his torsion balance is irrelevant. Could this be restored to something like it was in April 2009 before Celebration1981 (a user subsequently blocked) put it into this form?--Keith Edkins ( Talk ) 11:01, 4 January 2010 (UTC)

Newton's Theory Applies Only to Point Masses?

The present article says Newton's theory applies only to point masses. What does this mean? On the face of it, the statement seems to be false. Newton himself, in the Principia, certainly did not consider "point masses" at all, he always insisted on finite density, so the mass of a single point would be zero. So what does it mean to say that Newtonian gravity applies only to point masses?Urgent01 (talk) 17:27, 19 April 2010 (UTC)

Recent work showing non-equivalence of gravitational and inertial mass

I am not qualified to update the article properly but I wanted to bring the following paper to the attention of someone who can do it justice. Recent work has shown that in the quantum world, these must be different and in fact can be significantly different. The paper describing this work is [1] while the blog describing it is [2]. --Sgaragan (talk) 13:00, 15 June 2010 (UTC)

Direction of weight in space elevator

Einstein inoculated general relativity with the help of equivalence principle and spaceship/space elevator but I don't understand in which direction a person feel sensation of his weight = mg?

Upward means towards the centre of elevator/along "g" OR

Downward means towards the floor of elevator/ opposite to the direction of "g".

Further, shouldn't a person of mass m inside space-elevator of gravitating mass M moves towards its centre due to universal law of gravitation [F=GMm/R^2]?Khattak#1-420 —Preceding unsigned comment added by 68.147.41.231 (talk) 02:50, 9 January 2011 (UTC)

In flat space, the effects of motions are equal for any two experiments; in curved space this cannot be true

The Einsteinian equivalence principle states a.o. that the local effects of motion in a curved space (gravitation) are indistinguishable from those of an accelerated observer in flat space, without exception. Is this really true? Here on earth experiments have shown the effect of measuring time at different heights, indicating that we are in a curved space. In flat space, the effects of motions are equal for any two experiments, indicating the experiments were done in flat space. However, if "local" means a single point, different heights are not applicable and then I have said nothing. — Preceding unsigned comment added by 82.171.197.206 (talk) 10:09, 8 March 2012 (UTC)

Eötvös experiment

See also: Eötvös experiment

I believe that this level of detail on the Eötvös gravimeter is not required on the present page. Therefore an removing it. If any body feels otherwise, please put this back.--Suneet (talk) 13:02, 9 October 2011 (UTC)

Loránd Eötvös (Vásárosnaményi Báró Eötvös Loránd) invented the gravitational balance. The Eötvös gravimeter is a sensitive, portable instrument for measuring varying densities of buried geological strata. Ore deposits are more dense, petroleum and caves less dense than average rock. It determines (airborne suspension) force and horizontal gradient of local gravity. The Eötvös torsion balance is an equivalence principle test. It was substantially improved by Robert H. Dicke in the early 1950s.

Modern Eötvös balances are sensitive to path divergence of suspended paired opposed test masses as the Earth spins about its axis (horizontal inertial acceleration; maximum at 44.9519° latitude, WGS84 geoid) and falls around the sun (gravitational acceleration; maximum at ~4 January perihelion and minimum at ~4 July aphelion). An Eötvös balance requires its own isolation bunker plus multiple levels of temperature, vibration, and field exclusion. Its equivalence principle sensitivity is limited by the vibrations of its own atoms, hence there is a preference to operate near 4 kelvin rather than at room temperature.

Proposed geometric test of the weak equivalence principle

While on vandalism patrol, I had reverted an edit made by 67.86.70.182 He kindly wrote back and explained why he made this particular edit, which included several references. I'm including the conversation below.

My removal of the "Proposed geometric test" section was not vandalism; it's basically an advertisement for "Uncle" Al Schwartz's Eötvös torsion experiment. I think it would be a fine experiment to run, but until it actually is (or at least proposed in a proper journal paper) it doesn't belong here. 67.86.70.182 (talk) 16:57, 4 July 2011 (UTC) Thanks for your reply and explanation. I agree that the external link needs to be removed. There are several other sourced references that seem pertinent and independent of the Eötvös experiment. What would happen if we removed all references to the mazepath website, but left the rest in there? There are other hypotheticals in this article, so it does not seem to violate the tone of the article as a whole. Would appreciate your additional thoughts. 78.26 (talk) 17:54, 4 July 2011 (UTC) That sounds reasonable. Shall we move further details to the article's discussion page? 67.86.70.182 (talk) 18:37, 4 July 2011 (UTC)

I made said edits, but would appreciate others who are familiar with the subject reviewing the paragraph. Perhaps it doesn't belong here at all. Thanks! 78.26 (talk) 02:02, 5 July 2011 (UTC)

I have cut the section. It is far too specific and technical for a general encyclopedia article on the equivalence principle. If people want to go this deep into the topic, they can check the literature. -Jordgette [talk] 21:58, 3 June 2012 (UTC)

This "Uncle" Al Schwartz character is persistent. I only just recently removed a re-insertion of his incomprehensible, jargon-filled original research which had persisted unnoticed from 26 July 2012‎ until now. Stigmatella aurantiaca (talk) 02:19, 9 February 2013 (UTC)

Rotation and the equivalence principle

Assume an observer who can do any experiment in the following cases.

1. Given x,y,z is a frame of reference in 3 dimensional space that is accelerated in the direction z and the observer at a fixed position at p=x1,y1,z1.

The direction d of gravity is equal to the -z direction and zero perpendicular to d.

The path of a free falling mass, that is dropped at p, follows d.

When moving uniformly in the d direction, gravitation is not affected.

When moving uniformly in a direction perpendicular to d, gravitation is not affected.

2. Given x,y,z is a frame of reference in 3 dimensional space, a mass at m = x = y = z = 0 and the observer located at a fixed distance from m, i.e. at p=x1,y1,z1.

The direction d of gravity is positive in the p to m direction and zero perpendicular to d.

The path of a free falling mass, that is dropped at p, follows d.

When moving uniformly in the d direction, gravitation is increasing.

When moving uniformly in a direction perpendicular to d, gravitation is decreasing and d is changing.

3. Given x,y,z is a frame of reference in 3 dimensional space that rotates around the z-axis and the observer located at a fixed distance from the z axis, i.e. at p=x1,y1.

The direction d of gravity is positive in the z to p direction and zero perpendicular to d.

The path of a free falling mass, that is dropped at p, deviates from d.

When moving uniformly in the d direction, gravitation is decreasing and a force perpendicular to d is felt, resulting in a change of d.

When moving uniformly in a direction perpendicular to d, gravitation is increasing and d is changing.

Conclusions.

- All three cases imply either a rigid body or a massless observer, because otherwise the observer cannot have a fixed position.

- If in case 2 and 3 the fixed distance is great with respect to the distances measured at the experiments, the results will resemble case 1.

- In nature, always combinations of cases 2 and 3 are found, be it solar systems or (classical) atoms, however, maybe there are exceptions. — Preceding unsigned comment added by 82.171.197.206 (talk) 11:19, 11 March 2012 (UTC)

- Maybe nobody considered rotation in this way. — Preceding unsigned comment added by 82.171.197.206 (talk) 11:05, 11 March 2012 (UTC)

Statement on photons in "The weak equivalence principle"

I believe the statement made on photons in the section "The weak equivalence principle" is incorrect as it stands. There is a factor of 2 in the deflection of photons by a spherical mass between the infalling trajectory at infinity and the outgoing trajectory at infinity when comparing the predictions of general relativity and of the equivalence principle alone. This factor comes (see for example Will's book "Was Einstein Right?", Oxford University Press, 1997) from the curvature of space, accidentally producing the same amount in deflection as the equivalence principle. But it would not be visible in a local frame of reference, because locality of the frame means it is so small that space(-time) curvature effects are negligible. In any case, the weak equivalence principle should hold for photons just as for any other (non-gravitating) particle. The question is not whether photons suffer the same acceleration as massive particles but whether the acceleration they suffer is the same in a homogeneous gravitational field and in a uniformly accelerating frame. Weak refers to all experiments not involving gravity. Whether gravitons behave the same in homogeneous gravitational fields and uniformly accelerated frames is out of the scope of the weak equivalence principle. It is the subject matter, so to speak, of the strong equivalence principle. Krenska (talk) 09:30, 19 June 2012 (UTC)

I have removed that statement. As I understand it, from the viewpoint of an observer on the surface of a gravitating body (or in an accelerating rocket), photons fall exactly like anything else. I have tidied up the reference to subjects which don't contradict the EP.--Keith Edkins ( Talk ) 16:52, 8 February 2013 (UTC)

Geometric EP test

Geometric EP test inclusion is important. Bench EP tests and Nordtvedt effect plus lunar laser ranging validate the EP. 1.74 solar-mass 465.1 Hz pulsar PSR J1903+0327 plus a 1.05 solar-mass star are a stellar binary system [arxiv:0805.2396]. 15.3% [AP4 model, arxiv:astro-ph/0002232] vs. 0.0001% gravitational binding energy, 1.8×10¹¹ vs. 30 surface gees, 2×10⁸ gauss vs. 5 gauss magnetic field; compressed superfluid neutrons and superconductive protons [arxiv:1011.6142] vs. proton-electron plasma, extraordinary isospin and lepton number divergence; plus pulsar 11% of lightspeed equatorial spin velocity are EP-inert for orbit, periastron precession, and gravitation radiation orbital decay. Relativistic and quantum mechanical extreme divergences validate the EP. What remains to falsify the EP?

The vacuum is observed parity-even toward massless boson photons but trace parity-odd towards fermionic matter. Fundamentally test vacuum geometry toward mass with geometric Eötvös experiments. The universe paints with a broad palette. Somebody should look. — Preceding unsigned comment added by 68.4.88.182 (talk) 17:55, 18 August 2012 (UTC)

Please do not reinsert your original research into the article. Wikipedia is not a forum for you to espouse your pet theories. Stigmatella aurantiaca (talk) 02:22, 9 February 2013 (UTC)

Geometric EP Test again

I removed the following original research by User:Spironis

• No composition or field contrast measurably violates the Equivalence Principle (EP). EP tests ignore test mass geometry, physical chirality, for the vacuum is observed to be mirror-symmetric toward massless boson photons. However, matter is massed fermions. Matter falls with half the acceleration photons fall in a given gravitational field. Photon vacuum symmetries are not identical to fermionic matter vacuum symmetries. Paired socks appear identical to a left foot (that is not mirror-symmetric). Paired shoes fit a left foot with different energies. If local left and right shoes fit into the vacuum with trace different energies, they vacuum free fall along trace different minimum action trajectories, violating the EP. This geometric EP falsification arises from Einstein-Cartan-Kibble-Sciama chiral spacetime torsion.
• Crystallography's shoe boxes are eleven pairs of enantiomorphic space groups . Periodic lattices test spacetime isotropy overall. Spacetime geometry, the EP, must be tested with massed chiral geometry. Enantiomorphic crystallographic space groups include P3₁21 versus P3₂21 single crystal α-quartz and P3₁ versus P3₂ single crystal γ-glycine. 3₁ screw axes are geometrically right-handed, 3₂ are left-handed. Control experiments contrast each α-quartz shoe against an amorphous fused silica sock, or each γ-glycine shoe against an achiral P2₁/n α-glycine sock. Somebody should look.

Please do no re-insert your original research into this article. Wikipedia is not a forum for you to espouse your pet theories. Your proposal superficially sounds interesting, and you seem facile in your use of jargon, but in the end, it is obvious that your proposal has no theoretical justification. Einstein-Cartan theory does not support your proposal. Your proposal is, so far as I can see, a wild stab in the dark, and it has never been set forth in a peer-reviewed journal. Stigmatella aurantiaca (talk) 19:47, 11 February 2013 (UTC)

Why two tables for tests of WEP?

There are two separate tables listing tests of the weak equivalence principle. There is some overlap, and I can't see why they shouldn't be merged. Thirteenangrymen (talk) 13:45, 30 October 2014 (UTC)

Where is the fallacy?

"being at rest on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being accelerated by its engines."

I know Einstein said this (or the equivalent), but I can think of it least two ways in which they do not appear to be equivalent:

1) If I am on the Earth, the force on my head is (marginally) smaller than that on my feet, whereas on an accelarating spaceship it is not; and

2) On the spaceship, the forces on my right and left sides are parallel; whereas on Earth, they are not: they meet at the centre of the Earth.

Where am I going wrong? Are these objections so stupid that no one has brought them up before? Paul Magnussen (talk) 00:06, 13 September 2013 (UTC)

I understand that both effects would be negligible if you're tiny enough — Preceding unsigned comment added by 77.242.202.229 (talk) 13:36, 7 February 2014 (UTC)

Answer: The the geometry of the gravitational field differed, if it was from a infinite flane, you couldn't tell. Then again the force would not drop off with distance either, but is iss theoretically concevible.

The weak equivalence principle refers strictly only to a constantly accelerated spaceship and a uniform gravitational field. The Earth's gravitational field is only approximately uniform. The WEP therefore applies only in a "sufficiently small" region.Ericlord (talk) 13:33, 15 January 2015 (UTC)

Paragraph should be checked

Although the equivalence principle guided the development of general relativity, it is not a founding principle of relativity but rather a simple consequence of the geometrical nature of the theory. In general relativity, objects in free-fall follow geodesics of spacetime, and what we perceive as the force of gravity is instead a result of our being unable to follow those geodesics of spacetime, because the mechanical resistance of matter prevents us from doing so.

What does this mean (in particular, the last words)? 78.15.203.91 (talk) 19:42, 19 September 2014 (UTC)

The final words don't mean anything. They are nonesense.Ericlord (talk) 13:37, 15 January 2015 (UTC)

Where is the fallacy2?

If you drop a clock in an accelerating elevator in space, it is not accelerating and hence can't be effected by time dilation from the acceleration.

So it would immediately resume normal time and tick faster than you experience time. If they are equivalent, then time dilation should also stop in a gravity field if you let gravity act on a clock (dropped or thrown).

You are essentially accelerating when you are stationary on earth, falling is like not accelerating relative to bent space(space-time).

I guess it is only kinda equivalent, either that or a clock dropped into a black hole will (all things being equal) appear to move at a normal rate to an observer at a safe distance as long as it freefalls. — Preceding unsigned comment added by 121.99.177.211 (talk) 22:16, 26 February 2014 (UTC)

"If you drop a clock in an accelerating elevator in space, it is not accelerating and hence can't be effected by time dilation from the acceleration". That's not correct. Time dilation is not about a single clock it's about the discrepancy in the passage time for two clocks (ie. the dropped clock and the clock of the observer standing on the floor of the elevator. So the two situations are equivalent - "You are essentially accelerating when you are stationary on earth, falling is like not accelerating...".Ericlord (talk) 14:08, 15 January 2015 (UTC)

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Equivalence Principle is False

• In his book Einstein's Mistakes, pages 226-227, Hans Ohanian describes several of many known situations all of which falsify Einstein's Equivalence Principle. Inertial accelerative effects are simply NOT the same thing as gravity. Einstein was wrong. One simple example is to simply release a coin while on a Merry-Go-Round, to see immediately the equivalence principle is simply false. Ohanian's book should be included in the Wikipedia article. 47.201.179.7 (talk) 14:05, 9 May 2017 (UTC).

• It is impossible to accelerate an orbiter on a circular trajectory. If the thrust increases or decreases, the trajectory becomes an ellipse instead of a circle. The only possible way to accelerate an orbiter on its circular orbit would be to simulate a mass increase of the body around which the mobile is orbiting. If the Einstein's equivalence principle would be right, this simulation could be performed with an engine, as far as the mechanical acceleration should be equivalent to a gravitational acceleration. This is not the case, and this is why the space rendez-vous is so difficult to calculate in astronautics. Ref : An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition, Richard H. Battin, AIAA EDUCATION SERIES, 1999, Chapter 11, paragraph 11.1, page 516.

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A contrarian viewpoint

The general theory of relativity is amongst others based on the equivalence principle. However a charge does not radiate in a gravitational field while it does when accelerated in a non-inertial field. Vasily Yanchilin concludes in his book The Quantum Theory of Gravitation (2003) (referring to other authors) that the gtr is wrong. In Wikipedia's article this should be discussed. One more argument against the gtr is that it assumes c to be constant in vacuum. But there is no real vacuum and everywhere radiation exists, which has a mass equivalent. When photons go "outward" in the universe they will be slowed down (compare curving around mass) unless the universe is infinite without a Big Bang. Time is a physical reality and not something abstract as it concerns physical processes and is measured on these like with frequency of radiation. Slowing down of time near supposed black holes contradicts the speed of processes around the Big Bang. The latter did not originate from a point, which is a mathematical thing and does not exist in physics because it has no dimensions. NIST says it has a clock precise to one second in several billion years. This should be adjusted to precision of one or more billionth per second. Jitso Keizer janjitso@hotmail.com www.janjitso.blogspot.com. — Preceding unsigned comment added by 145.108.106.189 (talk • contribs) 8:49, 18 May 2015 (UTC)

First, sign your comments with four tildes, not by posting your email address and website.

Second, please see WP:RSUW for an explanation on why the book you mention does not belong in this article.

Third, I assume you were the one who added the four dubious tags in October 2020, which I have removed. The reasons you provided show a fundamental lack of understanding of the basics of general relativity, and most of what you've written above is incorrect both mathematically and empirically. General relativity is not a subject you can make advances in without a thorough understanding of both the mathematics and the concepts involved, and as GR has been as thoroughly tested as any scientific theory, hopefully you realize that contradicting tens of thousands of the brightest minds who spent lifetimes studying when you don't understand the basic concepts is unlikely to be fruitful. At the very least, you could ask experts to clarify your understanding, but the talk page for the article is not the appropriate place to educate you. See also Dunning-Kruger effect. TricksterWolf (talk) 18:08, 10 December 2020 (UTC)

Note: I have thrown an {{unsigned}} template at the old comment, made way back here. - DVdm (talk) 21:57, 10 December 2020 (UTC)

Reorganization proposal

Rather than WEP, WEP test, EEP, EEP test, SEP, SEP test, I think the article would be clearer organized as Types: WEP, EEP, SEP, then Tests: WEP EEP, SEP. Johnjbarton (talk) 00:27, 20 December 2023 (UTC)

Resolved

Johnjbarton (talk) 04:08, 21 December 2023 (UTC)

Need a section on tidal forces

One of the 'next layer' topics mentioned but not coherently covered is the issue of tidal forces. One source on the history side is

• Norton, John. "What was Einstein's principle of equivalence?." Studies in history and philosophy of science Part A 16.3 (1985): 203-246.

Johnjbarton (talk) 17:37, 21 December 2023 (UTC)

Also the role of Mach to the History section, very clearly part of Einstein's thinking as well as Dicke. The Mach non-coordinate-system idea is tricky to describe however. Johnjbarton (talk) 17:41, 21 December 2023 (UTC)

Further Reading too long but...

The Further reading section is too long but it has a lot of hints for additions to the article that should be followed up and added as inline citations. Johnjbarton (talk) 04:20, 21 December 2023 (UTC)

I cut the Further reading down by moving refs in to the text or deleting those that were specialized.

Resolved

Johnjbarton (talk) 19:42, 21 December 2023 (UTC)

Why two tables of experimental results?

The WEP test section has two tables that seem to mostly overlap. I wonder why? Johnjbarton (talk) 00:31, 22 December 2023 (UTC)

Looks like no one wanted to merge the tables. I will pull a few items from the first table as text examples then delete it in favor of the second one. Johnjbarton (talk) 02:23, 22 December 2023 (UTC)

I merged the tables. The main thing lost was the comments about acceleration towards Sun, but these were not explain in any way so they were mysterious. Johnjbarton (talk) 17:44, 22 December 2023 (UTC)

Are the Chae experimental results notable?

The section "Tests of the strong equivalence principle" ends with a paragraph on a report that supports MOND. The work was publish in 2020 and challenges are online Milky Way and M31 rotation curves: ΛCDM vs. MOND. A puzzling published letter: ["A cautionary tale in fitting galaxy rotation curves with Bayesian techniques Does Newton’s constant vary from galaxy to galaxy?" https://doi.org/10.1051/0004-6361/202040101]] ends its abstract with:

• "When these effects are taken into account, the SPARC data are consistent with a constant GN (and constant g†)."

(Chae is one of the authors).

Should this paragraph be deleted? @XOR'easter opinion? Johnjbarton (talk) 19:44, 23 December 2023 (UTC)

I think we can cut that paragraph. I'm not convinced the debate over this study is noteworthy enough to include here, and certainly the text we currently have on it repeats the authors' POV as fact, which we shouldn't do. XOR'easter (talk) 20:30, 23 December 2023 (UTC)

I deleted the paragraph. In case this comes up again, I came upon two more challenges to the Chae work:

• Paranjape, Aseem; Sheth, Ravi K (2022-10-04). "The phenomenology of the external field effect in cold dark matter models". Monthly Notices of the Royal Astronomical Society. 517 (1): 130–139. doi:10.1093/mnras/stac2689. ISSN 0035-8711.{{cite journal}}: CS1 maint: unflagged free DOI (link)
• Freundlich, Jonathan; Famaey, Benoit; Oria, Pierre-Antoine; Bílek, Michal; Müller, Oliver; Ibata, Rodrigo (2022-02-01). "Probing the radial acceleration relation and the strong equivalence principle with the Coma cluster ultra-diffuse galaxies". Astronomy & Astrophysics. 658: A26. doi:10.1051/0004-6361/202142060. ISSN 0004-6361.

Johnjbarton (talk) 16:56, 27 December 2023 (UTC)

Wikipedia: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#Physical_characteristics 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'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,

{{{

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.

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.

}}}

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 <<Wikipedia is committed to presenting information backed by sources, not by logic or expertise>>".

The too-long-for, <<The paragraph is too long for the scale of the history section and it distracts from the "main event" in the article>> 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 <<History>> 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'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'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'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)