Dear Callaway,

Have the Einstein field equations changed their meaning?

I get an answer by the reading of your introduction citing  Weinberg.

useful only for distances much larger than about 10 (to the -33rd) centimeters, and particle energies much less than an energy equivalent to the mass of 10 (to the 19th) protons.

This limitation of the applicability of the equation makes a huge difference in their meaning.  It means that it cannot be applies in the early phase of the universe. This remove a big chunk of the original meaning.

P.S.

 This mean that we do not have a theory of the early phase of the universe so we do not have a theory of the origin of the universe.  It is not surprising given that the expression ''theory of the origin of the universe''  assumes the existence of a theory at the origin which necessarily bring the problem of the origin of the theory itself.  It is the unsolbable problem of saying something without making any prior assumption. So our only open option is to go in the direction of creating minimal initial creation framework.

https://en.wikipedia.org/wiki/Einstein_field_equations

Mainz, Germany,

Dear Gharaee,

This is the very article I linked to in the question. Do you want to say something about it?

H.G. Callaway

They are just tired of the GR. They are unwilling to understand within GR the Quantum effects and dark matter. My contribution: 

http://www.ijser.org/onlineResearchPaperViewer.aspx?On-the-value-of-David-Bohms-Quantum-Mechanics.pdf

https://www.morebooks.de/store/gb/book/simplest-explanation-of-dark-matter-and-dark-energy/isbn/978-3-659-50275-0

Mainz, Germany

Dear Martila,

Was that a "yes" or a "no"? I don't see that you attempt to answer the question about a change in meaning of the equations. Perhaps you think to answer indirectly? Can you respond to the argument from Weinberg?

H.G. Callaway

Dear Callaway,

I will make a citation from the Wiki article mentioned above: "

"""For many years the cosmological constant was almost universally considered to be 0. However, recent improved astronomical techniques have found that a positive value of A is needed to explain the accelerating [expanding] universe."""

This is just one possible sense in which the meaning of the equations changed with the time. They were not thought for an expanding universe. The equation have no a unique solution. Different solutions agree more or less with different models of the universe, and new qualitative reflections on the equations bring new interpretations and finally new meanings. 

On the other hand, the problem why only second derivatives play a rolle is very deep. The problem is not new, being already there in Newton's equation F = m x''. As a student I was influenced by Frenel's equations for 3-dimensional curves and I believed that the answer for the problem in the case of Newton's equation is related to the fact that we are in a 3-dimensional space. Now I am more skeptic with this explanation in the case of Newton's equation, and I dare no explanation for Einstein's equations.

Last but not least, thank you for a new very nice question and subject of reflection.

Prunescu

Mainz, Germany

Dear Prunescu,

Many thanks for your thoughtful reflections on the question. Weinberg is also at a loss, in this short piece, to explain the limitation to second derivatives, except perhaps as a matter of greatest possible simplicity. So, you are in good company.

A change in the value of the cosmological constant is a possible reading of a change in meaning, but I think this is not chiefly the kind of thing Weinberg is getting at. If we had a new, more precise determination of Newton's gravitational constant, and plugged it into Einstein's equations, that would not seem to change their meaning in any very significant sense. We might learn something of the meaning of the Einstein equations, I believe, by considering the consequences, in particular circumstances, of using different values for the gravitational or the cosmological constant --in effect this is an aspect of their usage. I suppose we are going to look at the use of the equations in exploring their meaning. 

I take it that the point is that the same equations are used in an "effective field theory," where they have a different meaning. Weinberg also argues that the Dirac equation and Maxwell's equations now have different meanings, and generally, that equations may survive in physics by changing their meanings.

H.G. Callaway

1) Why usually are no higher derivatives in the theory? I think it is linked with the fact, that inertial systems of reference are moving without acceleration. Thus, one shall only know the position and the speed. 2) Perhaps after the successes of quantum field theory (QFT) the GR is indeed considered as the effective theory: there are no microscopic vacuum fluctuations in GR. However, is the QFT correct? According to David Bohm's interpretation of quantum effects - hardly.

Mainz, Germany

Dear Martila,

I see very clearly that you want to argue against QFT in favor of Bohm's interpretation of quantum mechanics. But the question here is not, Is QFT true? The question is whether the Einstein equations have a different meaning in the revised theoretical setting than they originally had. If Bohm were completely right in everything he says, it still might be that Einstein's equations do, or do not, have a different meaning in the setting Weinberg gives to them.

H.G. Callaway

Dear Callaway,

Have the Einstein field equations changed their meaning?

I get an answer by the reading of your introduction citing  Weinberg.

useful only for distances much larger than about 10 (to the -33rd) centimeters, and particle energies much less than an energy equivalent to the mass of 10 (to the 19th) protons.

This limitation of the applicability of the equation makes a huge difference in their meaning.  It means that it cannot be applies in the early phase of the universe. This remove a big chunk of the original meaning.

P.S.

 This mean that we do not have a theory of the early phase of the universe so we do not have a theory of the origin of the universe.  It is not surprising given that the expression ''theory of the origin of the universe''  assumes the existence of a theory at the origin which necessarily bring the problem of the origin of the theory itself.  It is the unsolbable problem of saying something without making any prior assumption. So our only open option is to go in the direction of creating minimal initial creation framework.

I have difficulties understanding the exact meaning of the question that is being asked here. The objects (the Einstein tensor and the energy-momentum tensor) appearing in Einstein's Field Equations have certainly not changed their meaning, and the astonishingly broad range of successful applications of the equations has not shrunk; in fact, the range of interesting applications has grown ever broader, and practical applications, such as the GPS, have emerged! However, the following two features of the equations may be subject to change as time goes by:

1. The known range of validity and the degree of accuracy of the Field Equations; (we may know more about the distance- and energy scales of phenomena that are accurately described by the Field Equations, as well as possible limitations of their applicability or of the precision of the description they provide).

2. Nowadays, we may regard the Field Equations as an effective description of gravitational phenomena at relatively "large" distance scales, rather than as a fundamental theory of space, time and gravitation valid to arbitrarily small distance scales and compatible with principles of quantum theory. It is fashionable to imagine that, at very tiny distance scales, the structure of space and time might be radically different from the one of a classical Lorentzian manifold. However, it appears that nobody really knows a compelling alternative description. (Speculations have been made by many famous people, including, for example, Alexander Grothendieck,...). One might expect that the status of general relativity and of Einstein's Field Equations is analogous to the status of the Navier-Stokes Equations in fluid dynamics: They merely provide an effective description of phenomena at large distance scales and in the absence of quantum effects, but ignore new structure (in the case of fluids the atomistic and quantum-mechanical structure of matter) that becomes manifest only at very small distance scales.

As long as there isn't any unified description of the structure of space, time and gravitation and of quantum phenomena, we are entitled to expect that a deeper and more unified theory will lead to modifications of basic concepts of theoretical physics and the introduction of new concepts and ideas in our description of Nature. In the light of such new discoveries, General Relativity may then appear as an effective theory only useful for a description of phenomena in a certain range of scales. However, as with Newtonian mechanics or classical electrodynamics, it is safe to expect that, in a broad range of distance- and energy scales (up to cosmic scales), General Relativity will remain an extraordinarily useful and successful description of space, time and gravitation. After all, the same remains true about the Newtonian description of space, time and gravitation. However, it may not be applicable to correctly describe phenomena happening very shortly after the Big Bang or in the vicinity of very tiny black holes.

Revolutions in Physics do not invalidate older theories; they clarify the range of applicability of those theories and bring along new theories successful in describing phenomena in realms that have previously been inaccessible. Usually, the new theories reproduce the older theories in appropriate limiting regimes. They do not invalidate the older theories. There is absolutely no reason to expect that this will not be the case for General Relativity!

Well, that is what I can say without thinking more deeply about your question.

Mainz, Germany

Dear Brassard,

I see that Weinberg's argument convinces you. That is not surprising, since he is a fine writer and very convincing. My short exposition does not do him justice, and I recommend his book, Lake Views. But I see, too, that Fröhlich has expressed some skepticism about the question itself, and I think that well worth close attention. But let me first turn to your comment. You wrote:

I get an answer by the reading of your introduction citing  Weinberg.

useful only for distances much larger than about 10 (to the -33rd) centimeters, and particle energies much less than an energy equivalent to the mass of 10 (to the 19th) protons.

This limitation of the applicability of the equation makes a huge difference in their meaning.  It means that it cannot be applied in the early phase of the universe. This removes a big chunk of the original meaning.

This mean that we do not have a theory of the early phase of the universe so we do not have a theory of the origin of the universe.

---end quotation

I agree that it cannot be applied to the earliest phase of the universe. But it seems to go much further to say that " we do not have a theory of the origin of the universe." The problem is that we have too many theories of the origin of the universe, and too little theory and observational evidence to constrain them. But both the passage from Weinberg and your comments remind me of a quotation from Hawking:

… we know that the theory of general relativity must be modified. Because the classical (i.e. non quantum-mechanical) version predicts points of infinite density—singularities—it prognosticates its own failure…

                                —Stephen Hawking 2005, A Briefer History of Time.

---end quotation.

I used this quotation at the opening to my 2014 edition of Eddington's The Nature of the Physical World, and I would like to recommend my Introduction to readers of this thread (I hold the copyright.) I put it up this morning:

https://www.researchgate.net/publication/278673181_Introduction_A.S._Eddington_Physics_and_Philosophy

The point of the quotation is that if we modify GR by restricting its domain of application, then we have changed its meaning, though the mathematical formulas remain the same, orthographically, letter for letter and symbol for symbol. More basically, this involves placing Einstein's field equations within a new or augmenting, theoretical context. Moreover, as Hawking emphasizes, the singularities of infinite density predicted by GR are, on the face of things, physical impossibilities, and as Hawking has it, the original theory, thus fails.  But on the other hand, treating GR as an "effective field theory," we have something valuable and true. So, it could not be that the theory judged false and failing in its predictions is the same theory which is true and useful. Or, so it seems to me.

H.G. Callaway

Chapter Introduction: A.S. Eddington, Physics and Philosophy

Mainz, Germany

Dear Fröhlich,

What you say in your posting seems to me mostly on the mark and very informative. You add detail which may prove to be of use to those reading along, and which could very well help the discussion along. Some of this might be well worth coming back to at some point.

For now, allow me to address your doubts or puzzle about the meaning of the question. You wrote:

I have difficulties understanding the exact meaning of the question that is being asked here. The objects (the Einstein tensor and the energy-momentum tensor) appearing in Einstein's Field Equations have certainly not changed their meaning, and the astonishingly broad range of successful applications of the equations has not shrunk; in fact, the range of interesting applications has grown ever broader, and practical applications, such as the GPS, have emerged! However, the following two features of the equations may be subject to change as time goes by:

1. The known range of validity and the degree of accuracy of the Field Equations; (we may know more about the distance- and energy scales of phenomena that are accurately described by the Field Equations, as well as possible limitations of their applicability or of the precision of the description they provide).

---end quotation

First off, then I think that no one here wants to challenge the usefulness of the Einstein equations or of GR. Much the same could be said about Newtonian mechanics, of course. Both have a validity in relation to limited or restricted physical domains. I think that is just the point of Weinberg writing of GR as an "effective field theory." I am yet to encounter the physicist or philosopher, for that matter, who doubts of the genius of Einstein or Newton as scientists.

I take it that the Einstein field equations state certain complex relationships among physical variables. But as reinterpreted, they state the same relationships among physical variables within a limited domain. This restriction, as I've argued, amounts to a change of meaning of the equations. Let me make a very simple analogy. Suppose someone had said "All swans are white," everyone agrees and thinks this a fine generalization, and only later is it discovered that  their are black swans in Australia. In consequence, we get a reformulation: "All non-Australian swans are white." This is an explicit reformulation, of course, which makes the difference in meaning explicit. Regarding the field equations, on the other hand, the reformulation is more a matter of a difference in usage --as involved in excluding application to certain extreme conditions of scale and energy. Much of your posting in fact describes the restrictions on usage in considerable details --which is all to the good.

My point is that the same equations used in differing theoretical contexts can take on a different meaning, or interpretation. Weinberg himself writes of the need to "reinterpret" the equations. I hope these brief comments help in clarifying the sense of the question. 

H.G. Callaway

Dear H.G. Callaway,

A scientific model has a life cycle. The relation between the observable in the model is sometime first observed into a very specific experimental set-up.  Then it become a theory where these relations are assumed to be always the same in whatever context.  Then it finished its life cycle by being realistically limited to a specific context and this last phase often allow the discovery of a more general model under which it is subsumed.  

We are often told that the scientific model is falsified and so shown to be untrue. It is only untrue as an uncontextualize generalization.  But it is in the last phase of the life cycle that the model is better known in the sense as its domain of validity is circumscribed.  Newton physics is better known today now that we know when it is applicable and when it is not.  Maybe we should replace ''falsification of a theory'' by ''contextualization of the theory''.

Mainz, Germany

Dear Brassard,

I like your idea of a cycle, though I doubt that the terminology you employ is quite so definite as might be required to generalize the kind of point you are making in just those terms.  Sometime things go in such a cycle, and perhaps sometimes not. My impression is that there have been times when "theory" was treated in somewhat the way you suggest for "model," and that once "theory" came to be regarded as including things less hypothetical, then "model" came into play the role of talk about the more hypothetical. So, as I see the matter, there is a standing tension connected with the difference between what is better established and what if less firmly established, and much felt discomfort about that difference. The words tend to shift around in degree as people avoid the discomfort in various semantic settings. But I have no strong objection to what you say about a cycle.

However that may be, the current tendency is to contrast "model" as something more hypothetical with established "theory," as in, say, "relativity theory." (There are, of course, many and diverse uses of the words.) However, I sense of hint of anachronism is your talk of "uncontextualized generalization."

When Einstein proposed GR, it made universal claims, implying, e.g., (as came to be recognized) the singularities which we found Hawking objecting to in my quotation from Hawking. (Finding solutions to Einstein's equations is no easy matter, of course. There were times, e.g., when Einstein himself held that GR implied gravitational waves, and other times when he rejected the idea.) We cannot now read a "contextualization" back into what Einstein claimed so as to protect it against possible falsification--the same can be said for Newtonian mechanics.  What physicists can do is reformulate or reinterpret GR --to create a better alternative, drawing on Einstein's insights. Speaking of this, we may want to say that the validity of GR has been circumscribed, as you suggest. But actually, what we have is a revised theory, and one not open to the same objections, an "effective field theory" of gravitation. This is a different critter. The "uncircumscribed" theory is thereby rejected.

You can't take falsification out of science --not even to honor the greats!

H.G. Callaway

Dear H.G. Callaway,

I agree we can't take falsification out of science but I was searching a better expression for it.  The word ''falsification'' is popular now it is just a new and better way to speak about the ''truth''.  Falsification is less bold and more limited way to speak of truth.  I was searching for a term that is even more limited that falsification and play the same role.  Falsification wrongly suggest that once falsified a theory become untrue and fall.  Contextualization suggest finding the truth boundary of a model.

Mainz, Germany

Dear Brassard,

"Contextualization" means seeing something in its actual context, and we might say that the Einstein equations have now been placed in a new or altered theoretical context, since they are treated as an "effective field theory;" and it is exactly this development which shows the boundary or limits of their applicability.

"True" and "false" come along naturally with logic, and they are not to be avoided. Thinking of a theory as a set of axioms and in physical application, including relevant statements of initial conditions of a physical system, if any of the logical consequences are shown false, then the theory is shown false. That simply belongs to the meaning of "logical consequence," and, generally, if any of the consequences of a logically valid argument are false, then at least one premise of the argument is also false.

The aim of empirical testing of any theory is to check its predictions. From a more theoretical perspective one wants to develop its consequences as avenues of empirical testing and observational consequences. The predictions are either found true or found wanting, and that is fundamental and unavoidable in the practice of science.  I see nothing to object to in the use of the word "falsification" or "confirmation" (or "collaboration" as some prefer).

A possible problem arises here, in view of the following objections from Fröhlich's posting, above:

Revolutions in Physics do not invalidate older theories; they clarify the range of applicability of those theories and bring along new theories successful in describing phenomena in realms that have previously been inaccessible. Usually, the new theories reproduce the older theories in appropriate limiting regimes. They do not invalidate the older theories. There is absolutely no reason to expect that this will not be the case for General Relativity!

---end quotation

No doubt, GR is extremely well confirmed, and it is in fact gaining applications in empirical physics! My question here concerns the meaning of "invalidate," where the claim is made that revolutions "do not invalidate older theories." If this only means that the older theories can continue to be employed within newly recognized limits of validity, then of course, I have no objection to this. GR is, for instance, employed in current projects seeking direct evidence of gravitational waves. Newtonian theory is employed in sending landing vehicles to Mars. Clearly, no one objects to the use of older theories within limited domains of applicability. Still it is the spotting of false consequences which leads to the recognition of limits of applicability, and in that degree, the older theory is invalidated (in application to its former, broader domain of application) and something new arises in its place. According to Fröhlich, "the new theories reproduce the older theories in appropriate limiting regimes." but I think we could just as easily say that the older theory has been modified to avoid its unwanted consequences.

H.G. Callaway

SCIENCE

AND HYPOTHESIS

BY

H. POINCARÉ

https://www.gutenberg.org/files/37157/37157-pdf.pdf

CHAPTER X.

THE THEORIES OF MODERN PHYSICS.

Significance of Physical Theories.—The ephemeral nature

of scientific theories takes by surprise the man of

the world. Their brief period of prosperity ended, he

sees them abandoned one after another; he sees ruins

piled upon ruins; he predicts that the theories in fashion

to-day will in a short time succumb in their turn, and he

concludes that they are absolutely in vain. This is what

he calls the bankruptcy of science.

His scepticism is superficial; he does not take into

account the object of scientific theories and the part they

play, or he would understand that the ruins may be still

good for something. No theory seemed established on

firmer ground than Fresnel’s, which attributed light to

the movements of the ether. Then if Maxwell’s theory

is to-day preferred, does that mean that Fresnel’s work

was in vain? No; for Fresnel’s object was not to know

whether there really is an ether, if it is or is not formed

of atoms, if these atoms really move in this way or that;

his object was to predict optical phenomena.

This Fresnel’s theory enables us to do to-day as well

as it did before Maxwell’s time. The differential equa-

the theories of modern physics. 179

tions are always true, they may be always integrated

by the same methods, and the results of this integration

still preserve their value. It cannot be said that this

is reducing physical theories to simple practical recipes;

these equations express relations, and if the equations

remain true, it is because the relations preserve their reality.

They teach us now, as they did then, that there

is such and such a relation between this thing and that;

only, the something which we then called motion, we now

call electric current. But these are merely names of the

images we substituted for the real objects which Nature

will hide for ever from our eyes. The true relations between

these real objects are the only reality we can attain,

and the sole condition is that the same relations shall exist

between these objects as between the images we are

forced to put in their place. If the relations are known

to us, what does it matter if we think it convenient to

replace one image by another?

That a given periodic phenomenon (an electric oscillation,

for instance) is really due to the vibration of a

given atom, which, behaving like a pendulum, is really

displaced in this manner or that, all this is neither certain

nor essential. But that there is between the electric oscillation,

the movement of the pendulum, and all periodic

science and hypothesis 180

phenomena an intimate relationship which corresponds

to a profound reality; that this relationship, this similarity,

or rather this parallelism, is continued in the details;

that it is a consequence of more general principles such

as that of the conservation of energy, and that of least

action; this we may affirm; this is the truth which will

ever remain the same in whatever garb we may see fit to

clothe it.

Many theories of dispersion have been proposed. The

first were imperfect, and contained but little truth. Then

came that of Helmholtz, and this in its turn was modified

in different ways; its author himself conceived another

theory, founded on Maxwell’s principles. But the remarkable

thing is, that all the scientists who followed

Helmholtz obtain the same equations, although their

starting-points were to all appearance widely separated.

I venture to say that these theories are all simultaneously

true; not merely because they express a true relation—

that between absorption and abnormal dispersion. In

the premisses of these theories the part that is true is

the part common to all: it is the affirmation of this or

that relation between certain things, which some call by

one name and some by another.''

Mainz, Germany

Dear Brassard,

An interesting passage, in several ways, but we lack your commentary to see which points you think to emphasize in the present context of discussion. It seems that various distinct point from this passage might be relevant, but you are yet to say how you see the passage or how it fits into the discussion. Is this a reply to what went before in this thread? How so?

H.G. Callaway

Dear H.G. Callaway,

In this text Poincarre show that old and so called obsolotete theories are still valid.  He showed that the relational content remain stable accross changes but the metaphysical clothing, the images onto which the relational is garbed constantly changes.   It make me wonder in the light of limits of the field equations, what is the clothing and what is the core relational core that will survive. 

Mainz, Germany

Dear Brassard,

Yes, I see the questions in the offing here. I think they might well be quite interesting and relevant to the thread. Let me get back to you, svp, but for now, I'll be off on some travels.

H.G. Callaway

Dear H.G. Callaway,

I recently discover an interesting fellow:  Michel Mizony. I only found text, paper and book written in French.  He is a high ranking mathematical physicist specialist of relativity.  He elaborate a great deal on the mathematical pluralism of Poincarre and the Kantian notion of the aprio of space time.  He demostrate that any theory expressed into one geometrical framework can be translated into another geometrical framework.  He translated General Relativity in Euclidean Geometry.  He is also convinced that general relativity is compatible with quantum mechanics based on the property of the Poincarre group at their common basis.  He used the latest mathematical tools to re-explore the structure of the existing theory.

http://www.decitre.fr/livres/la-relativite-generale-aujourd-hui-ou-l-observateur-oublie-9782843016400.html

Why do people not have the slightest inhibition to disseminate half-baked ideas?

Dear Jurg,

Because a social network is not a journal nor a conference. it is the perfect place to disseminate half-baked ideas.

Mainz, Germany

Dear Martila,

You concentrate on the question of second derivatives. You wrote:

Why usually are no higher derivatives in the theory? I think it is linked with the fact, that inertial systems of reference are moving without acceleration. Thus, one shall only know the position and the speed.

---end quotation

However, I don't follow your reasoning here. Perhaps you could explain more fully what you have in mind. The Einstein field equations belong to GR, and GR concerns both inertial frames of reference (as in SR) and also accelerating frames of reference. Have you left something out here?

H.G. Callaway

Mainz, Germany

Dear all,

Here follows a short quotation from a 1954 paper by Niels Bohr, which strikes me as of interest for the present thread --in relation to the topic of meaning change in science. Bohr wrote:

The main point to realize is that all knowledge presents itself within a conceptual framework adapted to account for previous experience and that any such frame may prove too narrow to comprehend new experiences. Scientific research in many domains of knowledge has indeed time and again proved the necessity of abandoning or remolding points of view which, because of their fruitfulness and apparently unrestricted applicability, were regarded as indispensable for rational explanation. Although such developments have been initiated by special studies, they entail a general lesson of importance for the problem of unity of knowledge. In fact, the widening of the conceptual framework not only has served to restore order within the respective branches of knowledge, but has also disclosed analogies in our position with respect to analysis and synthesis of experience in apparently separate domains of knowledge, suggesting the possibility of an ever more embracing objective description (pp. 67-68).

---end quotation

The quotation comes from Niels Bohr (1954) “Unity of Knowledge” reprinted in Bohr (1961/2010) Atomic Physics and Human Knowledge. NY: Dover. pp. 67-82.

If we can imagine that the Einstein field equations have changed their meaning, in terms of Weinberg's argument, and various points in our subsequent discussion, then what Bohr has to say strikes me as a generalization of the kind of point involved. See what you think.

H.G. Callaway

It is NOT that Einstein's Field Equations have changed their meaning! They provide an astonishingly accurate description of space, time and gravitation, of the connection between curvature of space-time and gravitational fields, and of the motion of bodies and light in gravitational fields at macroscopic distance scales (of the order of milimeters). What HAS changed is our view of what a fundamental theory of space, time and gravitation might or ought to look like. We would say that the idea of a classical Lorentzian manifold as the right model of space-time will presumably have to be revised when it comes to describe gravitational effects at very tiny distance scales. Classical space-time only describes Nature in some limiting regime, albeit one that captures a great many phenomena that we are able to study experimentally. We don't really know what a successful starting point for a generalization of our concept of space and time will look like, although string theory provides a bag of interesting hints towards paths leading in promising directions. (For example, in classical differential geometry, curves are a fundamental building block. In "generalized geometry", it may be something like surfaces embedded into some "target" that may be fundemantal building blocks. - Who knows?) It would be important to extract from attempts such as string theory general conceptual ideas about what it is that we are trying to do. Some people have tried to do that. (It may incidentally be advisable to first better understand the fundamental message and contents of quantum mechanics, before attacking a unification of quantum theory with theories of gravitation.) But, unfortunately, most young researchers have to solve often fairly uninteresting, but technically challenging problems, in order to move forward in their careers. This brings me to the main point of my comments: It would be more important to debate whether the meaning of the endeavor of science has changed and whether the sociology of the scientific community has changed - they certainly have - than to meditate whether the meaning of Einstein's Field Equations has changed - it has not.

Mainz, Germany

Dear Fröhlich,

Many thanks for your forceful posting, above. You make your position abundantly clear, saying, the "meaning of Einstein's Field Equations ... has not" changed.

However, I do not see any argument which is nearly as clear or any detailed reply to Weinberg. Let me stipulate then, that so far as is known, no prediction of GR has every been found false on grounds of direct physical measurements. There is that much justification for being pretty conservative about GR. Even the prediction of gravitational waves, a long debated consequence, inspires continuing confidence among experimentalists--though gravitational waves have not yet been detected and for decades it was unclear whether they were a genuine consequence of GR. 

It is purely theoretical tensions or conflicts between GR and QFT which chiefly inspire attempts at "new physics" beyond the "Standard Model" of particle physics. There are many alternatives theories of quantum gravity, all more or less speculative, and very little direct evidence for deciding among them. But I do not think that the idea that the field equations have been reinterpreted depends on confirming any version of "new physics" beyond the Standard Model. What the change in meaning depends on is instead the motivational fulcrum on which all the new proposals seem to turn: the idea that GR breaks down in its prediction of singularities beyond the Planck length. Contemporary physics has come to the conviction that points of infinite density are not physically real, and in consequence the domain of application of GR, and the field equations, has to be limited. 

If theory T makes false predictions and theory T2 does not, then they cannot have the same meaning. But treating GR as a "limit" or "effective field theory" amounts to removing the undesired consequences.

That's the way I see it in any case. No doubt, other things have changed in science, too.

H.G. Callaway

The idea that General Relativity and the model of space-time it is based on (Lorentzian manifolds) are "effective theoretical descriptions" valid only in a certain range of scales, from millimeters (to be pessimistic) to scales of the order of the visible universe, and for phenomena that do not directly reveal the quantum nature of reality, appears to be standard, nowadays. I subscribe to it for reasons I could explain at length. (The arguments are somewhat analogous to those that say that Navier-Stokes equations provide an effective description of fluids valid on macroscopic scales and not taking into account their atomistic structure.) I don't see any point in further dwelling on these matters for ever. Let's move on and debate what's going wrong in the scientific community and elsewhere in the world - that's more important! Our situation is quite dramatic!

Mainz, Germany

Dear Fröhlich,

Thanks for your reply. Apparently you have no intuitions about change in meaning or "reinterpretation." But I see no dispute on the physics involved. 

You wrote:

Let's move on and debate what's going wrong in the scientific community and elsewhere in the world - that's more important! Our situation is quite dramatic!

---end quotation

This sounds like a different question than the one we have been considering. It might make a good topic for discussion. I think you should explain the kinds of problems and the dramatic situation that you see.

H.G. Callaway

Problems with General Relativity

http://cosmoquest.org/forum/showthread.php?15196-Problems-with-General-Relativity

''General Relativity does not predict the velocity profile of stars in galaxies, the gravitational rates of attraction between clusters of galaxies and groups of clusters of galaxies. One could even include the anomalous deceleration of the pioneer spacecraft.

In order to describe the motion of celestial objects based upon the application of general relativity (which includes Newton’s laws of gravity). A myriad of adjustments or assumptions have to be made in order for observation to correspond to theory.

i. The motion of celestial objects is not conforming to the predicted relationships of General relativity and Newtonian physics. Stars in outer parts of spiral galaxies are moving too fast to be retained in a stable orbit. To fix this it is assumed that there has to be extra dark matter somewhere preserving structure. No evidence of the necessary amount of dark matter has been directly observed. Dark matter’s existence has only been inferred.

ii. The centers of galaxies have stars rotating around each other so fast that it appears there must be huge black holes in the center of galaxies. No direct observation of these million solar mass holes have been observed. There existence has been inferred due to celestial rates of rotation and as an explanation for intense energy production.

iii. The amount of dark matter assumed to exist increases as the scale of observation increases. Dark matter in spiral galaxies, more dark matter for clusters of galaxies, and more dark matter for groups of clusters of galaxies.

iv. In order to expand space with all this extra dark matter, and to account for acceleration, massive amounts of dark energy has to be added to the mix to keep the universe expanding. There is some unseen or unaccounted for force expanding space. ''

Mainz, Germany

Dear Brassard,

You make an interesting posting, including a large array of puzzles relevant to GR. I hope that no one will feel obligated to offer solutions to them all here. These things can become quite complicated, and I would reiterate here, a point made in similar contexts, that the objective is not to do physics. I do not propose to second guess the established theory in physics, but instead to understand better what the physicists are themselves doing. Generally, I think we do best to take more or less established physics at face value, and work from there. It is partly in this spirit that I see a certain justification in conservatism about GR, for instance. 

This is not to say, of course, they nothing could be learned by working through the puzzles in the text you linked to. But what we would prospectively learn is some physics; while the generally accepted physics is good enough for present purposes. To make good use of the puzzles and questions on offer for present purposes, it seems important to determine their relevancy to the present thread. But you do not offer to do this. 

One point of possible relevance, however, is as follows. You wrote:

In order to describe the motion of celestial objects based upon the application of general relativity (which includes Newton’s laws of gravity). A myriad of adjustments or assumptions have to be made in order for observation to correspond to theory.

---end quotation

Of interest here, of course is the postulation of dark matter, which is understood, generally to be composed of particles outside the standard model of particle physics. What is needed is some explanation of the observed rates of rotation of galaxies and the movements within galactic clusters, which given GR, must have more mass than can be observed. One might indeed view this as a kind of "epicycle" added to GR to reconcile it with observation. On the other hand, alternative theories of gravity have also been developed, or are under development, as a matter of mathematical physics. Is this a "problem" of GR? Well, in a certain sense, it certainly is. Is it a refutation or clear falsification of GR? I don't think so. More to the point is that though well confirmed, GR is not beyond question--and rightly so.

As far as I know, observations by reference to gravitational lensing have tended to confirm the presence of dark matter in galaxies and galactic clusters. Obviously, this would be a quantitative result, and alternative approaches are not thereby ruled out of consideration. Confirmation would depend on an agreement between the observed lensing and the amount of curvature on the one hand, and the amount of dark matter needed to make the rotation/movement data square. 

But it is by reference to GR that we understand the very problem here; and general conservatism about GR serves that purpose as well. Lacking clear-cut failure of its predictions, that is how the situation will likely remain. But we don't get a change of meaning of the Einstein equations, as contrasted with a prospective or possible change, until and unless GR is restricted in its application in some fashion (or perhaps otherwise modified). In that way, this case differs from the considerations discussed by Weinberg.

H.G. Callaway

I don't know it is right but we can look also for DIrac equation and it's interpratation and how we take this equation. Oryginaly work of Dirac was taking Schrodinger eq. at present we take Dirac eq from marging QM and Special Relativity in QFT framework. The equations are the same but objects in equations not, so even if they "look" the same they are "speak" about something different thing.  i think that more understanding comes from "representations" of operators like wave equation and it's always classical interpretation. 

In : Absence of an Effective Horizon for Black Holes in Gravity's Rainbow

Ahmed Farag Ali, Mir Faizal, Barun Majumder

wrote that:

http://arxiv.org/abs/1406.1980

"The most important lesson from this paper is that

space and time exist only beyond a certain scale,"

Ali concluded. "There is no space and time below

that scale. Hence, it is meaningless to define

particles, matter, or any object, including black

holes, that exist in space and time below that scale.

Thus, as long as we keep ourselves confined to the

scales at which both space and time exist, we get

sensible physical answers. However, when we try

to ask questions at length and time intervals that

are below the scales at which space and time exist,

we end up getting paradoxes and problems."

 “rainbow gravity” posits that gravity’s effects on space and time are experienced differently by different wavelengths resolve some discrepancies between theories of general relativity and quantum mechanics.

Rainbow gravity theory predict the creation of micro-black hole in the LHC at energy level of 10 TeV. So this physical mathematical theory may soon be falsified or enter the realm of empirical science.

Philadelphia, PA

Dear Brassard & readers,

Illustrating the thesis that the Einstein field equations have changed their meaning, I think it generally best to stick to the least controversial developments modifying GR. Such we have in viewing GR as an "effective field theory." However, "Gravity's Rainbow" is apparently interesting enough to have engaged some of the  experimentalists at CERN, and it thereby recommends itself, though it is apparently not a widely held view. The key or central idea seems to be that gravity effects different wave-lengths of electromagnetic radiation by differing degrees of bending or curvature--on analogy with a prism. Whether this idea is consistent with the general approach to space-time in GR remains unclear to me. If gravity just is the curvature of space-time, then how could it be curved in differing degrees for different wave-lengths? The approach seems to treat gravity more like a force than is distinctive of GR.

I quickly read through the paper you quoted from and linked to in your posting. This kind of proposal apparently creates problems for elements of Leonard Susskind's reaction to Hawking on information loss. (See Susskind's 2008 book, The Black Hole Wars.)  The idea, however, that there is no black hole horizon, if it cannot be so precisely located as to defy the Heisenberg uncertainty principle seems to me, at first impression, to go too far. Still, the rejection of an infinite time, from the perspective of the distant observer, regarding something falling into a black hole seems reasonable, given a rejection of distance or spatial measurements beyond the Planck length.

In consequence there seems to be a general feature of the "Gravity's Rainbow" approach, viz., the introduction of minimal lengths and durations, by reference to the Plank constant--something found in alternatives to Gravity's Rainbow as well-- and which makes for similar problems in Susskind's criticisms of Hawking. It seems the infinite duration of objects falling into a black hole, for the distant observer, should go the way of points of infinite density at the singularity of a back hole.

I've watched some quite marvelous lectures of late on related themes. I'll see if I can't find a reference to some of these, or related papers, perhaps one at a time. One idea which seems worth exploring is that there is a "loss of locality" beyond the Planck scale --so that things still happen, or are, at least interrelated (and time is preserved) but the distinctness of locations of events or elements is lost into a kind of generalized inter-relatedness. Instead of ordered spatial relations in which A is next to B, and B next to C (but A is not next to C), say, A is equally in (some sort of ) relation to both B and C. While loop quantum gravity attempts to get along without time, at the most fundamental level, other approaches apparently attempt to get along without (full-blown) spatial relations. 

To reiterate your quotation, the following seems to me appealing:

Thus, as long as we keep ourselves confined to the

scales at which both space and time exist, we get

sensible physical answers. However, when we try

to ask questions at length and time intervals that

are below the scales at which space and time exist,

we end up getting paradoxes and problems."

---end quotation.

The idea that there are no length or time intervals "below the scales at which space and time exist" certainly calls into question the classical interpretation of the Einstein field equations --in light of quantum theory.

H.G. Callaway

Dear H.G. Callaway,

I am not understanding much of the rainbow gravity theory.  The idea that space - time would be different for different wavelenght or energy level is puzzling.  

In this scientific american article, http://www.scientificamerican.com/article/rainbow-gravity-universe-beginning/ it is said that the theory was pionnered by Lee Smolin and Joao Magueijo  http://arxiv.org/pdf/gr-qc/0305055v2.pdf

. Smolin is critical of the current interpretation of the rainbow gravity and see rainbow gravity as a particular case of a larger idea  called relative locality.

Wikipedia:

Relative locality is a proposed physical phenomenon that different observers would disagree on whether two space-time events are coincident.[1] This is in contrast to special relativity and general relativity in which different observers may disagree on whether two distant events occur at the same time but if an observer infers that two events are at the same spacetime position then all observers will agree.

When a light signal exchange procedure is used to infer spacetime coordinates of distant events from the travel time of photons, information about the photon's energy is discarded with the assumption that the frequency of light doesn't matter. It is also usually assumed that distant observers construct the same spacetime. This assumption of absolute locality implies that momentum space is flat. However research into quantum gravity has indicated that momentum space might be curved[2] which would imply relative locality.[3] To regain an absolute arena for invariance one would combine spacetime and momentum space into a phase space.

Philadelphia, PA

Dear Brassard,

Thanks for your further suggestion. Perhaps I should say, here, that it is not the point of this thread, so far as I'm concerned, to seek out named allies in action, for any particular purposes, but instead to examine the particular ideas stated above and what arguments can be offered in support or against them. 

If the arguments on offer above are somehow inadequate, on your view, please say how and why. That having been established, we might have reason to seek further illustrations. Otherwise, perhaps you think there is a different reason to want to examine further possible modifications of GR. If so, you might better say what those reasons are.

I do not propose to survey here, all possible departures from GR. I suspect that it is sufficient for purposes of this question and thread if it is recognized that many proposals have been made and some have been provisionally accepted. We no longer attribute quite the same status to classical GR, and though it has failed no empirical tests, and people are obviously concerned to save the successes of GR, its pretty clear, on theoretical grounds, that something has to go--especially at very high energies.

H.G. Callaway

The existence of black holes and their horizon, and Big Bang are the mathematics of GR and the other forces described by the mathematic of quantum theory.  These are theoretical objects that exist at singularities of the equations.  To beleive that the equations are valid at the infinite is to beleive into an infinite accuracy of these equations.  If there is a plank scale beyond which locality do not exist then it immediatly invalidate the equation at the plank scales and the theoretical existence of these objects as singularities cease to exist. There are plenty of experimental evidences that a very massive object lies at the center of all galaxies but none of these evidences necessarily implies that these massive objects are black holes, singularities in GR. There are plenty of evidence that the universe was before 13.7 billion years ago in a dense state but none of that necessarily implies that it was an initial singularities.  Someone has to believe in the infinite accuracty and adequacy of a mathematical model of reality and this require an infinite belief in science.  The only science I know is approximative and all approximations break down at infity.

Philadelphia, PA

Dear Brassard,

I believe that it is generally held that, consistent with quantum theory, there can be black holes, as predicted by the Einstein field equations, though the location of the event horizon be somewhat imprecise, to the degree required by the uncertainty principle; and likewise, the big bang theory is not objectionable on grounds of quantum theory alone, though the postulated singularity (whether of a black hole or before the big bang) is objectionable. You seem to be throwing the cosmological babies out with the overly idealized bathwater.

The idea is to recover something quite like GR, avoiding the singularities, at some limit of energy. length, duration, etc. GR has, after all, stood every empirical test to which it has been subjected.

H.G. Callaway

Dear H.G. Callaway,

GR and all other well established physical theories have been tested within a limited accuracy and in certain situations and these are thus valid within established accuracy in these specific situations.  I take it as a principle that a theory or its equations have a finite or limited accuracy.  If it is the case then any physical equation loose its meaning at its singularities because any finite departure of the representational validity of the equation become infinite and thus the equation become non representative of reality in these extreme situations.  It is a reasoning that I think hold for any physical equation.  So these elementary considerations on accuracy of a physical model prevent me to believe into the physical existence of black hole or an initial cosmic singularity. 

Regards

Philadelphia, PA

Dear Brassard,

I think we agree about the topic of "singularities," in general terms, and I would not be inclined to dispute your emphasis on theories having, prima facie, "a finite or limited accuracy." What I do not follow, in your recent postings, is your inclination to identify black holes with the alleged singularities of black holes; or correspondingly, the big bang with the alleged singularity of its origin. I do not see that you are making any argument for this, though I do not suppose that no argument is possible.

But let me see if I follow what you are currently saying. You wrote:

I take it as a principle that a theory or its equations have a finite or limited accuracy. If it is the case then any physical equation loose its meaning at its singularities because any finite departure of the representational validity of the equation become infinite and thus the equation become non representative of reality in these extreme situations.

---end quotation

I suspect that this is something of an over-reaction to the problems of contemporary physics. It may indeed be that "a theory or its equations have a finite or limited accuracy." (That is a general reason not to be dogmatic.) But I think that what concerns contemporary physics is more specific. It is specifically the success of QFT in particular, and the standard model of particle physics, which suggest that the singularities of GR, such as points of infinite density, are un-physical.  In the general case, it remains open to theory to interpret infinities in other ways. For example, if we are concerned with detection or observation of radiation "at infinity" in relation to a source, as with theories of gravitational radiation, then this seems to be regularly understood to mean something like "far away enough" that the observer is no effect on the source. In other cases, the interpretation of mathematical infinities may be left open to further consideration, but not always prejudged to be a matter of things of no physical concern or reality.

In any case, and however that may be, it does not seem to follow on the supposition of the un-physical status of the GR-inspired singularities of black holes that there are no black holes or no event horizons of black holes.  I am aware that Hawking has recently made some related claims, but if this is what concerns you, then I think we need to see the specifics of the arguments.

I take it that all measurements are of limited accuracy, though, of course, some are much more accurate and precise than others. But it has never or rarely been the established practice to qualify generalization merely in terms of the accuracy or degree of precision of supporting measurements. A ground of doubt that applies everywhere has little specific relevancy to any particular law or generalization. 

Again, regarding GR in particular there are situations or kinds of situations in which its predictions can be calculated and tested, and other where this is much more difficult. But the reasonable expectation is, for instance, that gravitational waves, say, will be detected. This is a reasonable scientific judgment.

To this point, they have not been detected. But hundreds of millions of dollars have been spent on the building and calibration of instruments designed to detect gravitational waves. Most physicists seem quite confident that they will be detected. It strikes me that if, in general, since,

As you put it,

GR and all other well established physical theories have been tested within a limited accuracy and in certain situations and these are thus valid within established accuracy in these specific situations.

---end quotation

if we conclude from these observation that GR is only valid with in its already tested  applications, then  this would seem to make non-sense out of the hunt for gravitational waves. It would be just as reasonable not to expect them. Moreover, it seems that on this supposition, the failure to detect gravitational waves, as predicted by GR would actually be nothing against GR!

You seem, then, to be headed off toward a very doubtful version of positivism equating a theory or its meaning with the evidence so far successfully accumulated. That, I take it, would be a mistake. On the contrary, it is just because GR does predict singularities, at the centers of black holes, say, and because we have reason to think that these could not be physical, that physicists think to modify GR--which in fact has, up to the present, never been found wanting in the tests so far made of its predictions. 

H.G. Callaway

The question whether there are black holes is not one of belief, Louis, but one of observational evidence! Giant black holes -- those expected to exist in the center of many galaxies, in particular of our milky way -- do not have very large space-time curvature at their event horizons. There is no reason whatsoever why General Relativity should not provide a very accurate description of such objects all the way from very remote space-time regions right down to their event horizons, (which is all one might ever be able to see as an outside observer). But the punchline of my remarks is that people such as Reinhard Genzel and his collaborators have gathered hard and convincing evidence that there actually IS a giant black hole near the center of our milky way! (Their data are on stars orbiting around an invisible center of gravitational pull.) -- I am not against philosophical reflection. There are good reasons to think about where we come from and where we are headed for and why we are so happy or unhappy. But when it comes to observing Nature and constructing models or theories organizing the observational material then it is not wrong to recall what Richard P. Feynman said about this endeavor: "It's not philosophy we are after, but the behavior of real things."

Philadelphia, PA

Dear Fröhlich,

This is also the way I understand the present evidence in astrophysics. Massive black holes are known to exist, with fairly direct observational evidence regarding the one at the center of the Milky Way. 

Regarding philosophy, there is a certain wisdom of later Wittgenstein to the effect that "Philosophy leaves everything as it was." At the least, it is not the office pf philosophy to dispute the results of the sciences. But clarification does belong to the goals of philosophy.

Still, we may wonder what Hawking, the theorist of the Hawking radiation and entropy of black holes, may have had in mind, more recently, in holding that there are no black holes.

Many thanks for your brief comments.

H.G. Callaway

Dear Callaway,

I am all in favor of philosophical clarification of many issues; (although, in general, not of issues that can be subjected to experimental and observational tests -- these can only be clarified by observations and experiments). Furthermore, I am all in favor of philosophical reflection. -- But I have always been a rebel disliking authorities. I don't imagine that Hawking has superior insights into the question of whether black holes exist or not. But should he have such superior insights one must hope that he will succeed in communicating his reasoning process. If not then feel free to keep wondering what he may have (had) in mind. Myself, I won't! I feel it may actually be more fun to wonder whether Pierre de Fermat had a proof of his "last theorem". In all likelihood, he did not; and in all likelihood Hawking does not have a convincing case against the existence of something like event horizons surrounding regions in space where an invisible object exerts a strong gravitational pull on visible objects near that region -- objects one customarily calls black holes. -- It's time to return to the drawing board!

Philadelphia, PA

Dear Fröhlich,

Thanks for your further comments.

Though I have placed a methodological emphasis on established or accepted theory and results, this is not to be taken as anything dogmatic. The aim is to better understand what is, in fact, going on within contemporary theoretical physics. I assume that such clarification may be useful and welcome, both to the defenders of existing or established views and to the rebellious critical inclinations of others. It seems clear that before anyone enters into a serious criticism of established theory and results, they may better want to be clear on exactly what they wish to place under criticism. For those disinclined to authority, I would encourage them first to clearly state what they aim to criticize, ideally so as to clearly capture what is involved.

I must certainly admit to some considerable admiration for Hawking's accomplishments, and I think there can be little doubt that they enter very significantly into the contemporary nexus of GR and QFT. But basically, it is Hawking's significance in contemporary physics and contemporary developments, which chiefly concerns me. I did read his short recent paper, but I offer, to this point, no comments on it. I wonder if we will hear from Brassard on this.

Lastly, I would say there is some, often more limited, role for philosophical clarification, even regarding issues subject to experimental and observational tests. A classical example is Eddington-like observational evidence in support of GR. I would say, in such cases, that we basically only understand the significance of the observations supporting GR in light of the theory. If we had only Newtonian theory to work with, I suspect that no one might even have thought of making the observations. Still, both the Newtonians and their critics could make the same observations, and see their relevancy, once an alternative theory of gravity was in hand.

Even the observational evidence for a black hole at the center of the Milky Way, surely depends on some sort of theory of orbital motions, and there would be no calculation of the mass of the central black hole, or even the very concept, in total independence of physical theory. To hold to the contrary that this is something purely observational simply takes the relevant theory for granted without proper acknowledgement of its needed role in the interpretation of observational data.

Perhaps you'll agree.

H.G. Callaway 

Philadelphia, PA

Dear all, 

I want to make available to those who have followed this question and thread the outline which I used for my presentation at the recent Boulder Conference on the Philosophy of Science at the University of Colorado in Boulder. (The paper itself is still a work in progress.) 

See:

https://www.researchgate.net/publication/309591694_Have_the_Einstein_Field_Equations_Changed_their_Meaning_General_Relativity_as_an_Effective_Field_Theory

This is an expansion of the outline I spoke from in my presentation this past July at the Foundations2016 conference at the LSE in London. I've added a short section concerned with renormalization. 

Comments invited.

H.G. Callaway

Conference Paper Have the Einstein Field Equations Changed their Meaning? Gen...

Dear Callaway,

1. 4  Flat space is not representative of Newtonian physics since flat space is a space without masses.

https://en.wikipedia.org/wiki/Newton%E2%80%93Cartan_theory

VI H.  An experimental deviation from theoretical expectation extremely rarely lead to a paradigm change.  And the Eddington expedition was successfull at help the paradigm change to GR only because GR was already available and making a prediction that was totally counter intuitive in Newtonian physics and this prediction was testable.  Apparently Eddington results should not have been conclusive given that the gravity effect was not clearly detected given the level of accuracy of this experiement.  It was dam ready to fall and it is why it was not pointed out.  

Dear H.G.

Let me slightly change the subtitle of your work: Classical Mechanics as an effective theory (which is quantum mechanics?). It seems that the answer is no, because these are two radically different theories, one of which uses the term trajectories, and the second uses only probabilities.

With regards

Jerzy Hanckowiak

'I don’t know,” he writes, “any place where Einstein explains the motivation for this assumption.'

I believe it is in the letters of Einstein with Herbert. Second order was the most his method could contain and still remain covariant.

It means that at extreme high energy GR is expected to give wrong predictions. It leads to TGD and other high energy proposals that use different math and allow extreme folding of space time more than a second order equation.

In my project last year for high speed transport in deep space, one of the conclusions was that constants become variables at high speed, except Planck constant remains constant over the range where GR is accurate.

Hierarchy of Plancks is the mechanism preferred in Squeezed Quantum States and Scale Relativity to make predictions about the ultimate failure of GR in prolonged acceleration. It requires an understanding of velocity different from the original GR. Cosmic Microwave Background is proposed by some famous scientists and reputed by others as a zero speed reference frame anywhere.

There are differences of opinions about original GR preferred by some researchers and present of revisions by others. Stephen Hawking and Roger Penrose made first serious deviation from original GR understanding. The field equations give a black hole no volume contained inside and nothing at all except a singularity distorted by curvature no matter how large the event horizon may be.

Hawking and Penrose in Nature of Space and Time gave new meaning to black holes. First black holes are only black from a great distance. Up closer they may be red, blue, or white hot. Second the black holes are in equilibrium with their surroundings by showing a black body radiator profile from great distance.

A number of other researchers have elaborated on the inside of an event horizon, and the fate of black holes in collapse of a false vacuum.

In answer to the question, there is gradual change of understanding by some researchers, and a rigid support for the original field equations by others.

The question is important for ultimate survival of the human race, in which the original GR points to extinction and some variations point to continuation.