upriver, in this post in the ATM section of BAUT, raises two interesting questions:I suspect that at least the first is one that many folk have wondered, so I've started this thread to see what sort of answers there are!

Einstein wrote that gravitation, inertia, and centrifugal effects all arise from the motion of matter relative to the local vacuum in which it is embedded. He called this the GR ether.

Quotes from Einstein's "On the Ether" 1924

"The fact that centrifugal effects arise in a (rotating) body, the material points of which do not change their distances from one another, shows that this ether is not to be supposed a phantasy of the Newtonian theory, but that there corresponds to the concept a certain reality in nature."

and on Mach:

"He sought to escape the hypothesis of the 'ether of mechanics' by explaining inertia in terms of the immediate interaction between the piece of matter under investigation and all other matter in the universe. This idea is logically possible, but, as a theory involving action-at-a-distance, it does not today merit serious consideration."

and on the relevance of the GR ether in the face of advances in quantum theory:

"But even if these possibilies should mature into genuine theories, we will not be able to do without the ether in theoretical physics, i.e. a continuum which is equipped with physical properties; for the general theory of relativity, whose basic points of view physicists will surely always maintain, excludes direct distant action. But every contiguous action theory presumes continuous fields, and therefore also the existence of an 'ether'."

There you have it, from the good doctor himself. The paper is Chapter One of Saunder and Brown's book "The Philosophy of Vacuum". I will not elaborate on my interpretation of this ether concept, although I have summarized it on ATM.

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

When a Foucault pendulum is released and assumes it's plane of motion fixed relative to the distant stars, it is not possible for it to interrogate them at it's moment of release. So, since it can not "know" them to find it's way, they must determine it's local path.

Do I misunderstand your last sentence? Are you saying that the distant stars determine the local path of the pendulum?

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

Actually, I recall an old Machian reference to this, so I will not claim it as my idea. In it, he said pretty much the same thing. I have no idea what source I was reading at the time. I do recall it was a quote in a text by another author, whether in a journal, textbook, or magazine..I remember not. Perhaps someone else does. But like you, I have realized for a long time the vacuum is not empty, with the principal entities being the , the local deformation of Minkowski space-time, the neutrino sea and the zero-point radiation..not necessarily in order of importance. Pete.

It seems to me this thread is not about inertia, it is about, "how, or why, can you tell when you are in an accelerating reference frame?" Inertia has to do with how much you accelerate when a force is applied, so it requires not only be able to tell you are accelerating, but also how much you accelerate when a force that has somehow been callibrated is applied. But I agree the more interesting part of this is simply how you can tell you are accelerating in the first place, and that is what the posts have been about. Apparently, you are accelerating relative to the local vacuum, and you can tell because of the appearance of mysterious gravity effects that have no explainable source other than your acceleration. So here's my question for those more knowledgeable in GR: if you enter a rotating reference frame, and observe centrifugal forces that act very similarly to gravity, can those centifugal forces be treated as a gravity-like curvature of the rotating spacetime, or would that not work because they don't behave like real gravity, i.e., they are repulsive and unbounded?

From the context of the original post from which Nereid clipped the questions, (here: Einstein over-exalted?) I assume the OP wanted to know how inertia can be explained in GR. In other words, what mechanical concept lies behind GR inertia. This is a simple question, but it cuts to the heart of the problems Einstein had with his own theories. With thought-experiments and fitting, he made his theories of relativity describe the physical world pretty well. Unfortunately, while he continued to try to discover just what his theories were modeling so he could unite gravitation with other fundamental forces, a generation of physicists learned to deal with his math and elevated the mathematical approximation to the status of reality. This gives rise to some pretty odd concepts, like massless corpuscular photons hurtling along geodesics in curved space-time.

Einstein himself did not believe in this concept, and he insisted that in space there must exist a medium through which light waves can propagate, saying that light could not cross "empty" space. Read his Leyden address of 1920 and read "Uber den Ather" ("On the Ether") of 1924 to see where he was headed with this. I guarantee that it will change the way you look at relativity.

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

That's an interesting insight, although at present I don't know what Einstein meant about a local ether. It surprises me that he didn't want light to propagate through nothing, in the sense that it seems to me a crucial element of relativity is that if two objects in empty space communicate via light, then the only relevant effect is the relative speed between the objects, not the speed of either relative to the space they are in. The former is unique, the latter is observer-dependent. In this light, the "nothingness" of space is seen as an advantage, since it explains why there is only one velocity of relevance, rather than two.

Lifted from John Baez's site:

"according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position." Einstein 1920

In other words, you cannot have gravitational lensing in "empty space" unless the space has optical properties (i.e. an index of refraction) at each position in space, so that light can travel slower in more dense locales and faster in sparser ones. By 1924, Einstein was sure that the EM ether and his GR gravitational ether were one and the same, but quantum theory was in its infancy and the quantum vacuum (a seething Zero Point Energy field filled with virtual particle-antiparticle pairs) would have been considered a pretty crazy idea. His idea for a GR ether was decades ahead of the rest of physics.

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

I think another way to say it is that you would need to alter the speed of light if you wanted to get a curved path in a flat spacetime. If instead you curve the spacetime, then you can have a constant speed of light. So if this is correct, then curvature is seen as a way to achieve SR results locally within the context of GR. Alternatively, you may allow the speed of light to vary, and not curve the spacetime, but that's not the usual formulation. I may be wrong here, I'm trying to understand the possible pedagogies. Also, in terms of the vacuum, I would certainly expect that two observers in relative motion to each other would nevertheless observe the same vacuum, so how zero-point oscillations relate to a local ether is not obvious.

Hi, Ken G:

Buy, beg, or borrow Sander and Brown' book "The Philosopy of Vacuum" and read chapter one - Einstein's 1924 paper "On the Ether". See if you can keep the book for a while, so you can refer to that chapter after reviewing my model of quantum gravitation on ATM. By the 1920's Einstein was trying to get beyond the mathematical model of "space-time-curvature" and determine just what was being distorted by the presence of matter. He needed a dynamical ether that could be conditioned by the matter and energy embedded in it, and it also had to be responsible for the transmission of EM waves through space.

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

Maybe it isn't just that the ether is distorted by matter, but also that matter itself is a distortion of the ether, created by the ether, and made of ether.

Einstein, 1930
"...that now it appears that space will have to be regarded as a primary thing and that matter is derived from it, so to speak, as a secondary result. Space is now having its revenge, so to speak, and is eating up matter."

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

Far Out! But what is that about space eating up matter?

It's not a literal statement - it is a statement that expresses the ground-shift in Einstein's perceived importance between material objects and the location in which they exist.

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

Yes, where does inertia come from in GR? What is the mechanical cause?

My particular take on Einstein's etheric model of GR would not be welcome here. Since this is not the ATM subforum, we will have to let a GR conventionalist explain how inertia arises.

Inertia was one of Feynman's favorite examples when he was explaining the difference between what we "know" and what we "understand", so I'm looking forward to the concordance answer.

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The ether of general relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in its locally variable properties by ponderable matter.

Albert Einstein, "On the Ether", 1924

Nothing that I've ever seen of GR would contain an answer to where inertia comes from, unless I missed it. GR is a relativistic description of gravity, inertia is something different. You have to simply tack on inertia when doing calculations in GR, just as you had to with Newton's equations. All GR does is give you a way to understand why inertia and gravitational mass are the same, via the equivalence principle. No physical theory can explain itself, theories are assumptions that are used to explain other things.

Upriver it seems you are asking what is the cause of inertial mass, since inertial mass itself is defined and measured by its inertia, or resistance to a change in motion: it takes a force to accelerate it, and the measured amount of force ‘defines‘ both the ‘mass‘ and its ‘inertia‘ (without really defining either). It seems to me there has to be an opposition of forces, rather than a force accelerating a kilogram of ‘stuff‘. You would think that the ‘inertial’ force opposing the accelerating force would be gravitational force, which causes an acceleration toward a common gravitational center. So then you have look at gravitational mass, which again is defined only by a measured ’effect’ between bodies. Inertial mass and gravitational mass are considered to be indistinguishable I think. Once again you are faced with the problem of ‘stuff‘. If mass ‘contains’ a measurable amount of energy, you find that the ‘stuff’ that resists acceleration is actually a container, or form, of energy. So one form of energy - the ‘stuff’ at rest or in ‘constant‘ motion - resists the action of another form of energy - either a collisional force created by other ‘stuff’ already accelerated, or a non-collisional force emanating from other ‘stuff’, e.g. magnetism.

Then what is energy? If it is indeed the ‘property’, or the quantity of the ‘property’, of changing the state of a system, then ‘mass’ itself is some ‘thing’ that is changing. Eventually this ‘property‘ has to be expressed as a force, causing a change in motion (speed or direction), and any ‘mass‘ is itself the effect of a force - not a gravitational force, which governs the behavior of ’masses‘ toward each other, but a more fundamental force governing the behavior of an isolated body of ‘matter‘.

If ‘space’, the ‘ether’, and the ‘vacuum’ are thought of as identifying the same system (perhaps a field), and it is a dynamic system, I believe it is also a fundamental system out of which ‘mass’ is created - a field of force. I believe the idea of rest mass, and then of inertial mass in general (and following that, gravitational mass), is a kind of misnomer, in that no body of ‘matter’ is ever at rest - it, or its components, rotate. So (in this scenario) mass is angular momentum, and what is resisting a change in its motion is already rotating itself. Angular momentum represents a continual acceleration which must be produced by a force. So what is accelerated? What if the ‘stuff’ (as in the 50-kilogram bar in Paris, which is losing weight) isn’t ‘stuff’ at all, but rotational motion? Then inertia is the resistance of an energetic system (undergoing continual angular acceleration by the field) to other forces. So the ‘mechanical cause’ of inertia in this scenario is rotation. (This is opposite to what seems to be the mainstream view, that rotation of large bodies is an effect of gravitational motion.) And the field and its creation, ‘mass’, are different ‘forms’ of energy, which is not a measurable ‘property’ but a fundamental ability - the ability to move.

That quote comes from Einstein's 1916 book, Crown paperback edition, page 76, and the concept originated with his 1911 "gravitational redshift" theory. In the 1911 theory, light slows down in a gravity field, and it slows down more in a stronger gravity field, and this is what makes a beam of light curve as it passes a massive astronomical body.

This idea of light slowing down in a gravity field is discussed in several Einstein papers in the 1911-1914 era. See Volume 4 of "The Collected Papers of Albert Einstein."

Also, Max Abraham noted in 1912 that in the gradually developing and changing Einstein "relativity" theory, Einstein had gravity acting like an "ether" for light. In the developing Einstein theories from around 1907 through about 1920, a gravitational field is not required for light to propagate, but a gravitational field does have an effect on light by causing it to slow down in str