I think that the most successful theory of gravity is that the orbit of planet can be explained with this theory and the orbit of satellite was designed with this theory. To design an orbit of a satellite, the three of the factors of the orbit: 1) The radius, 2) The inclination angle, 3) The eccentricity, must be calculated. And, the Newtonian theory of gravity is the only theory that can calculate the three factors. In another words, if there was not the Newtonian theory of gravity, the orbit of the satellite could not be designed. It was known that, from Einstein’s field equation, the orbit of planet can be deduced. And it was used to explain the advance of the Mercury perihelion. But, I cannot find the method to calculate the three factors with Einstein’s field equation.
In designing an orbit of a satellite with Newtonian theory, besides the gravitational force, other kinds of force are involved, such as the mv2/r, the light pressure of the sun.The orbit is affected by these kinds of force. And, these kinds of force are interacting with the gravitational force.
How to distinguish these kinds of force form the curved space. Or, all of kinds of force are the curved space?
to describe elliptical motion initial velocity and radius are needed!
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The question is:How to determine the r and v with geodesic equation?
In addition, the elliptical motion only is determined with the direction of v.
"It was known that, from Einstein’s field equation, the orbit of planet can be deduced. And it was used to explain the advance of the Mercury perihelion. But, I cannot find the method to calculate the three factors with Einstein’s field equation."
Exactly, Yin! The problem with general relativity is that always new linear equations are "invented" to describe general relativity, like the Minkowski space, Schwarzschild, Kerr.... They even falsely pretend that gravitomagnetism (Heaviside's theory) can be deduced, because they need it to explain issues.
Indeed, the theory that perfectly models gravity is that of Oliver Heaviside (1893):
This theory is the transposition of electromagnetism into gravity: the Coulomb force equation is totally like Newton's gravity force equation. So, when masses are moving, one can state that there is a magnetic-like field generated. This way, you can perfectly explain numerous phenomena, like Prof. Oleg Jefimenko has shown (theoretical development with numerous examples in his excellent books).
By testing it on cosmic phenomena, one always find the solution through gravitomagnetism. You find the link annexed (PDF file).
(Between brackets: Anatoli Vankov has proven that the calculus of the missing perihelion advance is wrong, and obtained by multiple approximations. Without the approximations, the advance is zero.)
http://gsjournal.net/books/De-Mees-Gravitomagnetism-and-Coriolis-Gravity-2011-A4.pdf
The question is good.
I think the tensor theory of curved spacetime can eventuate to repetitive perturbations and thus linear solutions maybe don't describe the reality under heavy conditions just like in an extreme gravitational field or at elementary particle scale level. It seems to me that the cyclic quantum mechanical backreactions are obvious. There is so much to explore. Hoping the "black hole" and the "event horizon" could set estimated as being observable or not observable.
Let me mention that the Shapiro time delay approaches infinity for light passing close to a black hole.
I found that in this case, also the distance down into the funnel approaches infinity. This implication of the recently recovered global validity of c in the equivalence principle (Progress in Physics, latest issue) entails that "stretching" has acquired an equal rank to "curvature" in the differential geometry of gravitation.
Chaos theory has stressed stretching over curvature, general relativity has stressed curvature over stretching. Now a rapprochement is in sight.
We use GR to compute the orbit of Mercury. GR has been verified to high accuracy in analysing the orbits of satellites. Where do you get this curious idea?
@Thierry de Mees: the Mercury precession can be calculated exactly from the Schwarzschild solution. What ``multiple approximations'' are we talking about?
Do you think the Schwarzschild solution is a pure curved space tensor theory solution?
Dear F. Leyvraz: the study of Anatoli Vankov has shown that there are several approximations that have been used to calculate the Mercury advance. When looking at the detailed calculus, he found another result. If you take the time to look at his annexed paper, you will find out why.
Article Einstein's Paper:“Explanation of the Perihelion Motion of Me...
Dear Yin Zhu: GR cannot calculate that. For the calculus of the binaries' decay, gravitomagnetism has been used. Also for the Gravity Probe B, it has been used.
The calculus is annexed.
Research Elliptical Fly-By and Expected Gyro-gravitational Orbit Accelerations
Dear Dr. Thierry De Mees, thank you very much for your intrducing the interesting papers. I shall study them. If you are interested, please reference:
Observation of the Direction and Neutralization of Gravitational Field
https://www.researchgate.net/publication/286192164_Observation_of_the_Direction_and_Neutralization_of_Gravitational_Field_V7
Working Paper Observation of the Direction and Neutralization of Gravitati...
Dear Yin Zhu: Thank you for your link. It is an interesting working paper.
You write: "For example, if there was the gravitomagnetic effect, the Newtonian gravitational constant G for the high speed stars/planets should be different from the low speed ones"
In fact, the gravitational constant doesn't change in gravitomagnetism.
Further, I would suggest to name the Fig. 2 in your paper "gyrotational" (from the Greek word 'gyros', round) instead of "gravitational", because the closed loops are occasioned by the rotation of the objects. Indeed, some gyrotation effects, even if very small, will on the long term change the shape of a system: planetary system, Saturn rings, and so on.
The Newtonian gravity is divergent, independently from the north and south pole.
Maybe my book will inspire you to solve the issues regarding the Roche or Hill sphere.
Anatoli Vankov spends a lot of time discussing Einstein's paper on the subject. This may be good science history, and conceivably he may be right about the ``mistakes'' he fnds in Einstein's paper (though I very much doubt it), but surely this is all irrelevant: we are asking about issues of mathematics, and physics, not about who said what when. The Schwarzschild solution *in its present form* is readily checked to be a solution of Einstein's equations (no matter what peculiar form Schwarzschild himself gave to it. Again, this is history). And the geodesics on the Schwarzschild metric are readily computed to yield Mercury's precession.
Dear Dr. F. Leyvraz, it is a well known story that "And the geodesics on the Schwarzschild metric are readily computed to yield Mercury's precession."
But, I am certain, no body can use GR to compute the three of the factors of the orbit: 1) The radius, 2) The inclination angle, 3) The eccentricity.
So, this is a bad story.
Yin> I am certain, no body can use GR to...
Everybody taking a university level physics course containing introduction to general relativity would(should?) be taught to do that! It does not even involve the solution of any differential equations, only exploitation of rotation and time translation symmetry. From these you can calculate the conserved angular momentum vector, and a conserved energy, from the initial data. The angular momentum determines the plane of motion. The energy determines whether the orbit is bound and stable or not, and for a bound stable orbit the maximum and minimum radius of that orbit. The only difference from the same analysis of Kepler motion is that this case require the solution of a cubic algebraic equation, instead of a quadratic one. (I am talking about motion in the Schwarzschild geometry.)
Yin> So, this is a bad story.
Yes, extremely bad! You should be ashamed of posting such ignorant silliness.
I think the issue is about the Schwarzschild solution how it was converted from the tensor theory, not about Schwarzschild-applications.
Kåre: with such a reasoning, I can prove that gravitomagnetism is in fact Newton's gravity theory, by adding a motion in Newton's equation. Honest scientists, like Jefimenko who extended Newton's gravity to gravitomagnetism by determining that the energy equilibrium is broken when a mass moves against another, will however not pretend that gravitomagnetism is in fact Newton's gravity theory.
Indeed, GR proponents need to get considerable things out of the bag of tricks to get at Kerr's metric, which is absolutely not a pure derivation from GR. The first trick being to define the equatorial plane of a body's angular momentum as the plane of action, without any physical or other ground whatsoever. They just know to where they need to come (thanks to gravitomagnetism and/or observation) and they fit the calculus to it.
Instead, gravitomagnetism precisely physically shows why and to what extend orbiting objects come toward the equatorial plane, and it explains why the orbits at the edge of a disc galaxy are much less bound to that equatorial plane. It also shows that some angles with the equatorial plane are less bound as well, which opens a track to explain angular quanta in particle physics. I will add a paper that calculates these issues in a separate post, if requested.
Finally, I must say that your way of trying to silence someone who is justly questioning GR, is abominable.
Dear Dr. Kåre Olaussen,
Thank you very much for your answer.
This question has been discussed many times from May 25, 2014. And no body claimed that the three factors can be calculated with GR. So, I said "I am certain, no body can use GR to compute the three of the factors".
Now, you gave a method to calculate them. It seems you are right. But, we know, there is a distance between this method and a real (calculated) result. If you should have a calculation for the three factors, I should thank you very much.
Check the following link:
https://en.wikipedia.org/wiki/Schwarzschild_geodesics
Best wishes, Francois
Yin> So, your calculation is needed.
No! If you are unable to do the calculations from expositions in a large number of textbooks, or the wikipedia article linked to above, no amount of calculations from my side will help. You really have to do it yourself.
A couple of points:
1. The direction of the angular momentum can be calculated from the initial data, as the direction of r0 x v0. This is sufficient to find the orbital plane, and to find the rotation needed for transformation to a coordinate system where the angular momentum points along the new z-axis. This is the most messy part, and usually skipped in textbooks (but of course important for practical description of satellite orbits). But it is exactly the same mess for the Kepler problem and Schwarzschild geodesics.
2. The exposition in the Wikipedia article contains a lot of material. To calculate the maximum and minimum radii, scroll down to the section about Effective Radial Potential, and set the radial velocity to zero. The gives you a cubic equation in 1/r. It is useful to plot the potential, and see how the possible solutions can vary with the energy E. There is a couple of possibilities not found in the Kepler problem; you may fall into the black hole, and it is possible for light to circulate in an orbit with radius 3/2 of the Schwarzschild radius (this is an unstable solution, though).
Thierry> Finally, I must say that your way of trying to silence someone who is justly questioning GR, is abominable.
I did not (mean to) criticize the opening question of this thread, only one specific post. Now, as Yin has explained, after almost two years and quite a few not-that-useful answers, he had reasons to believe that his question could not be answered. So, maybe I should move a considerable amount of my critique from him to earlier contributors.
I never want to silence posters on Q&A. But some posts obviously discourage serious scientists from participating.
Thierry> I can prove that gravitomagnetism is in fact Newton's gravity theory, by adding a motion in Newton's equation.
What is the action or Lagrangian for gravitomagnetism coupled to matter? Is it in any way different from the linear approximation of GR? You are right that the derivations of the Kerr or Kerr-Newman metrics look difficult, with a lot of required interpretation and analysis of the solutions. But, in the solar system, the linear approximation is (almost more than) good enough for all observable effects.
Dear Kåre,
The Schwarzschild solution would be valid only when the orbiting test mass itself was negleckted and the circumstances are near the peaceful spherical orbit. When an orbit for example with extreme eccentricity is considered, the unstability cannot be avoided. Besides, Lense-Thirring effect and many more could make it impossible to design the orbit with Schwarzschild when true GR solution can succeed, but - it's unknown. For varying situations we have Kerr, Kerr-Newman, Reissner-Nordström, etc. It seems to be challenging to get a good simplyfied and functional useful metric for all cases...
I think the GTR unifying with the quantum mechanics can be a pretty simple and even exact solution but we don't have it yet.
Esa @
It seems to me that the linearized equations are more than sufficient for the analysis of genuine GR effects (i.e., post-Newton). They also make it much simpler to incorporate all other more trivial (non-relativistic) kind of perturbations. For satellite orbits, GR corrections to the Kepler solution is probably not the first thing to worry about.
It is hard to find physical situations where a symbiosis of quantum mechanics and general relativity have to be considered. The closest thing I can think of is the unavoidable depolarization of polarized beams in high-energy accelerators, which to some extent can be interpreted as due to an analogy to Hawking radiation.
Francois Leyvraz: nice link: they need 4 approximations in order to get the Mercury advance, while that advance is in fact extremely tiny. I am curious to know the error calculus. Oh no, Vankov found already, the advance is in fact zero.
Kåre: which linear approximation of GR you mean Minkowski (the magical extension of SR)? or Schwarzschild? or Kerr? or any other of the palmares? Soon they will have an adapted metric for every single case, and they will call it all GR.
Or do you mean the hijacked and wrongly alleged gravitomagnetism-ersatz? The latter, I guess.
Well, the need of oblate spheres for "the linearized GR" to imitate gravitomagnetism is enough reason to reject all of GR.
Gravitomagnetism does not need that. It uses full spheres. And it really solves the issues of our planetary system without pretending that the sun and all the planets are oblate.
The GR proponents even need to pretend an oblateness that is related to their individual spin, in order to get the correct results...
Thierry > Gravitomagnetism ... really solves the issues of our planetary system without pretending that the sun and all the planets are oblate.
Please explain how your equations manage to generate an attractive force between the earth and the moon. The equations look identical to those of electrodynamics, where they imply that equal charges repel each other. The same thing happens here, as follows from a calculation you can do in your head.
Apart from this sign, which kills the theory before it gets off the ground, the theory has other problems: Should the source of a static gravity field be the density of invariant mass? Then they could behave correctly under Lorentz transformations. However, invariant mass is not conserved, but can convert to energy, leading to a non-conserved four-current source for gravitomagnetism, and in turn an inconsistent system of equations. (Maxwell equations are consistent only because the electromagnetic field has a conserved electric four-current as source.)
Instead one must interpret the source (in the static non-relativistic limit) to be energy density (divided by c2). But this is only one component of a symmetric, conserved energy-momentum 2-tensor (with ten independent components), which therefore must be the real source of gravity. This points directly towards general relativity, with some modifications allowed (scalar-tensor theories).
Gravitomagnetism is not even allowed to enter the game. Well, I am sure you have been told this many times already, if you have tried to get your ideas published in physics journals.
Kåre Olaussen>Please consider this problem: The Newtonian gravitational effect varied in the (altitude) height of 1cm can be detected with an atomic clock. While the time effect of GR only can be detected on the (altitude) height of more than 17cm. But, the experiments claimed to prove the time effect of GR has not observed the Newtonian gravitational effect . Why?
In the textbook to deduce the orbit of a satellite with Schwarzschild geodesics, the time effect of GR need be used. Is it valid?
Many books gave the method to deduce the orbit of a satellite with GR. But, no book gives a real orbit of a satellite. Shall you give a real orbit with 1) The radius, 2) The inclination angle, 3) The eccentricity.
@ Thierry: I actually read Vankov, and his analysis is badly done.He connects the issue of orbital precession with the issue of a shift in the mean radius, which, as he claims, affects the circumference. Obviously, the precession depends on the difference between radial and angular frequency, an issue Vankov never addresses.
In fact, what you have is an equation that can be exactly solved in terms of elliptic functions. The approximations made in the limit of large radii (large, that is, in units of the Schwarzschild radius) are *controlled* approximations, that is, it is iin principle straightforward, though tedious, to estimate the mistake made, which, furthermore, is quadratic in the small parameter. Since the small parameter is very small indeed, the corrections are truly negligible. In any case, you can easily either integrate the equation numerically, to any degree of precision desired, or evaluate elliptic functions, again to extremely high precision.
``they need 4 approximations in order to get the Mercury advance, while that advance is in fact extremely tiny. I am curious to know the error calculus.'' This shows a peculiar misunderstanding of perturbation analyses. When a small parameter exists, one uses this smallness to obtain, one after the other, terms of first order in the parameter, in the second, and so on. The smaller the parameter, the more reliable the approach, since the square of, say, 0.001 is much smaller *relative* to 0.001, than is the square of 0.01 relative to 0.01. So the fact that the effect is very small, which you are quite correct in pointing out, is in fact a guarantee that such approximations are extremely accurate in relative terms.
``But, no book gives a real orbit of a satellite. Shall you give a real orbit with 1) The radius, 2) The inclination angle, 3) The eccentricity.''
The orbit not being an ellipse, it cannot be characterised using ``radius'' by which I assume you mean semi-major axis, or eccentricity. It can be given as a formula involving elliptic functions. It can also be approximated, to first order by an ellipse, to second order, Vankov and Thhierry notwithstanding, by an ellipse undergoing precession. .
Kåre: please stop this puppetry. Nobody can get from Maxwells equations why electrons attract or repell either. You put the signs by yourself.
Neither does Newton's equations explain why there is attraction.
Concerning your invariant mass. First you infect gravitomagnetism with general relativity inventions, then you "prove" gravitomagnetism wrong. But if you calculate back from a second frame to the first frame, indeed, there is gravitational induction. The Lorentz equations are not identical, because the SR interpretation is wrong for gravitomagnetism.
Einstein omitted to calculate back like Oleg Jefimenko did. Then he would have discovered that there is gravitational induction.
Gravitomagnetism doesn't work the GR way, of course!
But none of the annexed successes of gravitomagnetism can be undone. Neither the Gravity Probe B result, nor the need of gravitomagnetism to explain the decay of binaries.
F. Leyvraz: that looks interesting. Since Vankov is still alive and since his calculus is not my crusade, maybe would it be better that I connect you both, so it can be discussed thoroughly? I am interested in the very truth, aren't we all?
Yin> The Newtonian gravitational effect varied in the (altitude) height of 1cm can be detected with an atomic clock. While the time effect of GR only can be detected on the (altitude) height of more than 17cm.
Can you tell us which published observations you are talking about? It is impossible to know what the facts behind your statements are, but there seems to be some confusion involved.
Yin> Many books gave the method to deduce the orbit of a satellite with GR.
Yes. So why did you ask the question of this thread then? There is a 6-dimensional continuous space of initial conditions, plus the masses of the Schwarzschild geometry and the satellite. Textbooks teach you how to calculate the orbit parameters you ask for from this information. What exactly prevents you from doing this from the information given? In particular, if you already know how to do it for Kepler motion, as you say?
Of course, as Leyvraz points out, the notation of radius and eccentricity, which may have very precise definitions for ellipses, must be replaced by quantities like maximum and minimum radii.
Kåre>
1. It is generally reported that as the altitude height is varied less than 1cm, the readings of the high precision atomic clock is different. The time effect of GR is 17cm please see:
Müller H, Peters A, Chu S. A precision measurement of the gravitational redshift by
the interference of matter waves, Nature, 2010, 463(7283): 926-929
Chu's work was questioned by some people.
2. We know, in Newtonian theory of gravity, the orbit of a satellite is described with the Largrange Equatios. In it, the semimajor, inclination angle and The eccentricity are described with different equations. It is notable, all these are based on the question GMm/R^2=mv^2/R. So, the radius R is important.
The crucial problem for GR is that none of such equations was obtained in GR although a method to deduce the orbit was presented. However, the maximum and minimum radii cannot be used for a real orbit.
Thierry> You put the signs by yourself.
No, you don't. Because you can't (if you are taking your craft seriously). That is why I asked for the Lagrangian of your model; that helps you stay honest and consistent.
Thierry> Gravitomagnetism doesn't work the GR way, of course!
That is good to hear, since it obviously cannot work al all.
Kåre: I repeat: First you infect gravitomagnetism with general relativity inventions, then you "prove" gravitomagnetism wrong.
Spacetime is a chimera, so, there is no Lagrangian.
Yin> Müller H, Peters A, Chu S. A precision measurement of the gravitational redshift by
Yes, that is a beautiful experiment, which I already knew about. It probably represents the-state-of-the art for such measurements. But there have been some time for improvements during the last six years, I didn't check.
Yin> It is generally reported...
So, where is this published? "Generally reported" do not sound like serious science. In any case it is a question of measuring the same effect. It has nothing to do with "Newtonian" or "General relativity" effects (and, as such, gravitational redshift is not a very strong test of GR).
Yin> the orbit of a satellite is described with the Largrange Equatios.
Are you talking about the Euler-Lagrange differential equations of motion? Which obviously also exists for the GR solutions. So, I assume you must be talking about something else. But what?
Yin> However, the maximum and minimum radii cannot be used for a real orbit.
What??? For an ellipse, that information is equivalent to the information about semi-major radius and eccentricity. If you can't work out the connection yourself, it is not due to lack of ability, but just ill will. And, as have been repeatedly said here, the GR solution is extremely well approximated by an ellipse in practical cases; it is only the small precession of its axes which is (barely) noticeable.
@ Thierry: I will gladly talk with Vankov if you believe there is any meaning to it. However, you might just as well refer him to the Wikipedia page I gave: this is a *controlled* approximate treatment. It gives a result which is clearly non-zero.
Now, another issue: consider a star of 3x the sun's mass, with a spin rate of 10 days at the equator, and a retrograde orbiting, small exoplanet at 45% inclination from the star's equatorial plane.
Since Einstein's GR equation is totally symmetrical without any preference, how can you possibly determine if the perihelion of the exoplanet will be an advance or a retardation, and with report to which parameters?
F. Leyvraz: I have send a request to Vankov, but he doesn't follow RG.
I am somewhat confused by your question. The spin should lead one to consider a Kerr metric, and this would be far more complex. However, if we view it as well approximated by a Schwarzschild metric, that is, if we disregard the spin, then the orbit will precess forward, in the sense that the perihelion will turn in the same direction as the orbit does (or maybe the other way around, signs are easy to confuse).
The rotational symmetry does not preclude such behaviour. In fact, it happens in Newtonian mechanics, whenever you have a centrally symmetric potential close to Kepler. Whether the orbit precesses forward or backward then depends on the details of the potential. That the Kepler potential does not precess is due to yet another kind of symmetry, called the hidden symmetry of the Kepler problem. But that is another issue.
F. Leyvraz: So, basically, you say: Assuming that the star doesn't spin, for a perfectly circular orbit, the relativistic orbital velocity will always be faster than the Newtonian orbital velocity?
What you say is indeed true, since the additional potential in the Schwarzschild metric is attractive. But this is not, or at least not obviously, equivalent to the precession issue. That pertains to non-circular orbits. Both in GR and in Newtonian physics, such orbits perform an oscillation from smallest to largest radius and back, at the same time as they turn around the center. Precession arises whenever these frequencies are different, in particular slightly different: if, say, the radial frequency is slightly slower than the period with which the angle phi increases by 2 pi, then the radius attains its maximum after an angular motion slightly larger than 2 pi, so that one has a positive precession. For the 1/r potential, the two frequencies are exactly equal. For r^2, the radial frequency is exactly twice the angular one. In neither case do we have precession: whenever the angle phi increases by 2 pi, the radius has performed either one or two full oscillations. It is a theorem by Bruns that only these two potentials have that feature.
I believe Vankov's computations are affected by similar misunderstandings.
Dear Dr. Kåre Olaussen,
As question cannot be agreed by each other, I shall discuss it one by one and step by step. Now, let's discuss the first problem:
Is Einstein's gravitational time dilation valid? Please see:
https://www.researchgate.net/publication/292970880_A_comparison_between_Newtonian_gravitational_time_effect_and_Einstein%27s_gravitational_time_dilation
Dear Dr. F. Leyvraz, you are welcomed to discuss this problem.
This problem is the first condition for the orbit in GR
Data A comparison between Newtonian gravitational time effect and...
Yin> Is Einstein's gravitational time dilation valid?
Now I think I understand what you mean by the Newtonian effect, the real physical effect caused by the acceleration of gravity. That has absolutely no measurable effects on atomic clocks. Why? Heuristically, because they already feel accelerations of order 1020g due to atomic forces.
But are you sure it is possible to detect the change in pendulum rate when it is lifted 1 cm higher in the gravity field? That leads to a relative change in g of order 10-9. The daily changes in the effective value of g due to the sun and the moon are much larger than that.
And, by the way, both the Newton and Einstein effects you refer to are correctly implemented in the orbit equations.
Yes, calculation of orbits in the Schwarzschild geometric does not have many practical uses: Perihel motion of Mercury, bending of light around the Sun and Jupiter, and the Shapiro effect for similar light-rays. But to do the really important corrections you want to get paid.
F. Leyvraz: So, you say: For a non-spinning star and for a perfectly circular orbit, the relativistic orbital velocity will always be faster than the Newtonian orbital velocity.
Where is the energy coming from? From the central mass, I guess?
Secondly, you speak of the Bruns theorem, but what happens if the central mass is a perfect sphere with a perfectly distributed mass (linear from 0 to R), so, there is no oscillation?
Then, do you say for a perfect central mass: the perihelion advance doesn't appear for circular orbits? So, it only appears when there is an eccentricity?
Yin> which experiment proved the Einstein's gravitational time dilation?
The paper by Stephen Chu and collaborators (as you listed) is probably the most accurate one. There are many earlier, as referred to by them, where the one by Pound and Rebka was the first.
Isn't it strange that Stephen Chu in his Abstract speaks of the factor 1+U/c², being measured up to a precision of 7.10^(-9), while 1+U/c² is only an appoximation of sqrt(1-U/(2c²) resulting in a relative error difference of 1% at least?
Isn't it strange that he states "Our result supports the view that gravity is a manifestation of space-time curvature", while the gravitational time dilation follows from a separate reasoning, the equivalence principle, which is in fact independent from GR as a whole, and which could fit with much more theories?
@ Thierry:
``Then, do you say for a perfect central mass: the perihelion advance doesn't appear for circular orbits? So, it only appears when there is an eccentricity?''
The perihelion advance is not defined in a circular orbit, since there is no perihelion.
``Where the energy comes from?'': the potential energy in the effective description of a particle in GR has an additional attractive term proportional to 1/r^3. The energy does not come from anywhere. It is another expression for the energy than the Newtonian one which is being conserved.
Finally, non-circular orbits always go, by definition, between a maximum radius value and a minimum one. It is this radial oscillation I talked about, not any oscillation of the central mass.
Thierry> Isn't it strange that Stephen Chu...
No, that part is not strange. They need to perform a measurement where d\nu/nu is of order 10-8. They do not need to measure, or claim to measure, the coefficient of that ratio to 8 decimal places. For me, two decimals sounds fine.
Thierry> Isn't it strange that he states...
The formulations are a bit roundabout on this, as I read them. But I agree that the observation of gravitational redshift is not a very strong proof of GR. Any sensible theory of gravity must have this prediction; otherwise it would in principle be possible to make Perpetuum Mobile of the first kind.
F. Leyvraz:
So, you say: Assuming that the star doesn't spin, for a perfectly circular orbit, the relativistic orbital velocity will always be faster than the Newtonian orbital velocity, but it is not the perihelion advance mechanism.
““Where the energy comes from?'': the potential energy in the effective description of a particle in GR has an additional attractive term proportional to 1/r^3. The energy does not come from anywhere.”
So, you say, no energy from anywhere. Curious. The Gauss flux perfectly explains the 1/r^2 term. How come that there is no explanation for the 1/r^3 term?
Has that been derived directly from the GR equation? Or was there a metric used?
“Finally, non-circular orbits always go, by definition, between a maximum radius value and a minimum one. It is this radial oscillation I talked about, not any oscillation of the central mass.”
So, you just mean, non-circular orbits with an eccentricity? And so, the periheliun advance only appears when there is an eccentricity in the orbit?
Kåre: "The formulations are a bit roundabout on this, as I read them. But I agree that the observation of gravitational redshift is not a very strong proof of GR. Any sensible theory of gravity must have this prediction; otherwise it would in principle be possible to make Perpetuum Mobile of the first kind."
We are here talking of Nature, the journal with one of the greatest reputations over the entire world. Very few papers are even taken into consideration by Nature. The paper has been peer-reviewed and then accepted.
Since this is not about politics, but about science at the highest level of the planet, can we say that the peer-reviewed research has to be entirely reliable and unbiased?
Can we say that the conclusion was biased? So, can we say that the authors have in fact concluded a lie?
Can we say that Nature was not able to detect the false conclusion? Can we say that Nature is sharing in guilt of this downright lie? Can we say that Nature is in fact biased?
Thierry> Can we say that Nature was not able to detect the false conclusion?
Absolutely not! The paper is about some fantastically accurate methods of measuring frequency shifts, applied to some interesting effects in gravity and relativity. The conclusions are about the accuracy of their measurement, not really about what these measurements say about any theories of nature.
But there is a sentence of general nature, referring to space-time curvature, which I find misplaced, and which can lead to misinterpretations. The experiment does not measure the curvature of spacetime in any way.
Kåre: My question should of course read:
Can we say that Nature was not able to detect the false conclusion about the curvature of spacetime ?
Of course they had the means to detect that!
"They need to perform a measurement where d\nu/nu is of order 10^-8. They do not need to measure, or claim to measure, the coefficient of that ratio to 8 decimal places. For me, two decimals sounds fine."
Well, doesn't that mean that whatever the result is, sqrt(1-U/(2c²) or 1+U/c² , or any series that begins with 1+U/c² are all equally valid, and consequently that it doesn't confirm at all the alleged relativistic value of gravitational redshift?
So, weren't the authors biased by claiming that as well?
Can we say that Nature was not able to detect the false conclusion about the alleged relativistic value of gravitational redshift?
"The conclusions are about the accuracy of their measurement, not really about what these measurements say about any theories of nature"
I don't agree because the paper was not only a presentation of high technicity. The setup of the paper, as from the Abstract itself, contains clearly at least an unallowable statement on the alleged relativistic value of gravitational redshift, and moreover an unallowable statement concerning the alleged curvature of space-time.
So, what was the published value of the alleged high technicity anyway?
So, can't we say that, spites the highest level of peer-review, this paper shouldn't have appeared in the most influent and respected journal of the entire world?
Can't we say that,in fact, Nature has shown it is biased? Can't we say that,in fact, Nature is biased over the whole line when it comes to GR and to all what reports to it?
``Well, doesn't that mean that whatever the result is, sqrt(1-U/(2c²) or 1+U/c² , or any series that begins with 1+U/c² are all equally valid, and consequently that it doesn't confirm at all the alleged relativistic value of gravitational redshift?''
It confirms the existence of such a red shift, as well as the coefficient in the term U/c^2. That is pretty much all you can hope for. Any theory that differs from STR or GTR in terms of order U^2/c^4 is impossible to refute.
It does confirm the value of the gravitational red shift compared to all theories that predict a red shift with a significantly different prefactor in U/c^2.
Finally, in an experimental paper, one may argue that the experimental results are what matters. If the statement about space-time curvature is wrong, a referee could have asked for it to be appropriately changed. However, it does not modify the fact that this consequence of GTR was observed to high accuracy.
``So, you say, no energy from anywhere. Curious. The Gauss flux perfectly explains the 1/r^2 term. How come that there is no explanation for the 1/r^3 term?''
First a misunderstanding: 1/r^3 is the modified *potential* energy, so should be compared to the Newtonian 1/r, not 1/r^2.
Gauss flux ``explains'' 1/r term: after a fashion, yes. But eventually, we simply set the potential energy of gravity to 1/r on the basis of observations. Gauss flux stands for the fact that 1/r is the solution to Laplace's equation. This was rather a coincidence in Newtonian mechanics, whereas it follows as a consequence of Einstein's equations in the limit v/c
F. Leyvraz: "However, it does not modify the fact that this consequence of GTR was observed to high accuracy."
Here you say "n'importe quoi". I have just proven step by step that it doesn't prove any GRT consequence whatsoever.
"Gauss flux stands for the fact that 1/r is the solution to Laplace's equation. This was rather a coincidence in Newtonian mechanics..."
That is also "n'importe quoi". You deny the real physics, which is the flux of gravitational energy. Of course it explians the 1/r^2 term of Newtonian gravity force, which indeed corresponds with the Newtonian 1/r potential energy. There in no coincidence whatsoever.
"As to there being no perihelion precession for circular orbits, I can only repeat what I said before: a circular orbit has no perihelion, so it cannot precess."
My phrase was: Assuming that the star doesn't spin, for a perfectly circular orbit, the relativistic orbital velocity will always be faster than the Newtonian orbital velocity, but it is not the perihelion advance mechanism.
So what do you say finally, will the relativistic orbital velocity always be faster than the Newtonian orbital velocity or not? And is that due to the same mechanism as with the perihelion advance or not?
``That is also "n'importe quoi". You deny the real physics, which is the flux of gravitational energy. Of course it explians the 1/r^2 term of Newtonian gravity force, which indeed corresponds with the Newtonian 1/r potential energy. There in no coincidence whatsoever.''
Neither Newton nor anybody else ever seriously claimed gravity to arise from any kind of flux, of ``gravitational energy'' or otherwise. Le Sage did, but his theory never really was equivalent to Newton's. The first really basic *explanation* of Laplace's equation for Newton's potential was given by the low-speed limit of Einstein's equations. (If you know another reference, I would be glad to hear about it). And higher order corrections to the low-speed limit give an attractive 1/r^3.
``Assuming that the star doesn't spin, for a perfectly circular orbit, the relativistic orbital velocity will always be faster than the Newtonian orbital velocity, but it is not the perihelion advance mechanism.''
That is correct. Of course, one might argue that such statements are coordinate dependent, hence meaningless. So one should make appropriate caveats about the fact that we properly identify variables with the corresponding Newtonian variables in the low-speed limit.
``Here you say "n'importe quoi". I have just proven step by step that it doesn't prove any GRT consequence whatsoever.''
There is a problem of logic here. You are, of course, right in saying that it does not prove GR: no experiment *ever* proves anything. This experiment confirms a prediction of GR. That is, GR predicts an effect, and the experiment shows that the effect is indeed found, and that the size of the effect is compatible with the GR prediction.
That is pretty much all an experiment can do. Of course, it only shows the leading order of the power series, but that is not a serious limitation. It invalidates any theory predicting either a zero effect, or an effect having a significantly different prefactor.
An important issue is the other one that Kare and yourself raised: the prediction is not specific to GR, but follows from the equivalence principle in general. So the experiment verifies this particular instance of the equivalence principle. In any case, it is a valid answer to Yin Zhu's question, as to whether time dilation was observed.
It was.
F. Leyvraz: "Neither Newton nor anybody else ever seriously claimed gravity to arise from any kind of flux."
It's not relevant who found that, but the flux explanantion is valid in 95% of sciences (except perhaps in some weird theories). Gauss' flux is doing excellent work. The 1/r^3 term has no physical explanation.
"This experiment confirms a prediction of GR."
That is a lie. The equivalence principle is embedded in the biased equivalence of inertial and gravitational mass by introducing the gravity constant G. Newton did that. Of course that has nothing to do with GR.
What happened is that Doppler found that light is frequence-sensitive and Planck found that an energy shift gives a frequency shift. Of course that has nothing to do with GR.
"the prediction is not specific to GR"
Of course! (as I said) This annihilates all your prose in favor of the authors and Nature, and it confirms their overwhelming bias and the uselessness of the paper.
" it is a valid answer to Yin Zhu's question, as to whether time dilation was observed"
NO, it is only valid in a biased mind. Energy loss of light is not time dilatation!
F. Leyvraz: "higher order corrections to the low-speed limit give an attractive 1/r^3."
Now we come to the essence: is the attractive 1/r^3 always valid for orbiting planets about non-spinning spherical central stars, for orbits with high eccentricity and with low eccentricity?
I suppose you will say "yes".
"Among others, the 1/r^3 perturbation causes precession."
Among what others?
``is the attractive 1/r^3 always valid for orbiting planets about non-spinning spherical central stars, for orbits with high eccentricity and with low eccentricity?''
As you surmise, the answer is ``yes''. The issue turns not so much on eccentricity as on whether the orbit comes close to the Schwarzschild radius, that is, whether the low-speed approximation holds throughout. For the Sun, since the Schwarzschild radius is only a few km. there is no issue.
``Among others'': maybe that was poorly expressed. I meant to say that essentially any potential perturbation will cause precession, except possibly for some extremely special cases.
`` Energy loss of light is not time dilatation!'' But this is not the issue. What was observed, in this and other experiments, is that the rate at which certain processes proceed, is modified by a constant factor. According to theory, all imaginable processes should be slowed down by the same factor. Thus a Cs atom will emit lower frequency radiation at the top of a tower, than at the bottom. And similarly for all other processes whereby time is measured.
That is the prediction of GR: I do not see that a shift in the emission frequencies of atoms follow from Newtonian physics. It may follow from the equivalence principle, but stated in this way it goes considerably beyond classical physics.
As far as `time dilation'' is concerned, it is a common way of expressing the fact that all known time standards are slowed down by the same factor. Is that something you would deny? Do you then suggest a way of distinguishing what happens in gravity from an ordinary time dilation?
``It's not relevant who found that, but the flux explanation is valid in 95% of sciences (except perhaps in some weird theories). Gauss' flux is doing excellent work.''
About 95 % of sciences I shall say nothing. No doubt the heat equation is excellent in describing heat propagation, and Laplace's equation is important there. But as far as ``explaining'' gravitation is concerned, I am not aware of any serious work providing an explicit link between Laplace's equation and the 1/r form of the gravitational potential. It is, of course, clear that 1/r *is* a solution of Laplace's equation, but I am not aware of anyone claiming a physical relationship between the two.
Again, the first explanatory connection I am aware of is given by the low-speed limit of Einstein's equations: these then lead to motion in a potential which solves the Laplace equation with the density as a source term. Next order corrections lead to the 1/r^3 term, which is also essentially exact for geodesics in a Schwarzschild metric.
Because the arguments by some ones about this question are confused which are poor to know the current points of view about GR and about the orbit of a satellite, and neglect my arguments, I shall not reply every answer for this question. So, I sentence my knowledge about this problem next:
1) it is the maistream point of view: Relativity is used only in the GPS.
2) GR cannot be used to design a real orbit of a satellite. A real orbit is a perturbed one. It is always perturbed by 1) the tidal force of the Sun and Moon, 2) the pressure of the light radiation of the Sun, and so on. GR cannot and have not used these factors to design an orbit.
3) my question is that under the condition that the Newtonian gravitational time effect is much larger than Einstein's gravitational time dilation, is the Schwarzschild geodeic equation valid? The Einstein's gravitational time dilation is the premise for this equation. But, the Newtonian gravitational time effect is neglected.
``A real orbit is a perturbed one. It is always perturbed by 1) the tidal force of the Sun and Moon, 2) the pressure of the light radiation of the Sun, and so on. GR cannot and have not used these factors to design an orbit.''
This is an important question, so let me try to give a detailed answer. GTR is a *generalisation* of Newtonian gravity. So if you start from 2 bodies, one much larger than the other, and nothing else, then you have a given Newtonian problem, the solution of which is the ellipse. This is what is generalised to the Schwarzschild metric.
If you now consider the Newtonian system of many particles, one of which is much larger than the others, then we have the usual Newtonian model for the Solar System. If the Solar mass dominates considerably, then the solution of the original two-body problem, the ellipse, can be used. But generally we need to introduce some corrections, via a scheme called perturbation theory. Then the planets still follow approximate ellipses, but the eccentrities, orientations and axis lengths of these ``local ellipses'' slowly vary in time.
This can also be generalised to GTR. In particular, if we assume that the velocities of the planets are small with respect to c, which is true enough since v/c is at most 10^(-4) for Mercury, then we may use the so-called Einstein-Infeld-Hoffmann (EIH) equations, which are correct up to an error of v^3/c^3. These are the GTR generalisation of Newton's equations for the many-body problem. Again, these cannot be solved exactly, but they can be solved approximately.
Such equations then do take tidal effects and in fact, all many-body gravitational effects into account. Light pressure must, of course, be added separately as an extra force, just as it also must be added to the Newtonian equations. There is no problem there in which Newtonian mechanics is superior to GTR.
On the other hand, full simulations with the EIH equations are being done, and they are the ones used to make the most accurate predictions of planetary positions.
Summarising: all the effects contained in traditional Newtonian mechanics are also present in GTR. Differences between the two theories appear in strong gravitational fields and/or at speeds close to the speed of light.
As to what you call the ``Newtonian gravitational time effect'' I have no idea what you mean. In Newtonian physics, clocks, and hence time, are altogether unaffected by gravity. The experimental effect of gravity on clocks, on the other hand, is well documented and agrees well with the prediction of GTR (and, to be fair, of several other theories compatible with the Equivalence principle).
Leyvraz> As to what you call the ``Newtonian gravitational time effect'' I have no idea what you mean.
If you want to have a good laugh at the start of the weekend, you should read the link attached. As I interpret the paper, it means that if you hang up a woodhead in a string of length L, and cut off 1 cm, this would be a situation of utmost gravity g, since a fraction of order 10-10 of sawdust will fall out.
But, to be a little bit more serious, Yin seems to believe that the rate of atomic clocks is governed by the acceleration of gravity, oblivious to estimates that typical accelerations in atoms are about 20 orders of magnitude larger.
Data A comparison between Newtonian gravitational time effect and...
When reading about the recent discovery of gravitational waves from a binary black hole merger, one realizes that the analysis of relativistic strongly gravitating two-body systems in GR must have reached a very sophisticated state.
In addition to its primary information, PRL 116, 061102 (2016) also provide a quite extensive bibliography to the history and status of the field. One is the linked 160 page article about inspiralling compact binaries, and gravitational radiation from such systems.
http://relativity.livingreviews.org/Articles/lrr-2014-2/download/lrr-2014-2Color.pdf
Spites the errors in the paper " A comparison between Newtonian gravitational time effect and Einstein's gravitational time dilation", to which Kåre referred, it is clear that it has never been proven at all that the SR time-dilatation is clock-independent.
Dear Dr. Thierry De Mees,
Physics is such a theory that is measurable. If it cannot be measured, it is not a scientific theory.
For example, if Einstein's gravitational time dilation is true, how can we know it by measurement?
In SR, if the time-dilatation is clock-independent, it also cannot be measured. It means that, it is not a complete theory.
`` it is clear that it has never been proven at all that the SR time-dilatation is clock-independent''
Indeed, it has not been proved, and it cannot be. This is because it is methodologically impossible to ``prove'' what is in fact a definition. A clock measures time. Two clocks either measure the same time, or they are not both of them clocks. The principle of relativity states that we cannot observe uniform rectilinear motion. Thus any two clocks which work identically in one reference frame, must also work identically in any other reference frame in rectilinear uniform motion. Hence, all clocks, which deserve the name, give the same time in all inertial reference frames. There is no proof of this, it is partly a definition, and partly the statement of the principle of relativity.
``For example, if Einstein's gravitational time dilation is true, how can we know it by measurement?''
We take two clocks at different heights and compare how they go. The Pound-Rebka experiment is a good example of how this is done: as a clock, we use the frequency of a very sharp gamma line in the emission spectrum of the nucleus of Fe^{57}. This gamma ray is emitted from above a tower, and a receiving block, which is capable of absorbing it, does not absorb it as much as expected, because the frequency at which it absorbs is different from that at which the original gamma ray was emitted, due to the gravitational time dilation.
You are right to ask such questions. The answers are not always trivial, but they are important.
Dear Yin: the SR interpretation is indeed short-sighted, as I explain further.
Dear F. Leyvraz: you first speak of SR to answer my "it is clear that it has never been proven at all that the SR time-dilatation is clock-independent''.
The SR interpretation is short-sighted because it works directly with masses. Another approach to get the SR equations is by calculating an electromagnetic event, say a Lorentz force F = q (E + vxB) from one moving reference frame to another reference frame. One has to take into account the retardation of the fields. By relating that to a mass, by F = ma, one gets the SR equations, as shown by Oleg Jefimenko.
That way, the SR equations are fully substantiated. However, when one fabricates a clock by using electromagnetic elements, the time retardation will depend from the structure (vibrating electron between charged rods, or spheres, or...) and also depend from the orientation with regard to the velocity. There are time-dilatation solutions with exponents of -3/4 or -5/4 (if I remember well) as well and not only -1/2.
This clearly shows that SR, or at least its interpretation, is incomplete.
When only atomic clocks are used, it might comply with SR's time retardation, but that is of course a practical limitation of the theory.
"The Pound-Rebka experiment" Your example is related to the equivalence principle and uses an atomic clock, so it might comply. This doesn't weaken my claim that it has never been proven that the SR time-dilatation is clock-independent.
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