The Equivalence Priniciple was first found and demonstrated experimentally by Newton for inertial an gravitational masses in a stationary system. The Eötvös experiments ran for a century and eventually made the EP become a law.
Einstein extended the EP to equate the effects of linear acceleration and gravitational fields which helped him to arrive to GR. Later on the EEP was restricted as a local property, although has to remain at a conjectural level, even though it is given as a fact by many.
Experiments supposed to check the validity of EEP, did only checked either LPI or LLI or WEP (Nasa GP-A tested only LPI not the EEP). The arbitrariness of the EEP is not trivial since it is given for granted the equivalence of the local effects of a linear accelerated motion with a static field.
In a paper of Giuliani it is reported what Einstein wrote in 1920 about the behaviour of clocks in centrifugal fields.
https://arxiv.org/pdf/1502.00990.pdf
Eddington in his famous book hinted an equivalence of the centrifugal fields with a gravitational one.
This kind of equivalence is much closer to real for three reasons:
a) much more in line with the Eötvös type experiment, since in the Eötvös torsion balance there is a comparison between a centrifuge force and a gravitational one.
b) Blueshift/redshift in a grav. field (Pound-Rebka-Snider) as well as in a centrifuge (Kunding) is an experimental fact after the 60's
c) time dilation due to a static gravitational field (atomic clocks in static comparison) and time dilation due to motion (pure inertial effects on GPS) is an experimental fact after the 70's
d) the equivalence is not restricted locally, but since also the centrifugeal field is radial, it can be found a suitable configuration such that the two fields match at superior orders (the c. field of a huge rotating sphere with a gravitational field of a planet).
The equivalence of with the centrifuge field is much more suitable than the one proposed by Einstein.
The latter is based mostly on conjectures and not on experimental facts:
a) The EP à la Einstein implies that time dilation for accelerated motion, has correspondence with the gravitational time dilation. Never been demonstrated experimentally (relativity of simultaneity).
b) The EP à la Einstein is true locally for constant active accelerations if the behaviour of GR is valid locally, or rather if locally the tidal effects of GR can be made vanish (but we are talking about a theory not about facts).
c) The EP à la Einstein is valid locally for zero acceleration (free fall) if the prediction of GR is valid locally, or rather if it is possible to make the gravitational field vanish locally (again it has to be assumed...)
Dear Stefano Quattrini,
The force field of a centrifuge is a force filed with the shape of a cylinder. The force field of a mass with gravity has the shape of a sphere. A cylinder is curved in one direction and a sphere is curved in two directions. Additional the force field in an elevator or rocket is flat. There is no curvature.
In GRT the gravity is explained with curvature of space and the field becomes flat in that curved space. The curvature of a centrifuge has a different metric and maximum away from the centre and minimum close to the centre. The acceleration field has no maximum. The gravity field has has the maximum close to the centre and the minimum far from the centre.
These 3 are very different. You want to find an equivalence principle between the centrifuge and the gravity. Then in terms of newtonian physics we would say that the mass in the centrifugal force equation is equal to the mass in the gravity equation.
mc=mg=m= rf/v2=fr2/GM
where m is the test mass, f is the force of gravity and the centrifugal force, r is the radius from the centre, M is the gravity creating mass, and G is the constant of gravity.
Is this a correct understanding of you question?
Regards,
Paul Gradenwitz
Dear Thierry,
https://www.merriam-webster.com/dictionary/centrifugal%20field
Dear Paul,
>
No.
It is evident that they are different eventually. It is the possibility to distinguish them from within a laboratory. If the cylinder is sufficiently large such that the surface seems flat, you cannot distinguish by making experiments if you are in a gravitational field or in a centrifugal field.
Thierry,
>
is not even a term used in Newtonian Physics, what is used is centripetal acceleration. And there is a reason...
I know that centrifugal force is a fictituous force due to the fact that the system is not inertial. But regardless of that a field can be defined since you can measure a force whenever you are in the rotating frame...
what is certainly true is that it has nothing to do with the Einstein Equivalence Prinicple.
Thierry,
you can find it yourself by reasoning on what is a force and what is an acceleration!!
hello Thierry,
The concept of centrifugal force as per our conventional thinking is fictitious but the truth is still not that the way of interpreting it in terms of inertia. Actually the concept of inertia is fictitious (i think we had talked about it previously).
Hello Stefano Quattrini,
The distinction and equivalence between inertial mass and gravitational mass for a same body which once projected in inertial frame and next in freefall in gravitational field is actually not a truthful ideology. All experiments which tried to prove it right are themselves in an enormous mythological errors. If you wish you could see Preprint A new course of relative acceleration within Classical regime
for why I am claiming so. Your question about "centrifugal" more or less is tried to cover within it too.
Dear Stefano Quattrini,
Your question got some attention.
Stefano>: If the cylinder is sufficiently large such that the surface seems flat, you cannot distinguish by making experiments if you are in a gravitational field or in a centrifugal field.
This is similar to the statement in a small enough domain the two forces are indistinguishable. But if we make approximations of the domain then the calculus we use should treat that approximation as acceptable. So the accuracy of the calculus should be less than the accuracy of the approximation. As soon as we use differential calculus we use a mathematical method that is by definition more accurate than an approximation. Differential calculus is about the quotient of the difference of values. If the values are approximated then the difference becomes zero and the quotient of zero by zero is undefined. As such we are not allowed to use differential equations. Without them we might have problems to use the GRT equations.
In a gravity field the shape of a drop becomes an ellipsoid with rotational symmetry along the longer axis. For centrifugal forces the droplet becomes an ellipsoid with the rotational symmetry along the shorter axis.
Differential calculus will always tell you that difference. Approximation will allow to call both a sphere.
Regards,
Paul Gradenwitz
Thierry,
Ok. Do you think that the centripetal force exists without an object on which such force is exerted? What is the centripetal force on a rotating disk for example?
Dear Paul,
>
it is similar to the statements that have been presented for the EEP, approximations.... with the difference big difference that
a) The EP à la Einstein implies that time dilation for accelerated motion, has correspondence with the gravitational time dilation. Never been demonstrated experimentally (relativity of simultaneity).
Dear Thierry De Mees,
I understand that you state that in vacuum there never can be a field that is called a centrifugal field. An object has to be diverted from its free fall trajectory and the subsequent reaction force of inertia comes into effect. If this diversion is onto a circular path then the force, the angular speed and the distance to a centre of a circle happen to have this special relation.
When I take a solid, liquid or gas object, so an object filled with mass, then the whole object can be spinning. The force here is everywhere subject to the same principle. A definition of a field is that I have a relation between a force and a geometrical location. So under that condition I think it is allowed to talk about a centrifugal force field. We should not object to such field only because we happen to know exactly why that field is there compared to the problem to tell exactly what is gravity and why that generates a field.
Regards,
Paul Gradenwitz
Stefano ≪What is the centripetal force on a rotating disk≫
The same forces that keeps the disk together: Mostly electrostatic forces. When the disk is set in rotation it stretches a little in the radial direction; that ultimately adds the extra internal local force that provides the centripetal acceleration. In the spin-up phase it also twists a little; that ultimately provides the extra internal shear force and torque the spins up the disk.
It is debatable to which extent General Relativity obeys some equivalence principle. For the dynamics of the universe, in the Friedman model, the expansion history depends on the matter equations of state. Although the first Friedman equation provide a unique relation between instantaneous expansion rate and total energy density. One way to look at this, is that various types of matter changes its energy density with expansion in various ways. Another way to look at this is to consider the second Friedman equation (the acceleration equation), which shows that acceleration also depends on pressure.
In the full Einstein equation, gravity couple to the entire energy momentum tensor. That provides the source for gravity at one position. Some piece of material in the gravity field at another position, must move in such a way that its energy-momentum tensor is covariantly conserved (that depends on the gravity field). In some cases this is sufficient to provide an equation of motion -- the geodesic equation. But if you introduce spin, there can in principle be a coupling between spin and local curvature. Then a particle with spin will not move in exactly the same way as a one without.
It's not debatable that, for forces that can be derived from a potential, it's possible to describe their effects exactly by a metric-and vice versa. It's a straightforward exercise to derive the correspondence. This is known as the equivalence principle.
For forces that cannot be derived from a potential-among these are the pseudoforces that act in a direction that's perpendicular to the velocity-the previous correspondence doesn't hold as is and needs to be generalized. And this has been done (e.g., most recently, in Article Hall effect in the presence of rotation
). In fact it was done when it was found how to describe spinning particles in curved spacetime, e.g. by Barducci et al.: http://inspirehep.net/record/110771Cf. also, the discussion about the Kerr black hole spacetime: http://eagle.phys.utk.edu/guidry/astro490/lectures/lecture490_ch13.pdf
Kare,
Yes but eventually you have to apply it per unit mass because it is variable so it is just acceleration. The term centripetal force is not used for that reason!!!
No, indeed, it's not. But just read the paper by Barducci et al.
While every textbook on general relativity mentions that the geodesic deviation equation is equivalent to Newton's second law, not all stress equally well what happens with non-potential forces, that couple to spin.
Conversely, it's possible to describe such forces as if the test particle, in fact, carried spin.
Dear Stefano,
I'm not sure to understand your question. The usual concept of the principle of equivalence is that non local experiment can distinguish between a freely falling nonrotating system and a uniformely moving system without gravitational field. Would you change this principle just introducing rotations too or substiting the gravitational force by another more general as the centripetal force too? Einstein's gravitational equations don't take into account the rotation symmetries and also their associate pseudo-forces as Coriolis, etc
Gravitational force is a fixed interaction force which can be made locally zero for a free falling bbserver. The weak equivalence principle states that all massive objects with the same initial velocity have the same trajectories given the equivalence inertial and gravitational mass. While the Einsteinian equivalence principle generalizes it for everywhere in the spacetime saying we can get non-local gravitation in a local inertial frame ("elevator"). And there is third possibility to employ the principle of equivalence not only for the interaction of gravitation but for other kind of interactions besides the gravitational ones (strong equivalence principle). Are you thinking in enlarging these kind of equivalence principles or you take into account a new point of view?
Dear Daniel,
>
or non local experiment can distinguish between an accelerated frame and a gravitational field. I'm not extending the validity of the EEP.
I am trying to find an alternative where the "equivalence" received experimental verification, in term of measurement of Time and forces.
In the case of absence of a centrifuge field the counterpart is to have no gravitation at all. The absence of acceleration or free falling in a gravitational field are equivalent locally.
The absence of a Gravitational field is equivalent also non locally to the absence of a centrifuge field.
So far the WEP received experimental verification (free falling experiments)
the LPI received experimental verification (Vessot and levine, HK)
the LLI received experimental verification
All the three together at once never received it (accelerators)
They would be valid together if
a) two co-accelerated clocks set in sync, do not stay in sync (given for granted but never verified)
b) two free falling clocks set in sync, stay in sync (given for granted but never verified) as if they were in deep space.
Dear Stefano,
Your question is:
Instead of the application of the EP à la Einstein, isn't it quite suitable an Equivalence between a centrifugal field and a gravitational field?
and an important answer is:
I am trying to find an alternative where the "equivalence" received experimental verification, in term of measurement of Time and forces.
The absence of a Gravitational field is equivalent also non locally to the absence of a centrifuge field.
which I agree. But I think that the answer is negative, you never can find an EP taking into account centrige field. The reason is simple but subtle. The trajectory followed in the equilibrium between gravitation and centrifuge fields provide you with a map of geodesics, which don't have a zero gravitational field. Thus you haven't a local flat spacetime as the EP definition needs.
Dear Stefano,
BTW if your idea, or wish, were true you had not found an experimental form to measure the EP, but a non-local form to define it!
Daniel ≪And there is third possibility to employ the principle of equivalence not only for the interaction of gravitation but for other kind of interactions besides the gravitational ones (strong equivalence principle).≫
I don't think an electrically charged satellite and an uncharged one, starting out with identical initial conditions in a Schwarzschild type gravitational field, would pass through the same orbit in the same time. I believe the charged satellite would radiate a little (electromagnetically), and experience some radiation reaction that would reduce its energy, momentum and angular momentum. How much would depend on its charge, but is should not be exactly zero. (Since I have not investigate electrodynamics in the Schwarzschild geometry, this is a belief.)
But this can only be realised as a thought experiment. In the real universe, there are other effects influencing the dynamics of celestial bodies, in particular small ones. Like the Yarkovski effect, and the Poynting-Robertson effect.
Added: An electric charge at rest in the gravitational field does not radiate; an electric charge undergoing centripetal acceleration will radiate (proportional to acceleration squared); an electric charge under constant linear acceleration does not seem to radiate, but you cannot maintain a linear acceleration forever.
Dear Kare,
According to Einstein’s equivalence principle, charges in free fall should not radiate, while charges supported at rest in gravitational fields should radiate. If one doesn't know enough electrodynamics can think that there is here a contradiction but it isn't true. The answer is that the radiation in Larmor for an electric charge is produced when there is a relative acceleration between charges and fields. Only in this case.
Thus in Schwarzschild metric or in others that you want, you are not going to have problems for the principle of equivalence of Einstein, sure!. This was shown in results simply from the analysis of radiating charges in antennas, X-ray tubes, and synchrotrons.
https://www.hindawi.com/journals/amp/2012/528631/
https://link.springer.com/article/10.1023%2FA%3A1026646928717
https://www.sciencedirect.com/science/article/pii/0003491663900514?via%3Dihub
https://arxiv.org/abs/1508.02287
@Daniel
Thank you for the references. Most of them seem to discuss only a constant, linearly accelerated charge, which I think I already understand. The paper by Grøn I must consider more carefully. The physical thought experiment of whether a neutral and charged satellite in the Schwarzschild geometry will follow the same worldline, does not seem to be addressed. Talk about different ways to do the energy accounting may not help with that.
Dear Kare,
As I told you the
The physical thought experiment of whether a neutral and charged satellite in the Schwarzschild geometry will follow the same worldline, does not seem to be addressed.
is a wasting of time and money because you are not going to find anything new. But perhaps I'm wrong....
My proposal for the simplest way to test the equivalence principle: Can you turn off the lights?
Explanation: In curved space electromagnetic waves do not (completely) travel with the speed of light. The same thing will also happen in flat spacetimes with even space dimensions.
I have not personally met many spacetimes with even space dimensions, but believe this effect could be demonstrated by sound waves confined to a two-dimensional volume.
Daniel
I have no ambitions of finding anything, only to understand what is already known. The paper by Øyvind Grøn gives reference to a good starting point: Article The Motion of Point Particles in Curved Spacetime
In the first part of their introduction, which is all I have read so far, they indicate a derivation which shows how the equivalence principle is violated in curved spacetimes, for charged particles, by an amount which depends on space curvature. Since this is a result which has been known since before I started to study physics, I tend to accept it, although I have not fully digested it yet.
Dear Daniel,
to my knowledge for the centrifugal field, the space-time is flat, although the same thing does not seem to be the case for the space which is not supposed to be flat...
KO> The paper by Coleman gives the complete analysis-along with the answer.
And, no, in curved spacetime, electromagnetic waves do travel at the speed of light-it's just not globally defined, like any other 4-vector. Apparently, one tends to forget the distinction between group velocity and phase velocity.
This doesn't have anything to do with the fact that in spacetimes of odd dimension, the magnetic field isn't a pseudovector.
Once more: in the presence of forces that can't be described by a scalar potential, but act in directions that are perpendicular to the velocity, the metric isn't sufficient to describe the geometry and additional fields are required. It's as if the particle had spin-and, in fact, if it does have spin these contributions are inevitable for the consistent description.
That was analyzed in the literature many years ago, by Papapetrou; a more recent (in 1976) and more direct approach was described by Barducci et al.
So the statement about the equivalence between pseudoforces and gravitation is incomplete, because it doesn't specify just what's meant by gravitation.
What tends to get forgotten is that the Poincaré group has two invariants: mass and spin. The former couples to the metric and can be identified with the inertial mass and this gives rise to the usual form of the equivalence principle, where the metric couples to the energy-momentum tensor of matter. This, in fact, takes care of forces that are described by a scalar potential.
Spin couples to forces that aren't described in terms of a scalar potential-and vice versa, such forces can be described as if matter carried spin at the scale one is looking at.
Indeed the distinction between forces that can be described in terms of a scalar potential and those that can't be actually relies in a choice of coordinates-what one calls position and what one calls momentum. It is known that in classical mechanics such a choice shouldn't affect the physics. And an example is provided by a particle in a homogeneous magnetic field, that can be described as a particle subject to the Coriolis force-if the dragging force can be neglected, that's the catch.
There have been experiments on ``spin-gravity coupling effects'', e.g. here:
Article Test of Einstein Equivalence Principle for 0-Spin and Half-I...
It is a test of the WEP, concerning the fact that angular momentum is conserved on spin particles in a gravitational field, or rather the spin is not altered by gravitation to the accuracy of the experiment.
Just like mass, spin is defined unambiguously in Minkowski spacetime. It's not ``altered by gravitation'' any more than mass is. What matters is that the quantitative way for describing all these effects is known-so instead of trying to guess it, it's much more efficient to learn it.
On the other hand it's not surprising that it's much harder to detect how spin probes spacetime than how a spinless particle probes spacetime.
The equivalence principle may have been introduced as an equivalence between inertial force and gravity as described by a metric-it's just much more general, simply because spin is a totally independent attribute than mass is and both are required to describe matter.
What is, historically, interesting, is how long it's taken for people to actually assimilate that position and momentum, that represent a choice of coordinates, couple to forces in a way that isn't that distinct as might have been believed. So the consequences for this symmetry can, in fact, be worked out and have interesting practical consequences.
So there's no sense in setting one sort of equivalence against another-both are present. It's just a historical accident that one has received more attention than the other-linked to technical issues, essentially. Now such issues aren't any longer that much of a problem.
Stam ≪The paper by Coleman gives the complete analysis-along with the answer≫
It is a nice paper which I have studied before. But it does not cover all issues, as can be seen by f.i. skimming through the Living Reviews in Relativity article that I linked above, Article The Motion of Point Particles in Curved Spacetime
The latter, f.i., has an interesting approach to the self-acceleration problem, which Coleman does not even mention (as far as I can remember).
Stam ≪And, no, in curved spacetime, electromagnetic waves do travel at the speed of light-it's just not globally defined, like any other 4-vector.≫
That is not the issue. The issue is that the causal propagator (aka retarded Green function) for the wave equation in curved spacetime does not have its full support on the backward light-cone, but also some support on the interior of the backward light-cone. That is a major complication, as you can see discussed in the article I linked. It is referred to as the tail terms in the equations of motions, which actually implies that the current force on a charged particle depends on its entire pre-history (among other things). The latter is encoded in the current electro-magnetic fields, so the full particle-field system can still be described by differential equations.
Stam ≪This doesn't have anything to do with the fact that in spacetimes of odd dimension, the magnetic field isn't a pseudovector.≫
Sure, it is a general property of the wave equation in odd-dimensional flat spacetimes, where again the causal propagator have some support on the interior of the backward lightcone. One can actually understand that without use of mathematics. A 2+1 dimensional space-time can be modelled as a 3+1 dimensional one, with complete symmetry in the z-direction. Then, a signal emitted from a point in 2-dimensional space must be modelled by a signal emitted synchronously from an entire rod in 3-dimensional space. Emitted signals will travel with various velocity-components in the z-direction, and therefore reach the receiver after various times. One can also follow this line of arguments to mathematically calculate the causal propagator.
Dear Stam,
Sorry, but most of the things that you are speaking on about spin and gravitation are nonsense for me. Einstein's gravitation doesn't take into account of rotational symmetries and less the spin. For doing it one needs to have Einstein-Cartan equations where there is a torsion besides a curvature for the spacetime manifold. And in all that I know never was found experimentally a torsion or an skew symmetric metric for the spacetime.
Dear Stefano,
I'm assuming a system without inner energy able to rotate a system, for instance the Earth around the Sun. Thus the Earth is trapped within a potential associated to a given energy-momentum tensor and therefore to a curvature. The geodesics of the Earth are where the force on our planet is zero and there you have not a flat spacetime as the EP needs to employ for its definition. I don't see how to define it in another form taking into account both forces: centripeta and gravitational, one depends of the position while the other of the velocity. Perhaps I don't understand you properly.
Daniel ≪And in all that I know never was found experimentally a torsion or an skew symmetric metric for the spacetime.≫
Torsion is not related to an antisymmetric contribution to the metric, only an antisymmetric contribution to the connection coefficients. I believe torsion is an unavoidable consequence of spin, which is known to exists. However, since it is difficult to align spin in a coherent manner, it is difficult to collect enough of it to generate any measurable torsion.
Also, in the Einstein-Cartan theory, torsion cannot propagate. So, it only has a local effect inside matter, where it is easily masked by many other kinds of interactions.
Dear Daniel,
infact the comparison can be made in these two cases with the advantage that they match also at the II order.
valid at the first and
II ORDER (including tidal effects) presence
a) static gravitational field: on a surface of a planet versus a
constant centrifuge field: on a surface of a huge rotating cylinder
II ORDER (including tidal effects) absence
b) wide area no gravitational field, far from planets: no tidal effects detected versus no centrifugal field, no acceleration detected in a wide area: no tidal effects detectable.
Dear Kare,
You are right, metric and torsion are independent. My last sentance was not well written. Thank you.
In elasticity of materials, for disclinations and dislocations, the torsion plays an interesting role and can be determined quite well. But in gravitation I never have found any result what it in some aspects strange because is one of the invariants as it happens with the curvature. For me this shows again the genious of Einstein and his physical intuition.
Dear Stefano,
What is fundamental in EP is to get one observer who has zero gravitation and which can see a flat metric, i.e. its curvature is zero. I cannot imagine a rotation helping to reach it. As I told you perhaps in such a case you needed to go to an Einstein-Cartan model and to find any condition on the curvature besides the torsion (this is just mathematics but I don't see the physics). What perturbations are you thinking about?
It doesn't matter whether it's called Einstein or Einstein-Cartan; what does matter is that spin contributes at all and how to compute its contribution. That its effects haven't been taken into account is the result of history not mathematics-the formulations are available-at least for more than forty years.
Experiments haven't found such contributions, to date, simply because they weren't sensitive enough. Now they've started to be able to probe them.
Dear Daniel,
>
infact it is not an option... in any case also in SR for rotations the metric is flat...
In any case so far I don't see any compelling reason why the two configurations cannot define an equivalence which is less limiting an more satisfactory than the EEP.
The invariant quantities that define manifolds are not limited to the invariants defined by the metric alone. And the physics, precisely, lies in the fact that particles possess not only mass, but, also, spin.
Once more: the mathematical formalism is known for, at least, forty years. It's just that real experiments have become possible only quite recently.
Dear Mohamed,
I agree with the fact that the EEP is not compatible with GR. And as a consequence GR can provide only a stationary geometric description.
On the other side the equivalence of a static gravitational filed and an accelerated reference frame is not viable.
The EEP is true only if it reduces to the WEP or the EP experimentally verified by EOTVOS.
Dear Mohamed,
yes it is compatible with Newtonian mechanics but not with the relativisitc mechanics when it is in a non-stationary case.
Since Newtonian mechanis is falsified if we apply the conservation of energy in *inelastic* scattering (which involves the mass energy relation), the relativistic mechanics which also Planck in 1906 pointed out, has to be used, involving the Lorentz factor and mass energy equivalence.
@Mohamed Hassani
Can you, please explain what does it mean "to define Mmentum-Energy 4-Vector in invariant manner for a system of particles in interaction"?
In particular: which features of such a M-E 4-Vector are required.
Regards, Joachim
“isn't it suitable instead an Equivalence between a centrifugal field and a gravitational field?”
Absolutely, if a dialectical view of this question is worth a cent. This will bring in “contradictions” and Newton’s Third Law of Motion in the understanding of the so far assumed one-sided and a "harmonious" cosmos. Article THE CONCEPTUAL DEFECT OF THE LAW OF UNIVERSAL GRAVITATION OR...
No amount of (ideal) mathematical juggling can eliminate the fact that "God’s intended" harmonious and everlasting creations are anything but – always changing through quantitative and qualitative leaps (even if infinitesimally) by resolving the dialectical contradictions; mediated by chance and necessity and never remaining in the same state and configurations at any instant! Any apparently stable configuaration is conditional and relative - its change is absolute!
Dear all,
as it emerges from this paper
https://arxiv.org/pdf/1502.00990.pdf
at page 3 there is the description of Einstein about the comparison of the behaviour of the clocks in a centrifugal field and a gravitational one..
Einstein wrote in 1920's
" If we denote by ϕ the effective potential difference of the centrifugal force between the position of the clock and the center of the disc, i.e. the work, taken as negative, that must be done against the centrifugal force on a unit mass for transporting it from the position of the clock on the rotating disc to the center of the disc"
which is basically what I described.
"Since, from the point of view of the disc, a gravitational field of potential ϕ appears, the result we have obtained will be valid in general for gravitational fields "
as usual some inaccuracies but he gave the right picture as well.
He actually put the adjective gravitational where he should not have put, it was just the case to avoid to write "a gravitational field of potential ϕ appears", it is just potential of a force ϕ which appears..
and it is true that such result is valid in general for gravitational fields, since it is the kinetic part of the SCHW solution obtained otherwise from more general considerations.
Gravity, like electromagnetism must be considered as an intrinsic property of matter itself!
Article Gravity – An Intrinsic Property of Matter! A Qualitative Gra...
Dear all,
there is an interesting paper I just found:
"We are proposing a new approach to investigate the physical effects of the centrifugal acceleration in an inertial reference system. Our proposal is based primarily on geometrical considerations, built on the extension of the equivalence principle. The equivalence principle is then used to derive an effective Schwarzschild radius. After having developed the equations, we propose an experiment to detect the effect of the centrifugal force on the time. We compute also the consequence on the unstable particle’s lifetime. The testability of our model is well reachable from our present technology. "
Article Clocks & Particles in a Centrifugal Field
what wrote in the paper should not though be seen as an extension of the EP but it should regard considerations on the rest-energy and energy conservation.
Dear all,
in regards to the falsification of the EP a' la Einstein, , you can find this script of mine, denying the existance of any offset due to co-accelerated motion which was instead initially supported by Einstein.
Deleted research item The research item mentioned here has been deleted
Preprint THE DOPPLER EFFECT IN ACCELERATED MOTION, RELATION AT HIGHER ORDERS
“isn't it suitable instead an Equivalence between a centrifugal field and a gravitational field?”
It is even worse than this! "Equivalence between a centrifugal field and a gravitational field” is not nearly enough! The rot in modern Fairy-Tale Cosmology goes all the way to Isaac Newton: Article KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Le...
I agree since the angular momenta forbid such equivalence, although there is a correspondence about the frequency shifts which depends strictly on the energies at stake.
Stefano Quattrini
Please see my comment posted just few minutes ago in the following forum:
https://www.researchgate.net/post/Is_Any_Effective_Refutation_of_Einsteins_Theories_of_Relativity_Possible#view=5f84938c3243337205050aef
Dear all,
Daniel Baldomir , Eric Lord , Kåre Olaussen
it is generally accepted that the longitudinal Doppler effect (LDE) is also a first order approximation of the gravitational redshift. That is considered a consequence of the Einstein EP.
Although the formulas are the same (1+gH/c2) and the Pound and Rebka experiments used the compensation with the LDE of the gravitational blueshift, there are substantial differences.
a) The LDE does not preserve the energy of photons:
b) the gravitational frequency-shift in a closed loop preserves the energy of the photon,
(DOPPLER ) LDE case: the energy of a photon changes according to
(Delta E)/E = gH/c2/(1+gH/c2)
in a gravitational field: (Delta E)/E = 0, a travelling photon does not exchange energy with the gravitational field....
it is the atom absorption energy level which is shifted.