When Einstein's general relativity theory predicted that light is bent in a gravitational field, Eddington verified that during a solar eclipse. He showed that some stars behind the sun were viisible, seemingly moved from their real position of almost 2 seconds of arc.
But I've read somewhere that Newton's theory predicted a smaller angle, but not zero. How is this possible? I thought that Newton's gravity only acts on things with non zero mass, and consequently not on photons.
Can anyone explain ?
I think that a rigorous answer would be, that this depends on the model you use for light. Newtonian physics, generally, does not predict the bending of light.
Newtonian mechanics does, if you are OK with "light particles", a model of light, where you have particles of mass m, moving asymptotically with a velocity of c. Then you can calculate the angle between the asymptotes of the hyperbolic orbit, and m drops out.
On the other hand, if you consider the wave equation, or Maxwell's equations, Newtonian physics does not predict the coupling to gravity at all.
See the https://en.wikipedia.org/wiki/Tests_of_general_relativity#Deflection_of_light_by_the_Sun and the relevant literature therein.
The misunderstanding is the following: Indeed, in Newtonian mechanics, a massless object can't be subject to a force. However the equivalence principle that, in the Newtonian approximation states that the inertial mass is equal to the gravitational mass, implies that the mass of any object cancels out in the equations of motion of the object in a gravitational field that, therefore, can be applied to the motion of light, described, according to Newton, as particles (of undefined mass). So, if one computes the trajectory of such a ``particle'', by solving the equation of motion, with boundary conditions that the ray start from the star and end at the Earth (both considered as points), one will not find a straight line, which would be the trajectory, were there no ``acceleration''.
One finds, in this way, that the ray is ``bent''. But, if one does do the calculation according to general relativity, one finds another value. And if one thinks a bit more carefully, one realizes that the Newtonian limit of the general relativistic calculation leads to no bending at all. The reason is that, in the Newtonian limit, the gravitational potential is a scalar field and the only way a scalar field can couple to the electromagnetic field in a relatvistically invariant way to describe gravitational effects, is by the product scalar field x trace of the energy-momentum tensor of the electromagnetic field. This trace, however, vanishes. Therefore, light, described as an electromagnetic wave, cannot be bent by a scalar contribution to the gravitational field.
“…light, described, according to Newton, as particles (of undefined mass)…”
- photons have defined concrete [seems equal] inertial and gravitational masses m= h*nu/c2; including – they change their energies when move between points with different gravity potentials.
Correspondingly, for example, red/blue shift for the case, when photons move orthogonally to Earth surface, exist and it [shift] is twice lesser then the GR “gravitational time dilation”; when the GR “time dilation” value is evidently twice larger then real value (not of a “time dilation”, of course) of clocks tick rate slowing down if clocks are on different heights.
And so “…one realizes that the Newtonian limit of the general relativistic calculation leads to no bending at all…”
- photons also bend their trajectories in Newton gravitational field, though possibly twice lesser then the GR bending value.
See alsohttps://www.researchgate.net/publication/265509276_The_informational_model_-_gravity and https://www.researchgate.net/publication/277710038_The_informational_model_-_gravity_a_next_experiment
Cheers
Article The informational model – gravity
Research The informational model – gravity; a next experiment
Take these two equations from Newtonian physics for a test particle with mass m: F = ma, vs. F = GMm / r2. For a freely falling test particle, these two would be equal: that is, the only force acting on the test particle will be the gravitational acceleration. Thus, ma = GMm / r2. But note that in this expression, m cancels and we're left with a = GM / r2. That is, the gravitational acceleration does not depend on the test particle's mass. So even when you take the limit of m going to 0, the acceleration remains constant.
Nice Thierry,
What do you think the probability could be that the amount the light approaching us being bent in toward the Sun is being underestimated in the parallax/triangulation measurements that are alleged to be accurate up a source up to 30k LY away whereas if the light source is 'only' :) up to 6k LY distant it would help confirm SPIRAL.
While a 5 fold distance might seem very material, when it comes to the actual difference in angle it is splitting hairs, I still have to do the math but suspect a hairbreadth vs 1/5th of a hairbreadth :) so not that improbable after all the issues involved that have room for such a tiny error.
advise, TY, r
Newton Gravity can be manipulated to give an approximation of bending light, but was not done in advance of Einstein GR. So it is just an exercise with approximate results.
Local gravity acceleration does not depend on the small mass of a falling object, only the mass of the sun or other large body. Then curvature is implied.
g = MG/r2
Radial velocity changes according to curvature
dvr/dt = g
Taken into the usual hyperbolic geometry, it leads to an answer for bending of light that is only half as large as GR and the accepted observations, unless a Lorentz transformation or other relativistic correction is applied, which would be a deviation from Newton Gravity.
Jerry : "Taken into the usual hyperbolic geometry, it leads to an answer for bending of light that is only half as large as GR". Can you provide more details or references?
Gravity not only exists between masses but also between any form of energies. i.e. grvity can exist between two masses or between a mass and a charge or between mass and a pure kinetic energy. Gravity can also exist between two charges or between two photons. Photons are pure kinetic energies. So the mass equivalence of this photon kinetic energy is used in calculations. m = E/c^2.
Then the question is why Newton's theory gives half the value of deflection of light compared to Einstein's theory which is experimentally verified. My answer to this question is that both Kepler and Newton overlooked a factor Cos(psi) + Sin(psi) defined in my article which is associated with the basic elliptical motion. This factor when considered, gives geodesic like trajectories without using Einstein's theory. This factor in conjunction with Newton's theory gives exact value for the deflection of light.
http://ptep-online.com/index_files/2015/PP-40-11.PDF
Article Periodic relativity: Basic framework of the theory
Hi Vikram and Thierry,
if the factors you both use are not the same to explain why the regular laws of physics alone are enough to explain the 'double' amount of light bending under Einstein's GR theory, than is it possible the actuality is the light bends even more than thought, once both your considerations are factored in?
or are they two different / independent ways to get to the same result?
Dear Vikram,
Photons do not alter their actual energy content referred to the emitter in a gravitational potential when they are absorbed. The bending of light which is explained by Einstein in his book, is entirely due to the tensor like structure of the background which guarantees that energy and momentum are conserved along geodesics for light.
Gravitation does not "attract" radiation which does not change its energy content referred to the emitter but changes only its momentum.
The force which is exerted to a particle of mass m or some bound energy and determines its slow down while exiting a gravitational potential well is not at all exerted to photons.
Hello Roger,
The factor I have pointed out is fundamental to elliptical motion and has nothing to do with Maxwell anology used by Thierry. What you call regular laws of physics, are actually incomplete without the factor I have proposed. This incompleteness is covered up in Einstein's GR theory by introducing factor 2 in the weak field approximation which is an ad hoc manipulation. Because of this manipulation Schwarzschild radius of event horizon is 2GM/c^2, where as in my theory it is GM/c^2. So it is possible to test my theory with Event Horizon Telescope. Predicted GR value for SgrA* is 52 micro-as and the measured value is 37 micro-as.
http://arxiv.org/pdf/0809.4677v1.pdf
Dear Stefano:
It is well known that GR violates conservation of energy particularly on a global scale. Changing momentum without changing energy content of the photon is violation of conservation of energy. My theory is able to generate geodesic like trajectories without the need for a tensor like background. If photons do not alter their actual energy content referred to the emitter in a gravitational potential, then how do you explain the gravitational redshift?
The force which is exerted to a particle of mass m or some bound energy and determines its slow down while exiting a gravitational potential well is exerted to photons as gravitational frequency shift.
“…Photons do not alter their actual energy content referred to the emitter in a gravitational potential…The force which is exerted to a particle of mass m or some bound energy and determines its slow down while exiting a gravitational potential well is not at all exerted to photons. ..”
- it seems is necessary a next time to point here that photons have defined concrete [seems equal] inertial and gravitational masses m= h*nu/c2; including – they change their energies when move between points with different gravity potentials.
And that this fact directly follows from Pound-Rebka-Snider experiments, where both interpretations:
– heretical (Pound and Rebka)’s interpretation that the measured by them “photons’ frequency” shift delta(omega)=gh/c2 appears because of changing photons’ energy at photons motion between points with different gravity potentials on different delta height, h;
- orthodox GR interpretation that photons “do not alter their actual energy” between these points and so in the experiments just predicted by GR difference of “gravitational time dilation” delta(omega)=gh/c2 was observed;
are evidently incorrect, even if one doesn’t mention that the “time dilation” phenomenon seems as rather strange for anybody who understands – what is the time.
The GR claim is evidently incorrect because of real difference of the rates of changing of internal states of material objects, which is a result of decreasing of mass of the system “Earth+Fe-57” because of the indeed real gravitational mass defect, is twice lesser then the GR prediction, i.e. it is equal to delta(omega)=gh/2c2
The Pound-Rebka interpretation is incorrect because of the rates’ difference above exists, and so photons really change relative frequency, but only on delta(omega)=gh/2c2.
And so in the PRS experiments at photons’ motion, say “up” to compensate the effects when the “red” nucleus Fe-57 radiated “red photon” that hit in “blue” nucleus Fe-57 and at that the photon lost its energy, in the experiments was necessary to move one of the nucleus so, that Doppler shift was equivalent to the frequency shift delta(omega)=gh/c2.
More – see links in the SS post on 1-st page.
Cheers
Dear Vikram,
It is well known that GR violates conservation of energy particularly on a global scale.
GR is ok for energy conservation regarding isolated systems. It is not ok regarding the non locality of the gravitational energy.
If photons do not alter their actual energy content referred to the emitter in a gravitational potential, then how do you explain the gravitational redshift?
it is due to how the same atoms emitter and receiver behave at different gravitational potentials.
And in any case if they altered their energy it means that some of their energy has been stored in the gravitational field. If you get a flux of photons in a unit time you get the power of the radiation. Do you think that the power of radiation gets lower by increasing the distance from the sun, provided that I consider the same amount of photons?
The force which is exerted to a particle of mass m or some bound energy and determines its slow down while exiting a gravitational potential well is exerted to photons as gravitational frequency shift.
No, there is no force which can act on photons, which can make any work on photons while travelling. Photons do not alter their energy content, but only their momentum the explanation of this is obvious with a variable speed of light.
From electromagnetism viewpoint, and in accordance with Maxwell's equations, there is a photon model from de Broglie's hypotheses that reveals that only half the energy of a localized photon possesses omnidirectional inertia (electromagnetic mass). When this is taken into account, Newton's equations directly give the double deflection angle given by GR, with the very same equations that Einstein used to demonstrate that the deflection amounts to only half the observed deflection:
http://www.omicsonline.com/open-access/on-de-broglies-doubleparticle-photon-hypothesis-2090-0902-1000153.pdf
Sergey,
- it seems is necessary a next time to point here that photons have defined concrete [seems equal] inertial and gravitational masses m= h*nu/c2;
Photons as "radiant energy" reveal a mass only after the absorption process but they are not photons anymore then. Either there is a mass defect when they are emitted, as large as you suggest.
Light is something which has a totally distinct nature from matter, it is only a mistake to think that radiant energy has a mass either inertial or relativistic while travelling.
Dear Stefano:
it is due to how the same atoms emitter and receiver behave at different gravitational potentials.
And in any case if they altered their energy it means that some of their energy has been stored in the gravitational field.
Your answer is very vague. It looks like you are not sure which of the two possibilities is correct. Besides, there are no mathematical support or experimental evidence to support your claim.
If you get a flux of photons in a unit time you get the power of the radiation. Do you think that the power of radiation gets lower by increasing the distance from the sun, provided that I consider the same amount of photons?
Answer is no.
No, there is no force which can act on photons, which can make any work on photons while travelling. Photons do not alter their energy content, but only their momentum the explanation of this is obvious with a variable speed of light.
GR does not support variable speed of light. It is based on local invariance of speed of light. The fact that the force acts on both momentum as well as energy content (frequency) is evident from eq.(2.23) in the following article which is derived from Lorentz equation (2.18). Subsequent equations point out the difference between classical acceleration and the Lorentz invariant acceleration. The later includes the component due to de Broglie force which is absent in the classical acceleration. GR runs into trouble when at one hand it uses Lorentz equation and on the other hand it equates gravitational mass with the classical mass. Therefore de Broglie force gets ignored in GR which in fact is part of the Lorentz force. When gravitational mass is equated to the relativistic mass as in my theory, this does not happen.
http://ptep-online.com/index_files/2015/PP-40-11.PDF
Vikram
It is easily demonstrated that all force equations are equivalent to classical force equation F=ma, even the Lorentz equation. See all mathematical derivation in the attached paper.
In GR, no force is involved. All motion is inertial.
http://www.ijerd.com/paper/vol6-issue6/F06062734.pdf
Dear Vikram,
"If you get a flux of photons in a unit time you get the power of the radiation. Do you think that the power of radiation gets lower by increasing the distance from the sun, provided that I consider the same amount of photons?
Answer is no."
So the consequence is that there is not net energy variation of photons crossing different gravitational potentials in the RF of the emitter.
"Your answer is very vague. It looks like you are not sure which of the two possibilities is correct. Besides, there are no mathematical support or experimental evidence to support your claim."
Which kind of mathematical support? I'm sure that the interpretation of the gravitational potential energy of photons is wrong, if you want I support it with the experiment of Vessot and Levine.
Stefano,
“…Light is something which has a totally distinct nature from matter…”
- photons are some rather banal material particles, which never reveal any mystical properties outside the relativity theories and only in these theories photons become be some powerful magic particles that force poor space, time, and spacetime to contract, to dilate, to curve, etc.; in order to provide photons “constant speed and constant energy/frequency in reference frames”.
Though both – the GR and the SR [and the reference frames as well] – are only some subjective abstract constrictions that were invented by a pair of some evidently non-mighty magically people.
More – see again SS posts on first and this pages, including the RG links in the post on 1-st page. Besides it could be useful to answer also – why so simple and cheap experiment [the link “…gravity; a next experiment ”], which can be made seems in a week now, doesn’t made till now? – when this experiment’s outcome will show difference between the two clocks [exposed on two different heights] showings twice lesser then the GR predicts – because it is wrong; and twice lesser then PRS experiments result – because of in this experiment the sum of two real effects was observed – of the real gravitational impact on the rate of permanent constant changes of internal state of Fe-57 nuclei and real photons energy losses/gains at motion between the nuclei.
Though the experiment was proposed a rather long time ago…
Cheers
"Though both – the GR and the SR [and the reference frames as well] – are only some subjective abstract constrictions that were invented by a pair of some evidently non-mighty magically people."
I'm a bit fed up to hear from a part of RG people that affirm GR and SR are totally failures and others who say the exact opposite, that there is nothing better and they are totally right and no need to change anything.
I see this attiutude far from belonging to intelligent people.
I see very very few instead who are able to appreciate the results of a theory and are capable to stress realistic limitations, because this and only thi is good Physics.
No model fits and will fit to an arbitrary accuracy the behaviour of phenomena, we have only to identify to which extent a model can be used. If we are not able to do that we are only doing some math or some speculation which most of the time are usless.
why so simple and cheap experiment [the link “…gravity; a next experiment ”], which can be made seems in a week now, doesn’t made till now?
I wonder also myself why some simple experiments like equally accelerated clocks or free falling clocks in a gravitational field were never considered before. In this case the accuracy of the atomic clocks was poor till the beginning of this century. Now it would be an experiment easy to do.
showings twice lesser then the GR predicts – because it is wrong;
so basically the GPS system does not work according to your opinion..
What about the measurement made with atomic clocks at different heights in a laboaratory as the one below?
https://www.uam.es/personal_pdi/ciencias/jcuevas/Teaching/Chou-Hume-Rosenband-Wineland-Science2010.pdf
Stefano ~
“…No model fits and will fit to an arbitrary accuracy the behaviour of phenomena, we have only to identify to which extent a model can be used…”
This is indeed often true in the science, but the SR/GR is the principal exclusion till now. And there are a number of corresponding points that, regrettably, determine such their “exclusive” status, first of all:
- till now in mainstream physics it is claimed that the theories haven’t any limitations and both are completely confirmed experimentally, and
- any attempts to point out in any mainstream source that the claim above is wrong, though they are quite reasonable and grounded, become be immediately obstructed with using quite non-scientific methods – by rejecting publishing of corresponding papers in the mainstream journals, a blunt, but intensive “defense” or even spam at discussions in the Net,
- in fact there are preventing executions of experiments, where the non-adequacy of these theories could be discovered,
- etc.
When these theories not only indeed have some limitations at physical applications. Besides, they are based on fundamentally wrong claim that the Matter’s spacetime is really the Minkowski/pseudo Riemannian spaces; at that the SR is unique theory, seems not only in physics, that is based on the [about total equivalence of all inertial reference frames] postulate, from which evidently non-sensical implications follow,
again etc.
Sorry, but such a situation in any science would seem as rather strange -?
Returning to the experiments in question.
“…I wonder also myself why some simple experiments like equally accelerated clocks or free falling clocks in a gravitational field were never considered ...”
- that is explainable – in such experiments rater probably a lot of problems can appear, first of all – here it is necessary to provide, to study and to prove the stability of clocks tick rates at acceleration, when, at that, the acceleration, if it is in reasonable limits, must be rather long, and – existent clocks stability isn’t known sufficiently to estimate possible experiments’ outcomes uncertainties, for example – at an impact of Earth magnetic field at clock’s rotation, etc.
“…basically the GPS system does not work according to your opinion…”
- the GPS system cannot be used at the GR testing, at least by two reasons: the synchronization procedure in the system is some analogue of the PRS experiment since two effects are involved – photons’ energy and clocks tick rate shifts; and the GPS clocks are subjected to many other impacts on orbits and so they are adjusted permanently by using data of stations on Earth.
***
When the experiment with comparing showings of a pair of stationary clocks [see SS posts above], after one of the clocks was exposed on other height is indeed quite simple and hasn’t practically unknown uncertainties. And, for example, if the heights difference of the clocks would be near 500 m (there are a lot of corresponding buildings on Earth now), after 1 hour exposition the difference will be near 10-10 s, what is well measured now and is twice lesser then the GR predicts and the PRS experiments outcomes.
Cheers
@André Michaud
In my theory all force equations are not equivalent to F=ma. In my theoy
Lorentz force = ma + de Broglie force.
http://ptep-online.com/index_files/2015/PP-40-11.PDF
Dear Stefano:
"If you get a flux of photons in a unit time you get the power of the radiation. Do you think that the power of radiation gets lower by increasing the distance from the sun, provided that I consider the same amount of photons?
In this example you have said nothing about different gravitational potential. Gravitational potential around the emitter and the receiver does not change by increasing the distance between the two.
No, there is no force which can act on photons, which can make any work on photons while travelling. Photons do not alter their energy content, but only their momentum the explanation of this is obvious with a variable speed of light.
In Vessot Levine Hydrogen Masser clock experiment, the amount of energy needed to reverse the spin of the electron is equivalent to a photon at the frequency of 1,420,405,751.786 hertz (Hz). This experiment only confirms that the gravitational force acts on the photon. Now Hydrogen Masser clocks are replaced by Cesium 133 atomic clocks in which outside the inner symmetric core of 54 electrons there is one 6S electron which has hyperfine splitting with frequency = 9,192,631,770 Hz which corresponds to 1 SI second. This clock also gives the same result and shows that gravitational force acts on the photon.
Apart from this you have not clarified what you mean by variable speed of light?
Vikram
The paper I refered to is not a theory. Just a mathematical derivation available for any body to verify.
@André Michaud
There is an error in your eqn.(13) for Gp. You cannot use Kepler's orbital period formula for deriving a new gravitational constant between proton and electron because of the presence of electrostatic attraction between the two. You can use Kepler's orbital period formula only if this Coulomb force was absent. In case of Sun and the planets this Coulomb force is absent. Therefore your derivation is invalid.
To answer this: "I thought that Newton's gravity only acts on things with non zero mass, and consequently not on photons." -- We have universality of free fall in Newton's theory (i.e. a weak form of the equivalence principle), so the trajectory of a particle in a gravitational field does not depend on the mass of a particle. That extends to zero or negative mass particles -- they all fall alike in a gravitational field.
The question then depends only on whether the kind of entities you consider interacts gravitationally. As long as you believe with Newton that light is made up of particles, you can (and von Soldner did in 1804) predict light deflection in a gravitational field. The answer is half the value predicted by Einstein in 1915 (but Einstein predicted the same value as von Soldner in 1911, albeit based on the wave picture of light).
If you believe that light is a wave phenomenon and no particles are involved, there is no reason in the Newtonial world view to assume it to interact with a gravitational field and then Newton's theory would predict zero deflection.
Thanks
I found von Soldner's article on the web : I'll read it...
https://en.wikisource.org/wiki/Translation:On_the_Deflection_of_a_Light_Ray_from_its_Rectilinear_Motion
Vikram
Since the inverse square interaction law is involved in both cases, the logic is clean and the derivation is authorized.
This simply confirms that separately equating F=ma with both the gravitational equation and the Coulomb equation as is made in standard textbooks is right, since all three equation reflect the use of the inverse square interaction law.
Each and every body in the Universe attract each other. According to this Newton's finding, let us assume that the bunch of photons as one body and star/other heavenly body as an another body. So the gravitational attraction of heavy object is more, so light bends towards the star.
I am astonished to see that some colleagues think that, in 1918, the classical theory predicted that light could be deviated by a gravitational field. Would anybody at that time still believed in light as particles, like Newton did? Science at that time should know that light is an amount of wave electromagnetic energy, and it was predicted that may act in well defined unique quantities of energy during emission (Planck's blackbody) and absortion (Einstein's photoelectric effect).
You will find an answer in my book. You can down load it from my profile. Regards
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