[fisherman]

The wiki makes the equivalence principle the foundation of the FE argument for universal acceleration, but it misrepresents what the equivalence principle says and what it means in the context of general relativity.

The equivalence principle demands that that mi = mg. Why should this be true in our universe? It has been about 85 years since the discovery of the Einstein equivalence principle, and hundreds of years since the discovery of Newton’s mass equivalence principle. Yet, it is still not understood why inertial mass exists in the first place, or why a mass opposes acceleration with a back acting inertial force. More importantly, it is also not known why there are two totally different physical definitions for inertial and gravitational mass (instead of just one).

The first problem with this statement is that according to the equivalence principle, inertial mass and gravitational mass don’t have two different physical definitions.  In fact, it explicitly says they are the same thing.

The second is that the equivalence principle offers an explanation as to why inertial mass exists in the first place. 

We then have the following law: The gravitational mass of a body is equal to its inertial mass. It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as “inertia” or as “weight” (lit. “heaviness”). In the following section we shall show to what extent this is actually the case, and how this question is connected with the general postulate of relativity.

Pg 77-78  The Meaning of Relativity by Albert Einstein

The unification of inertia and gravity is expressed in the geodesic equation:

Formally, the unity between inertia and gravity is expressed by the fact that the entire left side of d2 xν ds2 þ αβ ν ( )dxα ds dxβ ds ¼ 0 is tensorial (with respect to arbitrary coordinate transformations), whereas the two terms separately are not. In analogy to the Newtonian equations one would have to view the first as an expression for inertia, the second as an expression for the gravitational force.

https://einsteinpapers.press.princeton.edu/vol7-trans/358?highlightText=Formally

In other words, according to the geodesic equation inertia and gravity are the same thing because the two elements transform as tensors only when considered as a single entity.

In short, the wiki relies on the equivalence principle, which states that inertial mass and gravitational mass are the same thing, and explains why that's true, to make the argument that inertial mass and gravitational mass are not the same thing and there is no explanation for their equivalence.

That’s pretty much the mother of logical fallacies.

[Tom Bishop]

The first problem with this statement

That's a statement by a physicist. The problem is that you are not more qualified than the sources given on those pages. Why should we change anything based on what some person on an internet forum thinks?

In short, the wiki relies on the equivalence principle, which states that inertial mass and gravitational mass are the same thing, and explains why that's true, to make the argument that inertial mass and gravitational mass are not the same thing and there is no explanation for their equivalence.

Einstein came to his theory because of the unexplained empirical coincidence.

     "Whilst preparing a review article on his new special theory of relativity, [Einstein] became convinced that the key to the extension of the principle of relativity to accelerated motion lay in the remarkable and unexplained empirical coincidence of the equality of inertial and gravitational masses. To interpret and exploit this coincidence, he introduced a new and powerful physical principle, soon to be called the ‘principle of equivalence,’ upon which his search for a general theory of relativity would be based. ” —John Norton, What was Einstein's Principle of Equivalence?

On p.112 of Introductory Physics: Building Models to Describe Our World by astrophysicist Ryan Martin (bio), Et al., it says:

     “ As you recall, the weight of an object is given by the mass of the object multiplied by the strength of the gravitational field, g. There is no reason that the mass that is used to calculate weight, Fg = mg, has to be the same quantity as the mass that is used to calculate inertia F = ma. Thus, people will sometimes make the distinction between “gravitational mass” (the mass that you use to calculate weight and the force of gravity) and “inertial mass” as described above. Very precise experiments have been carried out to determine if the gravitational and inertial masses are equal. So far, experiments have been unable to detect any difference between the two quantities. As we will see, both Newton’s Universal Theory of Gravity and Einstein Theory of General Relativity assume that the two are indeed equal. In fact, it is a key requirement for Einstein’s Theory that the two be equal (the assumption that they are equal is called the “Equivalence Principle”). You should however keep in mind that there is no physical reason that the two are the same, and that as far as we know, it is a coincidence! ”

So we have astrophysicists calling it a coincidence, even after Einstein's theory, and that there is no physical reason that the two are the same.

Another quote:

     “ Einstein himself thought the equivalence principle deeply mysterious. ‘Mass,’ he wrote, ‘is defined by the resistance that a body opposes to its acceleration (inert mass). It is also measured by the weight of the body (heavy mass). That these two radically different definitions lead to the same value for the mass of a body is, in itself, an astonishing fact.’ Francis Everitt of Stanford put it more forcibly. ‘In truth, the equivalence principle is the weirdest apparent fact in all of physics,’ he said. ‘Have you noticed that when a physicist calls something a principle, he means something he believes with total conviction but doesn’t in the slightest degree understand.’ ” —Nigel Calde, Magic Universe - A Grand Tour of Modern Science, 2005

A deeply mysterious thing that physicists don't understand.

[fisherman]

That's a statement by a physicist. The problem is that you are not more qualified than the sources given on those pages. Why should we change anything based on what some person on an internet forum thinks?

It isn't about what I think.  It's about what Einstein, the guy who developed the principle, defined it as.  Why should we care about how anybody else defines it?  It's Einstein's principle he's the one who gets to define it.

Yes, he did at first think of it as "mysterious" and that's what led him to try and figure out why IM and GM are equivalent.  And he did figure it out...its because they are the same thing.

If you think that Einstein's reasoning is wrong, you are free to explain why.  Quoting people who don't think that Einstein reconciled IM and GM, or who are more likely unaware that he did, doesn't explain what's wrong with his reasoning.

[Tom Bishop]

What you quoted is the same thing those authors are talking about. You quoted:

We then have the following law: The gravitational mass of a body is equal to its inertial mass. It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as “inertia” or as “weight” (lit. “heaviness”). In the following section we shall show to what extent this is actually the case, and how this question is connected with the general postulate of relativity.

Pg 77-78  The Meaning of Relativity by Albert Einstein

I don't see how declaring the equivalency as a fact provides a physical process for why it should be so. And apparently those authors I quoted don't either.

Your next quote is about an equation:

The unification of inertia and gravity is expressed in the geodesic equation

An equation does not directly provide insight to a physical process behind physics.

[fisherman]

I don't see how declaring the equivalency as a fact provides a physical process for why it should be so. And apparently those authors I quoted don't either

That is more than just “declaring equivalency.”  It is an explanation as to why.  IM and GM are the same quality…as opposed to just the same quantity.  And Einstein made the point more than once.

Inertia and gravity are phenomena identical in nature.  From this and from the special theory of relativity it follows necessarily that the symmetric "fundamental tensor" determines the metric properties of space, the inertial behavior of bodies in space, as well as the gravitational effects.  We shall call the state of space which is described by this fundamental tensor, the "g-field"

https://einsteinpapers.press.princeton.edu/vol7-trans/49?highlightText=metric

If you want to play dueling experts, no problem.

The equality of inertial and gravitational mass, without which Galileo’s principle that all bodies fall alike would not hold, is an unexplained coincidence in Newtonian physics. To Einstein it suggested that there is an intimate connection between inertia and gravity. The universality of gravity’s marching orders makes it possible to move gravity from the column of assorted forces to the column of the space-time structure. General relativity combines the space-time structure (more accurately: The inertial structure of space-time) and the gravitational field into one inertio- gravitational field. This field specifies the trajectories of particles on which no additional forces are acting. Einstein thus removed the mystery of the equality of inertial and gravitational mass in Newton’s theory by making inertia and gravity two sides of the same coin.

http://philsci-archive.pitt.edu/4377/

Feel free to look up the author’s credentials if you have any doubts about his level of expertise on Einstein or general relativity.

An equation does not directly provide insight to a physical process behind physics

Einstein believed it does, at least in this case.  Can you explain why he is wrong?

[Tom Bishop]

I don't see how declaring the equivalency as a fact provides a physical process for why it should be so. And apparently those authors I quoted don't either

That is more than just “declaring equivalency.”  It is an explanation as to why.  IM and GM are the same quality…as opposed to just the same quantity.  And Einstein made the point more than once.

Inertia and gravity are phenomena identical in nature.  From this and from the special theory of relativity it follows necessarily that the symmetric "fundamental tensor" determines the metric properties of space, the inertial behavior of bodies in space, as well as the gravitational effects.  We shall call the state of space which is described by this fundamental tensor, the "g-field"

https://einsteinpapers.press.princeton.edu/vol7-trans/49?highlightText=metric

That's not an explanation of physical process. That's just a statement that says "Inertia and gravity are phenomena identical in nature."

If you want to play dueling experts, no problem.

The equality of inertial and gravitational mass, without which Galileo’s principle that all bodies fall alike would not hold, is an unexplained coincidence in Newtonian physics. To Einstein it suggested that there is an intimate connection between inertia and gravity. The universality of gravity’s marching orders makes it possible to move gravity from the column of assorted forces to the column of the space-time structure. General relativity combines the space-time structure (more accurately: The inertial structure of space-time) and the gravitational field into one inertio- gravitational field. This field specifies the trajectories of particles on which no additional forces are acting. Einstein thus removed the mystery of the equality of inertial and gravitational mass in Newton’s theory by making inertia and gravity two sides of the same coin.

http://philsci-archive.pitt.edu/4377/

Feel free to look up the author’s credentials if you have any doubts about his level of expertise on Einstein or general relativity.

That author describes himself as a "historian of science" rather than a physicist or an astrophysicist.

Various physicists disagree with this. Your author just says that Einstein did it by stating that they were the same, like you quote above.

An equation does not directly provide insight to a physical process behind physics

Einstein believed it does, at least in this case.  Can you explain why he is wrong?

Where does Einstein state that if you make an equation it explains why processes occur behind those equations?

[Tom Bishop]

Another quote from Anatoly Alekseyevich Logunov, a theoretical physcist:

https://pdfroom.com/books/the-theory-of-gravity/X623zYb6g4Z

"GRT does not comply with the equivalence principle,
does not explain the equality of the inert and active
gravitational masses, and gives no unique prediction
for gravitational effects. It does not contain the usual
conservation laws of energy–momentum and of angu-
lar momentum of matter."

GRT = General Relativity Theory, as defined earlier in the paper:

"Therein, also, critical comments are presented con-
cerning general relativity theory (GRT), which still remain in
force."

Here is another quote, from a publication of the AIAA on p.99:

"Newton proposed two formulas: the law of motion, F = ma, and the law of gravitation, F = GMm/r². The mass, m, has two distinct meanings in the two formulas, one as the receptacle of inertia, the other as the source and receptacle of gravitation; yet somehow the two are identical. Stated another way, if m_i and m_g are respectively inertial and gravitational mass, then for any two bodies A and B, regardless of what substance they are, the quantity



appears to be identically zero. It was just this identity that Einstein denominated a principle (weak equivalence) and extended (strong equivalence) to all the laws of phyics in accelerated frames, whether the acceleration is ineitial or gravitational in origin. Strong equivalence is the basis on which it becomes possible in general relativity to represent gravitation by a curvature of spacetime. Contrary to what is sometimes thought, however, general relativity does not explain equivalence. The principle is an assumption that, once made, allows the effects of gravity to be represented thus. The phenomenon remains a mystery and still needs testing."

[fisherman]

That's not an explanation of physical process. That's just a statement that says "Inertia and gravity are phenomena identical in nature."

The fact that they are identical in nature would explains the “mysterious coincidence”.  It’s kind of like explaining the “mysterious coincidence” that identical twins look like by pointing out they have the same DNA. 

Where does Einstein state that if you make an equation it explains why processes occur behind those equations?

I don’t know that he ever said that is the case in general, but he plainly states that in this case the formula reflects physical reality.  The equation expresses how gravitation and inertia effect a physical particle, and that physical effect is expressed in the formula by the fact that the two terms on the left can only be transformed as one entity.

Equation (90) express the influence of inertia and gravitation upon the material particle.  The unity of inertia and gravitation is formally expressed by the fact that the whole left hand side of (90) has the character of a tensor (with respect to any transformation of coordinates), but the two terms taken together separately do not have tensor character.

The fact that he considered this “unity” as an actual physical fact is also made plain by the way he analogized it to the electromagnetic field.

Therefore, the existence of the electric field was a relative one, depending on the state of motion of the coordinate system used; and only the electric and magnetic fields combined, aside from the state of motion of the observer or coordinate system, could be granted a kind of objective reality. This phenomenon of magneto-electric induction forced me to postulate the principle of (special) relativity. ….At that moment I got the happiest thought of my life in the following form:  In an example worth considering, the gravitational field has a relative existence only in a manner similar to the electric field generated by magneto-electric induction. Because for an observer in free-fall from the roof of a house there is during the fall—at least in his immediate vicinity—no gravitational field.[36] Namely, if the observer lets go of any bodies, they remain relative to him, in a state of rest or uniform motion, independent of their special chemical or physical nature.5[37] The observer, therefore, is justified in interpreting his state as being “at rest.”

https://einsteinpapers.press.princeton.edu/vol7-trans/152

As just a side observation, this quote is often used as an example of Einstein saying that accelerated motion is relative.  But if you actually read it, without any preconceived ideas of relativity, what he is saying is that the presence or absence of a gravitational field is what is relative.

That author describes himself as a "historian of science" rather than a physicist or an astrophysicist.

I guess he's being humble. 

https://docs.google.com/document/d/1lr0z_G9_BoUprc_P3kfRezm1K70_v35nrTERXQcOQ7M/preview
 He was also one of the editors of CPAE https://einsteinpapers.press.princeton.edu/
https://rd.springer.com/bookseries/4890
https://www.mpiwg-berlin.mpg.de/users/mjanssen
https://www.researchgate.net/scientific-contributions/Michel-Janssen-13021516
https://www.bookdepository.com/Genesis-General-Relativity-Michel-Janssen/9781402039997

He’s a frequent collaborator with John Norton, who as I point out below, is apparently respected enough to be quoted on your own wiki.

Your author just says that Einstein did it by stating that they were the same, like you quote above.

He does much more than just say "Einstein said this". He explains how Einstein solved the coincidence by combining gravity and inertia into one field. John Norton, in the exact same paper you quote in the wiki, makes the same point, using the same Einstein definition of the equivalence principle.

In short, we have seen in this section that the principle of equivalence enabled Einstein to see that one structure was responsible for inducing both inertial and gravitational fields and that the Minkowski metric was a special case of it. Einstein summarized this insight in a compact 1918 statement of the principle: Einstein's principle of Equivalence31 Principle of Equivalence: inertia and gravity arewesensgleich[identical in essence]. From this and from the results of the special theory of relativity it necessarily follows that the symmetrical \fundamental tensor" (g  ) determines the metrical properties of space, the inertial behavior of bodies in it, as well as gravitational action. (Einstein 1918a, p. 241)27

You should read the whole paper.  There are a lot of good insights in it.

The principle is an assumption that, once made, allows the effects of gravity to be represented thus. The phenomenon remains a mystery and still needs testing

.

Well, that's interesting.  Are you suggesting that the EP is not settled science?  That it still needs testing?