How could i calculate potential difference between : infinity to a point A , (general relativity formulation). Please explain how to calculate in simple terms...
Sourabh, I believe that gravitational potential is not widely used in GR. For static fields, you can calculate energy differences using the time dilation formula, however. This is one term of the metric, sometimes called gtt. In ordinary Schwarzschild coordinates |gtt|=(1-2GM/rc2)1/2. I indicated magnitude to disregard a minus sign that is a matter of convention.
Ordinarily you'd have for potential an expression like -GM/rc2. If you wrote an expression for the total energy E of an object, rest energy plus kinetic energy, which is at a radius r, and assuming you are at infinity, then you'd have Er =E∞(1-GM/rc2).
You can see that as long as r >> GM/c2, then (1-GM/rc2) ≈(1-2GM/rc2)1/2. But you cannot easily obtain an exact potential term because of the square root.
For a little more discussion you might find my paper on Hamiltonian analysis useful, but I only use the approximation.
Sourabh Singh,
gravitational potential is actually derived from the metric tensor, gamma44, in the simplification of the equation which brings to the geodesic motion.
The gravitational potential energy instead does not exist locally but only in the psudotensor. Sad but it is like that...
General relativity replaces the scalar Newtonian gravitational potential from Poisson's equation for gravity with a tensor potential that accurately reflects the contribution of mass-energy, pressure, and stress terms to gravity.
That said, for matter with negligible pressure and stress (negligible in the relativistic sense), in the first approximation all that remains is the Newtonian potential.
In this case, the metric can be written, with appropriately chosen coordinates, as a small perturbation of the Minkowski-metric tensor. In the conventional, diagonal matrix form, it is gmn = diag(1 + 2U, −1 + 2U, −1 + 2U, −1 + 2U). Here, U is the Newtonian potential in dimensionless form (divided by c2): thus, for a point source with mass M, at a radial distance r from the source, U = −GM / c2r.
When this metric is substituted back into Einstein's field equations, Poisson's equation is recovered as the "00" term in this equation: c2 ∆U = 4πGρ. where ∆ is the Laplace operator, ρ is the mass density.
However, this approximation loses its validity when the gravitational field is strong or when the matter source is relativistic (i.e., the energy present in the form of pressure or stresses is comparable in magnitude to the mass-energy associated with the rest mass of the source.) In this case, there is no scalar gravitational potential, not even in an approximate sense, and the full machinery of general relativity must be used. The simplistic notion of a potential difference between two points won't be of much use either, although I should note that the left-hand side of Einstein's field equations contains second derivatives of the metric, just as Poisson's equation contains a second derivative of the scalar potential, so one can see how the two are, in a sense, analogous.
When there is no gravitational field then the path of the particle in the medium is always a straight line and distance between two points of the path(geodesic) is given by euclidean geometry and metric potential is constant, however,in presence of strong gravitational field the geodesic is given by R-geometry and metric potential is a function of r . Thus metric potential is a consequence of gravity or vice versa
I like very much explanation given by professor Toth. I would provide an answer in exactly the same way. However, I would like to add(to complement) to Professor Toth comments some comments of mine which everybody can download directly from Research Gate. Please, read my paper http://adsabs.harvard.edu/abs/2010arXiv1006.4650K
Dear Sourabh,Nice Paper of Prof Arkady will certainly give you the answer.
t^(lambda)_(sigma) is Einstein's 'pseudotensor'. It is,
"the 'energy tensor' of the gravitational field." [Einstein, A. The Field Equations of Gravitation, Preussische Akademie der Wissenschaften, Sitzungsberchte, 1915 (part 2), 844-847]
"The quantities t^(alpha)_(sigma) we call the 'energy components' of the gravitational field." [Einstein, A. The Foundation of the General Theory of Relativity, Annalen der Physik, 49, 1916]
(1) Einstein's pseudotensor is not a tensor, and it is coordinate dependent. It is not therefore in keeping with Einstein's prescription that the equations of physics be independent of coordinates and covariant under tensor transformations.
(2) Einstein's pseudotensor acts 'like a tensor' only under linear transformations of coordinates.
(3) Assume that Einstein's pseudotensor has mathematical validity. Then contraction of Einstein's pseudotensor produces an invariant t, i.e. t = t^alpha)_(alpha). This invariant t and the pseudotensor appear in Einstein's field equations (Einstein, A. 1915, 1916). Examination of this invariant t reveals that it is a first-order intrinsic differential invariant. However, the pure mathematicians proved, in 1900, that such invariants do not exist. In other words, Riemannian metrics of any class do not admit of first-order intrinsic differential invariants. Thus, by the method of reductio ad absurdum, Einstein's pseudotensor is a meaningless collection of mathematical symbols. Consequently, contrary to Einstein's practice, it can't be used to represent any physical quantity, to model any physical phenomena, or to do any calculations.
(4) Einstein claimed that by means of his pseudotensor the usual conservation of energy and momentum for a closed system is secured by General Relativity. However, that is false, since by (3) above, t^(alpha)_(sigma) has no mathematical validity. Although it is still possible to determine a true tensor conservation law for General Relativity, it is in conflict with the usual conservation laws for a closed system determined from a vast array of experiments. General Relativity violates the usual conservation of energy and momentum for a closed system.
(5) By means of the pseudotensor, the energy of Einstein's 'gravitational waves' (which have never been detected) is calculated. However, by (3) above, such calculations have no mathematical validity, and hence no physical validity either.
What you are affirming is partly explained in the paper of an american mathematicians illustrating the ideas of Emmy Noether and Hilbert about SRT and GRT. I didn't know though that the pseudotensor is as you described. I strongly suspected it since all the experimental verifications of GRT are for steady state systems or systems without variation their of energy content.
My immediate reaction to Stephen Crothers's claim about the lack of meaning of Einstein´s pseudotensor is: !!
Raul,
Pseudotensors are a "patch" for non acceptable results. Feynman avoided such artifax with his Filed Gravitation Theory by adding the gravitational energy in the field equations.
Pseudotensor as a patch means that GRT does not work properly in some cases, it has issues with the energy conservation.
This is basically due to one pillar of the theory which is the LLI, Local Lorentz invariance. The Lorentz Group is omnipresent and unfortunately if you don't inject energy from without or give for granted that it exists somehow supposing an Hamiltionian, nothing in GRT moves.
According to the physicists it is impossible in General Relativity to obtain an expression for the energy of its 'gravitational field' which satisfies the following conditions: (1) when added to other forms of energy the sum is conserved, (2) is independent of coordinate systems. Einstein constructed his pseudotensor in order to satisfy (1). However, as I explained in my previous post, Einstein's pseudotensor has no validity even in mathematics, and so it is completely meaningless. The pseudotensor for Einstein's gravitational field alone is not unique. Others have been constructed. For example, the Landau-Lifshitz pseudotensor. However, it suffers from the very same fatal defects as Einstein's, as its contraction attests. It is astonishing that physicists do not know that first-order intrinsic differential invariants do not exist, and so such constructions as Einstein's are futile.
In any event, no pseudotensor can satisfy both conditions above, since none are tensors. The pseudotensors act 'like a tensor' only under linear transformations of coordinates. Consequently, their use violates the fundamental premise of General Relativity that all the equations of physics must be coordinate independent and be covariant under general tensor transformations.
However, contrary to the claims of the physicists, there is in fact a tensor relation that satisfies all the requirements of coordinate independence and covariance under general tensor transformations. This relation is what General Relativity must satisfy to be consistent with its own premises. The energy for Einstein's gravitational field is already accounted for in the Einstein tensor. After all, it describes Einstein's gravitational field. To this tensor must be added the energy-momentum tensor for material sources. Only the sum of the energy and momentum of the gravitational field and its material sources can be conserved, not individual parts. This is the usual conservation of energy and momentum for a closed system that has been established by a vast array of experiments, and which ipso facto Einstein tried to satisfy so that his theory is not in conflict with experimental facts. Mathematically this conservation is manifest in a vanishing divergence. However, a tensor divergence (covariant derivatives) is necessary for tensor relations. Pseudotensors, since they are not tensors, do not satisfy a tensor divergence. That is why Einstein resorted to an ordinary divergence (simple partial derivatives) of the sum of his pseudotensor for his gravitational field and his energy-momentum tensor for material sources. Since this ordinary divergence vanishes he claimed the usual conservation laws. But as explained already, this is false, since his pseudotensor is a meaningless collection of mathematical symbols.
Einstein's field equations must take the following form:
G_{uv}/k + T_{uv} = 0
This is a tensor equation. The energy components of Einstein's gravitational field are the G_{uv}/k. The energy-momentum components of the material sources of his gravitational field are the T_{uv}. Thus the field equations are also total energy-momentum equations. Since the above expression is a tensor equation it is coordinate independent, and it satisfies a tensor divergence. Taking the tensor divergence (denoting covariant derivatives by ;) yields,
[G_{uv}/k + T_{uv}]; = 0
This constitutes the required vanishing tensor divergence. It is in fact the only means by which General Relativity can satisfy its own premises.
However, the usual conservation of energy and momentum for a closed system is violated because the total energy-momentum of the system is always zero. This is in conflict with experiments. Thus, General Relativity cannot accord with the usual conservation laws and their associated experiments. It is therefore untenable. All attempts to salvage it by means of pseudotensors are futile. Pseudotensors are band-aids for a wound that will never heal. Consequently, physicists have merely contrived numerous methods, in ignorance, to try to make General Relativity consistent with is premises and with experimental reality. They have managed to construct a great mess that is completely detached from reality, and so try to make reality bend to their faulty theories, not realising that their theories are the real problem, in the footsteps of Einstein. They deceive themselves and their audience at every turn by inventing ever new 'exotic' matter and exotic processes with the aim of only saving their faulty theories at any cost. Theirs is a fruitless undertaking in wishful thinking.
If we're criticising GR1916, I think the situation is actually worse than that.
GR1916 seems to be a curvature-based theory of gravitation that can't properly cope with the effect of relative velocity on the shape of a moving gravitational field. So it's a theory of curvature and gravitation whose curvature-based arguments seem to break down if a gravity-source is moving. That's really not good.
Eric,
as Yurij Barishev once said GRT is like a theory of geometrical optics where nothing moves but light trajectories respond well.
With the "forced " LOCAL LORENTZ INVARIANCE which is not in agreement with the clock hypothesys (which specifically deals with energy) everything about the energy issue emerges.
LLI is good as a reference for EM fields not for radiation, which is basically the primary reason of the energy exchanges.
Stephen, interesting comment, I hope someday you evolve into fixing things, not just declaring them broken. ; )
Why is zero energy considered a problem? I have been assuming, due to my interest in inertia theory, that the background-free energy of a gravitational system is in fact zero.
If that at first makes no sense, realize two things:
A separate point ... you speak of "the fundamental premise of General Relativity that all the equations of physics must be coordinate independent." That very general statement seems to mean something different to me than it does to traditional relativists. We should be able to set up Euclidean coordinates as well as any curved ones, and write equations of motion. In that case we couldn't use geodesics, of course. Then space curved in a way that geodesics describe motion of free bodies is merely a mathematical artifact of solving for a coordinate system in which gravitational acceleration happens to be zero?
Robert,
"Energy is relative and not conserved across coordinate systems (either in the case of relative motion, or for different gravitational potentials)."
Yes maybe in GRT yes, that is the problem.
Stefano, in any gravitational theory I think. Saying "time dilation" and "energy is not conserved across coordinate systems" is essentially the same statement.
I always recommend to my students to go back to sources.In this case to a review article by Einstein dated by 1920. It it, much better than in any other book or paper on relativity, I had ever read or seen,he is explaining his theory in the most economical and precise way. Everything else is looking to me like a scum inside the kettle.....Thus, please, look up the original and use your brain. Also, remember that newtonian/lagrangian mechanics can be rewritten exactly in terms of equations for geodesics just those used in Einstein's theory of general relativity. E.g. look up book by Fomenko and Bolsinov http://www.amazon.com/Integrable-Hamiltonian-Systems-Geometry-Classification-ebook/dp/B00UV9J2IG/ref=sr_1_1?ie=UTF8&qid=1429568699&sr=8-1&keywords=bolsinov+and+fomenko , chapter 15 or my own book
http://www.amazon.com/Applications-Contact-Geometry-Topology-Physics/dp/9814412082/ref=sr_1_1?s=books&ie=UTF8&qid=1429568809&sr=1-1&keywords=kholodenko , pages 424-428
Dear Robert
"Stefano, in any gravitational theory I think. Saying "time dilation" and "energy is not conserved across coordinate systems" is essentially the same statement"
Newtonian is based on the gravitational conservative field.
Feynman, Thirring, Kalman Field gravitation Theory (FGT) is based on the Poincarè Group which fully complies the energy conservation theorems.
The GRT is intrinsically out of the local conservations, which makes it impossible to merge with theories which use the local conservations like Quantum Physics.
Either GRT dances alone and explains everything which cannot, or it is going to be replaced with a theory of gravitation complying the local conservation theorems.
All the paradoxes GRT shows is due to the fact that it cannot in anyway handle transitories of any kind. This is basically due to the fact that it does not respect the conservations.
Dear Professor Arkady,
"Also, remember that newtonian/lagrangian mechanics can be rewritten exactly in terms of equations for geodesics just those used in Einstein's theory of general relativity"
The Hamilton-jacobi action is postulated in order to explain the geodesic motion in term of the metric tensor, which is correct. THis then does not imply the GRT free-falling rule, due to its metric, according to which every free falling atomic clock falls with the same clock rate, which explicitly violates the energy conservation theorem and it is one of the flaws of GRT.
The Einstein Field Equations can be obtained from the Einstein-Hilbert Action, the FGT which include the gravitational energy satisfy the same action principle as shown by Feynman. Feynman explicitly affirmed that the Gravitational energy was missing in the GRT.
The matter is quite delicate and regards how the theories handle energy. It might be that also QM doesn't do it properly in local, but it is for sure that GRT doesn't it at all.
Article Energy-Momentum of the Gravitational Field: Crucial Point fo...
I kindly invite you also here:
https://www.researchgate.net/post/The_least_action_and_the_maximum_entropy_principle_are_the_governing_dynamics_according_to_Eddington_what_do_they_have_in_common
The inability of General Relativity to deal with moving bodies is easily evidenced by experiment. For instance, General Relativity cannot account for the simple experimental fact that two fixed suspended masses approach one another when released. This is reinforced by the fact that there are no known solutions to Einstein’s field equations for two or more bodies and no existence theorem by which it can even be asserted that his field equations contain latent configurations for two or more masses. In any event, GR fails due to its violation of the usual conservation of energy and momentum for a closed system, from which it has no escape.
There is no impetus to motion in General Relativity, unless one assumes that a time gradient is somehow a driver. However, that is a fantasy. Since gravity is not a force in GR, because it is spacetime curvature, gravitational forces cannot be invoked to initiate and drive motion anywhere.
All the contradictions and physical falsehoods that arise in GR are due to its invalidity as a physical theory. This is most profoundly evident in its failure to accommodate the usual conservation of energy and momentum for a closed system.
Robert, I understand your point, but I reiterate that I am not an inventor of theories, and so I can offer nobody an alternative theory, and I have no intention to try. My work is restricted to the analysis of certain current theories; in this case, here, General Relativity. It is legitimate science to correct theories that are faulty, or to eliminate faulty theories, as the case may be. I leave it to others to find workable theories. But in some 100 years it is astounding that physicists have not even been able to see the invalidity of Einstein’s theory of gravity. It is a time consuming and indeed full time occupation, to analyse this 100 years or more mountain of physical and mathematical falsehoods buried so deep in complicated mathematical apparatus, a job to which I have dedicated myself after discovering that General Relativity is unsound. One cannot unravel it by just saying it is false. This must be done by meticulous scientific method so that the proofs are clear.
Robert, consider the Compton Effect where only a photon and an electron are involved. The total energy energy and momentum of this system before impact of the photon on the stationary electron is not zero. After impact some photon energy and momentum is transferred to the electron. The total energy and momentum after impact is not zero. Energy and momentum are conserved so that the total energy and momentum of the system before impact is the same after impact. Any theory in which the total energy is always zero, even though conserved (at zero), does not meet the usual conservation of energy and momentum laws as illustrated by the familiar Compton Effect. Any number of such examples can be adduced. General Relativity fails to meet the experimental facts of the usual conservation laws for a closed system, and so it fails.
General Relativity is based upon the requirement that the equations of physics must not change under general tensor transformations. This requires the coordinate independence of all equations of physics. As explained, pseudotensors do not satisfy this basic premise because they only hold under linear transformations of coordinates. Such a major restriction contradicts the fundamental requirement of the theory. There is no way out of this. The pseudotensors are merely useless contrivances to try to keep afloat a theory that sunk to the bottom when it was conceived, because it was ill-conceived.
That Lagrangian/Newtonian equations can be written in equations of geodesics has no bearing whatsoever. Gravity is not curvature of spacetime in Newtonian theory; it is a force. There is no causal connexion between matter and space and time in Newtonian theory. Moreover, Newtonian theory is a linear theory, GR is a nonlinear theory. They are entirely different theories. Writing Newtonian and Lagrangian equations in some geodesic formalism does not make Newton’s theory nonlinear so that it can be given something of the mantle of Einstein’s fantasy. The fact is that General Relativity fails; it is riddled with physical falsehoods, contradictions, and invalid mathematics. I have already pointed out that no physicist knows that first-order intrinsic differential invariants do not exist; bearing in mind that they routinely use such related quantities to formulate and to calculate; clearly in ignorance. I find it astounding that they do so. And that they do so is the aetiology of all their whimsical constructions of ‘exotic’ and ‘dark’ matter, and exotic processes that have no basis in any experiment, to try to bolster that which has fallen down around their ears. They are so lost in their salvage attempts that they can’t even see that the ship is already on the seabed and covered in barnacles; a nautical wreck no less than the Hesperus. Cosmologists have demonstrated that they don’t even understand escape velocity, since they adorn their ‘black holes’ with an escape velocity and no escape velocity simultaneously at the same place, without realising it, just as they realise nothing with their invocation of ‘mathematical’ quantities that possess first-order intrinsic differential invariants (and are therefore not even mathematics). Physics is broken. Realising that it is broken is the first step to correction. There is now a lot to correct, so much so that one can only wonder it it is even possible.
Stephen
"It is a time consuming and indeed full time occupation, to analyse this 100 years or more mountain of physical and mathematical falsehoods buried so deep in complicated mathematical apparatus, a job to which I have dedicated myself after discovering that General Relativity is unsound."
There is something surely wrong in GRT but I don't throw away the baby with the dirty water..
I'm not so dramatic at GRT, it is 100 years old, time to retire but with honors.
Space-time makes sense, curvature makes sense, Schwartzshild metric has been verified experimentally to a certain extent, also in the Gravity probe A experiment, so prediction of time dilation is verified and Redshift too. Light is geometrically well treated. Trajectories predictions of steady state systems are good.
Close systems like binaries lose energy at the rate predicted by the EFE according to the gravitational wave emission.
It is not only GRT but the SEP (strong Equivalence principle) which needs to be reviewed.
The failure in quantization of the space-time and the non-merging with Quantum Physics is for sure a drawback of its weird metric with a "infinite number of infinitesimal generators", while the Poincarè infinitesimal generators are 7 for QM.
"General Relativity fails to meet the experimental facts of the usual conservation laws for a closed system, and so it fails."
Here I don't completely agree. To make GRT work you have to assume that there is an Hamiltionian, or know that the system is isolated, then in the case of steady state system the EFE guarantee a solution.
“Space-time makes sense, curvature makes sense, Schwarzschild metric has been verified experimentally to a certain extent, also in the Gravity probe A experiment, so prediction of time dilation is verified and Redshift too.” Stefano
Spacetime curvature does not make sense. For example, according to the cosmologists, the finite mass of their ‘black hole’ (‘Schwarzschild’ or otherwise) is concentrated at its ‘singularity’, where volume is zero, density is infinite, and spacetime infinitely curved. Gravity is not a force in GR, because it is spacetime curvature. Thus, the cosmologists assert that a finite mass produces infinite gravity. However, no finite mass can have zero volume, infinite density, or produce infinite gravity anywhere.
The ‘Schwarzschild radius’ is not even a distance let alone a radius in the ‘Schwarzschild metric’. The ‘Schwarzschild radius’ is therefore not the radius of anything in the ‘Schwarzschild metric’. Nonetheless the cosmologists always treat it as a radius and assert that their ‘Schwarzschild radius’ is the radius, rs = 2GM/c2, of their black hole ‘event horizon’ and that the ‘physical singularity’ is at r = 0, which they call the ‘origin’. Related to this, as I alluded to previously, the cosmologists assert, unwittingly, that at the event horizon (‘Schwarzschild radius’), their black hole has and does not have an escape speed (‘escape velocity’) simultaneously. However, nothing can have and not have an escape velocity simultaneously at the same place.
The Schwarzschild manifold is spatially infinite, and is asymptotically flat by definition. However, all three types of big bang universes alleged by cosmologists are either spatially infinite (two different cases) or spatially finite, depending upon their constant k-curvature. If k = -1 the big bang universe is negatively curved and spatially infinite; if k = 0 the big bang universe is flat and spatially infinite; if k = 1 the big bang universe is spatially finite and positively curved. The spatially infinite Schwarzschild universe cannot be inside a spatially finite big bang universe. Moreover, Schwarzschild spacetime does not even possess a k-curvature and so it again can’t be inside any big bang universe. And no big bang universe is asymptotically anything.
The Schwarzschild metric is eternal, i.e. it is static, and so it is not expanding. However, all three types of big bang universes alleged by cosmologists are non-static and are of finite age (~13.8 billion years), and are expanding.
Because GR is a nonlinear theory the Principle of Superposition does not hold. Consequently black hole universes cannot be superposed with themselves, with other black hole universes, or with any big bang universes. Similarly, no big bang universe can be superposed with itself, with any other big bang universes, or with any black hole universes. How do the cosmologists get their black hole big bang universes? They superpose! They superpose billions of times since they allege a supermassive black hole at the centre of ‘almost every galaxy’, and other black holes inside galaxies; all of which they superpose upon some unspecified big bang universe (since there are three of the latter). Let X be some black hole universe and Y some big bang universe. Then the linear combination (i.e. superposition) X + Y is not a universe. Indeed, X and Y pertain to completely different Einstein field equations and therefore have nothing whatsoever to do with one another.
“Close systems like binaries lose energy at the rate predicted by the EFE according to the gravitational wave emission.” Stefano
Upon what set of Einstein field equations and upon what solution thereto do you rely for the binary systems you refer to? As I have already mentioned, there are no known solutions to Einstein’s field equations for two or more masses and no existence theorem by which it can even be asserted that his field equations contain latent configurations for two or more masses. Furthermore, owing to the fact that the only means by which Einstein’s field equations are consistent with the tenets of the theory is such that the total energy is always zero. A consequence of this is that his gravitational energy cannot be localised, i.e. his gravitational waves do not exist! Furthermore, the wave equation for binaries such as you refer to, besides having no valid basis in Einstein’s field equations, is coordinate dependent, because it is obtained from a ‘linearisation’ of Einstein’s nonlinear theory. The speed of propagation of such ‘waves’ is therefore arbitrary. One can choose a different set of coordinates and get thereby a different speed of propagation. Einstein merely chose a system of coordinates deliberately to make the speed of propagation that of light. The energy of these alleged Einstein gravitational waves is calculated, as I have previously mentioned, by means of a pseudotensor. Which pseudotensor do you rely upon? No Einstein gravitational waves have ever been detected. They won’t be detected because they don’t exist.
As I said in my previous post, the cosmologists merely invent ever new ‘exotic’ matter and exotic processes at every turn in their attempts to try to save GR from imploding, and in doing so they have become so completely disconnected from reality that they do not realise that they are flogging the proverbial dead horse. Their black hole universes, their big bang universes, their superpositions of them all; their dark matter, their dark energy, their quintessence, their ‘nuclear pasta’, their higgsinos; their creation of the Universe from absolutely nothing is the epitome of creationism since their creator created itself out of nothing; their 'an almost infinite number’ of parallel universes (how close to ’infinite’ did they get?); their claims that the universe is a computer simulation from some other numinous place; their big bang Cosmic Microwave Background and mean temperature of the Universe at 2.725K blackbody; matter present and absent by the very same mathematical constraint; etc. etc., all contrivances, attest that physics is broken, and now steeped in sympathetic magic and mysticism.
Stephen,
you position risks to be as incorrect as the ones who think that GRT is totally correct..
Stefano:- No, that's not so. The points I made are valid. I await your attempts at refutation of the points I have made.
Stefano, I cannot figure out your complicate response to my comment about time dilation and energy conservation. My comment was very simple. If energy is measured by frequency, and time is dilated as a function of coordinates (or coordinate position), then energy varies with coordinate position. But in any one coordinates it is conserved. Nothing complicated about it. It's like velocity. It's relative. In fact, duh, kinetic energy is a function of velocity. (So is time dilation)
Stephen Crothers,
You sometimes make very interesting comments, but I have trouble getting a "conversation" going because I prefer to go past them and ask what might be reasonable, not just what isn't. :D
For example, you wrote: "The ‘Schwarzschild radius’ is not even a distance let alone a radius." If instead of taking the religious way of talking about GR, and just look at the "facts" implied by the Schwarzschild metric, not the doublespeak, we find the coordinate radius is quite real. It just isn't the length of measuring rods or tethers, except in the special case where the attractor mass is zero. This is like the special case of two observers in special relativity who are not moving relative to each other, and share the same length and time measurements. See the paper I've linked below for further explanation.
In fact, it is the physical reality of the coordinate radius, physically because we CAN write potential energy (as well as area) as a function of it, that we can indeed calculate and measure the proper radius. This physicality implies there are multiple interpretations of metric gravity, at least in the static case. One is a true curvature of space-time, which anyone who has read any of my papers or my coordinate thread knows I am suspicious of, and the other is that it is merely length contraction and time dilation. The fact that Einstein insisted "any coordinate system will do" is further evidence that one can "choose" a Euclidean coordinate system and simply write equations of motion appropriately. The equations of motion always have a correction factor for gravity. This correction factor happens to be zero in the "special" coordinates preferred by Einstein after he said any coordinate system will do. It is just as likely that this is because the special coordinates were carefully calculated to make the gravity correction factor zero as it is that they have any other physical meaning. The argument for their physical meaning involves uniform parallel fields (aka "equivalence") with all the difficulties Stefano Quattrini is fond of pointing out, and I have disposed of this argument, without directly saying so, in the paper below.
Then you write "Because GR is a nonlinear theory the Principle of Superposition does not hold." Quite true in GR. But not true of metric gravity generally. In an earlier version of the paper below I pointed this out. Unfortunately I have soft pedaled it for now, but the example is still there. If one takes just a slightly different potential function (very relevant to this thread) then in fact potential becomes linear and superimposable. Check it out. : )
For all you pure relativists who will read my remarks out of context and come unglued (some of you will be offended I'm even talking with Stephen), resist the temptation to even comment. These remarks are not directed at you and I'm well aware of how they differ in subtle ways from the religious orthodoxy of GR.
Robert,
"If energy is measured by frequency, and time is dilated as a function of coordinates (or coordinate position.."
Unfortunately not. The energy is measure by the frequency in its own reference frame and can be compared only in its reference frame, unless making a conversion considering the different time rate of different reference frames which alters the measurement of the frequency itself.
Article Gravitation, photons, clocks
I am not sure, Stefano, whether we have a misunderstanding of terminology, or a fundamental disagreement. If I measure a photon which originated deeper in a gravitational field, I do measure it in my frame. If I compare my measurement to a deeper observer, he obtains a higher value because of his slow clocks.
Therefore, the locally obtained measurement of energy is a reflection of the coordinate dependence of clock rates.
"If I measure a photon which originated deeper in a gravitational field, I do measure it in my frame. If I compare my measurement to a deeper observer, he obtains a higher value because of his slow clocks."
YES, If I measure the frequency of a photon.
"If I compare my measurement to a deeper observer, he obtains a higher value because of his slow clocks."
Yes he obtains an higher value of the frequency not an higher value of the energy.
"Therefore, the locally obtained measurement of energy is a reflection of the coordinate dependence of clock rates."
yes because I measure the energy using the frequency which is acquired altered at different gravitational potentials. But the actual energy is Always the same.
THe energy which I measure in my rest frame and Is sent to the other rest frame,
the emitted energy.
Stefano:- Following your pejorative remarks about me on this forum I await your refutations of my points. I suggest that you begin with just one, perhaps this one. (1) The 'Schwarzschild radius' r = rs = 2GM/c2 is not the radius of anything in the 'Schwarzschild' manifold, and so it is not the 'radius' of a black hole 'event horizon'.
Please provide your proof by which you maintain I am in error.
Stephen,
I appreciate very much your effort, really because you are basically against some consolidated theories presenting contradictions .
It is not so easy to find somebody competent (Yurij Barishev is too) who is against the mainstream where there are very competent people as well.
But still I'm not so extremist, maybe because I'm not so competent.... I look for truth in every reasoning of people, checking if it matches with reality of the physical experiments (which might be biased too though).
(1) The 'Schwarzschild radius' r = rs = 2GM/c2 is not the radius of anything in the 'Schwarzschild' manifold, and so it is not the 'radius' of a black hole 'event horizon'.
Yes you may be right in this consideration but still the Schwarzschild solution has been proven experimentally also in the Vessot and levine experiment to an extent of 70 parts over a million. It works for prediction of time dilation, quite well.
I allowed myself to carefully analyze such experiment directly from the NASA report
Article NASA GP-A REVIEW UPDATED VERSION
Re: "the Schwarzschild solution has been proven experimentally also in the Vessot and levine experiment to an extent of 70 parts over a million. It works for prediction of time dilation, quite well."
So, there you have the reality of the Schwarzschild so-called coordinate radius. It works "quite well." I think we should be questioning the reality of the proper radius, which is nothing but the inverse of the length of measuring rods, which as we know from special relativity are subject to change.
In the paper linked below, see Fig. 2 – "Potential of B is not dependent on proper radius changes." In other words, the proper radius has no physical effect on the physical properties of an object, its orbit, its time dilation, etc.
Stefano:- You did not address my point on the ‘Schwarzschild radius’. No theory that is logically inconsistent can be meaningful. Since it is easy to prove that the 'Schwarzschild radius' is not even a distance let alone the radius in the 'Schwarzschild' metric, it is totally meaningless to treat it as the radius. Consequently, everything that is based upon this metric is fallacious. It is by an alleged 'extension' of Droste's solution that the so-called 'Schwarzschild solution' is obtained (0
Stephen,
very interesting. But I would feel better to get rid of dark matter instead of black holes...
I know that Schwartzshild is not a full satisfactory solution because it cannot explain me the Redshift between two orbitating objects exchaning radiation in which a 1/2 appears in the equations due to the angular motion.
I'm not so expert as you in the metric and math, I analyze experiments and I find good suggestion that there is something really not working.
Einstein unfortunately in his haste to build a consistent theory didn't pay much attention on the soundness of it regarding the energy conservations.
The main mistake according to my opinion is its voluntary neglect of radiant energy in his equations explicitly saying that it was negligible respect to the other energies at stake. It makes everything like a reversible rubber wall and quite unphysical.
Stefano:- The dark matter etc. is already dead. It is part and parcel of the Big Bang phantasmagoria. With the demise of black holes, the Big Bang creationism is also defunct, taking with it all the 'exotic' stuff the cosmologists have invented ad hoc.
All this is explained in detail in my paper (available on my Researchgate profile):
General Relativity: In Acknowledgement,
Of Professor Gerardus ‘t Hooft, Nobel Laureate
I have relegated most of the mathematics to appendices so that the salient issues can be easily understood by any reader. The appendices nonetheless cover all the necessary mathematics.
According to Christopher Nolan, Matthew Mcconaughey and a robot can leave an event horizon, indeed, even the interior, and our future selves can construct a time lattice within a black hole allowing Mcconaughey to haunt his daughter's past.
Reading the posts in the last two days, I am seeing about the same level of intellect and logical consistency from the posters. Especially both sides of the Stefano-Stephen pseudo debate, because they very nearly agree but argue anyway.
You don't need century old assumptions to get curvature. Is it fun to argue with a century old dead man? You don't even need the field equation. Or tensors. See paper I linked yesterday. What you give up without the field equation is worm holes and time travel, like in the movie, because the curvature is strictly embedded in Euclidean 3-space.
Bringing the topic back around to potential, you can choose to give priority to potential instead of force and obtain linear potential, which is esthetically very satisfying. It still produces the common solar system gravitational effects.
Robert:- Your jibe of a pseudo-debate between Stefano and me is just another absurdity. Pick any one of the arguments I have adduced and prove me wrong. Don't forget that you can see all the details in my paper (cited above, and here: http://vixra.org/pdf/1409.0072v6.pdf). Perhaps you can explain to we, the great unwashed, how the cosmologists' black hole can have and not have an escape velocity simultaneously at the same place. Also, provide a proof that the 'Schwarzschild radius' is the radius of something in the 'Schwarzschild' metric.
Dear Stephen,
I will have a look for sure.
What you think of FGT of Thirring, Kalman and Feynman??
Stefano
Luiz:-
You said:- “I agree with yours suspicious on the real existence of a black hole .But note that the source on the empty Einstein equation is obtained by declaring that the space time is the manifold of full Euclidean space R4 MINUS the origin (where is supposed to live the gravitational energy source-out of the problem space time since there is not such mathematical object called Euclidean-Lorentzian singular manifold ) .”
No; the solution for Ruv = 0 is a 4-D pseudo-Riemannian (i.e. non-Euclidean) metric-space, as the components of the metric tensor are not constants. The ‘origin’ at ‘r = 0’ is NOT the origin at all, because this ‘r’ is not even a distance let alone the radius in the metric. Furthermore, although this false ‘origin’ at ‘r = 0’ is a boundary or border of the metric-space alleged by the cosmologists, it is nonetheless included by the them, since that is where they locate the finite mass of their ‘black hole’ and which they call a ‘physical singularity’, where volume is zero, density is infinite, and spacetime is ‘infinitely curved’. Now gravity is NOT a force in GR, because it is spacetime curvature. Thus, the cosmologists allege infinite gravity at their ‘physical singularity’. However, no finite mass possesses zero volume and infinite density, and no finite mass can produce infinite gravity anywhere. I have no suspicions about the non-existence of black holes. I have proven that black holes do not exist; they are the product of irrational imagination and invalid mathematics. It’s all over for the cosmologists.
You said:- “By introducing by hand the physical "boundary condition" that the fourth component of the obtained metric for "infinite light velocity " is the usual Newton Potential , one gets the Schwarzschild celebrated solution .That appears to be the usual thinking on the issue .Correct me , if I am wrong .With cosmological constant one imposes that at radial space time infinite the metris MUST reduces to the flat Minkwosky metric ,which by its tirn vanishes the introduced cosmological constant (this mechanism of vanishing cosmological constant only works for non compact space times”
No; by introducing Newton’s expression for escape speed the cosmologists introduced a mass into Hilbert’s ‘solution’, not Schwarzschild’s solution. Schwarzschild did not introduce Newton’s escape speed expression at all. The solution attributed to him generally in the literature is not his, it is Hilbert’s corruption. Newton’s expression for escape speed can’t appear in what is alleged to be the solution to a 1-body problem, since escape speed is an implicit 2-body relation. The cosmologists’ analogy with Newton is a farce. They slip in the Newtonian escape speed and 'event horizon radius' for their black hole by means of Newtonian potential, which can’t be determined without two masses anyhow. After all, Newtonian potential is defined as the work done per unit mass against the gravitational force produced by the two masses M and m. With ‘cosmological constant’ /\, de Sitter’s totally empty universe is obtained, from the ‘field equations’ Ruv = /\guv. de Sitter’s empty universe is meaningless, since the Universe is not empty, and his metric is not asymptotically anything and therefore does not approach flat Minkowski spacetime asymptotically. No metric containing the ‘cosmological constant’ is asymptotically Minkowski spacetime. And as I have shown already, according to Einstein and his followers, material sources are alleged to be both present and absent by the very same mathematical constraint, Tuv = 0. That is impossible! Schwarzschild spacetime contains no material sources for the very same reason de Sitter’s empty universe is empty (no material sources), Tuv = 0. This fact alone is sufficient to completely ruin black holes and big bangs, bearing in mind that the cosmologists retain the former in the latter.
Stephen, apparently you have not read anything I have written to you. My assertion is not that you are wrong, but that you ignore the problem of trying to figure out what it right. I think you are "wrong" to be entirely deconstructive and ignore the problem of constructing a correct theory of gravity. Now, how are you going to debate that?
Luiz C. L. Bothelo: You have not adduced any rational arguments in defensible of the indefensible. All your 'arguments' have no scientific or mathematical validity whatsoever. Your ad hominems don't count as scientific arguments either - they are irrelevant and futile drivel.
(1) Despite your plea, 'r' in the 'Schwarzschild solution' is NOT even a distance let alone the radius.
(2) Despite your plea, matter CANNOT be both present and absent by the very same mathematical constraint.
www.sjcrothers.plasmaresources.com/critics.html
Black holes and Big Bang creationism are products of irrational imagination and invalid mathematics.
A Few Things You Need to Know to Tell if a Nobel Laureate is Talking Nonsense, 10 July 2015,
http://vixra.org/pdf/1507.0067v1.pdf
Oh Stephen,
your vixra.org article teaches the remarkable fact that also Nobel Non-Laureates sometimes are talking nonsense.
Ulrich Mutze: Now you are talking nonsense. My points are clear and simple. You think otherwise - then provide your proofs instead of hot air.
Stephen Crothers: You ask for the impossible. If two persons hold different oppinions about a thought, one saying 'clear and simple' the other saying 'nonsense' then there is no reasonably sized argument which decides the question convincingly for both persons.
Ulrich Mutze: Your response is bereft of any scientific argument. You have failed to provide the required proofs. Your remarks are therefore irrelevant.
Crothers, S. J., A Nobel Laureate Talking Nonsense: Brian Schmidt, a Case Study,
16 July 2015, http://vixra.org/pdf/1507.0130v1.pdf
Luiz, the cylinders have the same rank of infinity, none is bigger.
One of the most mind-blowing facts a young mathematician learns is that, in a specific, rigorous way, there are exactly as many numbers between 0 and 1 as there are between 0 and 2, 0 and a million, or even in the entire set of real numbers! Don't worry, it's natural to feel dubious about that. It seems impossible that a set could be the “same size” as a set that contains it plus some other stuff! But that’s one of the marvelous mysteries of infinity.
.............................................................................. Evelyn Lamb
Luiz C. L. Bothelho,
It is certainly not I who is being ridiculous in public. Schmidt thinks that 'near infinite' is a scientific quantity, as he said, in public, on national television! No it is not. Just tell us all Luiz, how close to infinite did you get before you realised you were near to it? 'Near infinite' is utter rot! Schmidt is talking nonsense.
That which is infinite cannot get bigger - it 's already infinite. Schmidt does not even understand elementary mathematics - he used the infinite sequence 0,1,2,3,4 ... and claimed that by multiplying it by 2 the sequence 0,2,4,6,8, ... is twice as big as 0,1,2,3,4, .... That is utter rubbish. Infinity is not even a real number, so Schmidt's (2 x 'infinity') is claptrap. Schmidt doesn't even know that infinity is not a real number and hence can't be multiplied by anything, let alone by 2. Schmidt doesn't know what he is talking about, and neither do you.
Schmidt claimed that he and/or his friends measured 'near infinite'. No, neither he nor they did. He is talking rubbish.
Schmidt claimed that the Universe is embedded in four dimensions. Even by the theory used by the cosmologists that is patently false, since their mystical 'spacetime' is four-dimensional by a mathematical construction and not embedded in anything. The cosmologists, including Schmidt himself, assert that their expanding universe is not expanding into anything, and so it is not embedded in anything. So Schmidt is still talking nonsense.
That such nitwits as Schmidt get a Nobel Prize for such garbage attests to the intellectually decrepit state of physics and astronomy. That you are a proponent Luiz, of such drivel, speaks for itself.
Luiz Botelho,
Calling me a 'fool' is not a scientific argument, no matter how angry you get or how loud you scream it.
Your analogy with stereographic projection is false - there is no point at infinity, because infinity has no bound - it's limitless! So how close to infinite did you get Luiz before you realised you were near infinite?
You conveniently avoided addressing the specific claptrap of Schmidt. Schmidt did not make things simple to instruct the boy; Schmidt does not know what he is talking about, and revealed his ignorance on national television, for all to observe. Let's see, according to Schmidt, take the infinite sequence 0,1,2,3,4 ... and multiply all its terms by 2, to get, 0,2,4,6,8, ... According to Schmidt he has now doubled infinity, he has made infinity get bigger! That is utter rot. His other 'arguments' are no less incompetent.
Your infinite cylinder suffers from the very same errors committed by Schmidt and his fellow cosmologists. The increase of the area of the base of your infinite cylinder does not make the infinity of your infinite cylinder get bigger.
Cosmology is not science - it's mysticism and superstition cloaked in scientific and mathematical jargon, pretending to be science. Physics and astronomy are now intellectually decrepit. Schmidt is an example of how ridiculous things have become.
i can see one form of infinity.
( to distinguish b/w infinities we can introduce prime ('))
2*infinity=infinity'
2=infinity'/infinity
infinity' is double than that of infinity
Actually we cant distinguish b/w infinity & infinity' normally , and that is why we write ,infinity'/infinity= not-defined , it means 1,2,3........any number can be there , which depends on which number is multiplied by infinity. But in this case we know about it.
Does it means that infinity' > infinity ? Yes because both are divided to give 2 .i guess mathematically we have to do it like this,
This Question explains that idea very well:
we have a infinite plane area which have uniform charge density, calculate electric field at point P .
.
Intrigration(E.da)=Q/e.
Where
Q=charge , E=electric field , A=area , e.=epsilon ,sigma=area charge density.
1) integration( E.da) = 2AE (considering pill box)
2) Q/e.=sigma*A/e.
Solving this , here area is infinity
But if we think that both sides are equal to infinity , then sigma/e. have to be included in infinity. Hence we cant get any answer of electric field while canceling infinity on both sides.
But constants have to be outside from the infinity , then we can get answer ,
So, E=sigma/2e.
and that is why 2*infinity=infinity' (here infinity' is some answer)
so , infinty'/infinity = 2*infinity/infinity = 2
More over E=sigma/2e., is a experimentally correct answer ! (of course plane is not infinite in real cases but distance (where electric field is measured) should be very very less than the length of the edge of the plane). In that approximation we get experimentally valid electric field.
And that is why some infinities are bigger .
Luiz Botelho,
You have no defence Luiz, and neither does Schmidt. Schmidt does not know what he is talking about, and neither do you. That he addressed an 11 year old boy is irrelevant to his ignorance of elementary mathematics and physics, which he has revealed in public, as you have too. Schmidt's arguments are not simplifications or "loose affirmations" for boys or his national television audience - they are utter claptrap. He is a glowing example of what the Nobel Prize has becomes - a prize for nitwits conferred by nitwits for 'theories' that are nitwit.
Since infinity is not even a number, (2 x 'infinity') is a meaningless collection of symbols. Yet Schmidt told the audience on national television that it is double infinity, it is infinity getting bigger. His other arguments are just as asinine. Nonetheless you support Schmidt, in total disregard for the truth, in violation of elementary mathematics and elementary physics. People like Schmidt and you are symptomatic of the intellectual decrepitude that is now called physics and astronomy. Such hogwash must be eliminated from science.
Sourabh
Infinity is not a number, is a mathematical concept without numerical value.
It is not correct operate as you did.
Hugo alberto fernandez
I do agree with you sir. But this type of mathematics is doing well , when we deal with infinite plane having uniform charge density(uniform charge density plate of infinite size, even here mathematical concept is introduce in mathematical operation ) .
2*infinity=infinity => 2=1 ? No ,
so 2*infinity=infinity => 2=not defined quantity .This not defined quantity is equal to 2 ?
Please explain that sir, or recommend some books .
Sourabh Singh,
Ultimately numbers must be multiplied by numbers. Since infinity is not a number it cannot be multiplied by numbers. Thus (2 x 'infinity') is a meaningless concatenation of symbols. Similarly, ('infinity' + 1) is meaningless. To use 'infinity' in the usual arithmetic as a number you must first prove that 'infinity' is a number. Cantor's 'theory' of transfinite numbers has no relevance here.
Sourabh
Assume A=infinity=1+2+3+..., the addition of natural numbers.
Applying arithmetic rules we obtain: 2A = A+A = B => B>A
A=1+2+3+…
B=2+4+6+…
On the other hand, B is the addition of even numbers, while A is the addition of odd and even numbers. So, => A>B
This contradiction shows that arithmetic rules do not apply with infinities
I do not agree with Toth's answer.
The Newtonian gravitational potential means the existence of a gravitational force, which does not exist in GR.
The apparent analogy between Newton’s potential and a term in the metric (Schwarzschild) is by construction, as consequence of the adopted symmetry (spherical).
Any point source at rest, whatever be the source (charge, mass, etc.), will produce 1/r behavior at infinite
Infinity is NOT a real number. It never was and never will be. Let those who want to use 'infinity' as a real number first provide a proof that it is a real number.
Big Bang creationism is not science, because creationism is not science; it is mysticism. Yet cosmologists would have all and sundry 'believe' that the Universe created itself out of nothing! 'Believe' is the appropriate word, since cosmology is a belief system like any other form of mysticism.
Luiz Botelho,
No Luiz, it is not I who is ridiculous; you are. Give us all your proof that 'infinity' is a real number. We await your miracle with bated breath.
Let's recall what Professor Schmidt (Nobel Laureate for physics) claimed on Australian national television, for all to see. Take the infinite sequence 0,1,2,3,4, ... Now multiply each term by 2 to get the infinite sequence 0,2,4,6,8, ... According to Schmidt the infinite sequence 0,2,4,6,8, ... has multiplied infinity by 2 and so, like his phantasmagorical expanding infinite Big Bang universe, infinity has got bigger. No, that's utter hogwash. Schmidt doesn't know what he is talking about.
Big Bang creationism with its expanding universe and black hole is not science, because creationism is mysticism, not science. According to the Big Bang cosmologists, the Universe created itself out of nothing. This is the purest form of creationism - the creator created itself! Cosmologists ridicule all other creationisms. They claim that their creation myth is the one and only true creation myth, all others are false prophets!
Luiz,
Do not be so arrogant, if possible. You, as anyone, make mistakes too.
This is not right.
The EXTENDED REAL NUMBER SYSTEM adjoins two symbols (no numbers), +oo and –oo, having particular properties (with new added operative rules).
Those symbols are not numbers.
Arithmetic (“arithmos” means number), which only tries with numbers, is not modified. You can not introduce “arithmetic”, you added particular operative rules (justified with the limit operation) in order to include infinities.
Infinities are not numbers. Stephen is right
Besides, your example with cylinders is wrong in any branch of mathematics.
No infinite is bigger or smaller than another infinite
Of course, I may be wrong too. Let me know if you detect some mistake. I will be gratefully.
Hugo, you write "Of course, I may be wrong too."
I don't think so. You think in terms to which the categories of wrong and right don't meaningfully apply.
Hugo, that is just not true. There are infinities that are much larger than other infinities, & that can be proven just by naming the type of infinity (set), the type of the members of the set, & then in comparing them to one another, you see that one set rapidly outstrips the other in terms of the smaller infinity not having enough terms to keep up with the larger infinite set. The set of whole or counting numbers is infinite, but the set of rational numbers is far larger, so it's a larger infinity.
- Badges
- Science topic
- Similar topics
- Psychology