[McQueen (OP)]

           Einstein’s s equivalence principle, states that uniform acceleration is indistinguishable from a homogeneous gravitational field (the principle of equivalence). He illustrates this statement by demonstrating that the effect of gravity in free-fall is totally abolished in all possible experiments and general relativity reduces to special relativity, as in the inertial state. To make this issue more comprehensible: The Equivalence principle states that “inertial force and gravitational force are the same thing.” Or, that “acceleration and gravity are the same thing.”

   If we are to examine this issue on an absolutely level playing field, the first thing is to get rid of the sentient observer. We don’t give a flying f_ _ _ _   whether it is a man, a monkey  an elephant or a slab of stone in the accelerated room in space, it doesn’t  matter what it thinks or what it makes of it all; all that matters is its composition. Right!  Or, for the finicky in this forum, the mass of the object.

   Newton had an equation for the situation described by Einstein in which an object in an enclosed room somewhere in space experiences an acceleration of 1g.  It is not necessary to wonder what the object thinks about this experience, or whether the object discerns that it is in an earth like environment, all that matters is that the force it experiences depends on its mass and acceleration. What does this mean? It all comes down to how Newton thought of mass and of how the force of gravity acted on it.  Neither Newton nor Einstein were ever able to explain exactly what gravity was although, especially in Newton’s case, they were both able to explain how it worked. In Einstein’s case it might almost be said that he took Newton’s  gravitational force and replaced it with a gravitational potential that was represented by mass. (Same difference!) Here in Newton’s own words are the thoughts he had on where the cause of gravity might lie:

"I have not yet assigned a cause to gravity. Indeed, this force arises from some cause that penetrates as far as the centers of the sun and planets without any diminution of its power to act, and that acts not in proportion to the quantity of the surfaces of the particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter, and whose action is extended everywhere to immense distances, always decreasing as the squares of the distances." Principa Mathematica, Isaac Newton

   From the above it is clear that Newton’s definition of mass had to do with its density, or more accurately the density of the matter of which it was made.  Newton's law of universal gravitation states that every mass attracts every other mass in the universe, and the gravitational force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. But to Newton force and gravity were different.

        The crucial fact here is the equation F = ma. According to Einstein it is impossible to distinguish gravity from acceleration. Is that really true? Consider two objects in space. One of the objects weighs 20 kg and the other object weighs 10 gm. If a force of 10 N is applied to each of these objects what happens? The object weighing 10 gm acquires an acceleration of 100 m/s²  and travels 100 m in 1 second, while the object weighing 20 Kg  acquires an acceleration of 0.5m/s²  and travels a distance of 0.5m in one second. How can one equate acceleration due to a force with gravity?

   

[Bored chemist]

I think you missed a bit

The Equivalence principle states that “inertial force and gravitational force are the same thing.” Or, that “acceleration and gravity are the same thing.”

No, they "feel" the same, and are indistinguishable- unless you look out of the window,

[Origin]

Equivalence principle states that “inertial force and gravitational force are the same thing.”

No it doesn't.  It says you can't distinguish a difference.

From the above it is clear that Newton’s definition of mass had to do with its density, or more accurately the density of the matter of which it was made. 

No, it is quite clear Newton meant mass when he said mass.

How can one equate acceleration due to a force with gravity?

You are the only one who is doing that.

[alancalverd]

One of the objects weighs 20 kg and the other object weighs 10 gm. If a force of 10 N is applied to each of these objects what happens? The object weighing 10 gm acquires an acceleration of 100 m/s2  and travels 100 m in 1 second, while the object weighing 20 Kg  acquires an acceleration of 0.5m/s2  and travels a distance of 0.5m in one second. How can one equate acceleration due to a force with gravity?

That rather misses the point. A gravitational field that applied 10N to the 10 g object would, as Galileo, Newton and Einstein agree, apply 20 kN to the 20kg object, and the resultant accelerations would be identical. And the distance travelled would be 50 m in the first second. s = ut +½at² - or at least it did in 1957.

However it seems to me that the equivalence principle only really applies to infinitesimal or infinitely rigid bodies.

To a first order approximation, a gravitational field acts equally on all particles in the body. Hence "weightlessness" in orbit or free fall - the capsule and everything in it are falling at the same rate.. But any other acceleration requires a force to be applied to one end of the body, resulting in a compression in the direction of that force - what we measure with a g meter.

[evan_au]

If a force of 10 N is applied to each of these objects what happens?

To narrow the focus - you should not be applying the same force to two masses, you should be applying the same acceleration to two objects.
- Which is what would happen if they were in the same uniform gravitational field (eg the proverbial "top of the leaning tower of Pisa").

[McQueen (OP)]

That rather misses the point. A gravitational field that applied 10N to the 10 g object would, as Galileo, Newton and Einstein agree, apply 20 kN to the 20kg object, and the resultant accelerations would be identical. And the distance travelled would be 50 m in the first second. s = ut +½at2 - or at least it did in 1957.

To narrow the focus - you should not be applying the same force to two masses, you should be applying the same acceleration to two objects.

I am confused, why is gravity involved at all ? It was Einstein who stated that gravity was indistinguishable from acceleration, nothing there about a Universal gravitational field.  Whereas, I am referring to a force, giving rise to acceleration. What am I missing?  Are you saying that gravity is the only force that exists in the Universe?  I was under the impression that under Einstein’s equivalence principle, acceleration was indistinguishable from gravity.  Two objects in space, one weighing 10 gm and the other weighing 20 Kg experience different rates of acceleration when the same force is applied. If the stipulation is made that the force applied is due to a gravitational field,  how does it relate to equivalence?  Or if the stipulation is made that different forces are applied to the two objects so that they experience the same acceleration, it means that the force applied to each of the objects is different, which is self defeating. It is only when acceleration under a universal gravitational field is used that Newton’s formulas yield the same answers regardless of the mass of the objects. For instant, using  F = ma, then in the case of the mass of the 10 gm,  F = 0.01 x  10m/s²  = 0.1 N    and in the case of the 20 Kg mass F = 20 x 10m/s²  = 200 N. It takes more force to move the larger mass.  But using  u²  + v²   = 2as  or v² / 2a = S;   100/20 = 5m   and 100/ 20 = 5 m. So regardless of the fact that one mass is  2000  greater than  the other, if the same acceleration is applied to both, both will travel the same distance.

[Kryptid]

According to Einstein it is impossible to distinguish gravity from acceleration. Is that really true?

No, and I strongly doubt that Einstein ever actually said that.

[Bored chemist]

It was Einstein who stated that gravity was indistinguishable from acceleration,

What he said was that there's no way to distinguish them IF ALL THE INFORMATION YOU HAVE IS THE FORCE THAT ACTS ON YOU.

You keep ignoring the important bit.

[alancalverd]

I am confused, why is gravity involved at all ? It was Einstein who stated that gravity was indistinguishable from acceleration, nothing there about a Universal gravitational field. 

Which is why nobody else has mentioned one. All I have insisted upon is that your test objects be subjected to the same gravitational field, whereupon, as Galileo demonstrated, they behave identically, and as Cavendish demonstrated, F = GmM/r² holds for all m and M.

[McQueen (OP)]

I can see that my approach so far has been wrong. Instead of my making statements, perhaps it would be better, if I quote from a source.  Here is the definition of the equivalence principle taken from the Wikipedia article on equivalence:

In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.  Wikipedia

What does pseudo force imply, if two objects are accelerated by two different acceleration (pseudo-forces) they will experience different effects and know that the force pushing them  is not gravity.  For instance if they can communicate by radio and have instruments to measure the rate at things fall and so on.

[Eternal Student]

Hi.

Original question:  Einstein’s Equivalence Principle, is principle the right term?
Brief Answer:   Seems OK.  You could change "principle" for  "idea"  if that helps.

I am confused, why is gravity involved at all ? It was Einstein who stated that gravity was indistinguishable from acceleration, nothing there about a Universal gravitational field.  Whereas, I am referring to a force, giving rise to acceleration. What am I missing?  Are you saying that gravity is the only force that exists in the Universe?  I was under the impression that under Einstein’s equivalence principle, acceleration was indistinguishable from gravity.  Two objects in space, one weighing 10 gm and the other weighing 20 Kg experience different rates of acceleration when the same force is applied. If the stipulation is made that the force applied is due to a gravitational field,  how does it relate to equivalence?  Or if the stipulation is made that different forces are applied to the two objects so that they experience the same acceleration, it means that the force applied to each of the objects is different, which is self defeating. It is only when acceleration under a universal gravitational field is used that Newton’s formulas yield the same answers regardless of the mass of the objects. For instant, using  F = ma, then in the case of the mass of the 10 gm,  F = 0.01 x  10m/s2  = 0.1 N    and in the case of the 20 Kg mass F = 20 x 10m/s2  = 200 N. It takes more force to move the larger mass.  But using  u2  + v2   = 2as  or v2 / 2a = S;   100/20 = 5m   and 100/ 20 = 5 m. So regardless of the fact that one mass is  2000  greater than  the other, if the same acceleration is applied to both, both will travel the same distance.

     Other people have tried to answer some of this already but I'll try another way.
Early in the development of Einstein's theory, it was decided to stop thinking about gravity as a force.   Gravity is NOT a force.   Can I suggest you take the idea on-board now.   STOP thinking about gravity as a force.   Don't use the word "Force" for the next day.  Re-read what Einstein originally wrote and notice that he uses the word acceleration rather than Force. 
     Remember that acceleration is NOT the same as force.  Einstein did not care about Force, he didn't care where it may come from and he didn't even think gravity was a force.  Whatever it is or isn't that is tomorrow's problem.

   When tomorrow comes, we might recall that we often try and connect the two with Newton's third law   F = m . a  which shows that  Force is NOT the same as acceleration.   Two objects can have the same acceleration but totally different forces acting on them because the masses of the two objects could be different.  This means that if Einstein was correct and acceleration is what we need to focus on, then giving two objects the same acceleration will mean that we need to find two completely different forces from somewhere. 

     Alancalverd started talking about "a gravitational field" as if that might be the source of all these different forces we need but  she/he  has raced ahead a bit too far and accidentally jumped tracks trying to mix in some older Newtonian ideas that we absolutely must NOT take with us while developing Einstein's theory of gravity.  (Shame on you, Alancalverd).  Nobody needs to be worrying about what a field is at the moment and you (McQueen) are absolutely correct that such words do not feature in a basic description of the Equivalence Principle.

    Eventually Newtonian prejudice may get the better of us and you might hear people talking about something called a gravitational field.   You (McQueen) have correctly identified that this must be a mysterious thing that is somehow capable of supplying different amounts of force to different objects so that their accelerations will all be the same.   I can wholeheartedly recommend that you shove the idea away in a cupboard for the moment along with any old cauldrons and alchemy experiments and forget about it.  Einstein persisted for a long time with the idea that gravity is NOT a force and therefore he had no need to imagine such a thing as a "gravitational field".   Much, much later in the development of his theory of gravity, he would demonstrate that General relativity does correspond well with the earlier version of gravity as described by Newton and at that sort of time we may need to use terms such as a "gravitational field" because that is the language and terminology associated with the older existing theory.  The language and terminology that Einstein would develop uses a different field called "the metric field" but it will take him years to get it all figured out and so we people here in this forum shouldn't be too worried if it takes us a few years to understand it.

Best wishes to everyone.

[Origin]

What does pseudo force imply, if two objects are accelerated by two different acceleration (pseudo-forces) they will experience different effects and know that the force pushing them  is not gravity.  For instance if they can communicate by radio and have instruments to measure the rate at things fall and so on.

I am really baffled as to why this is confusing you.  If you are in a room with no windows the equivalency principle states you will not be able to distinguish between the room being on the earths surface and the room accelerating at 9.81 m/s^2 far from a gravity source.  What about that is hard to understand? 
The reason evan_au mentioned a uniform gravitational field, I believe, is because if the gravitational field was not uniform you could tell the difference between the 2 cases because a clock would run slower near the floor than near the ceiling.

[Eternal Student]

I can see that my approach so far has been wrong. Instead of my making statements, perhaps it would be better, if I quote from a source.  Here is the definition of the equivalence principle taken from the Wikipedia article on equivalence:

Hi again.
   I hope I didn't actually put you (McQueen) off too much with my earlier post.  You can carry on writing and doing whatever you want

   The Wikipedia quote you have provided is an attempt to describe something about the Equivalence Principle in terms of Newtonian Mechanics.  It's of very limited value and quality.  You can see where someone has put quotation marks around the word "force" in some vague attempt to avoid the reader thinking that it is a force.  Wikipedia is of varying quality and that piece of text is hardly worth discussing.

[Bored chemist]

For instance if they can communicate by radio and have instruments to measure the rate at things fall and so on.

Why do you resolutely ignore the important criterion?

IF ALL THE INFORMATION YOU HAVE IS THE FORCE THAT ACTS ON YOU.

No, they "feel" the same, and are indistinguishable- unless you look out of the window,

Do you not understand that it is important?