# Newton knew that his law of gravity is not final

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Just want to share what the great man wrote about it:

"That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left open to the consideration of my readers."

(It stayed open for 250 years.)

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I think it is still very much open.

GR is an accurate and very valid description of gravity (within its domain of applicability), but it isn’t an explanation, because it has nothing to say about the underlying mechanism. We simply don’t know yet how and why macroscopic spacetime with its observed degrees of freedom comes about; we can only describe its dynamics. This is why research into quantum gravity is so important.

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Newton asked about an agent mediating an act of one body upon another, conveying action and force from one to another, acting according to certain laws as opposed to an "innate" action at a distance. Today we know such an agent. The agent is gravitational field and it acts according to the laws of GR.

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Yes, but spacetime and its degrees of freedom is - at least in my opinion - only an effective description of gravity. I do not think it is fundamental at all, and the underlying mechanisms that give rise to the appearance of smooth spacetime aren’t yet known (though there are of course some interesting hypotheses out there).

To put it slightly differently - the domain of applicability of GR is limited, at least in a ‘downwards’ direction.

Edited by Markus Hanke
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Newton asked about an agent mediating an act of one body upon another, conveying action and force from one to another, acting according to certain laws as opposed to an "innate" action at a distance. Today we know such an agent. The agent is gravitational field and it acts according to the laws of GR.

I have heard differing descriptions or definitions of  a "gravitational  field" and my takeaway is that it is wrong to think of it as a physical object

Rather I have been assured it (like any field) is    just a set of measurements in space and time .

I am not sure ,given that definition  it can be said to mediate  a force between  two massive bodies (if that was what you were saying)

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Newton didn't ask for an explanation of gravity or for its fundamental underlying mechanism. My point is that we got the answer to what Sir Isaak asked for. The answer is GR.

@Markus Hanke says, that GR is not final in its own right. Susskind, Zee, and other authors say that many, or most theoretical physicists think so. Just 150 years more, since 100 years have already passed ...

@geordief says, that it is wrong to think of gravitational field as a physical object. I don't know what physical object means in this context. Are gravitational waves detected by LIGO "just a set of measurements in space and time" or a physical object? Didn't these waves mediate between those colliding stars and us?

Gravitational field, "like any field" ( @geordief ), propagates with finite speed and carries energy. Doesn't this tell that it is (they all are) more than just a set of measurements in space and time?

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Newton didn't ask for an explanation of gravity or for its fundamental underlying mechanism. My point is that we got the answer to what Sir Isaak asked for. The answer is GR.

@Markus Hanke says, that GR is not final in its own right. Susskind, Zee, and other authors say that many, or most theoretical physicists think so. Just 150 years more, since 100 years have already passed ...

@geordief says, that it is wrong to think of gravitational field as a physical object. I don't know what physical object means in this context. Are gravitational waves detected by LIGO "just a set of measurements in space and time" or a physical object? Didn't these waves mediate between those colliding stars and us?

Gravitational field, like any field ( @geordief ), propagates with finite speed and carries energy. Doesn't this tell that it is (they all are) more than just a set of measurements in space and time?

When I said my takeaway (from various earlier discussions) was that it was wrong to think that a field was a physical object  I was only saying that that interpretation seemed most persuasive to me

I didn't mean to suggest that I had weighed the evidence personally as that  would be well beyond my competence.

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Gravitational field, "like any field" ( @geordief ), propagates with finite speed and carries energy. Doesn't this tell that it is (they all are) more than just a set of measurements in space and time?

I don't think so.
Gravitational fields don't propagate, they are simply there.
What propagates are 'changes' to the gravitational field, such as the gravitational waves you mentioned. The gravitational field, as Geordief correctly stated, is simply a curvature at each point in space-time, as described by the metric.
This geometry is the field, and 'measurements in space and time' are the definition of the metric.

Newtonian gravity was not 'final', but neither is GR.
And I doubt Quantum gravity will be 'final' either.

Edited by MigL
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I agree with everything @MigL says here, with two small additions:

• what I refer to as "propagation of the field" is an idealized situation of a change from zero field to non-zero field = from no-field to field = from flat to curved; this is perhaps semantics
• I don't know if the answer to GR is necessarily Quantum gravity
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On 1/10/2022 at 10:24 AM, Genady said:

The agent is gravitational field and it acts according to the laws of GR.

What aspect of GR makes it a field theory ?

In other words what properties specified and used in GR form this 'gravitational field' ?

It should be noted that when GR was published in 1915 it described no such properties and did not conform to the then still developing definition of a Field Theory formalised by Kellogg in his 1929 book "Potential Theory".
This definition was in use for most of the 20th century.

In order to turn GR into a Field Theory it is necessary to modify both GR (via a non linear Lagrangian) and the definition of a field (theory).

Quite a lot of progress has been made towards this in the last few decades and there are postgrad lectures on the subject at MIT, including youtube lectures and padf papers.

A new term  "Effective Field Theory" has been coined, but note the caveat (from Wikipdia)  it is an approximation to the real thing.

Quote

In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model.

@geordief you have +1  for one post, have +1 for the other as well for being brave enough to ask rational questions.

Edit I should add that Effective Field Theory is not quite there yet, nor is it (yet) mainstream.
But it does answer Markus' points about scale, local v global variables and quantum considerations.

Edited by studiot
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Had that discussion with AJB a few years back.
The question was whether Gravity requires a field model or a geometric model.
His reply ... in GR, geometry is the field.

( thanks AJB )

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18 minutes ago, MigL said:

Had that discussion with AJB a few years back.
The question was whether Gravity requires a field model or a geometric model.
His reply ... in GR, geometry is the field.

( thanks AJB )

"in GR, geometry is the field" is said repeatedly by Zee in "Einstein Gravity in a Nutshell" (I think, there.)

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1 hour ago, MigL said:

Had that discussion with AJB a few years back.
The question was whether Gravity requires a field model or a geometric model.
His reply ... in GR, geometry is the field.

( thanks AJB )

Can you find that thread? I searched your quote (in quotes) and just came up with an earlier reminiscence  of yours of AJB's contribution.

Does "Geometry is the field" apply because in GR all geometry is entirely local?

And spacetime is the set of all local geometries?

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Zee, A.. Einstein Gravity in a Nutshell:

"the equivalence principle leads us directly to an understanding of the gravitational field as a manifestation of curved spacetime." (p. 280)

"the gravitational field and curved spacetime are effectively the same thing." (p. 285)

"We could say that there is no such thing as gravity, only curved  spacetime.  But you could say with equal justification that spacetime does not exist; there is only  the gravitational field. To me, it is just a matter of words, and the only relevant issue is which language you find more useful to think in." (p. 285)

"In Einstein’s theory, the gravitational field is equivalent to curved  spacetime." (p. 302)

And so on.

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Newton didn't ask for an explanation of gravity or for its fundamental underlying mechanism.

My interpretation of Newton’s words is that ultimately this is what he is asking for, hence my response.

Are gravitational waves detected by LIGO "just a set of measurements in space and time" or a physical object?

They’re measurements of space and time, but that doesn’t mean they don’t have physical consequences, so in that sense they are also a physical object. I don’t think one can cleanly distinguish between these.

Doesn't this tell that it is (they all are) more than just a set of measurements in space and time?

Energy is simply the conserved quantity associated with time-translation symmetry under Noether’s theorem, so it is itself a measurement of space and time.

14 hours ago, studiot said:

What aspect of GR makes it a field theory ?

I would say that the fundamental dynamical quantity of GR - the metric tensor - is in fact a tensor field; would this not make it a field theory?

Furthermore, one can write GR as a gauge theory, with the Lanczos tensor being the gauge potential. This should make it a field theory for sure, no?

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I hope you appreciate this ... I had to sift through about 27 pages of AJB's content to find it.

halfway down page ten, we have this exchange ...

On 7/4/2016 at 1:51 PM, MigL said:

And I've had this discussion with you before AJB, where I spoke of GR as a geometric theory, but you corrected me by saying that it is a field theory where the geometry is the field.

All classical field theories are geometric. The usual way of understanding the gravitational field is as a metric on space-time; but there are other ways of understanding this.

Edited by MigL
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I was playing with my hand sanitizer , suddenly i have ton of questions too about gravity

Doesn't the space should have something in it for the massive bodies to curve ?

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6 hours ago, dummy39 said:

Doesn't the space should have something in it for the massive bodies to curve ?

No. The geometry is curved; gravity exists even with no body to experience it.

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Thanks for the reply swansont ,

I watch lots of physics related documentaries in youtube but my knowledge is very limited in these subjects .

😅

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On 1/10/2022 at 2:58 AM, Markus Hanke said:

I think it is still very much open.

GR is an accurate and very valid description of gravity (within its domain of applicability), but it isn’t an explanation, because it has nothing to say about the underlying mechanism. We simply don’t know yet how and why macroscopic spacetime with its observed degrees of freedom comes about; we can only describe its dynamics. This is why research into quantum gravity is so important.

Ditto.

We can only attempt at an explanation when we have a theory (a law), plus its domain of applicability. We can take Newton's law of gravity, or GR, and try to explain planetary motion, or why the Moon is slowly sidling away from us by tidal interactions. To summarise, we can explain relatively complex phenomena in terms of simple laws by means of a mechanism spelled out in terms of that simple law. But fundamental physical laws have no mechanism.

Quote

No one has yet made up a theory of electricity for which
$$\nabla^{2}\phi=-\rho/\epsilon_{0}$$ is understood as a smoothed-out approximation to a mechanism
underneath, and which does not lead ultimately to some kind of an absurdity.

Richard Feynman

The Feynman Lectures on Physics Vol. II

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11 hours ago, joigus said:

To summarise, we can explain relatively complex phenomena in terms of simple laws by means of a mechanism spelled out in terms of that simple law. But fundamental physical laws have no mechanism.

That’s true. But so far as GR is concerned, it doesn’t exist in a vacuum - one has to also look at the wider context. For example, if, in addition to GR, we also take into account QFT, then we know that event horizons of Schwarzschild black holes carry entropy (as a function of horizon area). This implies that the bulk enclosed by the surface has a finite, well defined number of non-trivial degrees of freedom associated with it - which physically means that the bulk must have some kind of ‘structure’, or is granular, or is topologically non-trivial. This of course runs counter to a naïve application of GR alone, under which spacetime in the Schwarzschild bulk is everywhere smooth and continuous, and singly connected outside the singularity. More recent results (ref Netta Engelhardt et al) support this.

This is one of the indications that make me think that GR isn’t fundamental. In fact, I’ll eat my monk’s robes should it turn out to be - without salt and pepper, but perhaps with a bit of chilli 🌶 sauce.

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• 1 month later...

My opinion is that Einstein himself admitted his equations described a spacetime which was fluid, frictionless but nonetheless a medium that could bend and stretch. He didn't realise at first that gravitational waves could propagate through it, that spacetime is the field.

Which I think about as the surface of a lake being the field that waves propagate on, the propagation occurs below the surface though, it's a three dimensional wave.

Currently research into superfluid dynamics is hoping to probe the early state of the universe; when did inertia first appear? That kind of thig.

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