Mainz, Germany

Dear El Naschie, 

Perhaps your internet connection to the reading has some problem? I just checked and the Norton paper is 68 pp. That's long, I admit, but it is a good paper and widely referenced. Norton is a Professor at the University of Pittsburgh.

Whether GR is a "fundamental theory" is not the issue here. Instead the question concerns GR as it is, and whatever its ultimate status, as concerns the relationship of the equivalence principle and general covariance. What are the significance and relationship of these principles and how do they figure into a proper understanding of GR?   

Best wishes for your quick recovery and thank you for your expression of interest in the present question.

H.G. Callaway

"The equivalence principle tells us that the "force" of gravity is the same as the pseudo-force effecting unsupported bodies in an accelerated frame of reference"

Not exactly, there are a lot non equivalent definitions of the equivalence principle...it is a total disaster..

The only true EP is the one experimentally verified by the Etvos experiments till Dicke in 1964. THis is the WEP or weak equivalence principle, which is the one adopted also by Newton to define the orbits of planets, also called the NEP. The gravitational mass of a body is equivalent to its inertial mass.

The extension Einstein gave to EP, which I use to call the E-WEP, is based  on the indistingushabiltiy of  an accelerated system and a gravitational field at finite distance.  It is falsified by clocks in a gravitational field as written in my paper and such falsification is not certainly due to tidal phenomena.

The EEP and SEP are controversial and still some experiments have to be performed in order to test them properly...

Article A Falsification of the extension of the Equivalence Principle

Mainz, Germany

Dear El Nashie, 

Actually, I'm an American, and I am presently visiting in Mainz; I have live in Europe, off and on, over a period of 30 years, though. So, I sort of know how things go here. 

Let's see if other participants pick up on your offer of your papers. As I say, I don't think that the "fundamental" character of GR is quite to the focal point here, it is more a matter of the understanding the relationship of the equivalence principle and general covariance. Can you say something directly on that theme? 

H.G. Callaway

The equivalence principle establishes the (local) physical equivalence between a gravitational field, and an accelerated frame. Mathematically, this expresses through the fact that we can always choose (locally) a coordinate system, where the metric is Minkowskian (its first derivatives vanish), in such a frame no (local) gravitational effects are observed (the freely falling frame). Of course, non-local gravitational effects (tidal forces) cannot be eliminated by any choice of the coordinate system. The covariance principle just states that the relevant equations of the theory are written down in a tensorial form. As such, they are valid in any coordinate system. The Einstein equations are manifestly covariant, but we know that any theory (e.g. the newtonian mechanics) may be written covariantly.

Dear H.G. Callaway,

the equivalence principle is somehow vague and heuristic. But nevertheless, this Gedanken experiment may be interesting to think about: Consider a fictitious world where the electric charge and mass of the particles are equal in some gauge, and where no negative charges exist. In such a world, the weak equivalence principle holds, since all masses fall the same way. However, if you have a homogeneous magnetic field, the particles spiral, and since the radii and axes are arbitrary, you cannot transform this situation to an accelerated frame, the strong equivalence principle does not hold.

Sincerely, Andreas Aste.

Mainz, Germany

Dear Quattrini & contributors,  

Looking around a bit, I found the following webpage, and I think it may prove useful to readers, concerned with the distinction between the weak equivalence principle and the stronger one in Einstein. 

https://www.cfa.harvard.edu/pag/index_files/Page1098.htm

I'm interested to hear more about your criticism of the Einstein equivalence principle. You wrote:

The extension Einstein gave to EP, which I use to call the E-WEP, is based on the indistingushabiltiy of an accelerated system and a gravitational field at finite distance. It is falsified by clocks in a gravitational field as written in my paper.

--end quotation

I wonder if you can give some brief account of the issues involved as, for example, some description of the experimental design of the proposed tests and experiments. How is the principle falsified in the experiments you describe? What consequences do you see in this for RG?

Also, I am wondering if you differ with the other recent contributors regarding the definition or character of the equivalence principle in GR. I did take notice of your paper, but I am yet to study it at all closely. I think of the equivalence principle as chiefly resting on Einstein's thought experiment --as with the man in the elevator. 

H.G. Callaway 

A first and not detailed answer is that GR is another partial true theory, which can explain a portion of the reality, while leaves another portion unexplained. We have not a complete theory of gravity, despite the strong acceptance of GR, so my answer is:

• If you forget all the non experimental proofs of GR, you can keep it as a nice mathematical theory, which many people wish to be able to explain our cosmos, but it fails to do it...

Andreas...

That's why  somebody "magically" reformulated the SEP, considering only non charged objects.... IRF theory and SEP are strictly connected.

The local equivalence between:

a) Galilean RF (RF in constant speed in deep space far from masses) which is the widest accepted  definition of inertial reference frame IRF and

b) any radial free falling RF  in a gravitational field,  is something given for granted by Einstein. I personally consider it an arbitrary assumption, somebody has to demonstrate that internally things are really the same, not only deduced by the natural absence of "forces"...

True till a contrary proof comes out.??....it is just a principle....

But the II principle of thermodynamics is a sort of conclusion of the study of thermodynamics, a final deduction conirmed  by dayly experience too.

In GRT the IRF assumption and the SEP are at the basis of the theory....

Dear Callaway,

This is an interesting relationship between the equivalence principle of general relativity and general covariance. In principle both concepts are very different because the principle of equivalence corresponds to have equal the inertial mass and the gravitational one. This is to identify two formulae and phenomena that in principle are independent. Gravitation action seems to be quite different to the opposition to change of the state of motion, although the concept of acceleration is the same in both cases.

General covariance tell us that the form of one equation keeps equation under a group of transformations and can be Lorentz transformations of coordinates. Or what is the same we cannot see the change of physical phenomenon, for instance a wave in a diffusion effect. Mathematically speaking we cannot transform one kind of equation in another one non equivalent as an elliptic differential operator in a wave differential operator.

The idea then is that

d^2/t^2=GM/r^2

Seems to be non trivial to accept witout a long tought because the first term contains time while the second doesn't.

Dear Professor Callaway,

"I wonder if you can give some brief account of the issues involved as, for example, some description of the experimental design of the proposed tests and experiments. How is the principle falsified in the experiments you describe?"

What is falsified is the equivalence Einstein gave in the 1911 paper , which is the first version . In GRT the equivalence is local, infinitesimal, that cannot be under discussion in my paper.

Everything is based on the fact that two equally spaced (by H) and accelerated atomic oscillators (at low speed) can't delay, unless messing up the sequence of time events, which is unthinkable.  

While it is  experimentally demonstrated every day with atomic clocks in a gravitational  field (at distance H) that they delay, according to the P&R rate (1+gH/c2).

I was forgetting that you need also the linked paper. There is a mistake on the calculation of an exponential but the results come out Greater that 1 as well.

Article About Time dilation in accelerated frames

Mainz, Germany

Dear Low, 

Thanks for your brief accounts of the two chief subtopics here. You wrote:

General covariance. The laws of physics are tensorial (or, if you prefer, geometric) in nature. They can be expressed in a form which is independent of the choice of coordinates used to paramaterise space-time.

---end quotation

This statement seems to get fairly close to my related interest. I take it that when you speak of "the laws of physics" here, you are more specifically concerned with the laws formulated in GR--or laws of gravity and motion. Interesting that you can equate "tensorial" and "geometric." That the laws "can be expressed in a form which is independent of the choice of coordinates," seems the most interesting point in your account of general covariance. 

I take the general meaning of covariance to be that, though we must make use of some frames of reference, and related coordinates, in order to do physics and determine its laws, the laws should turn out the same in spite of possible differences in the frames of reference and coordinates employed. In that way, frames of reference are like units of measurement --in that differing units can be converted to one another.  Again, whenever we do experiments on physical hypotheses, we must use some particular frame of reference or other, and there is no universal (or Newtonian) frame of reference.

Space-time, I take it, can be viewed as a theoretical postulate of SR and GR, and that any given characterization of it, in a locality, presupposes that we employ some particular frame of reference --in order to be able to put in the parameters needed to characterize the particular space-time.  The general laws, of course, are to be distinguished from such a particular application. But it is as though the general laws have open places for variables related to particular conditions, and one must fill in the open variables in order to make a particular application--which brings us back to using some particular frames of reference or other.

I'm going into some detail here, in part, because I'm interested in the description of the observational set-up relevant to tests of GR. For instance, how might we best describe the observational set-up of Eddington's observations during the 1919 eclipse? The observations allow, from the perspective of GR for a determination of the curvature of space-time in the vicinity of the Sun, though, of course, Eddington was himself firmly planted on Terra firma --off the coast of West Africa. How does the frame of reference of Eddington's observations relate to the distant space-time in the vicinity of the Sun?

H.G. Callaway  

Dear Callaway, the relationship you have written between gravitational force and acceleration force, between equivalence principle and general covariance is in concordance with General Relativity.

The equivalence between gravitation and inertia to acceleration seems not to be exactly as stated, even inside GR. GR proves the following effect: in the neighborhood of some big mass, one has a dilation of time, exactly as when you run with constant speed v. You see the point: constant speed movement, and not accelerated movement. So the stated principle is much more a heuristic argument for (1) making more plausible the space curvature produced by gravitation and (2) expressing the hope that the property of matter called mass is the same when dealing with gravitation as when dealing with inertia, although those phaenomena are very different. In fact when I learnt physics in school, they told us that we are dealing with two different propertys of matter, gravitational mass and inertial mass, and the equivalence principle was the statement that they were approximatively equal. 

The general covariance is a much more fundamental principle, and is partially inherited from Gallileo and (in this form) from SR. However, if the observer is in the origin of the coordinates, this observer has in general no mass (!). If the observer had a mass, than its simple existence generates effects as time dilations in different other systems of reference, and the situation becomes already too complicated. 

The two concepts are independent: general covariance means that local translations are symmetries. The equivalence principle means that matter probes spacetime through the generally covariant coupling of the metric to the energy-momentum tensor of matter.  It is possible to write theories that are generally covariant, but don't obey the equivalence principle, if spacetime is described by fields in addition to the metric, e.g . scalar-tensor theories or supergravities. 

Since Einstein endeavored to unify electromagnetism and gravitation, he tried to generalize special relativity by taking rotations into account. Both the equivalence principle and general covariance are involved in this approach. The third principle involved is the so called “Mach principle”, which Norton also mentions.

In my opinion, though, equivalence principle and general covariance conflict with one another in an important respect. On the one hand, the heuristic equivalence principle set forth in the Gedankenexperiment on the momentarily free falling elevator cabin has no proper space-time description, because we perceive space and time as inherently different. On the other hand, once four-dimensional rotations are admitted in geometry, it is very hard to avoid rotations merging space and time. This conflict shows the difficulty to match a mathematical description with an intuitive one.

Mainz, Germany

Dear Vesely,

Thank you for your contribution. I think that the way that the equivalence principle and covariance entered into Einstein's project for  a "unified field theory" might well tell us something about how he understood these ideas. On the other hand, readers might like to keep to his treatment of the topics in GR, if there is any distinction in the treatments. 

I recently ran across a book which might interest you regarding this: Jerven van Donge, 2010, Einstein's Unification, Cambridge University Press; and there is a review of the book in the current issue of Science (March 25, 2015) written by Michael Janssen and titled "Beyond General Relativity." 

http://www.sciencemag.org/content/347/6226/1078.1.summary

Readers will need a subscription to get the review. 

I agree, of course, that there are very considerable difficulties involved in matching mathematical descriptions with more intuitive descriptions, and in an important sense, this is just the problem of the (ordinary language) interpretation of the formalism. See my comments of this morning under the question regarding whether objects can be said to move is space-time according to GR.

H.G. Callaway

In the order of General Relativity, General Covariance defines that "law of physics can be expressed with respect to any reference frame". About this possibility there aren't doubts: it is certainly possible.  The Principle of Relativity, in its only formulation, establishes instead that "laws of physics are invariant with respect to inertial reference frames". It is manifest that the Principle of Relativity defines not only a possible equivalence among reference frames but above all it defines a principle of invariance of laws of physics with respect to only inertial reference frames. That physical property of invariance isn't enclosed in the General Covariance. We can also think General Covariance includes Relativity but we cannot think, because it is wrong independently of what Einstein thought, General Covariance is a theory of relativity.

Mainz, Germany

Dear Prunescu & contributors,

You wrote:

The general covariance is a much more fundamental principle, and is partially inherited from Gallileo and (in this form) from SR.

---pause

Right, agreed. 

you continue:

However, if the observer is in the origin of the coordinates, this observer has in general no mass (!). If the observer had a mass, than its simple existence generates effects as time dilations in different other systems of reference, and the situation becomes already too complicated.

--end quote

This further statement may seem somewhat mystifying for some readers. I think you are stating a kind of idealization: it is sometimes quite safe to ignore the mass of the observer, since it is so small (and/or distant) in comparison to the parameters of the measurements being made by the observer. So, .e.g., if Eddington is sitting off the coast of West Africa, with his telescope, and on terra firma, making observations of the curvature of paths of light in the vicinity of the Sun, then the mass and distance of the Sun are so great in relation to Eddington, telescope and terra firma, that the contribution of the observer to the curvature of the paths of light in the vicinity of the Sun are negligible and safely ignored.

If we imagine an observer and telescope of very large mass, however, say out at the orbit of Mercury, then we would expect the influence of the observer to tell in the measurements. Is that about right?

H.G. Callaway

Mainz, Germany

Dear Low, 

you wrote:

Indeed, 'observer' is such a loaded word that I prefer just to talk about coordinate systems and coordinate values rather than observers and observations, whenever it is possible.

---end quotation

Thanks for your comment, though you seem quite distant from my own just prior. 

I expect that talking purely in terms of " coordinate systems and coordinate values rather than observers and observations, whenever it is possible," serves the purposes of mathematical idealization and simplification of actual observational or experimental work in physics. That is fine and good, I believe, when it actually facilitates our understanding of the physical processes --in more theoretical terms.

On the other hand, "observation" and detailed description of the observational or experimental set-up are crucial for the experimentalist, who is perhaps less likely to accept a theoretical simplification or idealization if the relationship to possible observational and experimental set-ups remains opaque or unclear. So, I would tend to think that your attitude reflects the perspective of a more theoretical interest.

When physics actually gets down to testing some hypothesis proposed, then there is a great deal of filling of details which becomes involved. Moreover, contemporary empiricisms tell us that we test our theories and hypotheses by reference to predictions and observational consequences. At that point, the experimentalists have to call the theorists down out of the mathematical clouds. If we can't finally understand the detailed relations of complex theory to the details of experimentation and observation, then we can't really test the theory. Right?

H.G. Callaway

My notion of observer regards the scientist who observes, measures, calculates and strives to understand what he has observed.It is possible the concept of observer regards a team of scientists. My notion of reference frame regards the system of space and of time where the physical event happens and it is necessary to describe the physical event. If I observe the fall of a body on the surface of the moon I think a reference frame on the moon is a preferred reference frame and the observer in that reference frame is a preferred observer. If I observe the fall of a body on the surface of the earth, similarly in that case a reference frame on the earth is a preferred reference frame and the observer in this reference frame is a preferred observer. The concept of preferred reference frame is relative and non-absolute.

Mainz, Germany

Dear Low,

I wonder if you can be more specific on the problems you see in the usage of "observation," and related terms. They seem central and crucial to science, so far as I can see --though they need not always be central to a particular problem.

You wrote:

All this I happily agree with: I'm really commenting that a careful use of terminology can at least reduce the potential confusion. In particular, in relativity 'observer' and 'observation' are two words which have, I think, led to considerable unnecessary confusion. 

---end quotation

In particular, do you see problems with related usage in the current thread? Is your caution a kind of overly generalized skepticism? Can you give specific examples of the ways in which these words become problematic in your view of the matter?

H.G. Callaway

I would go back to the Eulerian and Lagrangian observers, the view points of the fluid mechanics.

These are maybe more convincing  view points:

a) The Eulerian sees the things occurring from an external point of view, the river flows and he sits on its border and watches a particle flowing in the river.

b) The Lagrangian imagines to travel with the particle within the river.

Both descriptions have to agree somewhere....

The first is  a Kinematic view point in the literal sense, like a Cinema: the observer sits and watches

the second is Dynamical, it may not have a picture of where he is, but he feels the water around and the pushes and pulls.

 The Eintein's stress tensor concept is derived explicitly in his book from fluid mechanics equations. I wonder why did remain only a sort of Lagrangian observer in GRT: "detects forces and doesn't look outside" ...what about the other??

Mainz, Germany

Dear Low and Quattrini, 

The "Lagrangian observer" is required by a purely relational conception of motion in GR? Could that be the answer? 

Still, although we can't plausibly have an observer outside the overall gravitational field of the universe, we can imagine an observer, or observations made, from outside, or at great distance from, a local gravitational field. That is the case with Eddington's 1919 eclipse observations. Right?

H.G. Callaway

That's why there's the notion of a ``test particle'' (or ```test system'', if it's more than one), that probes a gravitational field, but whose modification of the gravitational field can be neglected. In fact that's how an ``observer'' is operationally defined and this can be made precise, by computing the correction to the metric induced by the energy-momentum tensor of the putative observer. So there isn't anything mysterious or metaphysical about the notion of ``observer'' or observation here.

Mainz, Germany

Dear Nicolis, 

In contrast to what you say above, it seems clear that one might consider an observation made which involves more than a negligible effect. Imagine a very massive body, or a telescope so large that it would influence --significantly interact with--the gravitational field of the Sun. One might still get a measurement of the bending of the paths of starlight in the vicinity of the Sun, though this would be a different reading from Eddington's.

You wrote:

That's why there's the notion of a ``test particle'' (or ```test system'', if it's more than one), that probes a gravitational field, but whose modification of the gravitational field can be neglected. In fact that's how an ``observer'' is operationally defined and this can be made precise, by computing the correction to the metric induced by the energy-momentum tensor of the putative observer.

--end quotation

Do you see yourself as disagreeing here? The differences of the measurements would still consort with the same physical laws; and all frames of reference are equally valid for the determination of physical law. 

I agree, of course, that "there isn't anything mysterious or metaphysical about the notion of 'observer' or observation here."  That is to say that our account of what may count as an observer or an observation must be consistent with physical law. 

H.G. Callaway

Actually, what Eddington measured was, precisely, an example of a ``test'' situation, where the gravitational field of the Sun affected the propagation of light, whose energy-momentum tensor had negligible effect on the metric. The deflection indeed illustrates the equivalence principle, since the metric couples to the energy-momentum tensor of the electromagnetic field. For stronger fields, the combined Einstein and Maxwell equations must be solved and  Reissner and Nordstrom found that the solution of the combined Einstein and Maxwell equations can be  the metric of a black hole that has mass and charge; and a special limit, the extremal limit, where, in appropriate units, the mass is equal to the charge, is of great importance, since quantum effects can be computed reliably then. 

Mainz, Germany

Dear Nicolis, 

Yes, very good. I see your point about a test particle in the Eddington example. Yet, it seems one might make a similar observation involving non-negligible test objects. 

You go on with some physics, but, as I read you, you don't really answer my questions. Was I unclear in constructing the interaction of gravitational fields in the observational situation? 

For Eddington, you say "The deflection indeed illustrates the equivalence principle, since the metric couples to the energy-momentum tensor of the electromagnetic field." 

It strikes me that your point would be helped along by some bridging explanation. You neglect to say how the equivalence principle (relating gravitation to accelerated frames of reference) relates to the coupling of the metric [of the gravitational field?] to the energy-momentum tensor of the electromagnetic field. Can you say a bit more on this --helpful to the non-specialist?

H.G. Callaway

I did address the questions: In the example of the deflection of light, Einstein's equations are solved and give rise to the metric of a massive body (the Sun)-which isn't the metric of flat space; then Maxwell's equations are solved for computing the propagation of the electromagnetic field, light, in this metric. 

In this case the right hand side of Einsten's equations is the energy-momentum tensor of a spherically symmetric massive body only, i.e. the solution, the metric, is the Schwarzschild metric, since the energy-momentum tensor of the electromagnetic field  is taken to give a negligible contribution-it's a probe of spacetime, that doesn't change it. But Maxwell's equations contain the metric. 

For stronger electromagnetic fields, the two sets of equations must be solved together, since the right hand side of Einstein's equations does include the energy-momentum tensor of the electromagnetic field, a known function of the electromagnetic field, that obeys Maxwell(s equations, in which the metric, also, enters. Therefore the metric will not be that of a single massive body, in this case, but will depend on the electromagnetic field. In this case light is no longer a probe of spacetime-it modifies spacetime and is, in turn, affected by it, since its propagation, described by the light-like geodesics in this spacetime, is  affected. 

Regarding the equivalence principle, this is a technical issue and words can only go so far. General covariance implies that, with the metric and the energy-momentum tensor there is one way to combine them. This way expresses mathematically that the energy-momentum tensor is a source for Einstein's equations and, thus, whatever the matter content is, it probes spacetime through this coupling to the metric. So if different matter configurations give rise to the same numerical value for the corresponding energy-momentum tensors, the spacetime will be affected the same way-whether it's an electromagnetic field, or a fluid, for instance, since the right hand side of Einstein's equations will be the same.  

Mainz, Germany

Dear Nicolis,

Again, you go through a great deal of physics in your reply. Yet, in the end, it seems you conflate the observer or observation with your talk of the test particle--so it seems to this reader. We can't substitute the one for the other. 

Eddington measured, more directly, the distance between the images of stars on his photographic plates. It is only given the specific observational set-up that this could be interpreted as an indirect measurement of the curved paths of light in the vicinity of the Sun. Right?

H.G. Callaway 

The observer *is*, by definition, a ``test system'' and the result of the interaction of the test system with the environment, defined in a certain way, is, by definition, an `` observation''. And  I gave some very explicit examples above, that show how the transition from ``test'' to mutual  ``interaction'' is realized. Of course the physical content must be taken into account.

Eddington's observations can only make sense, if the theory is understood. The observational setup is one, among many possible, that are described by the theory. The qualification ``indirect'' doesn't mean anything-any observation is ``mediated'' by something.  

Dear Prof. Callaway,

regarding the Eulerian-Lagrangian viewpoints approach, it seems that GRT is satisfiyed only with the second, the first is left to the old physics  or experimental phyisics which needs to refer to specific coordinate systems observing the phenomena globally (which makes me quite unconfortable).

The root of this choice in GRT is based mainly on the "Einstein's happiest thought" of the free falling RF as an Inertial RF:

the complete local equivalence between a free falling system and a Galilean RF. The Galiean  is an IRF since it proceeds with constant speed in deep space, is isolated from any external interaction. The free falling RF is defined also as an IRF but it is in relation with a gravitational body.

I really don't think it is was a very happy thought to base a so remarkably articulated theory on such an assumption, equating two systems which are in completely different  situations and affirm that they differ in a finite region only for tidal effects of the field.

As I said already other times, it has to be demonstrated that the physics in a free falling RF and the one on a Galilean RF are the same or equivalently there is no way to distinguish differences them from the inside.

This is at the base, according to my  very humble opinion,  of the  issues GRT has encountered with energy conservation.  

The symmetry group of special relativity, the Poincare' group,  has a finite number (7) of independent infinitesimal generators. GRT  is  group that has a continuously infinite number of independent infinitesimal generators. In Noether’s terminology such a group is an infinite continuous Group.

Field theories with a finite continuous symmetry group have what Hilbert called ‘proper energy theorems’. The GRT has instead ‘improper energy theorems’, there may not be energy conservation in finite parts of  the space-time, only globally the conservation is granted (if the system considered is isolated).

With a very good approximation in a strictly physical experimental view point, the Gravitational field occurs to be so far the best example of conservative field in which the QM and Newtonian Dynamics has been tested for 100 years together in remarkable experiments.

It is true that geodesic equation obtained by the Euler-Lagrange action, was built adopting  the space-time curvature tensor and can be seen collapse in Newtonian G equation. This is done by neglecting many terms having other effects, not only the ones which give more accurate predictions of the Newtonian gravitational interaction. So far so good.

But who assures me that all the possible effects of gravitation imparted by the space-time curvature physically disappear locally when a body free flows in it???Mathematics,??? Can't.

It is like asking the shopkeeper if his merchandise is good..

I'm quite pretty sure of the opposite, unfortunately....

Maybe I should repeat referring to the answer given by Synge in his `Relativity: the general theory':

``The Principle of Equivalence performed the essential office of midwife at the birth of general relativity, but, as Einstein remarked, the infant would never have

got beyond its long-clothes had it not been for Minkowski's concept.

I suggest that the midwife be now buried with appropriate honours

and the facts of absolute space-time faced.''

Willem de Muynck

Mainz, Germany

Dear Muynck, 

Good to hear from you. 

On needing to "face" the fact of "absolute space-time." Would you care to explain?

I'm puzzled. Would this be "absolute space-time" in GR, or are you proposing an alternative?

H.G. Callaway

Mainz, Germany

Dear Nicolis,

You wrote:

Eddington's observations can only make sense, if the theory is understood. The observational setup is one, among many possible, that are described by the theory. The qualification "indirect'' doesn't mean anything-any observation is "mediated'' by something.

---end quotation

I agree, of course, that the observations can only be understood, if we understand the theory. But I think you over-state the case in holding that "The observational setup is one, among many possible, that are described by the theory." Instead, the specifics of Eddington's 1919 set-up are one among many possible set-ups consistent with the theory. It goes too far to claim that all the possible observational set-ups are actually described by the theory. Some are surely, as yet, un-imagined. 

Along with the theory, we need to understand the specifics of Eddington's observational set-up. It is typical in experimental and observational reports, claiming to confirm theoretical predictions, that the instruments are specified along with techniques of calibration, etc. We need to know, or be in a position to reasonably judge, for instance, that Eddington had his telescope in an appropriate focus. Anyone wanting to replicate the results needs to know something of the details. Trying to replicate results is standard experimental practice.

It also seems a vast over-statement to claim that " 'indirect'  doesn't mean anything" because, as you put it, "any observation is 'mediated' by something." Apparently you have some argument for your claim that you are yet to explain. I fully agree that any observation is mediated in some way or other. Knowing the specific means employed in the observation is important to evaluation of the results. 

Your comments are welcome here, but you must admit that your replies are rather indirect. Rather than taking up the language of the question, you seem to translate the question into some other discourse, and then answer in those terms. I think you help the discussion along less than you might. 

H.G. Callaway

Dear Willem de Muynck,

Synge referred to the equivalence between accelerated motion and the gravitational field as initially affirmed by Einstein,  which is  falsified in the real gravitational field of earth by real atomic clocks.

To do without the SEP is a problem for GRT.

SEP = UFF (universality of free falls) + UCRLPI Universality of clockrates or Local position invariance + LLI (Local Lorentz invariance)...

GRT implies the SEP as long as I know...

it should be that No SEP implies no GRT.

Understanding the theory implies, also, modeling the experimental procedure and this is a core part of the subject, that's part of increasingly specialized courses. That's why content matters and general discussion becomes less useful, as one gets into technical issues. There's simply no substitute to studying  a *textbook* and solving exercises to learn a subject. (And while a study of the history of the subject can be fascinating, it can be an obstacle for understanding, since errors, inevitably are part of the historical process, but how they are corrected is what really matters. It doesn't really matter *who* affirmed what, but *what* was affirmed and what it means. And, once more, it's incorrect to identify the equivalence principle with the general theory of relativity. The symmetry principle is general covariance; the equivalence principle is consistent with general covariance, but is but a specific realization, for the case that the gravitational action depends only on the metric. So it's not correct that atomic clock measurements have falsified the equivalence principle. The only way they could have done that would be to show that the gravitational part of the action depends on fields other than the metric, scalars, vectors or spinors. This hasn't happened.)

Mainz, Germany

Dear Nicolis, 

Thanks for your further comment. 

You wrote:

And, once more, it's incorrect to identify the equivalence principle with the general theory of relativity.

---end quotation

I think it to the point here to emphasize that my question concerns the relationship between the equivalence principle and general covariance. Though Einstein stated that the equivalence principle was his original insight on general relativity, it is certainly not my intention to identify equivalence and GR. Here it matters quite a lot who said what. 

You also wrote:

The symmetry principle is general covariance; the equivalence principle is consistent with general covariance, but is but a specific realization, for the case that the gravitational action depends only on the metric.

---end quotation

Correct me if I am wrong about this, but I believe that the emphasis on general covariance as a matter of symmetry is a fairly recent innovation--following the standard model of particle physics. Otherwise it seems correct to me to hold that the equivalence principle is a specific case falling under general covariance. 

By the way, I generally agree that "It doesn't really matter who affirmed what, but what was affirmed and what it means." Still, your emphasis on this doesn't help bring the discussion along. 

H.G. Callaway

Mainz, Germany

Dear all,

Readers of this thread may find the following short article of interest:

http://news.stanford.edu/news/2007/october31/einstein-103107.html

Its a news item from Stanford University describing the experimental design of a test of the equivalence principle: "Physicists chase Einstein's Equivalence down a hole."

Though this dates from a few years back, it seemed to me to accurately represent the view which contemporary physics takes toward GR and the equivalence principle. The equivalence principle is not put beyond all doubt, but it is regarded as highly accurate in experimental terms. 

H.G. Callaway

Dear Callaway,

As far as I am aware, Synge's problem with the equivalence principle has nothing to do with any absolute space-time. At the place of the quote he simply referred to the well-known fact that the Riemann tensor of space-time would be non-zero if and only if there is a gravitational field. There, hence, cannot be any equivalence between a coordinate frame in a curved space-time and whichever coordinate frame in a flat one. This non-equivalence is just a consequence of general relativity, usually taken into account by stressing that so-called `momentarily comoving reference frames' are (approximately) valid only in a limited region of a space-time point for which the Christoffels are all  vanishing.

Regards,

Willem de Muynck

Dear Prof Callaway,

 "The equivalence principle is not put beyond all doubt, but it is regarded as highly accurate in experimental terms. "

This is the Einstein EP for free falling or UFF a part of the EEP. They are testing it  this year in the space laboratories under the ESA STE-QUEST project with matter waves.

It is not the one regarding the equivalence of accelerated RF with a static gravitational field of which Synge complained which I call the E-WEP and is just an euristic tool.

Mainz, Germany

Dear all, 

Let me take this opportunity to thank all the contributors and readers of the present question and thread of discussion. I believe that much has been accomplished in terms of understanding the two named principles and their relationship to GR, and more detailed questions have been opened. 

As I understand the matter, it appears to me that the Synge question is one among various objections to GR which have been answered over the course of time. Many of these go back several decades or more. This is not to say, of course, that further studies are not in order, or even, as we have seen, currently under way --seeking greater precision. I would emphasize the general question here, remind the participants that the intention of the question is not to do physics, but instead that the question aims to clarify and understand what it is that physics claims. We should keep the forest in sight while looking in detail at the tress on occasion. 

It seems to me that the principle of covariance stands out in the present discussion as crucial and central to GR. That seems to be philosophically of considerable importance and interest, since it tells us that the laws of physics must turn out the same in spite of the differences which come into view in considering the perspectives provided by differing frames of reference. 

More later, svp. 

H.G. Callaway

Philadelphia, PA

Dear all,

Here follows a link to a new paper of mine, partly based on our discussion, and on discussions on another RG tread:

https://www.researchgate.net/publication/275041797_What%27s_Wrong_with_Relativism_anyway?showFulltext=1&linkId=553125d90cf27acb0dea4b77

Have a look. Comments invited

H.G. Callaway

Research What's Wrong with Relativism, anyway?

" Is relativism a philosophy?" is a question in the proposed paper.

Relativism is only a philosophy. In physics and in science there isn't relativism, but only the Principle of Relativity is valid. Relativity is a very different concept from relativism.

Mainz, Germany

Dear Sasso, 

Many thanks for your comment. Of course, I agree entirely, and that is the point of my posting the link to the "Relativism" paper. 

I'll be visiting here in Europe over the next several months. 

H.G. Callaway

It is quite interesting regarding the argument of the Covariance the Voigt's transformations. These are infact covariant.

Since the Lorentz Transformations are invariant  they are not  directly suitable for GRT. For GRT the Local Lorentz invariance is used, but this approach is source of problems.

http://arxiv.org/abs/1411.2559

Charles,

mathematically yes there is no problem to treat it infact GRT is a mathematically sound theory, but physically it is not exactly the same..

The two principles are presented as independent, but they are connected by inaccuracies that come from approximations.

First equivalence is approximate and only precise to the second order terms. Gravity differs from place to place in a predictable way based on distance from the source, while other acceleration is often the same from place to place. Instantaneously they are indistinguishable at a point, but the differentials and gradients are not identical.

The error in equivalence introduced problems with covariance causing the terms higher than second order to be truncated. The curving of space is represented, but the higher order folding of space is not.

Einstein acknowledged in his non technical book of relativity that his theory was approximate and incomplete. He expected other scientists to improve on it quickly. That didn't happen although many have tried.

GR works very well until the kinetic energy goes high enough to fold space in layers. TGD takes up where GR leaves off and provides the folded layers, but with other math of difficult content while avoiding the inaccuracies.