Why was the Newtonian notion of "action at a distance" replaced by local interactions in Einstein's gravity?

Newtonian gravity can be-and has been-formulated in terms of a gravitational potential and field, in analogy to the Coulomb potential and electric field-so the statement about action at a distance is, simply, not true. Of course, just like Colomb's law, it is non-relativistic, in fact the non-relativistic limit of Einstein's theory, which is invariant under local Lorentz transformations. That's the point. And it turns out to be the field theory of the metric tensor. All this is standard material in courses on general relativity.

"Action at a distance" not always supposed to be a false idea. After EPR paper on the criticism of quantum mechanics, it turns out that the term " Spooky action " may be considered inevitably for "Entangled" states. Recently there suggested some connection between "worm hole" (a concept emerged originally from GR) and entangled states. these evidence convey that the recent trends are toward ruling out the concept of Action at a distance. Moreover the accepted mechanism for all forces

is a perturbation conducted by " Bosons" that for gravitation assumed to be gravitons.

However it sounds that the challenge for the existence of graviton has not been ended.

jean claude Dutailly

Action at a distance has been replaced by the concept of force field : an immaterial object, existing eveywhere and acting locally on charged particles, and similarly which propagates and depends on the presence of charges particles. In the classic picture there is no fundamental difference (at least with respect to the concept) between the electromagnetic field and gravitation. The introduction of fields rised several issues, one ot them being the geometry in which they are defined : because the value of the field depends formally on the location, and not on the distances to charged particles, geometry matters. The Michelson-Morley experiment is a consequence of this feature. Another issue is that the gravitational charge is identical to the inertial mass, and this lead to general relativity.

Action at a distance needs an infinite speed of propagation of

a signal. The signal originates from a source and it's effects

are observed at a particular point under consideration. However

according to Einstein maximum velocity at which a signal can

travel is c, the speed of light. This is the problem with "action at

a distance picture"

The connection between source point and field point is

produced by the Green’s functions G(x,x'). This is

essentially the propagator of a interaction which is under

consideration. It can be electromagnetism or gravitation.

Green’s functions are used to connect x with x' along the

light cone. Therefore again we see that the connection

speed is not instantaneous.

Action at a distance does imply infinite speed of propagation-the converse isn't true and that's what happens with Newtonian gravity (and electrostatics and magnetostatics). The notion of a field is well-defined, nevertheless, since invariance under Lorentz boosts isn't realized, the theory does not select a particular speed for propagating signals. The field theories are invariant under rotations, translations and Galilean boosts only.

The classical wave equation is an example of a model, where Lorentz invariance appears, only the speed is the speed that enters the wave equation. Its validity thus relies on the validity of the wave description. For sound waves and water waves, this description breaks down at the level where motion of molecules and atoms can be resolved-and it's interesting that this does occur. It's equally interesting that, for electromagnetic waves this *doesn't* happen and, the quantum description is quite different.

jean claude Dutailly

Actually action at a distance by itself does not imply infinite speed of propagation. The Newton's law, the laws for electrostattic, do not mention time. This is in the Ampère-Maxwell and Maxwell laws of magnetiism that the time, and the problem, appear, because the usual definition of the speed of propagation (as in the galilean geometry) is not consistent with the covariance of the equations. The Michelson and Morley was based on the idea that the speed could be added, and so a difference could be measured. All the preparatory work, by Poincaré and Lorentz, to the special relativity was motivated by this issue.

If you look at the Feynmann's diagram you see another form of interaction at a distance, even if the variable distance does not appear explicitely.

It can be retrieved from the EPR paper and following story that the main reason of Einstein opposition for "Entanglement" or action at a distant ( spooky action in Einstein's word) was not implication of "infinite velocity" in this action , but rather it means that the signal can be propagated even more than celerity (C). So i don't agree with Brahmachari and Nicolis but confirm Dutailly comment about infinity velocity.

@ Dutailly : The Feynmann diagram amplitude calculation sometimes requires the time ordering of vertices and this implies that internal lines are propagators with a definite velocity propagation and mediated by some particles (Bosons) , therefore it is not a type of "action at a distant".

It's not consistent to appeal to relativity in non-relativistic quantum mechanics-but this doesn't have anything to do with gravity, Newtonian or Einsteinian.

John A. Macken

Gravitational waves propagate in the medium of spacetime and experience impedance of c^3/G. These gravitational waves propagate at the speed of light and produce action at a distance. As John Archibald Wheeler said, “Empty space is not empty”. QED and QCD require that spacetime has energy density approximately 10^120 times greater than predicted by general relativity and observed in cosmology. I have written a paper (recently accepted for publication by Springer) which analyzes this difference and proposes a way that both can be correct and coexist. The energy density of vacuum takes on the properties of a force field. One result of this analysis is that gravity (curved spacetime) is the result of a nonlinear effect which scales with amplitude squared. The gravitational force and electromagnetic force are united when both are expressed as a wave disturbance in the proposed spacetime field. The equations for these two forces are identical except that the gravitational force equation has one term that is squared while the electromagnetic force equation has this term not squared. A preprint of this paper is available at: http://onlyspacetime.com/QM-Foundation.pdf

@ Charles Francis

Please review these sites for recent progression in determining the speed of "Entanglement" (i.e. spooky action) :

http://www.extremetech.com/extreme/150207-chinese-physicists-measure-speed-of-einsteins-spooky-action-at-a-distance-at-least-10000-times-faster-than-light

or:

arXiv:1303.0614

Regards

Once more, within the framework of non-relativistic (quantum) mechanics, the speed of light does *not* play any particular role. So there's as much sense in comparing the ``speed of entanglement'' to the speed of light in this context as there is in comparing the speed of response of a point on a rigid body (described within the context of classical mechanics) to a force applied at another point to the speed of light. In fact there's even less sense, since in the case of a rigid body there is a well-defined space-time framework, whereas in the case of entanglement in non-relativistic quantum mechanics, precisely, there isn't: entanglement does not appear in the classical limit.

I was thinking in the line of Green's functions. Consider source

coordinates x' and field coordinates x.

Then

phi(x) = int dx' rho(x') / |x-x'|

because G(x,x')= 1/|x-x'| we can write

phi(x)= int dx' G(x,x') rho(x')

Now if x' and x are four vectors then dx' --> d^4 x'

Thus the integration yields,

phi(x) is obtained where x is a four vector. Therefore some

information is obtained about the time dependence of phi at the

field point. Where phi is the potential at space-time point x.

Note that here we have not used the fact that signal

can have a maximum velocity c.

Yes, you have: when you've defined the norm and when you've defined the integration measure. Look at the difference between the solution of the d'Alembertian and the Laplace equations.

The measure is, also, important, else the result of the integration *won't* have the requisite properties.Both metric and measure are important. And by measure is meant, also, the prescription for dealing with the singularities, i.e. what happens when x and x' coincide. In Euclidian signature the solution is unique-in Lorentzian signature a prescription is required. This, of course, is standard material in mathematical methods for physics courses. For the subject at hand, cf. http://www.rand.org/content/dam/rand/pubs/research_memoranda/2006/RM2820.pdf

Actually the Green function defined above may be non-zero outside the light-cone and results in faster thn light speed, but practically in QFT the Green function turns out to be Retarded (Feynman) Green function which for space like interval (i.e. outside the light-cone) vanishes.

Requirement of causality principle (i.e. perturbation appears after source generation) leads to the "Definition" of Retarded propagators. this could be attained by deformation of integral contours. So this is just a handy mathematical trick to preserve Lorentz invariance and causality based on Jordan's lemma. Sorry, I did not find Coleman's article.

Once more: read this: http://www.rand.org/content/dam/rand/pubs/research_memoranda/2006/RM2820.pdf (which was mentioned four or five messages above this one).

For simplicity we can consider one space and one time direction.

x = X, t

x' = X', t'

|x-x'|=+Sqrt[ (X-X')^2 - (t-t')^2]

Because time cannot go back t'>t. The integration

has to be time ordered. I am not sure about the

measure, but time variable is monotonically

increasing. Because we are applying to actions

at distances, we can exclude the case x=x'

Look in Coleman's article, he explains the more general case in great detail. The statement about time ordering is not correct and the statement about action at a distance, also.

Coleman's article sounds to be out of date ( published 1961) there are too many

up to date articles and textbook in the related context. Moreover the fonts used in the article in some equation are difficult to understand.

It's better to judge a work by its content than by its date, or cover. In any case, its content is consistent with what anyone can say about the wave equation. Many people simply rediscover it. But if anyone thinks they can find something in contradiction, they had better check their calculations. This part is standard material in mathematical methods for physics for centuries-Coleman's work on the electromagnetic field clears up some more subtle issues-that have *not* been addressed, alas, elsewhere. But to understand *that* part, requires mastering some mathematics, first.

Coleman's article doesn't have anything to do with quantum electrodynamics, but with other issues, that touch on the subject being discussed here. Were his paper read then a lot of confusion that has appeared would be dissipated.

It can be resolved in *any* treatment-that's a question of personal taste-and *has* been resolved-it has been the subject of courses for decades.

Since Coleman's paper deals with *classical* electrodynamics of a *non-relativistic* particle, this isn't surprising. (It does deal with the wave equation for the electromagnetic field, that had led to some issues in the discussion.) Whatever method one uses will lead to an equivalent result-it's the latter that counts, not the former.

Judging paper by its title isn't as useful as having read (and understood) it. Of course, no one is forced to read anything.

Stefano Quattrini

I will try to stick to the question.

Action at a distance if it is not istantaneous doesn't imply infinite speed of signal propagation.

Newton and Coulomb laws implied istantaneous action at a distance since nothing else was specified , at the time when they were formulated everything appeared instantaneous no perception of delays was noticed. In fact they work fine as long as relative motion of bodies are far from light speed. They represent only a first order approximation of General Relativity and relativistic electrodynamics which include the effect of the finite speed propagation and space time warp.

Stefano Quattrini

I know it sounds absurd, but these laws have been formulated like that and till the finite speed of c has been experimentally found only phylosophical arguments could be used to sustain that interactions occured at finite speed.

Modern physics admits local actions regarding energy exchanges for sure. Quantum entanglement which Einstein himself defined as "spooky action at a distance", doesn't seem "so local" . Anton Zelinger experimentally demostrated this phenomenon for a distance of some hundred meters in his laboratory in Wien.

@ Quatrinni,

I would agree with you, that ,

"at the time when they were formulated everything appeared

instantaneous no perception of delays was noticed"

Even today they are used by Engineers and Technocrats. It is

sufficiently correct for them given today's technical standards.

For example to build a very good bridge or a very nice building

an engineer does not need to know Einstein's equations and

locality of interactions between energy-momentum

with space-time.

Einstein's equations are used mainly in Astrophysics and

Cosmology, as far as I know.

Well, fortunately, Einstein's equations are used when computing positions with the GPS-the Newtonian approximation for how electromagnetic waves probe spacetime gives wrong answers in that case. This is an interesting test of general relativity, in fact.

More precisely time dilation resulting Independently from both Especial and General relativity considered as correcting parameters for the clocks on sattelites GPS.

" Why was the Newtonian notion of "action at a distance" replaced by local interactions in Einstein's gravity? "

The idea of Newtonian gravity acting instantaneously over long distances is something that appears in educational texts, but if you read what Newton actually wrote, he describes gravitational deflection occurring because of a lightspeed gradient across the region surrounding the particle, analogous to the deflection of light that happens in a region where there's a gradient in refractive index.

In physics, a lot of the starting points that we use for comparative theory are based on statements that are historically wrong. This sometimes results in theoretical work and experimental testing work being compromised.

Eric Lord

Velocity of propagation, in gravity and in electromagnetism, comes into play only when there are accelerating sources. Coulomb's inverse square law refers to a STATIC charge and the STATIC electric field around it - that extends through the whole of space. The gravitational analogue is the Schwartzschild solution, which refers to the gravitational field of a STATIC mass - a STATIC gravitational field extending through the whole of space.

The term "Instantaneously " repeated many times in the discussion, apparently is in contradiction with "Relativity of Simultaneity" principle.So this Newtonian idea was ruled out after Especial Relativity before introduction of GR.

Manouchehr, it doesn't seem to have been a Newtonian idea.

What often happens in physics education is that teachers and lecturers ascribe "bad" ideas to old models in order to emphasise the progress that's been made since, or to highlight a shift in philosophical emphasis. A lot of these comparisons seem to be completely fictitious, but the more memorable ones survive to be taught to the next generation of students, and then the next ...

It's like that old canard about how before Christopher Columbus, people thought the world was flat. It's a nice story, but I've never seen anyone provide credible evidence of anyone seriously suggesting that the world was flat in the last two millennia - and Eratosthenes's figure for the Earth's circumference (a couple of hundred years BC) seems to have been more accurate than whatever value CC was using.

This has been going on for so long that we're now wallowing in science history disinformation, so much so that if you want to do any real comparative theory involving relativity theory, you have to work on the assumption that everything you've been told is wrong, unless you can find evidence to the contrary.

If you want to know what was REALLY taught before the C20th, ignore what the C20th textbooks //say// was taught back then, and actually check the original texts. You'll find that big chunks of what you probably believe to be standard peer-reviewed physics history are at odds with the historical record.

"at the time when they were formulated everything appeared

instantaneous no perception of delays was noticed"

Actually, that's not true, either. Newton pointed out that the finite speed of light meant that we observed the eclipses of Jupiter's moons to happen earlier or later than calculated, depending on how far away Jupiter was from the Earth at the time of observation. This effect had already been measured, and Newton supplied a calculated value of the speed of light based on these observational time-differences.

Yes, I know that some respected sources characterise the distinction between Newton's physics and Einstein's by saying that Newton believed that the speed of light was infinite ... it's a nice story for the physics classroom, but it's not factual.

"More precisely time dilation resulting Independently from both Especial and General relativity considered as correcting parameters for the clocks on sattelites GPS."

Another couple of corrective historical footnotes regarding GPS, time dilation and experimental testing:

[1] Velocity-related shifts

Transverse redshifts aren't unique to special relativity as implied or stated in some SR reference sources. If you do the calculations, you'll find that most old theories predicted a redshift in a detector aimed at 90 degrees to a moving object's path, where "90 degrees" is measured in the observer's frame. Einstein's argument extrapolating from transverse redshift to physical time dilation for a circling clockworks would be expected to work similarly in at least some of those other theories.

C19th Newtonian emission theory actually predicts a //Lorentz-squared// transverse redshift, although distinguishing this from the SR version is complicated by SR's Lorentz redefinitions of distances and times (and resulting nominal velocity values).

[2] Gravity-related shifts

Gravitational shifts were predicted from Newtonian mechanics back in 1783.

Einstein's 1911 presentation of the argument for gravitational shifts and a further argument that this led inevitably to gravitational time dilation predate general relativity, and Einstein's 1911 calculations used "Newtonian" Doppler equations rather than those of special relativity for simplicity, so it was a "Newtonian" calculation in the sense that the argument didn't require anything from special or general relativity. Essentially, he recreated Michell's C18th argument and pointed out that a clockrate that depended on gravitational environment was the apparently inevitable consequence.

Stefano Quattrini

I don't think Newton gave to the "light" the HONOR to be the maximum speed for everything. He might have estimated the speed, but never thought that gravitation itself or fields perturbations would be limited by that speed.

Only the LORENTZ factor could be accounted for time dilation/contraction at the beginning. Einstein's presentation of Gravitational Redshift though being a marvellous intuition, was not correctly derived from the equivalence principle and the special relativity equations in his paper. The title was "ON THE GRAVITATION OF ENERGY", but he didn't make any distinction between radiant and confined energy and it's experimentally verified that free energy does not gravitate. As you can see in the same paper there is the conjecture about the variable speed of light in a gravitational potential, which gave Birth to GR. In GR the Redshift is only a consequence of the clock hypothesys wrote also in OKUN's article: GRAVITATION, PHOTONS, CLOCKS.