In the 60's Schiff tried to demonstrate that some results of GRT could be derived from the WEP and special relativity in a simple way.
In his "On experimental test of the General Theory of Relativity"
he affirmed that WEP and the LLI were sufficient in order to determine the LPI or UCR.
The first to cast serious doubts on the paper was Rindler who in 1969 wrote in a "counter example to the Lenz-Schiff argument" about the simplistic and incorrect way in which he derived the light bending.
Unfortunately also the first part of the paper is flawed by two trivial mistakes which reveals
1) an arbitrary redefinition of the time dilation between RFs
the only accepted and acceptable is the operating definition applied also in the Hafele and Keating experiment which officially measure time dilation between clocks in a correct way.
2) an intrinsic misapplication of the equivalence principle.
The accelerated clocks inside were compared by "looking outside" referring to a clock at rest, which is not in line with the application of the principle which dictates that experiences have to be performed, as Einstein did, all inside the accelerated (or free falling) laboratory.
This double mistake allowed Schiff to provide the right approximated gravitational time dilation predicted by GRT.
Dear Stefano,
This is an interesting issue which war treated for many authors in different forms. In fact, locally and for a given observer always is possible to find one flat system of coordinates where GRT transforms in SRT, but the problem is to extend it globally starting in the flat metric of Minkowski. How is this question at present?
Again, time dilation is not possible.
Take a serie of pictures of the sky by night at 0m and 5000m of altitude with times.
Match the pictures of the sky and compare the times.
24 hours or 4.5 billion years later do it again.
Would you see now a difference of time? Following general relativity, you should. But is it true? No.
Because we are already 4.5 billion years later, then the difference should be minimum of 2 hours.
Actually, all our astronomical pictures of the sky are taken at same time, then there is no time dilation given by gravity (general relativity) or velocity (special relativity).
Another try :
Think about the film Interstellar :
The twin going downwards to a high gravity planet comes back next to the other twin stayed in the (geostationary) station at low gravity. Imagine they have watched all the time the position of the "sun". Once back, how can a twin see another (older or younger) position simultaneously to the other twin ?
Following Einstein, it means there is a day/night phenomenon when going downwards or upwards to the high gravity planet in order that when the two twins are together they see both an aged position of the star.
This day/night phenomenon (which is cumulative since creation of earth) is not seen on earth when going from 0m to 5000m. If general theory of relativity was right this phenomenon should be of more than 2 hours.
Following a time dilation (special or general relativity):
Or we have two similar pictures taken at different times;
Or we have two different pictures taken at same time.
Do you agree?
If pictures are the same at same time, where is time dilation?
In this case, if there is time dilation then your stars should move at different speeds, what is not acceptable with relativity.
Any theory within GRT is non sense !
This conjeture is related with the possibility of any theory of gravity that embodies weak equivalent principle ( WEP), necessarily embodies the Einstein equivalence principle (EEP), more than with the time dilatation. The question is how to define properly the equivalent principle for an observer locally, i.e. how to transform curved space-time in a flat one and viceverse.
Ni Ge,
Pictures can be taken at same time only when both of the cameras are at the same point of the spacetime. The resistance if futile because we have accepted light ray as a measuring tape. ;)
The first paper of this issue (if Stefano allow me) is:
L. I. Schiff, Am. J. Phys. 28, 340(1960).
and in the paper of 1977 appears a discussion with measurements of time dilatation for a positive and negative muons in a circular orbit:
Nature 268, 301 - 305 (28 July 1977)
Although the dilatation of time is obviously related with the equivalence principle of general relativity, I do not know how this can distinguish the different approaches in the literature and also I do not know more recent experiments on this issue too.
Dear Stefano:
Thank you for your perceptive point.
I would be interested in your (maximally critical if possible) response to my c-global paper: http://www.ptep-online.com/index_files/2015/PP-43-09.PDF
All the best,
Otto
I think The GTR needs strong equivalency principle. The geodesics for free fall are dependent on all gravitating bodies. The observed object itself affects also how the spacetime will be curved and how the gravity field changes with gravitational excitations ie gravitational waves.
It's very possible to get results near although without an understandig deep enough.
Schiff's conjecture, so named by Kip Thorne who now refuses to discuss the subject, is not mentioned in the 1960 paper. It is understood to be WEP+UGR→EEP. See http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.49.853
Schiff himself never defended the 1960 paper, possibly because he realized it was so full of errors:
My paper on the subject is currently in review and has been removed from RG for that reason, but if someone would like more detail they can request it from me.
Dear Daniel,
"This is an interesting issue which war treated for many authors in different forms. In fact, locally and for a given observer always is possible to find one flat system of coordinates where GRT transforms in SRT, but the problem is to extend it globally starting in the flat metric of Minkowski"
yess...it is impossible that phenomena of the SRT are confined to a virtually no space inside the GRT. I think we miss one dimension.
Don't you think that it is improper to still treat the physics with 4 dimensions (X,Y,Z,T)?
If we think of Newton he provided Phisycs with four independent dimensions, absolute because independent.
What we did after Maxwell is to reduce it to 3 and 1/2 or less....since T is not anymore independent.
Everything would be much easier if we regained the absolute time and make the speed of light be a further dimension ic, which takes care of all the relativity phenomena....
I think Minkowsky missed the opportunity with his strange dimension ict, he should have written ic, T giving 3 space dimensions, the time and the dynamics.
SR works dynamically because it deals basically with pointlike objects, we have to put some flash on the bones... and GRT works very fine only if we don't consider the EM interaction as a net energy exchange....which means that works by itself and basically works for steady states...no transitories....
Both theories would merge in the ic,T, and Gravitation would emerge from mass and electromagnetism through the least action principle in a natural way...
ic would be an F(x,y,z, dx/dt,dy/dt,dz/dt) implementing directly the least action principle....
Robert,
you are right but everything starts from that paper and the sad thing is that it is still mentioned as a conquest. In 2013 several authors referred still to that and even at the end of 2015.
I immediately spotted something strange as soon as I've seen it for the first time and I thought, if such collection of idiocies can be published and so many followed it and I was able to spot such trivial mistakes, then I can do much better than that....
was he talking about the gravitational redschiff ???
Well, Schiff's paper caused me a great deal of personal inconvenience because I did not think to look for rebuttals or criticisms, and like you spotted some inconsistencies, which caused me to "throw out the baby with the bathwater" so to speak. But the rebuttals have been published, themselves weak I think, and about all we can do is caution all to look for multiple references and citing papers.
I am sure that parts of Schiff's argument are correct, just not for the simple reasons he gave. It is the correct answer for the local relation between time and spatial curvature. I have some notes on an energy argument for that, but the world is not ready for such an obvious thing, that SR and GR should actually be related. Currently the Ricci tensor is the only accepted guardian of curvature in a vacuum.
Robert,
I am more and more convinced that the WEP and LLI are falsified and only UCR or LPI are valid.
There is not any Local lorentz invarance like described in GRT, this can be acheived only along circular orbits.
the SEP is not valid because infringes the energy conservation principle, unless it is implemented in circular orbits.
The WEP is valid but can be falsified by certain configurations so it is valid in 99,99% of cases but there are case when it is not.
the only valid is the EP tested in the Eotvos experiment for low speeds and the UCR/LPI tested in the Pound and rebka, HK and vessot and Levine experiments and Shapiro Delay.
You know what is one valid thing which emerges from the Schiff's paper? but I don't even know if he meant to:
Time dilation emerges from the actual energy difference per unit mass between reference frames.
I like your arguments Stefano (which view doesn't differ from Azzam K Almosallami),
What will be the proof against an equivalence principle/principle of reciprocity OR a galilean relativity taking into account light aberration and fields retardation?
P.S. For those who still don't know GRT is a dead end.
I am not against: time1 x velocity1 = time2 x velocity2
But i think (it is my a priori argument for an equivalence principle) that it would have some consequences on nature developpment (like chemical experiments).
Note: Almosallami uses a Minkowskian space-time with v=v as equivalence of an euclidian space-time with v=/=v
Dear Daniel,
you reported that the life time of muons were prolonged according to the prediction of the SR. The time dilation depends obviously on the difference of the energy per unit mass when the muon decays at rest in the lab or at relativistic speeds.
It is obvious that The acceleration, which is radial, does not have anything to do with the time dilation of the muon. It is clear though that in order to bring the muon to the speed of light you have to accelerate it linearly, increasing its speed. During this acceleration there is a time dilation as well but it is due to being at an higher energy level.
I don't know really to relate this with the equivalence principle though as for Fock, Singe, Lugounov, Eddington too it was just a tool to derive the GRT but it is devoid of physical meaning.
The only thing which can determine the time dilation is the ACTION which is a functional of the potential energy per unit mass + kinetic energy per unit mass of a body referred to a Reference Frame, nothing else.
Dear Stephano,
I agree with you that the experiment of the muon is not simple to relate with the weak principle of equivalence in one unique form. The dilatation of time in general relativity of a photon in a gravitational field with potential V is
(1+a)V/c^2
where a is fine constant of structure and c the velocity of light. There are many experiments but, from my humble point of view, they are not conclusive in this point
http://www.nature.com/nature/journal/v463/n7283/full/nature08776.html
http://arxiv.org/abs/1009.1838
Dear Daniel,
Exactly. It is disappointing how Physics has this open point and in general this is treated like it is all clear. It is intersting this paper too about the gravitational redshift you mentioned
Article On the gravitational redshift
Dear Stefano,
I'm afraid that I have lost here the equivalence principle of GR and therefore issues as Schiff's conjecture that you ask are not included. One interesting thing is that if the red shift is due to the potential of the field (gravitational or others) then you can do the same for the electromagnetic field or others. And in fact some people do measuring the lifetime of muons as a test.
http://arxiv.org/pdf/gr-qc/0104025v1.pdf
Dear Daniel,
The contribution of the EM fields is already part of the energy stress tensor of Einstein, via the various components.... in any case yes it should depend on the energy at stake provided that you don't count them twice..
Dear Stefano,
I didn't explain me enough well. Sorry.
I think that the Schiff's conjecture comes from trying to see if the weak equivalence principle in fact can be always reached in one unique form as the GRT of Einstein's assume. Geometrically speaking it is only a question to locally reduce the Riemann curvature to a flat Minkowskian one. And, as you said, the source of the curvature is the energy-momentum tensor independently if it is given by electromagnetic, gravitational field or even others. The question is that it is easy to imagine one lift falling in one gravitational field for applying the equivalence principle and to obtain the proper time dilatation, but how could you do in a magnetic field? Notice that the forces are not simple with respect to the motion of the physical observer.
In the formula 3 of the paper that I have attached, you can see how the redshifts of gravitation and magnetism are independent. In the case of gravitation only contributes with the square root of the pure temporal component of the metric, while for magnetism is directly the density of magnetic energy stored in the field respect to the scalar mass density. This is simple formulation that didn´t show anything respet to the equivalence principle.
Yes Daniel, if the Ep is conceived according to the Equivalence mass energy.
Dear Stefano,
Going to your presentation of the question:
"In the 60's Schiff tried to demonstrate that some results of GRT could be derived from the WEP and special relativity in a simple way".
I think that, although it was worked a lot in the literature the question to try to reduce the GRT to the SRT, it is clear that both theories are very different. One very basic difference is that while SRT works directly with the Lorentz group SO(1,3), while the GRT needs to use the 4-dimensional general linear group GL(4, R) for the Lorentz covariance (no invariance of Lorentz as in SRT). The Lorentz group is only a Cartan subgroup!
Physically Einstein could find their equivalence locally just using WEP but this is only one possibility among many others that I am afraid that need to be studied if gravitation has to be glued with the rest of interactions.
Daniel, exactly.. The dimensions are 4 but These should do not include time... should be 4 plus time, with or without gravitation. Time T measured at the observer at infinity should be kept as the reference, absolute time. No other way to escape such Chess mate among QM, SR and GR...
I would like to add the following text here in the hope that I can get criticism from the very researchers who have thought most about similar questions.
----------------------------
The Einstein Rocketship explained to Young and Old
It is fun to picture this most beautiful brainchild of a scientist who always called it “the happiest thought of my life.” What is it that is so “happy” about it? Can a thought be happy?
It is maximally simple and yet maximally absurd in its consequences. Such a coincidence is unprecedented. This lad was a gift to the planet.
Just embark on an Apollo-like rocketship in your mind. Unlike the real one, it is not filled with propellant throughout: In the middle it has a narrow passenger cabin that runs along the whole length and width of the ship. Therefore you can make simple experiments on board if you brought along your pocket laser-pointer and a pocket frequency counter. Thirdly, you may bring along a smoke-filled glass tube through which to send a laser pulse while the tube lies on the floor or is glued to the ceiling, so as to take snapshots of an internally advancing light pulse from above or below. The ship is assumed to be accelerating constantly in outer space while you make the measurements.
The same equipment (pointer, counter and tube) you can also use inside a huge church tower on earth, with predictably the same measurement results. The experiment is so simple that “mere thinking” suffices to make valid predictions. This is what Einstein did in 1907 with all the mentioned equipment not being available as of yet.
The least surprising prediction is that, when you hold the laser pointer horizontally at any height inside the accelerating rocketship, the horizontal light ray that comes out will be gently downward-curved inside the accelerating rocketship. This effect is very small since the rocketship is so slender. Moreover, von Soldner had already predicted gravitational light bending a century before in 1805.
The most famous surprise found by Einstein is the following: When the laser is pointing upwards from the floor and you count the pulses at the tip, the counter will show a reduced ticking rate compared to what is valid on the bottom – despite the maintained distance. For during the time the light is ascending with its limited universal velocity c, the tip did continue picking up speed away from the emission point. Hence a Doppler effect applies, like the slowed pitch of a receding ambulance.
This was Einstein’s main prediction. It appeared totally absurd at the time. Nonetheless Einstein’s “gravitational redshift” is confirmed everyday by the GPS in our cars. The satellites overhead make for the ceiling of a rather high church tower indeed (their fast motion does not abolish the effect).
Pointing the laser downwards from the tip will show the opposite effect – an increase in the count rate compared to what holds true above when measuring downstairs.
What else can we do with this mental or real toy? The second big implication seen by Einstein applies when the tube with the smoke in it is lying on the bottom while watched from the tip. Einstein predicted correctly that the light speed inside will look reduced from above: A second absurd prediction made out of the blue by sheer thinking. And when you look from the bottom up to the ceiling, the transversal speed of light will look increased there (a fact that remained unmentioned).
The correctly predicted observable change in c caused Einstein to fall silent on gravitation for almost 4 years. For the theory of special relativity with its by definition globally constant c had produced an implication that amounts to a contradiction-in-terms. This illogical state of affairs is still the accepted teaching of to date. I hope you did enjoy the ride. But: is there not something missing here?
When staring a bit longer into the Einstein-Apollo-rocket, we may suddenly realize that the light ray, while visibly “creeping” across the floor (or else visibly “zipping” across the ceiling), is not moving horizontally as this was assumed so far. The tilt – an upwards tilt in either case – is owed to the fact that when the propagating light ray reaches the next spot on the horizontal floor, the previous point has already fallen back a bit relative to the tip in the meantime (or else has come somewhat closer to the bottom from above, respectively). Hence the no longer horizontal light ray has re-gained in either case the universal speed c – as originally presupposed.
At this point, an encouragement from the part of the reader or listener is vital because the relative upwards slant seen is not part of the narrative since 1907. Can Einstein have possibly overlooked this detail?
The Virtual-Reality-like thoughts described – which hopefully will soon be part of a computer game – were so taxing for Einstein that they “singed” his brain as he once confessed. He feared to go crazy and looked for mental shelter from his longtime friend,, mathematician Marcel Grossmann, in order to continue functioning. Everyone knows that the most difficult dynamical equation of history would come out eventually: the Einstein field equation. Does that equation contain the “relative upwards slant” proportional to vertical distance that we just spotted jointly? The answer is in the negative.
But the present playful text is supposed to be a kindergarten version of Einstein’s equivalence principle between gravity and ordinary acceleration, is it not? Virtually all specialists (except Wolfgang Rindler) scoff at texts without equations: Can it be that the mathematically educated establishment has gone astray for so long?
“Thinking helps” according to Hewlett-Packard. The new “relative upwards slant” of light rays hugging the horizontal floor inside the Einstein rocketship, valid relative to above (or below), repairs the so far accepted violation of c as a global constant of nature in the vacuum. A well-known result from special relativity – that the speed of light inside a transversally receding light tube appears reduced (or increased if approaching) was overlooked. So everything is fine again: c remains a globally (and not just locally) valid constant of nature in a return to the pre-1911 Einstein.
Why be hesitant? The reader will be appalled to realize that the retrieved global c entails that the cosmos cannot expand any more since distant points can no longer recede from each other at more than c as everyone believes does occur. By denying the Big Bang you will make yourself a laughingstock among your peers when you tell them that you approve of the above “mental analog computer” of the Einstein-Apollo rocketship. So you will have to decide whether rather to trust your own firm judgment or let yourself be bullied into behaving like a dogmatist. In science and elsewhere, dogmas have a knack for being deadly. Therefore: Is the above conclusion (“relative upwards slant”) correct or is it not?
I for one am sure 99 percent of the time that it is vorrect. One reason to remain skeptical is the fact that it is such an immense fun to be more right than 3 ½ generations of specialists from the year 1911 on. This feeling, if legitimate, is accompanied by an immense gratitude to this young amateur scientist of 1907 who took on the whole establishment with the verve of a total outsider. I need not tell you that at present, the scientific community is gladly betting the planet on the above story being false. But this is another tale. Thank you for having lent me your ear, my young colleagues, gentlegirls and gentlemen.
(Talk planned to be given at the Nell-Breuning Schule Rottweil tomorrow.)
Dear Otto,
as I said the other time c is not constant at all, it is variable according to the gravitational potential and not only that.
Having admittend that c is always the same all over the space has been an hystorical mistake.
The time dilation which somebody says occurs for real in the Rocketship between the tail and the head is something very false and to a certain extent revals a very bad understanding of physics and of what really is time dilation.
The only equivalence principle which makes sense is the Newton Equivalence Principle.
The SEP on which GR is based is the complete physical equivalence between a free falling system in a grav field and a galilean system. This can be verified only in four cases
a) if everything is completely without motion
b) for light which maintains approximately the same speed.
c) for massive particles going close to speed of light which cannot be accelerated either, their speed is already maximum and any changes in momenta due to gravitation is negligible.
d) for circular motion orbits, where there is no energy exchange at all between the gravitating body and the gravitational field.
In all the other cases which represent the 99,99% of the cases in the universe the SEP cannot be vaild, because it excludes the gravitational interaction as energy exchange.
I am sorry but I do not understand what are you saying. Let me to put it step by step:
1. The velocity of the light only depends of the electromagnetic properties of the medium where it propagates:
c^(-1)= square root (permittivty.permeability)
Another thing is the frequency or the wave length that can depend of the gravitational potential. Notice that these parameters only give the phase velocity and no the group velocity which is the one important from the relativistic point of view.
2. If the light moves in an electromagnetic medium as water (dielectric) where its phase velocity is 3/4 c, then one charged particle which a velocity higher than the light in such a medium must produce a new conic propagation of light or Cherenkov radiation ( blue color of water in a nuclear reactor due to the decay of neutrons in charged high velocity particles).
3. Therefore, it is well tested that there is a limit of propagation of the energy and momentum for every particle in a medium. The maximum of the velocity of the light is in vacuum and only depends of the permittivity or permeability of the medium.
4. Concepts as global velocity of light are nonsense because every velocity is local by definition.
Dear Stefano,
I am not sure that we agree in the importance of equivalence principle which is obviously a key condition of GRT.
My humble point of view is that the equivalence principle only postulates the existence of a reference frame in which Lorentz invariants are defined on the whole world manifold. This is the theoretical justification of that the linear group GL(4, R ) might be reduced to the Lorentz group SO(3,1). Then the very definition of a pseudo-Riemannian metric on a differential manifold is associated to pseudo-Euclidean metric which provide as with special relativity as one particular case of GR.
This is a genial choice but a little arbitrary if we want to generalize gravitation to be interacting with other fields or even itself
Dear Daniel,
"I am sorry but I do not understand what are you saying. Let me to put it step by step:
1. The velocity of the light only depends of the electromagnetic properties of the medium where it propagates:
c^(-1)= square root (permittivty.permeability)
Another thing is the frequency or the wave length that can depend of the gravitational potential. Notice that these parameters only give the phase velocity and no the group velocity which is the one important from the relativistic point of view."
agree
"If the light moves in an electromagnetic medium as water (dielectric) where its phase velocity is 3/4 c, then one charged particle which a velocity higher than the light in such a medium must produce a new conic propagation of light or Cherenkov radiation ( blue color of water in a nuclear reactor due to the decay of neutrons in charged high velocity particles)."
agree
"Therefore, it is well tested that there is a limit of propagation of the energy and momentum for every particle in a medium. The maximum of the velocity of the light is in vacuum and only depends of the permittivity or permeability of the medium."
agree
"Concepts as global velocity of light are nonsense because every velocity is local by definition."
If you measure the speed of light Locally in vacumm you get c always, like in the MM experiment.
If you measure the speed of light which moves radially towards a massive body and you divide PATH LENGTH / TIME TAKEN (Shapiro Delay) you get a quantity smaller than c. Why I cannot define an average speed along a long path?
Dear Stefano,
Thank you very much for your answer, but I do not understand how is possible that having a curve at constant velocity c in every point, you can reach an average velocity different to c and lower. On the other hand I cannot see what is the reason to decrease its value without changing the electromagnetic values of the medium where it propagates
Dear Daniel
"My humble point of view is that the equivalence principle only postulates the existence of a reference frame in which Lorentz invariants are defined on the whole world manifold. This is the theoretical justification of that the linear group GL(4, R ) might be reduced to the Lorentz group SO(3,1). Then the very definition of a pseudo-Riemannian metric on a differential manifold is associated to pseudo-Euclidean metric which provide as with special relativity as one particular case of GR."
The Strong equivalence principle (SEP), at the base of GRT , as you say, is valid only strictly locally according to the prescription of GRT and that is the condition according to which you can pass (locally) from SR to GRT.
This is already much better than what described/applied by Schiff as the Equivalence principle.
Another thing is to be able to affirm that the SEP holds in the case most people think it holds.
Dear Daniel,
"Thank you very much for your answer, but I do not understand how is possible that having a curve at constant velocity c in every point, you can reach an average velocity different to c and lower"
Because local measurements are performed by local rods and clocks and for sure are affected in the same way by the variations predicted by relativity of clocks and rods, so you will always measure the speed as c.
There is this very interesting paper which talks about the variable coordinate speed of light in a gravitational potential
http://iopscience.iop.org/1367-2630/16/6/065008/
Dear Stefano,
Thank you very much for your reference and answer, but I can not agree with the results claimed in the paper for several reasons:
1. The formula 17 and 18 are for phase velocities and therefore it is obtained a shifting of different frequencies. In fact it is a redshifting.
2. The energies involved by the gravitational potentials are so small that NEVER is going to excite electron-positron pairs. Notice we need at least 2mc^2 rest energy of one electron.
3. A perturbation method in QED is not so simple as the one presented which only takes into account the gravitational one acting on mass m that is assumed to be the one of the dynamic mass of the photon. This again is possible, mathematically speaking, but neglects the electromagnetic potentials associated to electron-proton which are much much higher. Thus it is really difficult to assume as physicist.
4. I am sorry to be so strong in my arguments but this paper doesn't convince me at all that the velocity of light (carrying energy and momentum) is lower than c if the photons are in vacuum, even there is a gravitational field there. My simple argument is that non conservation of energy will be there because the gravitational potential cannot exchange it with photons, in all that I know and I hope to be right.
Dear Daniel,
"My simple argument is that non conservation of energy will be there because the gravitational potential cannot exchange it with photons, in all that I know and I hope to be right."
I belive and agree in the correctness of your exceptions. I only cited the paper in order to stress the (1) relation about the speed of light, but I did not go through the details.
infact the relation is [ co=c(1+2(phi)/c2)], he wrote it badly actually...
there is also this publication on astronomy which talks about the speed of light.
The lensing effect involving radiation is the same as the variation induced by a refractive medium.
"My simple argument is that non conservation of energy will be there because the gravitational potential cannot exchange it with photons, in all that I know and I hope to be right."
Why the light should infringe the energy conservation? The wavelength too varies with the speed so that the frequency/energy referred to the emission reference frames does not vary, the energy is conserved.
Article On the gravitational redshift
Dear Stefano,
I quite agree with this paper because it tries to explain the redshift effect using the conservation energy principle and Doppler effect in one atom. This far of explaining lower velocities of the light in vacuum under a gravitational potential, in fact they assume it constant and only changing in an scattering with an atom. This is absolutely true for the phase change in the velocities of the light and no the group velocity that needs much more ingredients.
Daniel,
in the (11) of the paper I reported it is clearly written the relation of the coordinate speed of light according to the gravitational potential. It is infact reported:
"A decrease of the speed of light near the Sun of this amount is not only
supported by the predicted and subsequently observed Shapiro delay33, but also indirectly by the deflection of light"
it is not necessarily a group velocity it might be also a single photon.
Dear Stefano,
I agree with you if :
"it is not necessarily a group velocity it might be also a single photon"
In any case, the interpretation of formula 11 needs to be justified deeply if we speak about the usual group velocity of the light IN VACUUM. Another thing is if you have scattering with atoms because they can absorb energy-momentum just changing parameters as the proper time associated to each state where the photon is emmited and absorved.
In any case this is my humble opinion on an issue that I didn't studied in all details.
Dear Daniel,
"in any case, the interpretation of formula 11 needs to be justified deeply if we speak about the usual group velocity of the light IN VACUUM."
I agree with you that it deserves attention.
What Eddington said is that a body going close to speed of light slows down its motion if free falling on a massive object instead of accelerating.
Einstein wrote down the relation of the variable speed of light in order to account for the gravitational light bending. That can give you the equivalent effect of the refraction index necessary to induce curvature to a the beam.
The germ of this, is written at the end of his paper of 1911 in which he pointed out the effect of gravitation on light and time but he did not have a theory yet to justify them properly.
The Shapiro delay effect is based on such physical property. The speed of the signal is not the same if I consider a long path across the solar system.
Some consider GRT as the theory according to which the speed of light is variable, a sort of geometrical optic.. not geometrodynamics as Misner Thorne and Wheeler would mean.
But i agree that this is a key point.
Another very interesting paper about the variable speed of light of LEV OKUN
"We define the critical coordinate velocity v c. A particle moving radially in Schwarzschild background with this velocity, v = c/√3, is neither accelerated, nor decelerated if gravitational field is weak"
http://arxiv.org/pdf/gr-qc/0111103.pdf
Dear Daniel,
it is quite peculiar this chain of reasoning:
a) delta(E)/E=delta(phi)/c2 , is the redshift relation.
Since E is a differentiable function and the gravitational potential is a differentiable function too I can write:
b) dE/E=d(phi)/c2 this has a trivial consequence by integration
E1/E2=e(delta(phi)/c2) which means
c) v1/v2=exp(delta(phi)/c2) the frequency ratio is exponential.
what would impede me to write such an exponential redshift?
Apparently nothing, but this would go against the time dilation established by GR with the Schw solution and proved in everyday situations with the GPS atomic cloks. We all recognize that a) is also an approximation of the Schwarzschild solution between the clocks.
But the only way to make that relation b) consistent with the Schw approximation, is to set c variable according to the ci=c(1+2phi/c2).
The differential equation dE/E=d(phi)/ci2 in such case does not bring to an exponential law c) , but it goes back to a)
Dear Stefano,
I understand your argument, but I am sorry to say that do not convince me: it is only mathematical. Let me try to summarize my opinion, which can be wrong obviously, but which I can understand.
1. The velocity of the light only depends of the electric and magnetic properties of the medium. In the case of the gravitation field, given that in all that I know, both fields gravitation-electromagnetic are independent, thus no transformation is allowed and gravitation can change the electric-magnetic properties of the vacuum.
2. The velocity of the light carry energy-momentum and this is the link with gravitation, but it is easy to see that the relationship between gravity-electromagnetism is so different in energy, to understand that only close to gravitational singularities is reasonable to think in mutual influence.
Dear Daniel,
"The velocity of the light only depends of the electric and magnetic properties of the medium. In the case of the gravitation field, given that in all that I know, both fields gravitation-electromagnetic are independent, thus no transformation is allowed and gravitation can change the electric-magnetic properties of the vacuum."
You teach me that the energy conservation has to hold in a isolated system and we see continuosly EM energy convert into Gravitational one. We don't know with our present theories how this can occur.
What if all the effect described by GR can be effectively described in a framework which maps the effects predicted by GR but the equations are expressed with a continously variable speed of light and the special relativity as well??
Dear Stefano,
An accepted fact is that the velocity of light is independent of the state of motion of the observer. Lorentz transformations and all the physical-mathematical basis, in all that I know, are out of "something like acceleration of light". On the other hand, I do not know how you could get it, whether we think on them as photons or as electromagnetic waves (Poynting vector).
Dear Daniel,
"An accepted fact is that the velocity of light is independent of the state of motion of the observer."
fortunately yes ( and the emitter).
"Lorentz transformations and all the physical-mathematical basis, in all that I know, are out of "something like acceleration of light".
yes because they postulate IRFs.
if I don't remember so badly, the Lorentz Transformations were conceived to justify the presence of the Aether driving the waves, since the Galilean Transformations were not anymore sufficient for the maxwell equations to pass from a RF to another...
The same reasoning I was doing about the gravitational redshift exponential law (wrong), this guy was making for free falling bodies in a gravitational field (maybe not so wrong).
Article Non-linear energy conservation theorem in the framework of S...
Dear Stefano,
You are right, the idea of Lorentz transformation was always against the old established concept of aether. In fact the Michelson-Morley experiment is nothing more than the Fizeau (1851) experiment made with much more accuracy. And Lorentz though that he was transforming the luminiferous aether in one stationary one. The important outcome was that he put justify the Fresnel coefficients in a very natural form assuming that the light propagates on the aether as if it were another kind of "water". In parallel Poincare showed that these transformations were a group and Einstein, in fact, saw that they didn't need at all the "aether". And what was more important, that the Galilean absolute time need to be substituted by another depending of the observer.
That is all, the velocity of the light is CONSTANT respect to every observer and emitter.
"That is all, the velocity of the light is CONSTANT respect to every observer and emitter."
The experiments say locally in vacuum it is always constant equal to c. If I measure it locally I detect it moving always at its characteristic speed.
The time it takes for a light beam to reach a planet and come back is more than the time it takes to cover the same distance in vacuum.. is it due to the fact that space-time is not euclidean? It is a possiblity..which is equivalent to say that the speed of light is variable... as described in the paper below... quite recent and quite lucky to have just found it.
http://arxiv.org/pdf/1503.06763.pdf
Respect to the paper that you have attached, it is only a consequence of trying to introduce a gravitational potential into special relativity using an equivalence principle. Mixing so many things you can obtain a disaster of results that it is not necessary to comment. Physically speaking although the mathematics are right. If we have a so beautiful theory as the Einstein's General Relativity, why are we needing to go to explore these "models"?.
There are many interesting possibilities, as to try to find new transformations changing the velocity of light or others, but you need to justify the physical achievements. It is clear that the mathematics is always possible.
The problem with global is that is difficult to measure it. In fact, in relativity it appears in a very strange form defined the concept of locality because it is a geometrical concept (Riemann) with a local chart (Minkowski) without taking into account of the topology which is the proper concept to distinguish local-global.
Dear Daniel,
"If we have a so beautiful theory as the Einstein's General Relativity, why are we needing to go to explore these "models"?."
Indeed. You know, the one in that paper (Non linear energy conservation) was the same attempt that Einstein made before diving into Riemanian geometry (Straumann reported such passage) the same exponential law came out of the combination of the EP and SR.
It was just to show you that the consequence of postulating c always constant because measured locally and applying the equivalence principle is a blind alley. With a constant speed of ligth you have to recurr to Reimanian geometry, you have to curve the space to explain gravitation and still there are issues...
"it is a geometrical concept (Riemann) with a local chart (Minkowski) without taking into account of the topology which is the proper concept to distinguish local-global."
this convinces me only if we consider SR along the surface of geoids, like the surface of Earth or like circular orbit.s Radial motion cannot be included since it crosses areas which can be exploited to perform correctly SR.
I don't know if it ever came to your mind but:
Newton used 4 full indepenent dimensions to describe laws
Einstein used a sort of 3 and 1/2 (Minkowsky, Riemann) instead of increasing the degree of freedom after 3 centuries Physics shrinked???
http://link.springer.com/article/10.1007%2Fs10701-008-9210-8
Yet another very interesting paper on the extensions of Hamiltonian and Lagrangians
http://arxiv.org/pdf/0811.0496v9.pdf
Dear Daniel,
could you give your opinion on the following paper?
Article Maxwell–Lorentz Electrodynamics Revisited via the Lagrangian...
Dear Stefano,
I have just taken a look to the long paper and I have only one weak opinion which I need to study more in detail for being definitive. Let me advance some basic points:
1. They do not use relativistic formulation and always speak about energy. Electrodynamics needs to be formulated in a relativistic form using the energy momentum tensor. Notice that this tensor contains more things that energy and momentum.
2. From the early beginning they seem to put as fundamental to work in the Lorentz gauge. If they formalism depends of this assumption then there is something wrong.
3.The potentiaas appear as the fundamental physical magnitudes and no the fields, that is very good for gluing electrodynamics with quantum theory but it has problems for obtaining the conservation laws of electrodynamics.
4. I cannot distinguish, at a first look, all that they find which could be new.
Dear Daniel,
a very happy new year... would you give me your very precious feedback to this page of mine..
Happy New Year Stefano,
I have just read your paper but I think that there are several typos. The gamma needs to have one square on the v as it has in c, etc..but what puzzes me a little is when you substitutes the values in the first example, to show that a>>1m/s2 when v=1 m/s and H=10m. Obviously a=0.1 m/s2. I suppose that these are just typos.
But what is more difficult to undestand for me is if you are with velocities much lower than the one of the velocity how you try to find differences in the measurements of time. The time must be Galilean and therefore independent of the observer in such a case.
Dear Daniel,
maybe it was not well explained. The idea is to give a sudden pulse to the two clocks the way they reach ASAP the speed v, long before the rear clock arrives at the position of C. The acceleration due to the pulse has to be much bigger than v2/2H this way (let's say 1000 times bigger).
"But what is more difficult to undestand for me is if you are with velocities much lower than the one of the velocity how you try to find differences in the measurements of time. The time must be Galilean and therefore independent of the observer in such a case. "
SR recites for sure (I give you the relevant papers if you want) that after equal acceleration two clocks have an offset of vH/c2 (and this is something I want to falsify) where v is the final speed and H is their reciprocal distance.
Dear Stefano,
If you assume that v/c tends to zero, then t=t'=t'' of different systems. That is to say, the time is absolute or Galilean.
If you use SR in one accelerated system, you have the relationships
v/c = tanh(at/c)
and the time no accelerate ti is related with the accelerated ta by
ta= (c/a) sh -1 (ati/c)
These are the usual expressions that I know for the accelerated systems having one inertial observer. The smartest form to work with them is using the tensorial formalism.
Dear Stefano,
if you want I can develop a little bit these expressions for taking into account your example. When t=H/c, you have
v/c = tanh(aH/c2)
which for small argument you can develop in series as
v/c = aH/c2 - (1/3)(aH/c2)3 + (2/15)(aH/c2)5 - (17/315) (aH/c2)7 + .......
It is reasonable to keep only the linear term within a relative small acceleration a, then the beta relativistic factor v/c can be approach by
v/c = aH/c2
Thus the gamma factor will be always one independently of the big or small that you take the distace H.
Dear Daniel,
"Thus the gamma factor will be always one independently of the big or small that you take the distace H."
Yes exactly, and what you just wrote corresponds, in the time dilation, to the interval
DeltaT'=DeltaT(1+aH/c2)
or DeltaT'=DeltaT+vH/c2
A finite variation of speed of two clocks, in regards to a IRF (initial rest frame), set at reciprocal distance H, should affect their reciprocal counted time the way the leading clock lags of vH/c2
Dear Stefano,
Sorry, but I cannot follow you. If you say that v/c is negligable this means that you are telling that H is not entering in your measurements of time as I have tried to show you in my last post. If you want to obtain the time explicitally, then you can make the approaches of hyperbolic sine, but this only wasting time because the important is the choice of v/c as negligable quantity. In fact this tells you that you are in Galilean absolute time as I have written yesterday and today only tried to enter in your systems or example.
Dear Daniel,
"Sorry, but I cannot follow you. If you say that v/c is negligable this means that you are telling that H is not entering in your measurements of time as I have tried to show you in my last post."
you are right in priniciple. Infact we have to see where v/c is negligible, you teach me that a quantity is negligible in comparison to another, not in general.
In this case I considered that v
Dear Stefano,
From my humble point of view you need to relax the physical conditions if you want to explain the twin paradox within the special relativity, v cannot be too small respect to c.
Dear Daniel,
from an experimental point of view I agree. From a theoretical one I agree a bit less since there is in any case a II order effect for how negligible it can be...
Dear Stefano,
I agree with you that, theoretically speaking, you can distinguish the time of the clocks only thinking in classical terms. But, if you introduce the quatum mechanics for doing the measurements of time, thus it would be almost impossible if not were impossible. Obviously it depends of the exact relationship.
But what is worse for me, and in some aspects contradictory, is that you use a series development considering v/c as neglegible and after that you use such value to consider the difference of times. That is not very pleasent for me. I think that you can do other approaches more consistent: theoretically and experimentally.
Sorry for being so negative.
Dear Daniel,
would it be possible to have your opinion about this old paper of Levi Civita?
"On the analytic expression that must be given to
the gravitational tensor in Einstein’s theory"
https://arxiv.org/pdf/physics/9906004.pdf
https://arxiv.org/pdf/physics/9906004.pdf
Dear Stefano,
It seems to me that everything is ok with the paper of Levi-Civita and the only problem is the interpretation that he does for the energy-momentum. He wants to separate the energy in different kinds: mechanics, elastic, etc--- using the D'Alambert mechanical concept.
It is clear that the derivative of Einstein's tensor must be zero for obtaining the local conservation of the energy-momentum but the separation in terms that neutralize is more difficult to see for me. The energy-momentum tensor doesn't distinguish the different kinds of energy in all that I know.
Dear Daniel,
Levi Civita talks about the Gravitational energy tensor which is something controversial and was named by Einstein as the Pseudotensor.
Dear Stefano,
I don't know exactly what are you thinking, but it is well known that the energy-momentum in gravitation within the context of Einstein's equations have some difficulties.
1. They are not infinitesimal generators associated to the translations as Noether's currents. For instance, this distinguish it clearly of the one defined in electrodynamics.
2. It is equal to the Einstein's pure geometrical tensor and therefore must follow pure geometrical rules as the equivalence with cuvature values of the space-time associated to different metrics. And obviouly their identities as the Bianchi's ones.
3. Separating contributions of the energy-tensor as pure gravitational, electromagnetic is non sense for me, as Levi-Civita does through the classical mechanical -D'Alambert theorem. Perhaps I have not understood it properly because Levi-Civita is an authority in the subject.
Sorry, it is not well written:
Separating contributions of the energy-tensor as pure gravitational, electromagnetic is non sense
must be
Separating contributions of the energy-tensor as pure gravitational from electromagnetic or elastic is non sense ,or at least to dangerous.
Dear all,
I would like to discuss with you the first part of the Schiff's paper of 1960, very simple but quite tricky.
Dear all,
I updated the crictics to Schiff.
Article A revisitation of the Schiff's derivation of the time dilati...
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