No, because it isn't true. General relativity does *not* assume that the speed of light changes, if the gravitational potential changes.

Actually, GR doesn't *assume* that the speed of light doesn't change, it *deduces* this from the assumption that Einstein-Hilbert action only involves the metric tensor and its derivatives, therefore one shows that at any one point one can work with Minkowski coordinates-where special relativity is valid-it's this result that shows that local inertial frames can, indeed, be defined.

The local speed of light in vacuum is c (celeritas). The mean global proper speed can be greater than c.

The ``mean global proper speed'' can't be unambiguously defined.

Hi Stam

To understand what I mean with the ``mean global proper speed''

I develop my previous email and I add one reference.

Of course, the local speed of light measured in a local linertial frame in vacuum in obviusly c in accord with general relativity.

However, the averaged or global speed of light can be greater than c, due to the fact that the average velocity of light over a finite path measured by different observers is not necessarily equal to c.

As a consequence of the time dilation in gravitational fields, this global speed can be greater or lesser than c.

See, for instance arXiv:1110.0813

Indeed-because, in a curved space-time, the relative velocity of two observers depends on the path, along which the velocity was transported from one to the other. So it cannot be unambiguously defined. This is a standard result in general relativity.

Indeed-I'd rather consider the Einstein-Hilbert action as input and Einstein's equations as output, than the other way around. At the ``classical'' level we're discussing this is, of course, a matter of taste and convenience. Whatever one does, however, the important point to take away, is, of course, that, at any given point, one can set up a Minkowski coordinate system and recover special relativity. How one does it is not that important.

Dear all

Thank you for your nice participation. My question is not about changing the speed of light locally because this is already known that speed of light is constant locally. What I meant is globally. can any wave at speed of light moves at a gravitational field with constant speed equals to c as measured by an observer out of this field?

I know you may say that general relativity assumes that the speed of light in vacuum must be changed because if the gravitational potential is changed and that the equations of general relativity are proven experimentally, but can we reformulate these equations assuming the constancy of speed of light globally not just locally?

sorry for late comment I was slightly busy in previous days.

thanks

Once more: in a curved space-time the relative speed of two observers that aren't at the same point cannot be unambiguously defined-it depends on the path used to parallel transport the velocity 4-vector from one to the other. Therefore the answer is No.

In the Theory of Reference Frames only the "physical speed" of light is constant and therefore it is a local constant with respect to the reference frame where the speed is measured. The relativistic speed and the speed in the gravitational field aren't constant.

I think that in the discussion we are mixing different concepts of speed of light with "relative" velocities v. gr.:

1º.- The local speed of light in vacuum measured in a local inertial frame in always c in accord with GR.

2º.- The averaged or global (proper) speed of light measured by an observer at he final point of a path can be lesser or grater than c.

See the reference in the my previous email and this another one:

PHYSICAL REVIEW D 85, 047501 (2012)

3º.- The "coordinate " speed of light lesser than c due to the Shapiro time (coordinate) delay in the presence of a grtavity field.

4º.- The "relative" velocity between two different observers is another matter and it has, in general, four different definitions, see for instance arXiv:gr-qc/0506032

I'd have thought these are standard exercises in a general relativity course-cf., for instance, Sean Carroll's lecture notes: http://arxiv.org/pdf/gr-qc/9712019.pdf

Dear all

I promised that I will up vote any answer in this question which has been down voted by someone we don't know. please feel free to participate we are not in a fighting here we just want to catch the reality, so please leave the down voting. if you want to say something just say it you may be right otherwise let the others participate.

Dear all

I would like to thank you for your nice answers. So we are agreed that speed of light is constant locally of course this what GR stated, but globally No. now let's move to an important point if a clock is moving at speed of light in a variable gravitational potential, will the clock encounter time dilation or not? according to GR and according to your opinion? if it is not agreed with GR please give it separately.

thanks

In the order of the Theory of Reference Frames (TR) a time relativistic effect has been demonstrated, but it is different with respect to time dilation considered in SR and GR.

In TR the time relativistic effect doesn't have kinematic nature, like in SR and GR, but is related to the variation of electrodynamic mass. Consequently not all physical systems have a time relativistic effect but only those systems that have electrodynamic mass like charged elementary particles.

Electtrodynamic mass changes with the speed and this variation of mass produces a time relativistic effect. Motion of a charged elementary particle in a gravitational field happens with variable speed and therefore a time relativistic effect exists for these particles.

This effect regards the internal characteristic clock of particle and doesn't regard the kinematic clock of the gravitational field. In fact for physical systems that don't have electrodynamic mass, like ordinary masses, that relativistic effect of time doesn't exist.

Experiments have proved gravitational field works on light.

Indeed, gravity does bend light-but this doesn't affect the speed of light.

Yes, because you think gravity bends space-time but it has to be still proved.

Light it self can be considered as clock throgh its frequency.

Its obvious that the frequency will be changed but remember

our clocks ticking rate is also changed within such varying gravitational potential.

So which clock is really varying in its rate in such potential?

That gravity bends spacetime has been shown, among other ways, (precession of the perihelion of Mercury, to cite just one example), also, through the variation of the period of the binary pulsars, which is an, indirect, detection of gravitational waves. Gravitational waves could not exist, if gravity did not affect spacetime

(cf. http://arxiv.org/pdf/gr-qc/9712019.pdf p. 149 and following).

What this *means* is that ``test particles'' in such a spacetime are affected.

And, once more, there were measurements of the period, these were compared to calculations, made on the basis of the full Einstein equations and the agreement is impressive-cf. the Nobel Prize in Physics to Hulse and Taylor in 1993, http://www.nobelprize.org/nobel_prizes/physics/laureates/1993/

While many measurements are ``weak field'' measurements, where the linearized equations have been used, ``strong field'' measurements, that test the non-linear aspects are reviewed here: relativity.livingreviews.org/open?pubNo=lrr-2008-9&page=articlese5.html

Gravitational lensing is the prototypical example where a gravitational source (RHS of Einstein's equations) affects spacetime (LHS of Einstein's equations)-and, in this spacetime, a ``test particle'', that follows a null geodesic, i.e. light, is affected:

http://astro.berkeley.edu/~jcohn/lens.html

Regarding clocks: cf. http://arxiv.org/pdf/gr-qc/9712019.pdf p. 109 and following.

A general theory would be able to explain also precession of the perihelion of other planets (Mars, Venus, etc.). The statement "Gravitational waves could not exist, if gravity did not affect spacetime" is altogether arbitrary. Anyway if the curvature of

spacetime is for you a satisfactory theory I don't intend to continue to squabble.

Best regards.

Nowhere has it been claimed that the other planets' perihelion doesn't, or can't, precess-simply that this precession is much more difficult to measure. It's a practical issue, not a conceptual one. The expressions for the precession aren't constructed *for* Mercury-they apply to any test particle.

Cf. for instance: http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node115.html

(for the Newtonian case-the relativistic correction for Mercury is given)

and

http://www.iap.fr/activites/seminaires/GReCO/2011/presentations/LePoncinLafitte/leponcinlafitte.pdf

for more tests on ``post-Newtonian'' parameters.

In fact the quadrupole moment of the sun has been measured and the consequences for the perihelion precession of Mercury are discussed here: http://arxiv.org/abs/astro-ph/9804258. The results for the ``post-Newtonian'' parameters are consistent with general relativity.

Dear Stam and Robet

I have no dought about space time curvature near gravitational potential,but I

think there is misunderstanding to the question. The question is about the

origin of the changing of frequency of the speed of light

wave in variable potential, is it due to changing the frequency of the wave itself or due to a difference of the clock ticking rates between the source and the observation region.

I hope it s clearer now.

In a curved spacetime, once more, it's not possible to compare the ``ticking rate'' of clocks that are not at the same point, since this rate is a component of a 4-vector. So, indeed, it's due to the curvature of space-time itself. I'd recommend, once more, the reference I gave in a previous message: http://arxiv.org/pdf/gr-qc/9712019.pdf p. 109 and following.

Dear Stam

The curvature of space time affect what ? the ticking of the measureing clocks or the ticking of the wave that moves at speed of light? this is a specific question,

please don't mension papers, just give the answer according to your understanding, because I want this specific point please.

Thanks

The curvature in space time is a means to represent the forces we encounter in nature through mathematical means that we can comprehend. Curved space time is a representation of the force of gravity and the effects on anything withing it's field or curvature. It has been proven time and time again that gravity does affect electromagnetic waves, and that clocks are affected by space-time drag, or frame dragging. Perhaps in the future someone would come up with another better representation but now Relativity and space-time is the best we have. So since it has been shown to represent reality it is no longer an assumption but the truest representation we have so far.

Dear Dr. Edwin,

I appreciate your non-dogmatic position.

Dear Edwin

I have no problem with space time curvature or assumtions of GR. I only try to

understand the interaction between wave at speed of light and two observational

clocks at different gravitational potential with gravitational potential changing.

Specially I want to know is the wave really affected by changing gravitational potential or our clocks which are only affected.

Regards

Dear Sadeem,

I have some difficulty to answer your question because I have a paper in progress just on this subject. I can give only some advance information: in actuality I am proving, in the order of the Theory of Reference Frames, the speed of light is affected by gravitational potential and therefore, also if in small manner, it changes in an useful space of the gravitational field. This effect isn't relativistic and therefore it has nothing in common with the Doppler effect. Relativistic effects of time aren't kinematic and are connected only with variations of electrodynamic mass. When my paper will be ready (in May), I will send you a copy.

Dear Sasso

Thank you for sharing some infirmation of your paper,I will be waiting to it.

Thanks

Dear Robert

Thank you for your effort. The importance of this question

is attempting to understand the weak point of GR which is near its singularity.

This start from understanding the mechanisim of light gravitation interaction

and chequing the consistency of basic principles adopted in GR.

There is no harm from asking such questions , because they can give new ideas.

Regards

Sadeem

The singularity of a Black Hole as I understand it is merely a projection of the tangents along the event horizon. There is a researcher in Denver university, that is studying this, I have not read his papers as of yet, but have seen an article. One of his ideas is that time reverses at the even horizon, and considering greens and stokes theorem, tat has possibilities. You may wish to check it out. It is great reading all your comments and questions, helps in understanding a great many things. Thanks

Thank you Dear Edwin

I think GR is a huge work if you want to solve its

singularity, this needs a team work not just from

the professionals in the field but also from other

related fields.

There are no evidences to prove black holes are true, only pulsars or magnetars have been found in the remains of supernova explosions. Even the so called supermassive black holes can spurt jets of massive particles. So the theory to solve the singularity problem of GR has to explain those phenomena at the same time.

For a recent review about astrophysical black holes, cf. http://arxiv.org/pdf/1312.6698v1.pdf

For singularities and general relativity the paper by Hawking and Penrose,

http://rspa.royalsocietypublishing.org/content/314/1519/529

is extremely well written.

According to GR, a star with 40 times solar mass should turn into a black hole, but in reality it turned into a magnetar.

http://www.space.com/755-origin-universes-powerful-magnets.html

Stephen Hawking: 'There are no black holes'

Notion of an 'event horizon', from which nothing can escape, is incompatible with quantum theory, physicist claims.

http://www.nature.com/news/stephen-hawking-there-are-no-black-holes-1.14583

Whether a star will collapse to a black hole depends on many factors-as mentioned in the review, there are objects consistent with black holes at lower fractions of solar masses.

And the paper on the magnetars doesn't say that a 40 solar mass star *must* become a black hole, but, instead, became a magnetar-the fact that it did isn't in contradiction with general relativity.

Regarding Hawking's statement, the way it is presented is, in fact, such an oversimplificaton as to distort the meaining of what he did write. I'd recommend reading his 1970 paper with Penrose, then his 1974 paper and then his own, latest paper and not rely on news summaries.

For astrophysical black holes, described by general relativity, which is a classical theory, the quantum effects of Hawking radiation are, anyway, very small-that's why it's, in practice, not possible to detect it.

I just want to share this interesting discussion with the fans of GR.

In 1915 Emmy Noether demonstrated that the conservation laws are consequences of properties ("symmetries") of the space and time.

Briefly :

- Homogeneity of space -> Conservation of momentum

- Isotropy of space -> Conservation of angular momentum

- Uniformity of time - > Energy Conservation .

These 3 symmetries are always present in Galileo-Newton space as in Minkowski space.

The General Relativity theory requires the loss of these symmetries to explain gravitation. Only the space isotropy may be possible with spherical symmetry condition (Schwarzschild), but this is a particular case.

Therefore, the Universal Principles are not valid in GR.

No, general relativity means that space-time symmetries are *local*, not *global*.

Does that mean the conservation laws are valid only locally but not globally?

The energy-momentum tensor is, indeed, *covariantly* conserved (i.e. using the covariant derivative, not the ordinary derivative)-so conserved charges (like mass or charge) can be unambiguously defined only at infinity-or on appropriate boundaries, if present.

How can you call those are conservation laws if they are just valid locally?

Precisely because there is a way to define quantities at infinity, or boundaries, that can be identified with conserved charges. This is explained in all general relativity courses, cf. Carroll's lecture notes, for instance.

In fact it's not special to general relativity-except for the property that these are space-time symmetries. In Yang-Mills theories the (internal) symmetry currents are covariantly conserved, also, since the particles that transmit the forces are, also, charged.

Curved space-time is impossible to be compatible with - Homogeneity of space - Isotropy of space - Uniformity of time.

Of course curved space-time can be compatible with homogeneity, isotropy of space and homogeneity of time; that's a consequence of what Killing showed, for instance. Cf. http://arxiv.org/pdf/gr-qc/9712019.pdf, p140 for example.

Fortunately we are not living in a universe defined by Friedmann-Robertson-Walker cosmology.

The curved space-time defined by GR is impossible to be compatible with - Homogeneity of space - Isotropy of space - Uniformity of time.

I have no interesting on pure math problem.

Why should I believe a text book telling me the conservation laws are valid only locally?

I am not a fan of GR who will give up the conservation laws in anyway.

Curvature of space-time is based on a tensor that defines an imaginary, linear or nonlinear, space-time element. In SR the speed of light cannot be exceeded because greater speeds involve imaginary masses, imaginary contractions, imaginary dilations. This principle instead isn't valid in GR where fundamentals are described just through imaginary quantities. See for example: http://arxiv.org/pdf/gr-qc/9712019.pdf .

What is impossible in a theory cannot be possible in another theory.

Dear all

I think the problem with GR is represented in its singularities which make it give

inconsistent solutions at such ranges. The problem is these ranges may

represent the key word in solving many mysitries like conservation laws globally applicable or unification.

No. First of all, there isn't any issue with conservation laws in general relativity-this is known and understood and is the topic of all general relativity courses.

(There are some subtle points, but they go beyond, rather than call into question, what is known and taught.)

Next, the singularities in general relativity are part of the theory-and this was most clearly set forth in the work of Hawking and Penrose in 1970, cited in a previous message.

http://www.worldscientific.com/doi/abs/10.1142/9789814504782_0047

The paper is also available on RG.

https://www.researchgate.net/publication/260490155_The_Theological_Basis_of_Big_Bang_Cosmology_and_the_Failure_of_General_Relativity

Article The Theological Basis of Big Bang Cosmology and the Failure ...

Robert Low,

We are living in a flat space-time universe, so I think the gravitation law of Newton still the best theory of gravitation, it might just need a little bit improvement from some proposals as below:

http://arxiv.org/abs/1001.0785

http://file.scirp.org/Html/16-7500855_23098.htm

Dear Robert and Stam

The singularities of special relativity and General Relativity form real obstacle on the way of solving many mysteries in physics. Even the black holes part include many fatal principles like the singularity in time which means the discontinuity in it. that's extremely illogical.

@Guoliang Liu

Have you read Kip Thorne's "Black Holes and Time Warps" book?

Chapter 11 "What is Reality?" argues that for most situations, whether we choose to model physics by assuming flat spacetime and light-warping gravitational fields, or by assuming curved spacetime, is irrelevant - if we can mathematically "map" between the two descriptions without losing anything, then both descriptions must be functionally identical, and statements about which type of universe we "really" live in become meaningless.

I guess that there may be extreme areas where the correspondence could break down, but most people who assert a strong preference for one description or the other probably aren't studying those areas.

Being able to jump between the two descriptions is useful, because some effects are very obvious in one description and aren't so easy to see in the other.

Eric Baird,

The electroweak coupling constant is a variable dimensionless constant, which implies the principle of general covariance is breaking down in microscopic scale. So it is impossible to fit the quantum theory into the framework of general relativity based on the principle of general covariance. We have to assume all of our measurements are referring to a clock sitting in the universal flat space-time reference frame, which is sitting infinitely far away from any gravitational fields, but still should be full of Higgs fields. Actually it is the only valid inertial reference frame in reality; if we talk about time dilation without referring to the preferred reference frame, then it can only lead to all kinds of paradoxes. By the way, general relativity curved space-time is incompatible with homogeneity of space; isotropy of space; uniformity of time, and will violate the conservation laws associated with those symmetries.

Hi Sadeem!

Actually, the idea that the speed of light depends on the gravitational environment goes at least as far back as Isaac Newton, and possibly further.

Newton's "Big Idea" for unifying various branches of physics was to treat the density of the aether (which he suggested might be either particulate or non-particulate) as being a function of the density of the gravitational field - gravitational attraction was then the result of particles being steered by a variation in the refractive index of the underlying medium due to gravitational field density.

Essentially, what Newton proposed was what we'd now think of as a curved-space model, complete with a little diagram of a particle being deflected and turned around (total internal reflection) by a gradual difference in refractive index that represented a gravitational field, giving the particle a parabolic trajectory.

Newton's argument led directly to the prediction of gravitational shifts (John Michell, 1783), and from there it was just one tiny additional step to show that gravitational shifts required gravitational time dilation (Einstein 1911). Once you have gravitational time dilation, then you know that any attempt to model gravity as curvature (like the ill-fated attempts of Gauss et al) have to be applied in four dimensions rather than three, and at that point, you're dealing with something that looks very like a modern general theory of relativity.

Einstein's early 1911 derivation of gravitational time dilation didn't rely on special or general relativity, it was a Newtonian derivation, so these arguments demonstrably aren't specific to our current general theory of relativity.

--Historical background--

Really, we should have derived gravitational time dilation back in 1811 rather than 1911, which would have meant that smart guys like Gauss in the C19th would have known to apply curvature in 4D rather than 3D, and developed a different four-dimensional theory of spacetime curvature to the one that we have now, without special relativity. Which would have been interesting.

The reason why we didn't is because of a screwup, and because of industry politics. It turned out that Newton ****ed up a basic relationship, and used the results in all his more advanced work. He assumed (reasonably but wrongly) that "bigge" particles and wavelengths carried more energy than small ones, and that this was why red light found it easier to jump across a barrier than blue. That inversion then got carried over into his aether model, so he had to describe the speed of light being faster in denser media rather than slower, and that in turn meant that instead of describing the metric-defining medium as being the gravitational field (as Einstein later did), Newton had to describe it as being //displaced// by the field - the inverted energy relationship meant that Newton's spatial densities were inverted, too.

English physicists didn't spot the mistake, and when the "continentals" used wave theory to predict that the speed of light needed to be /slower/ in glass than air, English physicists mocked them and argued that if wave theory disagreed with Newton then wave theory was wrong (even though Newton had described a "dual" relationship). "Wave theory" people were retards!

So the English guys bet their professional reputations on the idea that lightspeed was faster in glass then air, and when experiments showed the awful truth that this wasn't correct, there was a cover-up to save everybody's reputations. Histories tend to deal with this episode with a one-line sentence mentioning the drawing of a "discreet veil" over the issue to protect Newton's reputation, but given the unnecessary rift between the English and continental guys, eliminating references to the collective English physics community's screwup was quite a self-serving thing to do.

Unfortunately for all of us, the cover-up was thorough and very successful, to the extent that most professional English-speaking theoretical physicists nowadays seem to have no idea how far Newton got, or how he then cocked the thing up.

Part of the coverup involved eliminating references to anything that mentioned Newton's faulty work, and unfortunately John Michell's important pioneering piece on gravitational shifts and gravitational horizons had referenced one of Newton's offending passages, so Michell's piece disappeared from his posthumous bibliographies and profiles, even though it had been published in the Royal Society's journal (which was about as high-profile as you could get at the time for an English-language piece). Michell's work didn't seem to enter the mainstream citation chain until the 1960s, a somewhat unfortunate delay.

-----

So, if you're interested in the fundamental relationships between lightspeed descriptions and general relativity, unfortunately, almost everything that you read about the history and origins of the subject, and how GR compares with Newtonian theory (which has knock-on implications for testing methods and assessing the significance of results), is wrong. And nobody wants to tell you that it's wrong, because either they honestly don't know, or because it's professionally embarrassing to have to admit that the current format of our subject was partly shaped by a bunch of English physicists in the early 1800s who behaved like arseholes, and then suppressed information to save their reputations, and ended up f***ing us over.

The professional misconduct of those guys may have held back parts of gravitational physics for a century , and may even have ended up with us adopting the wrong theory. We're still dealing with the mess they left behind. And the b*****ds got away with it.

Hi Eric Baird

I agree that there was an interval of time that made the physics community at that time accepted or stick with theories that have some decrements in it. Nevertheless, there is no problem in accepting new theories, but the problem is in sticking with its concepts and considering it as a perfect and can't be made to be better, that's what really kills developing. I think there are many decrements in GR that needs to be completed and others that need to be modified, but just little researchers that think about that, because most researchers are attracted in applying GR not in modifying it!!!

@Guoliang, about conservation laws in GR: this is a quite difficult question.

First of all, a "covariant conservation law" nabla_m T^mn = 0 is simply an incorrect or at least confusing naming convention but not a conservation law, not even a local one.

But, on the other hand, there is some sort of energy conservation, but a very strange one.

Simply choose one system of coordinates and name it, without reason, the preferred one. Once the whole theory has diffeomorphism symmetry, part of this is also translational symmetry along the "preferred coordinates". And so you can apply Noether's theorem and obtain some conservation laws - standard conservation laws, with usual partial derivatives, partial_m (T^mn + G^mn)=0, written in these preferred coordinates. Here, the G^mn is some energy of the gravitational field.

But this depends on the choice of the preferred coordinates. Use other coordinates, and you obtain other energy densities of the gravitational field. Thus, according to the philosophy of GR, which requires to ignore everything which does not transform like a tensor as non-physical, these so-called pseudo-tensors cannot have any physical meaning.

On the other hand, whenever we make a computation, we have to use some coordinates anyway. And in these coordinates nobody can forbid us to use this pseudo-tensor. Thus, we have also a conservation law, for all practical purposes related with energy conservation everything is fine.

As a consequence, if one considers, for example, the post-Newtonian parameters (an approach used to compare different theories of gravity with observations in Solar systems and so on, there are also parameters which are connected to violations of energy or momentum by the given theory. From point of view of all these parameters, GR looks like a theory with energy and momentum conservation - to use this approach, one has to fix the coordinates of the solutions anyway, and then the pseudo-tensor works nicely.

Thus, we obtain a strange situation: On the one hand, GR does not predict any violations of energy or momentum conservation. On the other hand, the very conservation laws, which causes these conservations, are something conceptually incompatible with GR interpretation, thus, according to this philosophy GR does not have conservation laws.

If one thinks that all GR has to do is to fit observation, everything is fine - GR predicts some sort of energy and momentum conservation in agreement with observation.

If one thinks that energy and momentum conservation is something more fundamental, a deep insight into Nature, and that behind energy and momentum conservation something real - some real energy or momentum - has to be hidden, instead of energy conservation being a nice mathematical accident, then there is no energy conservation in GR and it should be modified.

Thanks Ilja another question what about speed of light is it affected by gravity or remains constant? can the ether move at speed of light in the absence of gravity? or in certain conditions thanks

Dear Sadeem, as long as somebody searches for GR validation, the failure is always present... What I cannot understand till now is why haven't we abandon GR yet. Any idea?

I don't know either, may be due to the high attention that it was attracted during the 20th century. Nevertheless I think the efforts that are payed to replace the GR are not enough because most of them are single works and no institute works or grants are payed towards this direction.

So, we can agree that no kind of 'a step forward' will be done in near future, just for scientific political reasons. Our hope is that after so many years and by using open platforms like RG, all past theories that are still on 'use' (usage and GR are incompatible words), will be rejected from scientific community and the strong political support for them will start to decrease...

Meanwhile, I don't think that it is good idea for somebody to work in GR field and try to publish his/her negative arguments against GR... He/she will never be published in a serious journal...