It is a common assumption that in General Relativity, electromagnetic fields cannot affect space-time curvature. But in a recent paper in Scirp, Dr. Algirdas Maknickas shows that this is not indeed case. He proves how electromagnetic field can change spacetime curvature. But alas, he does not provide any experimental data yet.
So, do you think that electromagnetic field can change spacetime curvature? Your comments are welcome.
I think that what you call a "common assumption"is really not an assumption at all, perhaps more like a possible misunderstanding.
Anything with energy-momentum affects curvature; the electromagnetic field is no exception. The energy-momentum tensor of the electromagnetic field is trace-free, which makes it very different from, say, the energy-momentum tensor of a perfect fluid. Nonetheless, solutions to the Einstein-Maxwell equations (sometimes referred to as electrovacuum solutions) exist, the simplest among them perhaps the Reissner-Nordström solution for the gravitational field of a charged black hole.
For reference, see, e.g., https://en.wikipedia.org/wiki/Einstein_field_equations#Einstein.E2.80.93Maxwell_equations, or the book, Exact Solutions to Einstein's Field Equations, by Stephani et al., which is a very comprehensive technical reference.
I think that what you call a "common assumption"is really not an assumption at all, perhaps more like a possible misunderstanding.
Anything with energy-momentum affects curvature; the electromagnetic field is no exception. The energy-momentum tensor of the electromagnetic field is trace-free, which makes it very different from, say, the energy-momentum tensor of a perfect fluid. Nonetheless, solutions to the Einstein-Maxwell equations (sometimes referred to as electrovacuum solutions) exist, the simplest among them perhaps the Reissner-Nordström solution for the gravitational field of a charged black hole.
For reference, see, e.g., https://en.wikipedia.org/wiki/Einstein_field_equations#Einstein.E2.80.93Maxwell_equations, or the book, Exact Solutions to Einstein's Field Equations, by Stephani et al., which is a very comprehensive technical reference.
It's not a ``common assumption'': it's *wrong*. (The tracelessness of the energy-momentum tensor of the electromagnetic field means that were a scalar field responsible for gravity, then it couldn't bend light-but that's of historical interest. It's relevant for the case where *additonal* scalar fields determine spacetime geometry, like in tensor-scalar theories-these scalars, by themselves, don't bend light either.) There are lecture notes available on the subject: http://arxiv.org/pdf/gr-qc/9712019.pdf chapter 7, p.201 and following.
I beleive yes, becuase in double slit experiment of photon we see interference pattern. Same pattern is observed for single electron bomabarded in double slit. I dont see wave interacting to create pattern but space time disturance creating those path for photon to travel.
In the double slit experiments spacetime is *fixed*, which means that it is not affected by the motion of the waves or particles in question-these are considered ``probes''. The way spacetime is affected by external fields is given by Einstein's equations, whose left hand side describe the geometry and right hand side (in traditional notation) describe matter, sepcified by the energy-momentum tensor. This is presented in all courses on general relativity and isn't anything new, anymore.
Dear Sirs:
Please see my experimental work and results on this topic. I would welcome more accurate endeavor in order to clarify the role of EM waves on gravity, especially in the dark.
Einstein's geometric theory of gravity used to be paraphrased by John Wheeler in essentially two statements: Spacetime tells matter how to move, and matter tells spacetime how to curve. With matter including light, the first statement has been widely explored and evidenced in various types of experiments. Though not as obvious, however, in the second statement, matter should in principle include light too, as proclaimed by Einstein's Special Theory of Relativity. This current research aimed to put the second statement under strict quantitative scrutiny using light as the added effective gravitating mass. The results showed, however, that even a dim light, of almost negligible equivalent effective mass, played overly significant role in Newton's gravitational formula, viz, the gravitational "constant" had to be increased in order to go with the evidenced gravitating force. Thus, though laden with successes on cosmological scales, the General Relativity theory appears to fall short on explaining influence from tiny bits of photons in the dark.
Matter does include light-however the experimental consequences are challenging to discern. This doesn't have anything to do with any *theoretical* issues for general relativity itself (beyond checking for deviations from Newton's law at submillimeter scales) and everything to do with carefully calibrating the experiment and simulating all possible effects that can affect the measurement-and there are experts on this at MIT. Since electromagnetic radiation is mediated by spin-1 particles, it's not clear how it would *enhance* gravitational *attraction*, however.
Not only does the electromagnetic field affects space-time curvature, but it can be found again from the curvature tensor only. Check "already unified theory" some decades ago.
The electromagnetic interaction is one of the components of the einstein stress energy momentum tensor. Atoms are bind electomagnetically. In case of plasmas it is the same.
Others are the rest mass of the elemetary particles and their momenta and the binding energy of nuclei with their momenta. One thing which should be out of the Tensor is the radiant energy.
Dear Dr. V. Toth, Stam, Bhushan, Claude and Stefano. Thank you for all your answers. I am no expert in General Relativitym but if i am correct, the right hand side of Einstein's equation is tensor matter, not an electromagnetic field tensor. So, according to Dr. Maknickas, unless we replace the matter tensor with electromagnetic field, then e.m. Field will not affect the curvature, is it correct? I do not discuss yet UFT.
@Chungpin. Thanks for your paper, i will read it soon. Btw do you have new equations on how e.m. Field can affect curvature? My interest includes possible detection of Brown effect. Best wishes
The energy-momentum tensor is *not* the electromagnetic field tensor-and it's not *possible* to have the electromagnetic field tensor appear as such-it's antisymmetric, whereas the LHS is symmetric... This is well-known physics of the level of classical electromagnetism and general relativity. The only way to couple matter to the metric tensor is through a symmetric tensor, namely its energy-momentum tensor (this statement is a way of expressing the equivalence principle). One then obtains Einstein's equations and can solve them-for spherically symmetric electrically charged black holes-analytically (the Reissner-Nordstrom solution). This is the subject of the textbooks and university courses on the subject and is the basis of any *further* research.
Victor Christianto: For pure (source-free) electromagnetic fields, the RHS of the Einstein field equations will be the electromagnetic stress energy tensor (https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor), given by Tmn = FmaFna − (1/4)gmnFabFab, where Fmn = ∇mAn − ∇nAm is the Maxwell tensor, formed from the 4-potential Am, and ∇m is the covariant derivative operator. Tmn for the electromagnetic field can be obtained by varying the vacuum EM Lagrangian density, L = (1/4)FabFab, with respect to the metric gmn. See also https://en.wikipedia.org/wiki/Covariant_formulation_of_classical_electromagnetism
Einstein's 1915 paper on GR derives the application of the Faraday tensors to the stress-energy tensor, which, of course, yields a symmetric tensor. If the Lagrangian is applied to this resultant tensor arrangement then the result is the energy density times l_{\mu \nu} l^{\mu \nu} where l is the four-velocity. The energy density would equate to h \nu per unit volume and as a result, a photon would have an extremely small gravitational field moving at the speed of light. You would have an incredibly difficult time measuring it. Although it is known that light red-shifts slightly as it passes through a gravitational field which would verify Einstein's work. Light also is very slightly polarized as it passes through a gravitational field, however, one must apply the effects of the off-diagonals.
@Stam, Dr. V. Toth, and Bruce, thank you for your answers. Best wishes
See equation (6) in the following post:
http://physicalprinciples.wordpress.com/2014/08/10/dark-matter-and-dark-energy-a-property-of-gravity/
http://physicalprinciples.wordpress.com/2014/08/10/dark-matter-and-dark-energy-a-property-of-gravity/
Dear Sirs:
All I want to say is:
Had Einstein seen the result of my primitive experiments, he might have given it a second thought, or even come up with a different GR theory. Thank you all.
@Chungpin, thanks for your file, i just read it. Your experiment is indeed very interesting. The gravitational constant can change ranging from 6 to 11 times 10^-11 Nm^2/s^2, that is very large ranging, so perhaps you can come up with a new theoretical model on how light affect gravitation? Best wishes
@Mihai. Thank you for your remarks, i agree with you that our intuition say: yes. But in theory, it is a long way to prove. I recall that Einstein around 1920s worked with Kaluza-Klein theory where electronagnetic field becomes the fifth dimension. Best wishes
@Eric, thanks for your answer. Does that equation imply that e.m. Field can alter the curvature? And if yes, then does it mean a new electrogravitic communication device? Your conments are welcome.
Hi Victor ~
Nothing new! It's just Einstein's field equations for gravity in the presence of electromagnetism: curvature on the LHS and energy-momentum of the electromagnetic field on the RHS. As Prof Toth pointed out, everything that has energy and momentum contributes to curvature, and electromagnetism is no exception. .
In any case, the reverse is well-known: spacetime curvature affects em fields. It was proved in the famous eclipse of 1919.
In Covariant theory of gravitation the EM field affects spacetime curvature, see https://en.wikiversity.org/wiki/Covariant_theory_of_gravitation
and http://vixra.org/abs/1404.0058 .
The EM field is a part of general field, see https://en.wikiversity.org/wiki/General_field
and change the metric as other fields.
Please see the reference of D Apsel, which also indicates that the electromagnetic field can also alter the space time structure.
General Relativity and Gravitation, Vol. 13, No. 6, 1981
General Relativity and Gravitation, Vol. 10, No. 4 (1979), pp. 297-306
International Journal of Theoretical Physics, Vol. 17, No. 8 (1978), pp. 643-649
We can obtained the additional redshift as an electromagnetic redshift analogous to gravitational redshift, this also indicates that electromagnetic field can also alter the space time structure.
I think that this question is much deeper than what is written, that anything with energy-momentum affects curvature; the electromagnetic field is no exception. We know that The stress–energy tensor needed by the Einstein RG equation is a that describes the density and flux of "energy and momentum"... but in "spacetime". If you do not want trouble then the answer is simple, and good or bad everyone has written in this way.
But if we want to get involved we need to understand "WHERE" in spacetime is this energy-momentum of which we are asking.
When we deal with massive particles or entities then we can infer the position in a 4d manifold, by the fact that we can see "That particle" at rest!
Now
Do you think that an em field is an aleph2 continuum of infinite virtual photons?
Do you think that an em field (also after the 2nd quantization) could be static?
What do you think the "Electromagnetism" is? If you agree on the fact that a photon is like a ball that after its emission reaches its destination travelling in the space, then all is clear.
But if you agree on the fact that a photon has no position, then the thing is a little different...
what I mean is that we still do not have the conceptual means suitable to unravel this question
Fulcoli ~
I agree with you entirely that this question, when thought about more deeply, raises other questions that cannot be answered within presently understood physical theory. The relationship between gravitational theory and quantum theory has remained elusive for a century. Thus, when you bring “photons” and “second quantization” into the discussion we simply do not have a theory to draw conclusions from. The gravitational theory we have (Einstein’s GR) is classical physics, and electromagnetic theory as Maxwell gave it to us is a classical field theory with a well-defined energy-momentum tensor that gives rise to curvature according to Einstein’s GR. That much is clear. It seems “reasonable to suppose” that this feature would be retained in a quantised version of the Einstein-Maxwell equations. But since that quantised version is unknown, that’s all that can be said.
“Non-locality” is an irreducible feature of quantum theory. Physicists have learned to live with it – its just the way Nature operates and we have to accept it. Einstein’s GR also has its own non-locality problems: there is no answer to the question “where in spacetime is the energy-momentum of the gravitational field”. But why should we expect there to be an answer?
The electromagnetic field affects in full the space-time curvature and is one of the prominent causes. The electromagnetic quanta should not, there would be problems with gravitational waves. If electromagnetic waves affected curvature there would be a gravitational wave associated at the same speed, would sound very hard to think.
The constituent of the EM field are not the EM waves or free energy quanta, EM waves are a secondary effect of the transients of the EM field, What is sure is that the energy content of the field in terms of EM energy tied to charges,which is by far the biggest contribution, affects the stress tensor. What is doubtful is that EM free energy affects the curvature.
@ Charles Francis
But only because we have chosen to integrate the propagator with the addition of a +ie, what can we say about this conservation if we used a -ie?
Charles you are very sure about it, I agree with you that the theory deveolped so far may tell that.. The packet division of the photon and arbitrary reconstruction at arbitrary distance which is proved to happen in QFT cannot be accounted by any stress tensor which is local.
Provided that what you affirm is true, what is obtained with the theory is a stress tensor which continuously reconfigures itself at the speed of light.
Or rather if you consider a fantastic number of 10^30 gamma photons pass in the vacuum, close to a mass without being absorbed, the mass would move towards them???
Charles I re-ask you the question. If what you affirm is true, it would imply that a fantastic number of 10^30 gamma photons passing in the vacuum, close to a mass without being absorbed, would make the mass move towards them and lose part of their energy , wouldn't it???
Ok the effects may no be of a "gravitational attraction", at least here we might agree...
Charles ~
"...energy is stored in the geometrical structure of spacetime, not at a particular place in spacetime. I think this is a perfectly good answer. Say rather that there is no reason that it should be stored locally."
Precisely. That's why I said 'there is no answer to the question “where in spacetime is the energy-momentum of the gravitational field?”' There have been many attempts to define energy-momentum "pseudotensors" so that, with particular coordinate conditions imposed, gravitational energy and momentum could be defined locally. Thas doesn't seem to me to be an acceptable procedure.
Charles ~
I’m not sure whether we disagree or not – I don’t think we do. In SR, an inertial observer can take an energy-momentum tensor and by integration say how much energy there is in an chosen region of space, how much energy flows across a particular surface patch, and so on. I don’t think its useful or necessary to look for an analogue of that for the gravitational field; that’s why I don’t like the “pseudotensor” ideas.
Eric said: 'there is no answer to the question “where in spacetime is the energy-momentum of the gravitational field?”
What kind of energy is stored in the ST due to its curvature, positive or negative??? Or rather with the annihilation of two objects would I get a flux of energy bigger or smaller than the double of one's contribution due only to special relativity??
Charles,
when you don't understand something you Always think that is the other person stupid or doesn't understand, I already noticed this behaviour.
I put in another way,
the calculation performed for annihilation between a positron and an electron, in special relativity, can't account for what happens to their gravitational interaction. So who accounts for the gravitational interaction energy???
@ Charles Francis
You said:
the answer is that energy is stored in the geometrical structure of spacetime, not at a particular place in spacetime. I think this is a
perfectly good answer. Say rather that there is no reason that it should be stored locally.
excuse me
but this expresses precisely the Einstein equation
that the energy is practically == curved spacetime
the original question asked whether the em field could be taken as a source of this deformation.
That the em field has energy, is ok, but
the answer was, where it would be located such energy? Otherwise the equations lose their meaning
and you say that this energy is in the same spacetime?
it is a dog that bites its own tail!
I do not exclude any a priori assumption ...but said in that way... I cant follow it.
to me the key point is the following: is the energy an entity or is it a qualification, an attribute, that applies to the entities?
(...I'd say only to the massive ones)?
We know that energy is measurable only through measurements of the "dynamic" and therefore applicable only to massive bodies..[when we
use thermal methods or concepts we are simply analyzing a micro-dynamic using a macro-revealer].
Then the question shifts to the concept of "action occurring at a distance" [respecting the causality principle] and we see that
energy is required to "express" the effect of the interaction, and it is transferred from one body to another, and the temporal hole
that elapses from emission till reception forces us to imagine that there is an entity (called field) that acts as an energy reservoir,
adapted to retain the flowing-energy (in transit into space) for the waiting time between the instant in which it is emitted and the one
in which it is received. First set of assumptions.
Moreover when we try to assign an energy amount to a "curved spacetime" we force the space-time. We give to it the characteristics of the
field, but we know that in RG the concept of field is completely abolished.
The fact that spacetime is curved is nothing more than an effect : spacetime modification arises from the assumption that everywhere and
always the light goes straight with a null spacetime interval... so we must redefine the concept of straight.
The spacetime is the "observable" effect of the light (massless messenger) used for measuring lenghts and times with the aid of masses,
but in order to explain the "Motion" we erase the concept of the force and use the trick of a trajectory (a geodesic) into a spacetime
curved where we move time against a space motion.
@Charles
nevermind all the rest
my question is:
is the energy an entity or is it a qualification, an attribute, that applies to the entities?
The real physical “entities” that are located in spacetime are scalars, vectors, tensors and spinors (and corresponding densities). Energy-momentum and curvature are tensors. Energy is not; it is only a component (an "attribute") of the energy-momentum tensor and, as such, is coordinate-dependent and hence not localizeable in a unique way.
It's a matter of terminology - I used the word "entities" because Fulcoli used it. I meant by it things that exist objectively in the real physical world independently of the reference system we use to observe and describe them. Stars, planets, electrons, elephants, physical fields etc are such "entities". Physical fields (eg., an energy-momentum tensor) in my view are not numerical quantities (I'm not a Pythagorian). They are "objects". Numbers are what we assign to them - they are attributes - not of the object itself but of the object and the chosen reference system taken together.
Yes, of course the word "tensor" is commonly used to denote a set of numbers - the "components" of the tensor. But when discussing physics the word also refers to something that actually exists out there in the real world. That is what physics is - it's about what exists objectively, in reality. An energy-momentum tensor for example is a physical field, constituted of more fundamental fields. Those fundamental fields are objectively real - they are the "thing in itself" that all real "stuff" is made of. Numbers (and mathematics in general) are simply a way of describing and predicting their behaviour and creating the illusion that we understand.
To say more would be to drift into philosophy and metaphysics. Let's not go there...
Nice examples of how electromagnetic fields affect spacetime curvature can be found in
R.E.Kates, Motion of an electrically or magnetically charged body with possibly strong internal gravity through external electromagnetic and gravitational fields, Phys. Rev. D 22, 1871 (1980) .
or
R.E.Kates, "Point-source idealization in classical field theories. I. Electromagnetic radiation damping of a system of two perturbed Reissner-Nordstrom singularities in the slow-motion limit" , Phys Ref D25, 2487 (1982).
Charles ~
“A physical quantity is defined by the series of operations and calculations of which it is the result” — Sir Arthur Stanley Eddington
But physical reality itself isn’t “a series of operations and calculations”.
“The classical electromagnetic field is not an object, but it is the force which we would measure if a test charge were placed at a point.”
I can’t agree. A test charge placed at a point feels a force because it is responding to something that is really there, and would be there even in the absence of the test charge. Otherwise, we are in danger of the ontological position that the only reality consists of what we can observe and measure. I agree that quantum theory does seem to support such a position – that’s why QM is so baffling, and why I suspect there is something wrong with the way quantum theory is currently formulated. The rocks on the far side of Pluto (or even those a few feet below the Earths surface) have never been, and will probably never be, observed. But they are surely there (Bishop Berkeley notwithstanding…).
“It is thus an assumption that a tensor describes an object.”
But not an unreasonable assumption.
“…a tensor cannot be two things at once.”
But a word can be used in two different senses.
“The fundamental stuff of which matter is made, electrons, photons, protons etc is something else altogether, and not a structure of mathematics.”
But physical fields are the fundamental stuff of which electrons, photons, protons etc are made. They don’t depend on our measurements and our mathematics for their existence.
Charles ~
I understand and appreciate your viewpoint. A variety of ways of thinking about and expressing things can be valuable and can lead to a more holistic understanding. Contradictions may be only apparent and disappear at a deeper level. (The puzzlement over “wave-particle duality” in the early days of the development of quantum mechanics is a case in point.)
“QED describes the possibility for the creation and annihilation of photons which carry the force. The photons do not have to be there when they are not being created and annihilated, since their presence also has to do with the placement of the test charge.” But there are regions of space where a test charge will feel a force when it is introduced and regions where it will not. The behaviour of the virtual photons is different. In the former case I would say there is “something there” even before the charge is introduced. That something is an electrostatic field.
Could it be that the fundamental “things” that constitute reality are neither particles nor “fields”, but “processes”? (Whatever that means.) One thing is certain, and that I think we can agree on - they are not observations, or measurements, or numbers....
Charles ~ thank you for a very stimulating discussion.
I don't think there's much more I can add. My curiosity is aroused - I intend to look into some of the contributions you've uploaded to RG. Any you would particularly recommend?
I'm afraid I'm not understanding the second paragraph in your most recent post. If a test charge feels a force at some some point in space but at another, there must be something different about the two points before the charge is introduced. "The potential for something to be there..." - what is that?
@Charles Francis
reading this last post you wrote it seems that you have some interesting ideas; I'd like to investigate in detail but I feel that we are close enough; in order to find out if we are tuned on the same wavelength I'd like to suggest these 2 experiments, one beside the other.
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser
and then
http://en.wikipedia.org/wiki/Purcell_effect
To you these two have a special meaning?
@Charles Francis Thank you for sharing these 3 works
@*
maybe: (this is just a lecture key) imagine that light is an oscillation of "something" [and here we must agree on the debacle: RealEntity vs Virtual vs Conceptual... what is real and what is a mind-map of? ] that is constrained on both its ends, bound between source and destination. To put it another way: the photon is never emitted from the Source/emitter that shoots it into space towards infinity, the photon is emitted when already "knows" its destination. A constrained oscillation of the electromagnetic field. For example, at this point, I can conveniently associate the dilation of the frequency for the wave with the concomitant distortion of the metric that indicates the "size" of the space in which the same oscillation exists.... as for example near a BlackHole horizon or in the FRLW scenario with the CMB.... but this is another big stuff. Nowadays there is a pragmatic vision, while mine is philosophical: imagine the simplest of situations. 2 electrons that scatter exchanging a photon: our reason leads us to say that the photon as a gauge boson is emitted and "after" is received, right? Only after this phenomenon the 2 electrons are kept into contact and therefore aware of each other. But before then either ignore the presence of the other. If so, why at a certain moment of their lives they (one of two) must emit a photon? So, according to the daily view of things it would be possible to emit a photon, leaving him free to go, and let it continue to infinity; and then maybe it would be possible to create along the way a charged and massive object able to receive it and let then the photon revealed. To me this not true, for me this is not a correct view. I read the work of Wheeler and Feynman, I realize that the advanced waves have the exact same quality compared to those delayed, in electromagnetism. In the
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser
it results easily the observation that a photon never travels but it is already everywhere in its path , as constitued of an infinite aleph2 amount of virtual photons moreover, if we want to support an argumentation that does not imply the fact that the photon (? can we use a different term?) is at the same time here and there [i.e. it lives only in the massive-charged matter, in what we call emitter and receiver], then we have to be able to give a location to the photon. But this is impossible, either prohibited by relativity than by quantum field theory: even at a conceptual level it is impossible to build a mathematical operator that may be associated (also in principle) with smtg that is more or less related to POSITION.
then for the
http://en.wikipedia.org/wiki/Purcell_effect
here you can see how a photon, without a contestual absorber can't be emitted. And this is possible only if a photon knows where its destination will be. So we can't emit a photon, then let it travel in space, and then capture it with an appropriate detector: the mechanism of energy flow is the cooperation of 2 parts: an emission of delayed waves and an emission of advanced waves, and the real/measurable flow occurs only if there is a correct matching of the 2.
It is a perverted corpuscular idea of a photon we get from our daily lives that leads to all the questions about an hypotetical photon motion and speed. The answers are not to say simple, but rather questions themselves should have no place if we understand what the photon really is (or what it isn’t). They are used in physical models and proved themselves useful as proxies in interactions (for the lack of better alternatives), but outside of the equations they make very little sense. No one have ever observed a photon. The only way to know where a photon is, is to get it absorbed by an electron – but then there is no photon any more, and it is still a question if there was one to begin with. All we know is that one electron somewhere emitted a portion of energy and then another somehow received it. There is definitely no ball of light traveling through the space between them, as was demonstrated by the double-slit experiment all the way back in 1800′s, so the question “how can photon travel” actually became invalid long before it could have come to any of our heads.
@Charles: your paper on qed seems interesting, i will read it soon. I really appreciate your attempt to avoid infinities. While i am not a specialist in qed, i think the founders of qed such as Dirac and Feynman did not accept such accepted methods to get rid of infinities. So did you succeed to remove infinities? Your comments are welcome. Thanks
@Charles: thank you for your answer. Btw, i just found another paper by Gupta et al who also try to remove infinity problem in qed. See http://arxiv.org/pdf/0901.3330v2.pdf. Best wishes
If we call visible light an electro magenetic field the experiments show that light can increase or decrease the weight of an object. Does that mean tHat the so called curvature of space is changed? Is there really physically such a thing or is it a mathematical concept. Facts are that light does change gravtitational force. You can read the resulsts in GRAVITYFORCES.COM
Spacetime is an imaginary concept or mathematical tool. Space and time does not have physical existence. So curvature of something which does not exist is meaningless. Energy and frequency have physical existence. Human mind mistakes frequency for time (period) and energy for space (wavelength). So first I like to rephrase your question as: "Does photon have a gravitational field?" My answer is: Yes. Gravity exists between different forms of energy. It does not matter what kind.
It helps the discussion to quantify spacetime and matter with dimensions, first. Contrary to the views of many, spacetime does have structure and this structure defines the geometry of matter. This is the foundation of my work. The basics of the theory are very easy to understand using simple Newtonian-type equations. All of it is based upon the same empirical data used by the SM.
Article A New Foundation for Physics
Yes, Every form of Energy will have its mass equivalent which can curve the geometry on which it is located.Einstein-Maxwell equations are very well studied and understood,in the context of astrophysical applications ,while trying to build models for high energy sources.
Einstein equate the energy and mass by equation E=mc^2 and mass create gravitation. Now we all know that electromagnetic field has energy very very larger than gravitational energy which implies that it must create curvature in spacetime.
Farhad,
may be electromagnetic field is itself curvature in space-time and Einstein's equation of gravity is definition (or connection) of energy-impuls tensor by (with) metric.
Eugene F Kislyakov,
Yes Sir, but if it is the curvature itself then the question arises that, how to write its line element or what will be the line element suitable for this case (I mean ds^2=?). I shall be thankful for the answer.
I am not god, Farhad. I am thinking about this. There were many attempts till now, but final decision is lacking.
Eugene F Kislyakov,
Thank you Sir very much, I will ask for help if needed
Farhad ~
The Reissner-Nordström metric (ds2 =...) is the static solution to the Einstein-Maxwell field equations corresponding to the gravitational field of a charged non-rotating, spherically symmetric body..
http://en.wikipedia.org/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric
Eric Lord,
Yes sir you are right, RN is a black hole solution which have a singularity at r=0, while I am searching a regular solution without a singularity purely created by the electromagnetic force.
the problem is what is the true expression of equivalence principle.
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