Vanishing of the Ricci tensor does not mean that the metric tensor vanishes. It does not even mean the metric is flat. (Some components of the Riemann tensor may still be non-zero. An example, where the Ricci tensor vanishes almost everywhere but spacetime is curved is the Schwarzschild solution.) Moreover, in the equations with non-vanishing cosmological term, the Ricci tensor will of course not vanish in vacuum. The "dark energy" will curve spacetime in that case. There are of course still solutions with zero average curvature, but these do not have Tμν=0, because there is matter in the universe and the standard Friedmann equations include the Tμν corresponding to the average matter density.

On the other hand, for Λ =0, Rμν =0 does not imply gμν =0. The Einstein equation is a partial differential equation, the solution of which depends on the boundary conditions. So gμν =0 is a solution, but an unphysical one. A frequent strategy in looking for solutions is to require them to become Minkowskian at infinity. That will exclude gμν =0 as a solution.

SW: Secondly, where is the dark matter? It should pervade the void

It is called "matter" because it behaves like matter, it isn't evenly distributed but clumps together due to gravity. The density profile of a dark matter halo should therefore be governed by the Virial Theorem. Think of dark matter particles in a halo as looking like tiny stars in a globular cluster, if only we could see them.

https://upload.wikimedia.org/wikipedia/commons/6/6a/A_Swarm_of_Ancient_Stars_-_GPN-2000-000930.jpg

Being just matter, they enter the SET in the usual way.

Vacuum regions contain gravitational field which itself contains energy. Void regions of universe also contain microwave background, which is a mass-less electromagnetic radiation which contains energy. CMBR contributes by the relation, Tμν = [FμαgαβFνβ -(1/4)gμνFδσFδσ] /μ0

Sofia,

It is far easier to derive the behavior of dark objects from a second order partial differential equation such as the wave equation. I suggest that you look at "Dark objects"; Preprint Dark objects

The docx versios is http://www.e-physics.eu/Dark%20objects.docx

The paper applies quaternionic differential calculus. It is not copyright protected, thus you can use the formulas. They fit in the editors of most discussion sites.

You may be interested in http://www.e-physics.eu/__QuaternionicDifferential.docx

Thanks, Hans,

But in matters of general relativity I am an ignorant. I have no means of judging if the equations you indicate are better than Einstein's equations.

Now, look what's written in Wikipedia https://en.wikipedia.org/wiki/Cosmological_constant

"Since the 1990s, studies have shown that around 68% of the mass–energy density of the universe can be attributed to so-called dark energy. The cosmological constant Λ is the simplest possible explanation for dark energy, and is used in the current standard model of cosmology known as the ΛCDM model. While dark energy is poorly understood at a fundamental level, the main required properties of dark energy are that it functions as a type of anti-gravity, it dilutes much more slowly than matter as the universe expands, and it clusters much more weakly than matter, or perhaps not at all."

Also, as we know, the cosmological constant in Einstein's equations and that calculated with QFT differ by 120 orders of magnitude. That's funny. By QFT, the universe should consist exclusively in dark energy.

Dear Sofia,

When you speak about a Quantum Field Theory in this context what is mean is that the energy is just an excited state of a given theoretical "field", which is not really physical (at least from my knowledge). it is just a mathematical structure as the spacetime actually is. I'm very scheptic of what is understood by the percentages of Dark Matter or Dark Energy that the specialists in cosmology say and it would be fantastic if anybody could explain your results (in Wikipedia) in understandable form for people not devoted to this "field" of knowledge.

Sofia,

Physical reality archives all its dynamic geometric data in a series of intertwined quaternionic separable Hilbert spaces. For example the life story of each elementary particle is archived in the eigenspace of a dedicated footprint operator in its private separable Hilbert space. Quaternionic eigenvalues are ideally suited as storage bins of a combination of a time-stamp and a three dimensional location. An elementary particle is a point-like object that hops around in an ongoing stochastic hopping path. This path recurrently results in a coherent hop landing location swarm. A location density distribution describes this swarm and equals the square of the modulus of the wavefunction of the elementary particle.

Elementary particles have no limbs. They can interact with other objects via the field that embeds them. The transfer of information via the field affects the information that observers can perceive. A Lorentz transform describes the conversion of the Euclidean storage format into the spacetime format that observers perceive. The Lorentz transform is a hyperbolic transform that introduces time interval dilation and length conversion. This transformation converts the coordinates from the observed scene to the perceived information. The information is further influenced by the fact that the hop landings of the elementary particles can deform the carrier field. Thus the field that transfers the information is no longer flat. The field is described by a quaternionic function that applies a flat quaternionic parameter space. Einstein uses tensor calculus to describe the transfer of information in a deformed field. It includes transformations, such as the Lorentz transformation. This is a complicated way of describing things. The behavior of the field can be described much simpler by quaternionic differential calculus and that includes the interaction between the field and point-like actuators. That means that the origin of gravitation can already be comprehended by using quaternionic differential calculus. The same holds for the origin of electromagnetic field behavior. Both are basic fields that obey the same partial differential equations. The fields differ in their start and boundary conditions. The field that represents the universe (our living space) exists always and everywhere. The electromagnetic field requires the nearby existence of sources or drains. The separable Hilbert spaces on which elementary particles reside carry these sources or drains.

In contrast to what QFT suggests, uses the Hilbert Book Model stochastic processes that own a characteristic function as a means to control coherence and binding. This offers a far easier comprehensible model than the weak and strong forces that QED and QCD apply. The stochastic hopping paths can produce the Lagrange equations that QFT uses as a starting point.

See: "Tracing the Structure of Physical Reality by Starting from Its Fundamentals"; in http://vixra.org/author/j_a_j_van_leunen

follow

Hans,

"Physical reality archives all its dynamic geometric data in a series of intertwined quaternionic separable Hilbert spaces. For example the life story of each elementary particle is archived in the eigenspace of a dedicated footprint operator in its private separable Hilbert space"

I don't belong to the general relativity domain, s.t. don't do metaphores with me. Speak simply, otherwise I won't understand. I have no idea what is a "dedicated footprint operator". And the rest of the text was non-understandable to me.

With kind regards

Respected Sir

You are requested to read my all articles from LinkedIn profile/Researchgate account and the article attached.

Regards with thanks.

I recommend to read:

Leandro Melendez-Lugo, Esteban Chávez-Alarcon, "On the Validity of Kepler´s laws and the enigma of dark matter", Jour. of Engineering Research and Appl., Vol. 8 [12] Dec 2018 pp 12-18.

Leandro Melendez-Lugo, Esteban Chavez-Alarcon, "On the dark matter conjeture and the anomalous galactic speeds", Inter. Jour. of Science and Engineering Invest., Vol 7 [83] Dec 2018 pp 54-61

At the start of quantum physics, the physicists were looking for a platform that they could use for modeling their theories. John von Neumann was one of the leading theorists. Schrodinger as well as Heisenberg designed useful theories. Dirac showed that these theories could be combined in a Hilbert space. John von Neumann doubted between projective geometries and Hilbert spaces. Finally the Hilbert spaces won the struggle.

A Hilbert space is a structure that is based upon a vector space. In addition to the properties of the vector space, the Hilbert space defines an inner product between each pair of vectors. That inner product gets a value that is taken from a number system and that number system must be the real numbers, the complex numbers or the quaternions. The inner product provides the superposition coefficients in the linear combination that creates new vectors from a series of mutually orthogonal vectors. Operators are maps of a Hilbert space onto another Hilbert space or of the Hilbert space into itself. If an operator maps a vector along itself, then the inner product provides the corresponding multiplication factor. This factor will be called the eigenvalue that this operator attaches to the vector and the vector will be called eigenvector of the operator. This mechanisme creates a way to archive eigenvalues in a structured way into the Hilbert space. Each operator manages its own eigenspace. For example a reference operator attaches all rational numbers of the selected number system to its eigenvectors. In this way a Hilbert space can manage its own private parameter space. Other operators manage eigenspaces that represent special sets of numbers. One of these operators is the footprint operator. It manages the hop landing locations of the ongoing hopping path of an elementary particle. A hop landing is described by the combination of a time-stamp and a three-dimensional location. This combination fits in a quaternionic eigenvalue. The hopping path results recurrently in a coherent hop landing location swarm. That swarm can be described by a location density distribution that uses the private parameter space of the Hilbert space. The square of the modulus of the wave function of the elementary particle equals this location density distribution.

This shows how the complete life story of the elementary particle archives in its private quaternionic Hilbert space.

Dark matter is an outrageous, ad hoc addition to the standard cosmological model to fit flat rotation curves of spiral galaxies. Note: NOT rising or falling RCs. The rising RCs falsify the dark matter suggestion. If a modification to an accepted model is to be made, Dark matter should be considered as matter part of the T

If you know where to look, then dark matter is a comprehensible phenomenon. The theory behind it was known for many centuries. Bounded in the footprint of elementary particles the field excitations that also can appear in less coherent ensembles cause the deformation of the embedding field whose strength we characterize with the property mass.

See: "Dark objects" ; http://vixra.org/abs/1901.0174

Hans,

I don't have problems with the history of physics, neither with quantum mechanics, but with the dark matter. Einstein's field equations do not refer to the quatum domain. I am very busy, s.t. please be kind, stick to the issue.

With kindest regards from me

John Hodge,

What you mean by RC?

"If a modification to an accepted model is to be made, Dark matter should be considered as matter part of the T"

I understand you. However, the dark matter itself is not considered a source that curves the space-time - it is supposed not to interact with objects. On the other hand, the disproportion between the QM prediction for the cosmological constant, and the relativity prediction, shows indeed how terribly sick is the concept of dark matter.

With the best regards

Dear Leandro Meléndez,

General relativity is not my domain, I am not competent in it. I see in your article different calculi. But, what you say about Einstein's field equations? Do you disagree with them?

With kind regards,

Sofia

Sofia,

Dark matter and dark energy are called dark because their effect when they operate in isolation is so tiny that no measuring equipment can ever detect them. Only when they operate in huge coherent ensembles, they become noticeable. In separation they are field excitations that are tens of billions times smaller than photons or elementary particles.

At cosmic scales dark matter objects appear as a thin halo around galaxies and they cause gravitational lensing.

In optics such halo is known as veiling glare. It lowers the brilliance of the images that imaging equipment produces. Veiling glare shows in the modulation transfer function of the imaging equipment as a quick drop in the amplitude of the MTF near zero frequency. In optics the cause of veiling glare is pluriform.

Sofia D. Wechsler :

RC - Rotation Curve. Specifically for this question it is the hydrogen HI line of free hydrogen usually beyond the luminous part of spiral galaxies.

The dark matter is supposed to add matter to the galaxy to raise the RC from the Newtonian calculation (Keplerian declining). Yhe problem with rising RCs is that the dark matter hypothesis suggests MORE matter. Yet the rising RCs are found in Low Surface Brightness (LSB) galaxies that have less matter than other measures calculate.

I know about the "T" thing. but the calculations make sense for most galaxies if dark matter is counted as part of T. It is not supposed to interact with light directly like the crystal spheres of ancient Greek models. But it is supposed to be gravitational. But that is the subject of the question.

Dark energy and dark matter is the situations arises after the symmetry breaking of the "Super Unified Gaussian Energy Group (SUT) of SU(11) until the next symmetry breaking of the Gaussian Unified Energy Group SU(5).

For details please read my above mentioned articles.

Dark matter is a contribution to the energy-momentum tensor, that's all. No problem of principle. It's, typically, described by the equation of state of a fluid.

How to solve Einstein's equations, both in the presence as well as in the absence of sources is understood in principle and done all the time in practice.

The statements made in the text about scalar curvature, etc are just misleading, that's all. It's not true, for instance, that dark matter is or should be uniformly distributed-any more or less than ordinary matter is.

I think the strength of the energy sources SU(6) are so strong that the exotic matter fluid changes to ordinary matter.

For details please read my articles.

Dr Narayan Kumar Bhadra,

I see that you ask me all the time to read your articles. But I am not so competent in general relativity to choose between theories. If you can offer an explanation in a post here on RG, without sending me to articles, and point to what you think that is wrong in Einstein's equations, it would be more useful to me.

With kind regards,

Sofia

Stam, my good friend,

How can the dark matter be a contribution to Tμν ? The dark matter doesn't curve the space-time.

Another issue: let me ask your opinion about the cosmological constant. I believe that the dark matter cannot be the quantum vacuum. The dark matter is supposed not to interact with bodies, while the quantum vacuum yes does. What you think of it?

With kindest regards

Yes Sir I apologize,

Of course sending you my explanation as you asked.

I think Einstein's theory is true for a particular physical Universe.

According to Einstein's GRT real time can not be defined out side the Gravitating sphere.

Thus we may be assumed that the space time as R + iR, where "R" stands for Einstein's 4-dimensional space time and (iR) is that for " D"-dimensions, an extra dimensions it is then compared with Kaluza-Klein cosmology we found some beautiful results that our universe appeared from something instead of nothing, our universe unfolded from 10- dimensional space-time instead of 4-dimensional space time.

From 10-dimensional to 7-dimensional flat Universe then maybe closed and unfolded matter atoms from 4-dimensional space time and so on. There may more and more will shown in my articles including living matters.

Dark matter is just matter, whose particles don't carry certain charges, that the known particles carry. The qualifier ``dark'' means precisely that.

Gravitationally it interacts just like all matter, through its energy-momentum tensor, and that's how its presence has been detected.

Dark matter can be perfectly well described as a fluid with a corresponding equation of state and that is sufficient to describe how it affects galaxies-which means that it curves spacetime as much as any other form of matter with the same energy-momentum tensor does.

This is elementary general relativity! Internal properties (such as electric, weak, strong charge, or other; more exotic charges, or baryon or lepton number) are irrelevant, only energy and momentum are relevant for gravitational interactions.

How to know a theory/hypothsis is a theory for gravity? I think, the only evidence is that whether it can explain and design the orbit.

An orbit is always determined with N-body problem. Einstein's general relativity is unable to process the N-body problem. So, it is not a theory for gravity. Factually, it is just a faked story. Please see:

Preprint Is the math in current physics beautiful?

Data Anti-ethics and pseudoscience: On Albert Einstein's theory o...

Dear Sofia,

Stam is right!!!

DM gives a strong contribution to the Stress tensor Tμν and that is probably the only contribution it has at any level since it does not contribute to the EM tensor or the YANG MILLS field due to the fact that it does not interact with EM waves or there is nothing related to Quarks....

It is dark only because its origin is unknown, but it is basically totally transparent and in addition it does not attract conventional matter....

It is a very strange entity which involves some of the properties of gravitation (curvature) but it is not able to exert a gravitational force which otherwise would attract other bodies.

You never find such "entity" mixed with conventional matter, you find it always well separated from it...

The fact that it does contribute to the Tμν ,as previously said, does not mean that on the other side of the equations the Ricci tensors are both "engaged", the metric tensor which is a generalization of the Newtonian gravitational attraction is very likely not involved at all. The Ricci Curvature tensor is instead certainly involved.

From one side DM represents the crisis of the current models of gravitation (Newtonian) including GR, on the other side it represents a confirmation of some of the characteristics of GR which Newtonian gravitation is completely missing.

The HP of matter was made also as a consequence of the properties of the Majorana Fermions, the Neutralini..

These particles were among the particles predicted by the models of Ettore Majorana (probably the greatest of the geniuses of the '900). Neutralini behave like Neutrini in regards to the absence of interactions with conventional matter but at the same time, unlike their relatives, they are very very "massive".

Dear Stefano,

If DM don't have electromagnetic, weak or strong fields, what are you going to introduce in the energy-momentum tensor for obtaining the Einstein tensor?

The fundamental idea of DM is that the orbital speeds of galaxies with respect stars do not follow the rules found in other orbital systems such as planets with respect to their star. Stars revolve around their galaxy's centre at equal or increasing speed over a large range of distances. In contrast, the orbital velocities of planets in planetary systems and moons orbiting planets decline with distance. In the latter cases, this reflects the mass distributions within those systems. The mass estimations for galaxies based on the light they emit are far too low to explain the velocity observations and I don't know what is the real accuracy in the astrophysical measurements. What is very strange is to accept the existance of the Dark Matter or the Dark Energy without knowing its fields and to say that is straightforward to calculate an energy-tensor associated to them. How?

Dear Daniel,

Dear Stefano,

I absolutely agree with you, but you cannot calculate the energy-tensor Tμν with the present knowledge as you have said and Stam first than you.

It can be only assumed that you have a density of something with a given pressure for a gas of ???? for explaining this different scale gravitational behaviour. Yes that could be a possibility but the problem is related with spiral galaxies having a different result than for stars and so on.

From my humble point of view there are more possibilities to explain these gravitational features taking into account that we don't know the relationship of this interaction at different scales. Even we don't know how the Standard Model could be related with gravitation.

Finally notice that all these calculations come with the comparition of brightness of these galaxies (electromagnetic interaction which is the only one long range besides gravitation) with the their "trajectories" for their inner stars. Frankly this is pure speculation and you cannot calculate any kind of energy-momentum seriously. In fact all these results as the acceleration of the expansion of the Universe (Dark Energy) are beyond of what Einstein's equations could seriously describe.

Stefano

"... but it is not able to exert a gravitational force which otherwise would attract other bodies. "

DM was introduced to be the "missing mass" in galaxy Rotation Curve (RC) observations. That is, introduced to gravitationally attract stellar and gas (hydrogen) mass. Wasn't it?

This is an example of how the equation of state of dark matter can be determined: Article Dark matter equation of state from rotational curves of galaxies

From that the energy momentum tensor is deduced in the standard way. (For more details see, for instance: https://www.nikhef.nl/~t32/relhyd.pdf for a summary and https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5256005/ for a comprehensive review; or any textbook on fluid mechanics.)

The particle content of dark matter isn't relevant (just as the particle content of known matter isn't relevant) for describing gravitational effects, since only the energy-momentum tensor matters for these.

My Stam,

You have a custom to answer to some questions of mine that they are not relevant. To whom aren't they relevant? If I ask, I do this because it's interesting to me. I wanted your opinion on the assumption that the dark matter is the quantum vacuum. More exactly, what your intuition tells you about this? Doesn't this assumption seem a miscalculation or a misconception? But you tell me that it's not relevant.

Now the article you indicate, with rotational curves of galaxies, seems interesting. But unfortunately, I can't read it immediately. I am unbearably busy. (And I am not young. I see that the amount of things I can do per day, is smaller than years ago. It's irritating but this is how God built the human being.)

There is though something new for me: I was told until now that dark matter interracts with nothing. But I understand that it produces a lens effect on the light from objects behind the lens. If so, the dark matter curves the space, s.t. it should be indeed on the RHS of Einstein's field equation. Though, in this case it should be part of the tensor Tμν, it should not be of a form Λgμν . What you say?

With kindest regards

Stefano, my dear,

You say "The fact that it does contribute to the Tμν ,as previously said, does not mean . . ."

I understand that the dark matter is represented in the term Λgμν. If the dark matter is a source, it should to be part of Tμν , shouldn't it? As gμν is the solution of the EFE, it's circularity to assume Λgμν also a source, and it should render the solution of the EFE unstable.

Now, I don't know what is HP. Please explain.

With kind regards

Dear Sofia,

You are talking about dark energy.. the lambda refers to the external energy which is meant to accelerate the expansion.

Dear Stefano, Daniel, Stam, John, and others,

It is said here that in a spiral galaxy, the velocity of a star increases with the distance from the galaxy center. But in that case the arms of the galaxy should have been straight radial lines. The situation is not so, see the attached figure. The form of the arms of the galaxy shows that stars distant from the center remaim "behind" stars closer to the center, i.e. rotate more slowly. So, obviously the distant stars have orbital velocity smaller than the stars closer to the center.

This is a silly discussion, Einsteins addition of the Cosmological term was simply a mistake, on his own admission.

He was trying to make the Universe static, when it was really expanding.

The conclusion about the metric tensor is only true if you keep this term. There is no problem with the usual form of the Einstein equation.

That empty space is obtained by setting the Riccci tensor equal to zero is out of question.

This comes from an age when dark matter is still not very widley discussed, and one still does not yet know about its gravitational properties.

Dear Stam,

Don't pulling my leg please! Do you know what is an energy-momentum tensor? Do you know what is the difference with an equation of state?

Dark matter equation of state from rotational curves of galaxies

No tensor energy is there.

https://www.nikhef.nl/~t32/relhyd.pdf

Usual calculus of relativistic fluids without calculating the tensor energy-momentum for the dark matter at all. And finally you look for a basic study of relativistic fluids

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5256005/

I hope a little bit more for a person who has so high ranking and which always is able to distinguish between what is relevant (for him?) or not.

Please if you want to be serious show the energy-momentum tensor of the dark matter and don't try to confuse us with general calculations for fluids.

Dear Juan,

Although the interpretation that Einstein gave to his cosmological constant was wrong, nowadays it represents a repulsion force which is employed in many models of cosmology for explaining the acceleration expansion of the Universe. The Hubble constant is not enough and the dark energy is another simple hypothesis (as aether or phlogist) that is not better explained. Einstein's equations need an exam when they are employed in so special conditions where its basic assumptions are in doubt. For me it is more serious the hypothesis of the Eisntein's cosmological constant than the huge amount of Dark Energy needed in the other models.

Dear Daniel,

you have to recognize though that the energy momentum tensor does not specify anything about the nature of what is contained inside. It is difficult to deny at the same time that what is named as DM is nor mass neither energy....but it has a lensing effect.

I understand that you support the fact that GR is not enough to justify that behaviour of DM? In other words, for you, GR is falsified by DM, which is not so unreasonable and it is what some groups of astronomer are trying to prove also..

The energy-momentum tensor of dark matter can be perfectly well describe as that of a fluid with an equation of state, i.e. the relation between pressure and density.

And, once more, for gravitational effects, of whatever form of matter, only the energy-momentum tensor is relevant. So the observations lead to the equation of state of dark matter, which leads to the energy-momentum tensor, whose appearance on the RHS of Einstein's equations leads to how the metric deviates from the spacetime, defined by the known forms of matter, for example. Or, more relevantly, perhaps, how this form of matter affects the motion of distributions of known forms of matter.This is nothing more or less than fluid dynamics. The equations acquire additional terms, that's all.

The same approach holds for any other form of matter. So the only new feature of dark matter is that it's an additional contribution to that of known matter. Nothing more or less. At the level of gravitational effects, nothing else matters.

All this is consistent with GR. And there can't be any inconsistency this way. New forms of matter don't affect invariance under general coordinate transformations, nor the property that only the metric describes the spacetime geometry and matter couples to it through its energy-momentum tensor. And deviations from the latter property don't describes inconsistencies of GR-they describe generalizations.

Logical inconsistency≠incompleteness.

Stam,

Instead of repeating the same, please write every component of the energy-momentum tensor for dark matter. Please go ahead, don't be worry if it is not relevant for you, at least it is for me. It seems that it is not difficult because you have written that it is inmediate and without any kind of difficulties. Go ahead and write it explicitally!

Dear Stefano,

" you have to recognize though that the energy momentum tensor does not specify anything about the nature of what is contained inside."

No! The energy-momentum tensor of a fluid is very different than the one of electromagnetism, for instance. In the fluid you don't have a Poynting vector and so on....

It's the energy-momentum tensor of a fluid, cf. the references. It's been written in every review on the subject.

So just look it up, if you're interested.

While the expression of the energy-momentum tensor of different forms of matter depends on the field content, only its value matters for Einstein's equations.

So whatever the content is, the same values of the energy-momentum tensor will affect spacetime the same way, whether they are produced by electromagnetic fields or by dark matter.

And whatever the field content, the energy momentum tensor of any form of matter, is covariantly conserved. That's the analog of Poynting's theorem for the case of electromagnetism in flat spacetime.

This is elementary stuff, it doesn't make sense discussing general relativity, if this isn't known.

Stam,

What is viscosity of such fluid? Please, write it instead to say that it is in the papers devoted to the fluids of one star. Or even if you don't want (or don't know it) to write it please tell me one only paper where the energy-momentum for the dark energy is written explicitally. Only one paper!

Dark energy≠dark matter. Dark energy is perfectly well described by the cosmological constant. It doesn't have anything to do with dark matter, that's just a normal fluid, at the scales where it's relevant.

Its viscosity has been studied, e.g. Preprint Viscous dark matter and 21 cm cosmology

i know, but answer my questions please!

Dear Stefano,

Let me to show you that the energy-momentum tensor is not so obvious for dark matter. Please read the paper:

https://aip.scitation.org/doi/abs/10.1063/1.4913334?journalCode=apc

I'm not under any obligation to do so. I've provided the references, so look them up yourself.

Try to contribute substance, instead of rhetoric. And it would be a good idea to actually study the paper linked to.

``Non-conventional'' doesn't mean anything. And what matters are the conclusions, not the title.

In particular, in a relativistic framework, the individual components of tensors aren't meaningful anyway-that's why the energy conditions, that involve invariant quantities, are only of relevance. And that's why the starting point of the paper is wrong.

However, fortunately, that turns out not to be of any relevance.

if one actually reads the paper, one finds that they aren't dealing with anything ``unconventional'' at all. They're simply studying different ways of parametrizing the effects of dark matter when dealing with galaxies, where Einstein's equation aren't directly used.

It isn't true that the most effective way of doing this is by dealing directly with Einstein's equations-but, of course, any conclusions drawn from the many different ways of solving them, when studying galaxies-which is what they're interested in-are consistent.

So the paper, in fact, implies the opposite of what was claimed by its posting...

When dealing with Einstein's equations, fields are, either, part of the geometry, or part of matter. By field redefinitions, it's possible to map some properties of one to the other-but not always. There are conditions. All this is known, or should be.

Ok. Don't be worry. You have only provided papers without answering obvious questions and I understand that this is not relevant for you. Have a good sunday Stam!

Dear Daniel,

Dear Stefano,

There are many different energy-momenta tensors(in QCD, in QED, in CED,ect , right? You can make analogies between fluids and electromagnetic fields, right? But physically they are very different things, for instance you never are going to find a Poynting vector associated to the fluid because you haven't the equivalence between "electric" and "magnetic" fieds. In the same form that you don't have in electrodynamics anything equivalent to the Reynolds number. The fields in fluids are purely defined in the tangent space of the real velocities while in electrodynamics are quantum objects as photons.......

In any case this is not the problem in this thread, the problem is that you need to introduce the dark matter as a physical model for obtaining an energy-momentum tensor for the Einstein's equations, and you ( and nobody) don't have it. What you measure is a curvature which is not the expected by the corresponding masses measured mainly using the electromagnetic interaction. Therefore you cannot write explicitally the components of any kind of energy momentum tensor in one-to-one form.

What has made me to intervene is that Stam first and you after gave the idea that this was a very usual calculation in cosmology and the energy-momentum was straightforward to calculate for relating Einstein equations with dark matter. That is not true and you create a faulse idea to Sofia. Dark matter is a subject of research and for the moment belongs to the kingdom of hypothesis, as the aether was in another moment for electromagnetism. Nothing more!

Dear Stefano,

Respect to the link that you have send, that is obviously only a mathematical analogy but physically are absolutely different things. You never could get an electromotrice energy in fluids using a kind of Faraday's law, sure! Or you never could get "fluid radiation" in the space, as the electromagnetic waves.

Daniel and Stam,

This is MY thread! In a thread of mine people are all COLLEGA. We ellucidate things we DO NOT QUARREL. Please be KIND with one another. None of us is a youngster, mature people learn to be patient.

Many times, divergences stem from the fact that people don't speak of the same thing. Unfortunately, general relativity is not my field of competence, for being able to help.

Now, would someone explain me what is the difference between "dark energy" and "dark matter"? Equations don't satisfy me, I prefer first of al phenomenology! For instance, the e.m. field has energy, but it is introduced in the tensor Tμν after dividing by c2. Dividing in this way, one obtains for the energy, some equivalent of a mass. Then, why there is no such equivalece between dark energy and dark matter? I mean, why should the dark energy appear on the LHS, and not on the RHS divided by c2? It seems to me that the terminology "dark energy" is improper: Λ is not energy, maybe it has another phenomenological meaning. Indeed, Einstein introduced it for obtaining a static universe i.e. for regulating the acceleration of the cellestial bodies, (but now it was discovered that the universe is accelerating).

A second question: you speak of a viscosity of the dark matter. Wow! If the dark matter is viscous it should disturb the movement of the bodies passing through it. Is there some evidence that such a thing happens?

Third question: why this "dark matter" can't be just cosmic dust and debris?

With kind regards!

Sofia D. Wechsler

I'll try

"Dark energy" was suggested to explain the SN1a (supernova at some distance from us). The data suggested these objects were accelerating away from us when the model of the universe when redshift suggesting slowing expansion. Big bang gave initial expansion velocity. After the initial "bang", the universe expansion was supposed to be slowing. So, the energy to cause accelerating expansion was suggested. This brought to mind the "cosmological constant" being an energy in the EFE. The argument then turns to whether it belongs on the LHS or RHS - it works either way.

"Dark matter" was developed to explain rotation curves (RC) of hydrogen gas (HI) in the outer region (beyond the stars) was greater than the Newtonian, Keplerian decline allows. I mentioned this before. This is sometimes referred to an older term - "missig mass problem". For inside galaxies, the idea of energy doesn't quite work because it would have to be repulsive from the center of spiral galaxies. The difficulty is the rotation of stars close to the center of galaxies DO show a Keplerian decline of from 4000+ km/s to near zero. As radius increases, the RC of stars (H\alpha line and others) increases from the near zero of the bulge in the visible region of the disc.

The term "dark matter" was copied from earlier work by Zwicky concerning rotation of galaxies around the galaxy clusters. A great deal of missing, non-luminous mass needed to be in the intergalactic region to explain the cluster movement. Later with X-ray observations this extra mass was found - it exists and

Sofia D. Wechsler (continued)

it exists and it is baryionic. It's mostly rocks, (presumably from nova), hydrogen with low density. That is, nothing mysterious requiring new models. But in Zwick's time it was not visible and light seems to pass thru clusters with no aberration - hence "dark". The amount of this extra mass was greater than the mass of all the galaxies in a cluster combined (big distances between galaxies compared to the size of galaxies.) Lifting the term for a similar "missing mass" in galaxies has been confusing.

Did I leave anything? Unclear?

Dear John,

I am glad. Thank you ! So, you confirm my naive thought that the dark mass is not a mistery but it is dust, debris, barionic matter.

However, please tell me: during the big bang debris, dust, couldn't have existed because barions did not form at that time. So, the dark matter should have appear later, changing the tableau of mass distribution in the universe. Do you think that I a right? I mean, I don't intend to say that additional mass appeared, but besides stellar and planetar masses the universe became filled with non-luminous "garbage". Am I right?

With kind regards

Sofia,

Photons are obviously carriers of energy. The Einstein-Planck relation E=h v. proves this. However, photons are structured objects and the above formula in fact states that the photon is a string of equidistant energy packages that each carry a standard amount of energy. The annihilation photon of an electron has a frequency of 1020 . If it has a length of 3 centimeter, then it contains about 1010 energy packages. This means that a single standard energy package contains a tenth of a billionth of the energy that is contained in an electron. This amount of energy is so tiny, that no instrument can detect such energy package in isolation. So it is rightfully called a dark energy object.

Similarly the footprint of an electron must contain about 1010 puls responses that together deform the field that embeds the hop landings of the electron. Thus each of these pulse responses correspond to one tenth of a billionth of the mass of the electron. Also the effect of this pulse response cannot be detected by any instrument. So it is rightfully called dark matter. It corresponds to the effect of the Green's function of the field. The Green's function has some volume and the spherical pulse response injects this volume into the field. In response the field gets deformed, but the dynamic pulse response acts as a shock front and spreads the injected volume over the field. Thus the deformation is only temporary and quickly fades away. Thanks to the fact that the electron keeps hopping, the deformation is recurrently repeated and in this way the deformation becomes sufficiently persistent and travels with the electron.

Both the standard energy packages that make up photons and the spherical pulse responses that constitute the footprint of elementary particles can appear as free objects. Far more of these objects stay free than are contained in coherent ensembles.

Baryons are already conglomerates of elementary particles and each elementary particle owns a footprint that contains a huge set of spherical pulse responses. The dark objects discussed above are field excitations that are caused by point-like actuators. Photons and elementary particles are conglomerates of enormous sets of such field excitations.

JH: A great deal of missing, non-luminous mass needed to be in the intergalactic region to explain the cluster movement. Later with X-ray observations this extra mass was found - it exists and it is baryionic. It's mostly rocks, (presumably from nova), hydrogen with low density. That is, nothing mysterious requiring new models.

More hydrogen was found but the baryonic total remains about a factor of 6 less than the mass needed.

There is also the flatness of the universe to be considered, that also requires a lot of extra mass and/or energy, the peaks in the CMBR and the amount of deuterium in the early universe all of which are resolved by dark matter (plus dark energy for flatness).

The most common error I see is people assuming that there is only one piece of evidence for dark matter, that is far from the truth.

HvL: However, photons are structured objects and the above formula in fact states that the photon is a string of equidistant energy packages that each carry a standard amount of energy

The photoelectric effect shows that is not the case, photons are either absorbed or not as single items. A string of pulses could be cut by a fast shutter but this never happens.

George,

Atoms are the emitters of photons and they also play the role of absorbent.

In scintillating material it shows that the atoms can absorb part of the energy of the photon. What is left over of this energy is turned into kinetic energy.

The photoelectric effect frees an electron. This requires a fixed amount of energy.

Sofia D. Wechsler

I apologize for misleading you. Poor writing I guess.

The original "dark matter" of Zwicky in clusters is considered found and it is baryonic. However, the "dark matter" of galaxy Rotation Curves (RC) is different. It is not baryonic. The name was just appropriated because at the time it looked to be similar - but it is not. The confusion is similar names for different phenomena - a common propaganda ploy.

I think the RC stuff is not matter and doesn't exist.

Nice play on words: dark matter and "make light." :)

Einstein's field equations only work if hypothetical dark matter behaves the same as ordinary matter, and if one puts in an exact ratio between the two. Many believe, based upon observations, that in some cases dark matter reacts differently. Also these field equations involve an energy factor and related tensors, the dark energy hypothesis and energy tensors of dark matter, as well as possible uneven expansion rates of the universe, could interfere with this.

For these reasons, and others, Einstein's field equations may no longer be applicable to the observable universe according to present day theory and related hypothesis.

Forrest

You are correct. This is why dark matter in the RC verity does not exist. Another model should be created which puts an outward force on the outer matter (hydrogen) in galaxies. It would be nice if this stuff helped explain the metalicity-radius relation, relation of central parameter to disc parameters, and other galaxy relations.

To everybody,

I am not enough competent in general relativity to be able to follow all the details in the posts above. But I have two questions:

1. What is the purpose of EFE, to describe the average behavior of the universe, or local behavior of different regions in galaxies?

2. Don't you think that the term "dark energy" is badly chosen? Energy (divided by c2) has to stay in the RHS of EFE, not on the LHS. So, Λ should not represent an energy, but something else, some sort of a pressure, which dictates if the universe in its generality is static, or expanding, or accelerating. I understand that Einstein added the term Λgμν in EFE "by hand", artificially, i.e. it's not so clear where from comes this pressure. Am I right?

Dear Dr.

I think you are right.

I have a work:Preprint Anti-ethics and pseudoscience: On Albert Einstein's theory o...

It is shown that the conclusion from the arguments and discussions in the reseachgate showing that Einstein's theory of relativity is just a faked story. Therefore, the "dark energy", "dark mass" and "big bang" are just faked stories based on another faked story (Einstein's theory of relativity).

Best regards.

Zhu

Thanks for this discussion.

I think one major issue has remained unobserved. Just look at the Planck-Einstein relation; E= hv and keep in mind that photons are quantized!

This simple observation means that the the minimum frequency of light is 1 Hz.

This further MUST mean that the spectral density of radiation in 1 Hz must be enormous. It's even observed as the background noice of

The Einstein-Planck equation E = h v suggests that a photon is a string of equidistant energy packages that each contain a standard amount of energy. It also suggests that at least at the instant of emission all photons feature the same spatial length. Since the universe continuously expands that length increases as well. If the energy packages move with light speed. also the emission duration shows the same behavior as the photon length.

The energy packages are field excitations. These field excitations are solutions of second order partial differential equations. The only field excitations that obey the sketched conditions are the one-dimensional shock fronts that are the result of one-dimensional pulses. During travel, they keep the shape and the amplitude of the front. Thus the front determines the energy of the energy package.

Shock fronts that are solutions of second order partial differential equations occur only in odd numbers of participating dimensions. Thus, besides the one-dimensional shock fronts also three-dimensional shock fronts exist. Over time, these spherical shock fronts integrate into the Green's function of the field. This Green's function has volume. Thus, the spherical shock front represents a bit of volume that spreads over the field. Initially it locally deforms the field, but that deformation quickly fades away. The injected volume stays inside the field and persistently expands it.

A mechanism that keeps producing isotropic pulses will keep injecting a bit of volume into the field. This causes the continuous expansion of the field and it can cause an ongoing deformation of the field.

If the field was originally empty then at that instant then at that instant it was equal to the parameter space of the function that describes the field. That parameter space is a flat field. If the mechanism works spread over the spatial part of the parameter space, then spread over that spatial part the mechanisme produced little temporary bumps that represented the injection locations. If these bumps form coherent swarms, then the bumps become conglomerates and combine into larger bumps that represent a persistent deformation. We know these larger and persistent bumps as elementary particles. Together they form all massive objects that exist in the field. We call this field our universe.

JJ: This simple observation means that the the minimum frequency of light is 1 Hz.

No, it has nothing to do with units of measurement. It means that any large amount of EM energy must be composed of an integer number of photons, but each can have any frequency, frequency is not quantised.

HvL: The Einstein-Planck equation E = h v suggests that a photon is a string of equidistant energy packages

No it doesn't, it says that any single photon has a specific energy. Splitting it into a string of n packages would mean that each package contained (on average) energy of E/n which is never observed.

@Hans van Leunen The Einstein-Planck equation E = h v suggests that a photon is a string of equidistant energy packages that each contain a standard amount of energy.

This view of photons runs contrary to the experimental results in

Martin Pitzer , Christian Ozga , Catmarna K¨ustner-Wetekam , Philipp Reiß , Andr´e Knie , Arno Ehresmann , Till Jahnke , Alexandre Giuliani , Laurent Nahon

State-dependent fragmentation of protonated uracil and uridine

https://arxiv.org/pdf/1902.02042.pdf

See pages 3-4, where photon energy varies in the range 4 to 9.5 eV.

Hi George Dishman

If so, then i am simply wrong, and I have understand the meaning of the quantum wrong. I have no problem with that either, but then;

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

" In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. "

The problem with the concept of "wave" is that wave has also wave length. I think it's rather a cycle, and the wave length is merely the distance traveled during one cycle.

Hi Jouni,

Wikipedia: "In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. "

I had to read that a couple of times, Wikipedia isn't always clear. What this is saying is that if you think of a classical macroscopic wave such as from a radio transmitter, it has to have the form of a lot of individual photons, it isn't continuous. It's a bit like looking at a wave on the ocean and realising that it is made of lots of water molecules.

Each photon then has the energy E=hf where f is the frequency of the wave. The frequency can have any value, it isn't quantised, but the wave is a continuous flow of particles each of which has energy E.

Hi George Dishman

It very easy to understand the need for couple of reading times. Here's more;

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

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

Particulary;

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

What I meant in my comment about being "wrong", is that I simply found it useless to talk about how my conceptual Idea is "wrong" within some "standard model" etc.

Ie. If the coordinate system is attached to Earth, then it's wrong to say that Earth rotates around the sun. As it simply can't do that in that kind of concept.

I am talking about new concept for gravity;

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

And this concept just works very nicely when the single photon can only be constructed in energy amounts which is h multiplied with Integer.

-Quantized quantums. Ok?

George,

The text in Wikipedia that you mention is not rigorous. I won't stay to dissect it, I'll tell you the correct form. Consider a MONOCHROMATIC electro-magnetic (e.m.) wave. A quantum of the energy of such a field is equal to hf. You can't obtain in practice a wave of frequency f and with energy which is a fraction of hf. A wave of frequency f comes always in quanta, i.e. contains only an integer number of quanta.

". . . if you think of a classical macroscopic wave such as from a radio transmitter, it has to have the form of a lot of individual photons, it isn't continuous. It's a bit like looking at a wave on the ocean and realising that it is made of lots of water molecules."

Not at all! A photon doesn't have the obligation to be monochromatic. Usually it is not monochromatic, it is a superposition of a continuum of frequencies, ψ = ∫ω exp{i(ҟx - ωt)}, where ҟ = 2π/λ and ω = 2πf. The wave from the radio-transmitter has some width Δf. It does contain a lot of individual photons, otherwise its intensity would be terribly small, but each photon is a superposition of frequencies. The number of photons establishes the intensity of the wave.

Dear John Hodge,

Thanks for that. Yes, I have written such a "no dark matter" paper, the abstract of which can be seen here on Researchgate.

Preprint Background-Field Flow Dynamics as an alternative to dark mat...

I believe the statistics contained within the paper is strong evidence against the existence of dark matter.

I recommend to read:

Leandro Meléndez-Lugo Journal of Engineering Research and Application www.ijera.com ISSN: 2248-9622 Vol. 8, Issue 12 (Part -I) Dec 2018, pp 12-18 www.ijera.com DOI: 10.9790/9622-0812021218 12 | P a g e On the validity of Kepler's laws and the enigma of dark matter Leandro Meléndez-Lugo*, Esteban Chávez-Alarcón*

I recommend to read:

International Journal of Science and Engineering Investigations vol. 7, issue 83, December 2018 ISSN: 2251-8843 On the Dark Matter Conjecture and the Anomalous Galactic Speeds Leandro Melendez-Lugo1 , Esteban Chavez-Alarcón2

You can assume the field is made out of photons, each with energy hf = hbar omega,

or you can proceed like this:

E=pc (set rest mass zero in Einstein formula)

=hc/lambda (1)

(Saying it is made out of different photons or different wave lengths is the same.)

(One has to know that de Broglie holds for photons also)

But a phase angle phi for a wave is

phi/(2 pi) = x/lambda

Taking a time derivative on both sides

omega= (2 pi) (c/lambda)

(photons move at light speed)

Now replace c in (1)

Get

E= (h/lamda) (lambda omega)/(2 pi) = hbar omega =hf

Light is just a mixture of photons of different energies. Things are easier if you do not change the definition of photon.

SW: The text in Wikipedia that you mention is not rigorous.

Yes, I think I said that too.

SW: Consider a MONOCHROMATIC electro-magnetic (e.m.) wave. A quantum of the energy of such a field is equal to hf. You can't obtain in practice a wave of frequency f and with energy which is a fraction of hf. A wave of frequency f comes always in quanta, i.e. contains only an integer number of quanta.

Right, that's what I said, and any broadband signal of width Δf can be broken into monochromatic frequencies by a Fourier Transform giving you a distribution of energy versus frequency.

SW: It does contain a lot of individual photons, otherwise its intensity would be terribly small

Right, and each photon then carries energy hf.

SW: each photon is a superposition of frequencies

No, each photon has a single frequency (which is subject to the uncertainty principle of course), the classical wave is the summation over the flow of photons so could loosely be called a 'superposition of photons'.

SW: The number of photons establishes the intensity of the wave.

Right.

Dear Jouni,

JJ: And this concept just works very nicely when the single photon can only be constructed in energy amounts which is h multiplied with Integer. -Quantized quantums. Ok?

The concept may sound OK but the unit of quantisation cannot be dependent on our choice of units. 1 Hz is the inverse of 1 second which was derived by factors of 60 due to the Babylonians preference for that number (it is easy to divide by numerous factors so simplified mental arithmetic) and the fact that we divided Earth's day by the number of visible constellations to get the hour. The physics of nature cannot be determined by such human conventions.

James,

The energy of photons has a huge range. The annihilation photon energy of electrons equals the energy equivalent of the electron mass. The energy of a single energy package in a photon equals about 10-10 of that energy. It is the lowest energy a photon can contain. This is about 10-10 times 0.5 MeV = 50 micro eV

Tau leptons have a mass of 1776.82 MeV/c2 (compared to 105.7 MeV/c2 for muons and 0.511 MeV/c2 for electrons). Since their interactions are very similar to those of the electron, a tau can be thought of as a much heavier version of the electron.

Dear George Dishman

This kind of conversation I Like to continue; I fully agree about your units. Speed of light is a constant, no matter what is our unit definition for time and lenght.

One full cycle is also an accountable thing without an any unit; If it's rotation, jump, step, click, what ever, it doesn't matter; it's an Integer.

Now Hz is 1/s Yes, but as the speed of light is also m/s, this second is cancelled out, and we have only "light length/integer" which in meters is 299 792 458 m. And this length sort of defines the difference between planet and sun.

The radius of Jupiter is 69 911 000 m, (roughly 1/4 from the length) and according to observations it already radiates much more (unexplained) heat than it receives from the sun.

Brown dwarf's are said to have a mass of 13 to 75–80 times that of a Jupiter.

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

Well this length math of mine gives a factor of 78.7

Edit; I do know also here that the mass and length are not comparable units, but as the masses are calculated through gravity, etc the systematic mistake with the concept of "mass" is just corrected here.

Earlier I implied that a wave monochromatic may be the same as the photon, roughly what George sais.

How to interprate? After some thought, this is the way I found;

How does the frequency f originate? It is a sustained frequency coming from the wave as it moves past some fixed point in space, say an atom. This creates the energy hf, and causes electron promotion (or expulsion), an abrupt response to a continued stimulation. That is the only reason it seems that a particle came in (it really is not)

Examine the interference experiment with a single photon. The position of the minima on the screen is partly related to the energy (frequency) of the light/photon. This seems to me to suggest the photon can be made of particles whereby the number of such particles determine its energy.

Dear Sirs,

After I went throught these thoughts (mainly guided by R. Feynman) it came apparent to me that the reason for the "probability amplitude" is that if the light vector is pointing on wrong direction it can't be absorbed. This means that the photon "cycle" (frequency) is half of the time going through everything. It(photon) just can't be absorbed if the vector is not pointing on the direction of the propagation. And if the "cycle" (frequency) is 1 (Hz), then the photon can be absorbed only once in a second, and the rest of the time it's "invisible" and just goes through. (This all is just my brain flow...)

Anyhow, through these kind of thinking I considered the reason on phase transitions. And I actually made some success, if such is considered the observations on true nature;

Working Paper STATES OF MATTER defined from The Speed of Light

Shortly said the solid matter is constantly kept on interaction through photon exchange, where photons goes through the neighbor atom.

In Kinetic gas the distance is enough, to keep the atoms separated without entering in to each other's free space.

In Plasma the photons are so far away that they again are able to go through, which makes the interactions random.

In electric matter the it further may turn to 1-dimensional!!!??

....but somehow this is beyond my imagination...

Dear Stefano Quattrini

"It is dark only because its origin is unknown, but it is basically totally transparent and in addition it does not attract conventional matter..."

Not correct, it attracts conventional matter, but only via the gravitational force.

Dear Daniel Baldomir

The contribution of standard cold dark matter to the Tmn is very simple, it is the same as for dust. The contribution of dark energy is simply Einstein's cosmological term, nothing else. So, both things are quite simple, nothing is unknown in these models.

If the simplest model (dust) for dark matter fails, one will have to start with some more complicate models. There are certainly already some minor disagreements, and correspondingly also more complicate models. But AFAIK it is not yet established that the simplest CDM model really fails.

Dear Ilja Schmelzer

sorry but this is where everybody agree, DM it does not attract conventional matter due mainly to the fact that it would not be possible to exchange electromagnetic energy.

By the way, do you know another way to attract matter which is not via the gravitational force?

Dear Ilja,

Nobody in this thread has doubt that there are models for trying to explain the gravitational interaction of the dark matter and other physical features. That is not at all one problem. My discussion was due to understand the "physical model" of dark matter. Let me to present you some problems that I see as a humble theorecitian in Physics:

1. Einstein's gravitation hasn't account of the angular momentum and only employs the energy-momentum tensor as generators of the translations in the Poincarè group. This is one limit of interpretation measurements because this matter is needed only in the spiral galaxies provided of an enourmous rotational energy in their disk of stars where the gravitation doesn't coincides with our "tested" gravitational models.

2. Without having a "physical model" there are many degrees of interpretation of what is there attracting more than the Einstein's equations. Name the word energy-momentum tensor for introducing, the cosmological constante or both it is one possibility, but that is only a pure theoretical speculation. You can write an action and theoretically you find an enery-tensor associated to the generators of the translations by the Noether's currents. Al that is made in a table without needing to watch what dark matter is. Notice that obviously the explicit components explaining where the density of energy, its flux or its stress are impossible to be written while a "physical" model is given. In all that I know there are even problems for putting the different measuments in a general agreement for different "dark matter" associated to different galaxies.

https://www.scientificamerican.com/article/dark-matter-doubts/

3. In fact and what in the practice better works , is applied is the Newton's gravitation for taking into account explicitly the velocities of the rotation. The Einstein's gravitation is not "necessary" due to the flatness of these cosmological spiral galaxies. It is true that the cosmological constant could play a role (as I have mentiones previously and you seems to agree) but this belongs to the dream's kingdom while the source of the gravitation is not known.

https://arxiv.org/abs/astro-ph/0612434

Actually Rμν vanish does not mean gμν should also vanish. In void, guv may not vanish. Make a comparison with electric field and potential, potential vanishes does not mean field vanishes, and vice versa

If you understand the origin of inertia, then you can understand the gravitational force. Both have nothing to do with electromagnetic interaction. The EM field and the gravitation field are fundamentally different fields They differ in the way they attract or repel and they differ in their start and boundary conditions. The EM field relies on the neighborhood of electrical charges. These charges are carried by elementary particles. The gravitation field is always and everywhere present. In fact it is the local version of the field that represents our universe. The universe is the living space of all elementary particles.

See: Preprint Mass and Field Deformation

Respected Sir

You are requested to read my all articles and the article "Revised Standard Model of Physics and Origin of Biology" and "The Complex Quantum State of Consciousness-IOSR" etc. from LinkedIn profile/Researchgate account or through Google Search in the title name or my name

Dr Narayan Kumar Bhadra

Dear Daniel,

>

this is interesting....we should go much deeper into this... but you don't mean only the spin do you? (CARTAN tried to deal with it)

Dear Stefano,

No, the spin is a pure quantum concept that is out of gravitation. What is important here is to introduce the six conservation components due to the angular momentum as generators in the Lorentz group, i.e. the Poincaré group without translations.

Dear Stefano,

SQ: "It is dark only because its origin is unknown, but it is basically totally transparent and in addition it does not

attract conventional matter..."

IS: Not correct, it attracts conventional matter, but only via the gravitational force.

SQ: sorry but this is where everybody agree, DM it does not attract conventional matter due mainly to the fact that it would not be possible to exchange electromagnetic energy.

You seem to have got the wrong end of the stick here Stefano, DM does clump through gravity but doesn't feel radiation pressure so that meant it could start increasing its density and forming halos when normal matter was still kept uniform prior to the release of the CMBR. Once the matter became free to move, the gravity of the DM halos pulled it in and galaxies formed very rapidly. Without that mechanism, we could not explain how galaxies exist at all, the first ones should just be starting to form.

SQ: By the way, do you know another way to attract matter which is not via the gravitational force?

Via the Coulomb force. DM cannot do that because it doesn't interact through EM.

Dear George,

I'm sure that the remarks that you did to Stefano were well knew by him. This was just due to write matter instead of mass in most of the cases. But you have let me worried with your explanation

Once the matter became free to move, the gravity of the DM halos pulled it in and galaxies formed very rapidly. Without that mechanism, we could not explain how galaxies exist at all, the first ones should just be starting to form

Do you think that DM is necessary for understanding the formation of galaxies?

Dear George,

>

this is too trivial, you did not catch the implicit of NEUTRAL...

Dear Daniel,

DB:

how do you introduce the AM as generators in the Poincarè group?

Dear Stefano,

Frankly speaking I don't know how this can be done, what I know is the limit of Einstein gravitation for taking into account the rotations SO(3). This was observed very soon by Élie Cartan and he introduced the torsion besides the curvature as independent geometrical objects in such a form that torsion is related with the angular momentum and curvature with energy-momentum tensor. The main mistake made by Cartan was to assume the covariant derivative of the energy-momentum tensor as a necessary conservation law when this is forbidden when a torsion is included in the geometry of the spacetime. The conservation law doesn't follow directly working on the energy-momentum tensor but employing the Bianchi's identities and in fact both theories are the same in vacuum where the torsion is zero. This is quite trivial and too simple as if we wanted to say that the polarization of the vacuum were zero because P is zero without matter in electrodynamics.

Nowadays I'm quite far of working in these interesting difficulties but when a long time ago was working something in this field, for me this was an important issue not fully developed and which needed an improvement in the General Relativity. What I can say is that Dark Matter or Dark Energy concepts are too easy to invent for avoiding to show our present knowledge of Gravitation Interaction out of our Sun system. For instance, let me to present a very interesting paper summarizing 153 galaxies measurements seen that the Dark Matter is not well correlated with was thought should be obtained.

https://arxiv.org/pdf/1609.05917.pdf