Is Gravity a Force?

[TheVat]

@studiot

 

At this point,  I would love to delete that post, lol,  and apparently sending false implications regarding orbital motion.   FtR,  I know that the near-earth area is not a closed cosmos packed into a compact Reimannian sphere in which I could with a large telescope inspect my bald spot in back.   That would be a cool sci-fi story,  however. 

I'm also aware that orbiting objects,  though they may have constant speed, do not have constant velocity and are therefore under acceleration.   I was indeed trying to whimsically point out that some usages of the term "force" can be misleading, pointing to why Einstein and others preferred to categorize gravitation as geometry.

Edited September 5, 2021 by TheVat
Gjfmwritnfrg

[StringJunky]

On 9/4/2021 at 9:32 AM, joigus said:

I think the word we're all fumbling for here when we say 'reality' is in fact 'ontology'.

One of the most important lessons of 20th-century physics is, I think, Nature doesn't care a great deal about our entities.

I think @swansont, @MigL, @beecee, and myself; and perhaps most eloquently @DrDon have drawn arguments along these lines.

Nature is probably connected all the way down to the most fundamental level. That's why such a thing as unification of physical laws is possible in the first place. But distinctions emerge. It is the business of physics to elucidate what connections/distinctions appear/disappear, and when (at what scale) they are relevant. Entities don't present themselves as 'solid' immovable categories; rather, as useful instruments for the scale of description given.

Terms as bosonization (a fermion can be seen as a pair of bosons with a 'twist' between them), dualities (a strongly-coupled interaction in one region of space can be seen as a weakly-coupled one on the boundary of that region) etc., strongly suggest that any entities that we may propose are simply instrumental, and what emerges as really robust are physical principles, patterns, rather than 'things'.

Lorentz invariance, locality, unitarity, symmetries and conservation laws. Those are the main characters in this play. Weinberg was a master at bringing out how they interplay.

Einstein was one of the most brilliant theorists of all time, but this revolution caught him at a point in his life when he was already too set in his --ontological?-- ways. Weinberg was able to take home the lesson much more efficiently for what the 2nd half of the 20th century physics needed.

Maybe nothing is, and everything emerges, in some kind of bootstrap mechanism of substantiation of entities in a grand cosmic scheme of which the building blocks are actually patterns and principles, and not things. --I'm getting blah, blah.  

I'm also glad that professor Lincoln has spent some time among us, be it ever so briefly.

Very good. Pat on the head, Sir! Your post heads in the direction of how my own sense of science has been emerging. It has been regularly reiterated by swansont over the years that physics is about behaviour, so we need to get rid of these 'thingies'. 

Quote

Reification (fallacy)

Reification (also known as concretism, hypostatization, or the fallacy of misplaced concreteness) is a fallacy of ambiguity, when an abstraction (abstract belief or hypothetical construct) is treated as if it were a concrete real event or physical entity.[1][2] In other words, it is the error of treating something that is not concrete, such as an idea, as a concrete thing. A common case of reification is the confusion of a model with reality: "the map is not the territory".  https://en.wikipedia.org/wiki/Reification_(fallacy)

 

[swansont]

9 minutes ago, TheVat said:

I was indeed trying to whimsically point out that casual usages of the term "force" can be misleading, pointing to why Einstein and others preferred to categorize gravitation as geometry.

I’m not sure “preference” tells the story here. It’s where the ideas led him. A spinning wheel’s circumference can’t be described by 2pi*r owing to length contraction leads you to a non-Cartesian system.

Add to this the notion that don’t feel gravity in freefall, you feel a force of something else when you aren’t in freefall, leads you to the idea that being stationary in a gravitational field is the accelerated frame.

[TheVat]

5 minutes ago, swansont said:

I’m not sure “preference” tells the story here. It’s where the ideas led him. A spinning wheel’s circumference can’t be described by 2pi*r owing to length contraction leads you to a non-Cartesian system.

Add to this the notion that don’t feel gravity in freefall, you feel a force of something else when you aren’t in freefall, leads you to the idea that being stationary in a gravitational field is the accelerated frame.

Thanks, and that last sentence is as concise a description of the equivalence principle as I've ever encountered.   Now I can stop wondering why you get the special hat.  I used "preference" loosely,  so the semantic point is a fair one,  given that I did not mean Al selected GR on a whim.   <g>

[beecee]

1 hour ago, MigL said:

Invoking A Einstein, and his quotes, doesn't help the situation, as he didn't know about Black Holes, nor about gravitational effects on approaching Planck scales.

And going on a sometimes faulty memory, didn't the great man reject the BH hypothetical, which is all it was at that time?

1 hour ago, MigL said:

So I don't see the point of quoting A Einstein, and his beliefs, nor about expecting one theory or the other to fully describe 'reality' or be 'true'.
Obviously neither is, and we are faced with two prospects ...
1 - We don't have a full description of 'reality' yet.
2 - We may never be able to fully describe 'reality.

Bingo!  GR is not an all purpose TOE, and until we have one, [1] and [2] remain obviously valid.

[swansont]

2 hours ago, MigL said:

So I don't see the point of quoting A Einstein, and his beliefs, nor about expecting one theory or the other to fully describe 'reality' or be 'true'.
Obviously neither is, and we are faced with two prospects ...
1 - We don't have a full description of 'reality' yet.
2 - We may never be able to fully describe 'reality.

To this I would add that even if one person thinks a particular model is reality (especially if its their theory), it doesn’t mean that this is true of all of physics. “this bit is real” says nothing about the rest.

(plus all the counterexamples, of course)

[Davy_Jones]

Just a couple of thoughts for all to ponder for now . . .

Can you bear one more Einstein quote? Just one last time, I promise.

Quote

"If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: Don't listen to their words, fix your attention on their deeds." 

What Einstein is telling us here, and as is well known to philosophers and historians of science, is that scientists--with the best of intentions--frequently misdescribe what it is that they are doing.

If it's any consolation, don't feel too bad; everybody else in the human race does it too, at least from time to time.

I very humbly and respectfully suggest that's what's been happening here, at least to some extent.

 

Whenever some annoying philosophical asshole (e.g. me LOL) gatecrashes the physicists party and asks questions about truth and reality, what we hear is something like the following (paraphrased with elements picked from various comments throughout the thread, either explicitly stated or implicitly implied):

 

"Oh, don't be silly. You obviously know nothing about physics. We just construct models which can be regarded as simply tools, and describe behavior. We don't use words like truth and reality and belief, or if we do, we hedge them with 'scare quotes'. Our models (which we prefer to the word theory) are simply instruments, not the kinds of things that can even be true or false. Science does not address questions such as "What is the fundamental nature of gravity? or the fundamental nature of anything else; we leave that to metaphysicians and philosophers and other degenerates. We simply describe behavior; physics is not in the business of going behind the scenes and offering explanations to 'why' questions."

 

(Having fun here, folks. Don't take this too seriously )

 

But, but . . . after that annoying philosophical asshole has been given a good beating and ignominiously thrown out the door head first, the physicists crawl out their shells again, look around nervously, and revert to their normal modes of speech.

 

Now, I've only been up for an hour or so this morning. Over a nice breakfast and a mug of coffee I enjoyed Prof. Don Lincoln's (see earlier in thread) lecture 18, "The Case for Cosmic Inflation".

Prof. Lincoln ends the lecture with this:

"Ok, so that's the story of inflation which is most certainly not a theory that you should believe outright. But it's a theory that is a very good candidate to explain the observed uniformity of matter in the universe and the flatness of space. It might be true, and if it is, it will definitely make the news."

 

After that, I had a quick browse through your wonderful forums here. First thing to catch my beady reptilian eye was a passage from Wiki which @TheVat posted a few hours ago in the thread "Why does it seem to us that the universe is expanding where there is no gravity" . . .

 

"Since the 1990s, dark energy has been the most accepted premise to account for the accelerated expansion. As of 2021, there are active areas of cosmology research aimed at understanding the fundamental nature of dark energy..."

Conclusion: I very humbly (grovel, grovel) suggest that comments such as those above are perfectly typical of the way physicists speak . . . when pests like me aren't around LOL.
 

Edited September 6, 2021 by Davy_Jones
typos

[beecee]

2 hours ago, Davy_Jones said:

If it's any consolation, don't feel too bad; everybody else in the human race does it too, at least from time to time.

Including philosophers.

Science is what we know: Philosophy is what we don't know.

                                                                                                        Bertrand Russell 

2 hours ago, Davy_Jones said:

Whenever some annoying philosophical asshole (e.g. me LOL) gatecrashes the physicists party and asks questions about truth and reality, what we hear is something like the following (paraphrased with elements picked from various comments throughout the thread, either explicitly stated or implicitly implied):

"There are no whole truths: all truths are half-truths. It is trying to treat them as whole truths that plays the devil". 

Alfred North Whitehead (1861-1947) English philosopher and mathematician.

"philosophy is to science as pornography is to sex".

Steve Jones:

2 hours ago, Davy_Jones said:

Prof. Lincoln ends the lecture with this:

"Ok, so that's the story of inflation which is most certainly not a theory that you should believe outright. But it's a theory that is a very good candidate to explain the observed uniformity of matter in the universe and the flatness of space. It might be true, and if it is, it will definitely make the news."

The BB theory of universal evolution of space and time, does have some  nagging problems with it; Inflation was speculated to eliminate those nagging problems, and does seem to account for that. While the BB has enough observational evidence to cement it as overwhelmingly supported, we have no evidence for inflation as far as I am aware. That's what Dr Lincoln is conveying.

2 hours ago, Davy_Jones said:

After that, I had a quick browse through your wonderful forums here. First thing to catch my beady reptilian eye was a passage from Wiki which @TheVat posted a few hours ago in the thread "Why does it seem to us that the universe is expanding where there is no gravity" . . .

 

"Since the 1990s, dark energy has been the most accepted premise to account for the accelerated expansion. As of 2021, there are active areas of cosmology research aimed at understanding the fundamental nature of dark energy..."
 

Scientists are actually unaware of the nature of whatever it is that makes the expansion rate of the universe accelerate...Hence the use of the terminology Dark Energy.

2 hours ago, Davy_Jones said:

Conclusion: I very humbly (grovel, grovel) suggest that comments such as those above are perfectly typical of the way physicists speak . . . when pests like me aren't around LOL.

I recommend you read Lawrence Krauss' book "A Universe from Nothing" 😉

"Philosophy consists very largely of one philosopher arguing that all others are jackasses. He usually proves it, and I should add that he also usually proves that he is one himself".

Henry Louis Mencken. 

[Markus Hanke]

18 hours ago, Davy_Jones said:

That is to say, "formalism", at least as I understand the term, implies precisely a mere mathematical structure or framework; a skeleton, if you like, bereft of any ontological commitments.

I am using formalism in the mathematical sense; ie akin to the ‘language’ used to write down the model. Usually this will be the language of tensor calculus and differential geometry.

 

18 hours ago, Davy_Jones said:

By speaking of formalism, is it not the case that you've already assumed the answer is no?

You need to choose a formalism to write down your model, otherwise you cannot extract any predictions from it - just as you need to choose a language when you write a forum post here. 

What I am attempting to point out is that this choice is not unique. Most texts on GR will use tensor calculus as their formalism, so you will see it written in terms of the metric, plus a couple more tensor fields built from the metric. But there are other choices that use completely different objects, yet still arrive at the same physical predictions. To pick just one example, you can write down GR using the Penrose spinor formalism - the basic object is now a rank-4 spinor, and the field equations become a constraint on that spinor. Or you could use the ADM formalism, which uses conjugate momenta. And so on. They all describe the same physics, but using very different languages.

So my point is simply this - if the “machinery behind the observable” is not unique, and to some degree interchangeable, in what sense then can this formalism itself be ontologically ‘real’?

It’s like language - you can say ‘table’ or ‘Tisch’ or โต๊ะ, but these are just conventions. What’s ontologically real is the object in your room which you can touch and bang your knee against, not the many different words. Or have you ever banged your knee on a word

18 hours ago, Davy_Jones said:

Now, given that Einstein (just to name one) clearly was able to construe GR as a (or an attempted) representation of how the universe really is, on what grounds do you base your claim that it cannot be read any other way but instrumentally?

What I wish to do is carefully distinguish between the observables of a model, and its formalism. The observables directly map to elements of physical reality, so they are ‘real’ in that sense. For GR that would be the outcome of measurements taken on test particles with clocks and rulers - GR is simply a set of correlations between gravitational sources, and such outcomes. The same is not true for the specific formalism, though - there are different ways to obtain these correlations, and the computational devices employed in doing so do not uniquely map into anything in the real world. Only observables do.

This is just my current view on this matter, which may evolve and change as I continue learning and pondering. I do not claim that it absolutely can’t be read any other way. One notable problem with this view of mine is that there is at least one computational device that is shared by all formalisms which I am aware of - space-time. Does that mean that space-time is ontologically real, even if it can’t be observed? Is it possible to formulate GR without recourse to any concept of space-time? And what about things like the Ahoronov-Bohm effect? What are the implications?

I shall continue to ponder.

To finish with a quote by George Box: “ All theories are wrong, but some are useful.”

P.S. What have all these disparate formalisms in common, that enables them to represent the same physics? The answer is that they capture the same symmetries - local Lorentz invariance, and global diffeomorphism invariance. For example, both tensors and spinors are representations of the Lorentz group. So really, the most fundamental thing that models and reality have in common - why they can map into each other - are symmetries. The same is true of course in quantum physics.

Edited September 6, 2021 by Markus Hanke

[Davy_Jones]

Thanks again, @Markus Hanke

Perhaps a little off-topic, but I'm genuinely curious . . .

1 hour ago, Markus Hanke said:

You need to choose a formalism to write down your model, otherwise you cannot extract any predictions from it - just as you need to choose a language when you write a forum post here. 

What I am attempting to point out is that this choice is not unique. Most texts on GR will use tensor calculus as their formalism, so you will see it written in terms of the metric, plus a couple more tensor fields built from the metric. But there are other choices that use completely different objects, yet still arrive at the same physical predictions.

This calls to mind the position known as conventionalism, associated particularly with Henri Poincaré. 

We see this kind of thing, for example, in the so-called "units of selection" brouhaha in evolutionary biology. There are those who hold that there is a fact of the matter as to what is being selected (individual orgamisms, groups of organisms, genes, etc.); others claim this is simply a matter of convenience or convention -- pragmatics, if you like.

More pertinent to general relativity, Poincaré maintained that there is no fact of the matter as to whether space is Euclidean or not. Again, which system we choose to adopt is purely a matter of pragmatics, simplicity, convenience, convention . . .

Quote

However, Poincaré did not share Kantian views in all branches of philosophy and mathematics. For example, in geometry, Poincaré believed that the structure of non-Euclidean space can be known analytically. Poincaré held that convention plays an important role in physics. His view (and some later, more extreme versions of it) came to be known as "conventionalism". Poincaré believed that Newton's first law was not empirical but is a conventional framework assumption for mechanics (Gargani, 2012). He also believed that the geometry of physical space is conventional. He considered examples in which either the geometry of the physical fields or gradients of temperature can be changed, either describing a space as non-Euclidean measured by rigid rulers, or as a Euclidean space where the rulers are expanded or shrunk by a variable heat distribution. However, Poincaré thought that we were so accustomed to Euclidean geometry that we would prefer to change the physical laws to save Euclidean geometry rather than shift to a non-Euclidean physical geometry.

https://en.wikipedia.org/wiki/Henri_Poincaré

 

Is this a position you subscribe to yourself? Or do you believe there is a fact of the matter as to the geometry of physical space? How about other physicists?
 

Edited September 6, 2021 by Davy_Jones

[Markus Hanke]

29 minutes ago, Davy_Jones said:

Is this a position you subscribe to yourself? Or do you believe there is a fact of the matter as to the geometry of physical space? How about other physicists?

I think this is a matter of internal consistency. We know from experiment and observation that nature obeys certain fundamental symmetries - for example, from observing and playing around with a large number of particle interactions, and even before making any specific models, we will eventually notice that all these interactions are subject to what’s called CPT symmetry. Any model of particle physics we now develop must therefore reflect this symmetry (the current Standard Model does this). As it turns out, CPT symmetry implies that space time must have a certain local symmetry as well, called Lorentz invariance (this can be formally proven, and has been experimentally shown to high accuracy). This symmetry is not compatible with a Euclidean geometry - you need something that has different signs in the time and space parts of the metric, making it non-Euclidean. So you need non-Euclidean space time for internal consistency, or else there would be a conflict between particle physics and macroscopic physics. Poincare could not have known this, since the necessary observational data was not yet available to him. The other thing is that the strong and weak interactions are not invariant under rescaling, so shrinking and expanding rulers are not even an option.

However, it should be noted that, given non-Euclidean space-time, you can describe gravity in ways that don’t use curvature - notably with a concept called torsion. Einstein himself tried this, but failed for technical reasons. Only in the 1960s was a functioning model along these lines developed; it’s called Møller gravity. Spacetime here is completely flat, and gravity is due to torsion alone. The physical predictions are the same as in standard GR, because they obey the same symmetries.

Which, of course, further underlines my earlier point that the behind the scenes machinery of GR - such as curvature tensors - does not necessarily map into any element of reality. You can do away with curvature completely, and yet still obtain the same gravitational physics through other geometrical means. What both models share are again the underlying symmetries.

[TheVat]

15 hours ago, Davy_Jones said:

Just a couple of thoughts for all to ponder for now . . .

Can you bear one more Einstein quote? 
 

No.  😁

I was interested to learn that gravity can be described without a curvature tensor (Môller gravity, with torsion) and I hope those more capable might explore the epistemological implications.  My hope is that scientists generally do not have to carry the burden of "math is reality," at least not the way Max Tegmark does.  

[MigL]

15 hours ago, Davy_Jones said:

Whenever some annoying philosophical asshole (e.g. me LOL) gatecrashes the physicists party and asks questions about truth and reality

Don't sell yourself short...
This has been one of the most interesting discussions in quite a while.
It even brought Markus out of 'retirement'.
 

 

15 hours ago, Davy_Jones said:

"Oh, don't be silly. You obviously know nothing about physics. We just construct models which can be regarded as simply tools, and describe behavior. We don't use words like truth and reality and belief, or if we do, we hedge them with 'scare quotes'. Our models (which we prefer to the word theory) are simply instruments, not the kinds of things that can even be true or false. Science does not address questions such as "What is the fundamental nature of gravity? or the fundamental nature of anything else; we leave that to metaphysicians and philosophers and other degenerates. We simply describe behavior; physics is not in the business of going behind the scenes and offering explanations to 'why' questions."

They say that the first step on the path to better oneself is recognizing one's shortcomings.
You're on your way to becoming a much better Physicist.

 

15 hours ago, Davy_Jones said:

Conclusion: I very humbly (grovel, grovel) suggest that comments such as those above are perfectly typical of the way physicists speak . . . when pests like me aren't around LOL.

8 pages of ( very informative and interesting ) discussion, and that is your conclusion ?
That sometimes Physicists ( and people in general ) sometimes use inappropriate words to describe things/effects ?

 

10 hours ago, Markus Hanke said:

Only in the 1960s was a functioning model along these lines developed; it’s called Møller gravity.

You're only back briefly, and already we are learning and ggaining new interests.

[beecee]

2 hours ago, MigL said:

You're only back briefly, and already we are learning and ggaining new interests.

New one on me also! Another is the "Vector 4 Gravity" model by Carver Mead, and fervently pushed by an old mate of mine from another forum. This from what I understand makes the same predictions and matches the same observations as GR, except in relation to a small aspect re polarisation?

https://www.npl.washington.edu/av/altvw181.html

 LIGO and LIGO+Virgo have now detected about a dozen gravitational wave events.  Their observed polarization characteristics shy locations are consistent with Einstein's GR but not with Mead's G4v.  Nice try, Carver.

[swansont]

18 hours ago, Davy_Jones said:

Conclusion: I very humbly (grovel, grovel) suggest that comments such as those above are perfectly typical of the way physicists speak . . . when pests like me aren't around LOL.

I think it’s accurate to say physicists* use some vocabulary that doesn’t mean what a lay use of those words mean. Physicists also use jargon, because they understand what the jargon means, and in both cases if you hear the discussion without an appreciation for this, you will not get the same message. So yes, physicists might speak differently to a lay audience, for fear of being misunderstood.

*(true of all scientists, not just physicists)

[Davy_Jones]

2 hours ago, MigL said:

8 pages of ( very informative and interesting ) discussion, and that is your conclusion ?
That sometimes Physicists ( and people in general ) sometimes use inappropriate words to describe things/effects ?

Well, not entirely.

Any young Turk entering a lecture course on free will, say, or the mind-body problem, and expecting to come away with the answer (perhaps written on the back of a postage stamp), is in for a rude awakening.

That's not to say his Anatolian time has been wasted, though. A great deal can still be learned. E.g.

1. What some of the greatest thinkers have had to say about these things.

2. A better appreciation of the complexities involved can be achieved. E.g. When you hear a Daniel Dennett or a Steven Pinker (both compatibilists) tell you that free will is real, they have something quite different in mind from a John Searle, say.

 

So, I'm genuinely grateful to all who have contributed. Next time my children (if I ever have any) ask "Daddy, is gravity a force?" I'll tell them "Shut up and do your homework" . . . er, I mean, I'll tell them "Ah, it's not a simple question, son, but I can tell you what some very clever people have to say about this".
 

2 minutes ago, swansont said:

I think it’s accurate to say physicists* use some vocabulary that doesn’t mean what a lay use of those words mean. Physicists also use jargon, because they understand what the jargon means, and in both cases if you hear the discussion without an appreciation for this, you will not get the same message. So yes, physicists might speak differently to a lay audience, for fear of being misunderstood.

*(true of all scientists, not just physicists)

Point well taken. Obviously when Professor Lincoln, say, is delivering a series of lectures to a lay audience he will not be speaking the same way as he he does when talking to his peers.

 

If he did, I'd demand a refund.

[studiot]

3 hours ago, TheVat said:

No.  😁

I was interested to learn that gravity can be described without a curvature tensor (Môller gravity, with torsion) and I hope those more capable might explore the epistemological implications.  My hope is that scientists generally do not have to carry the burden of "math is reality," at least not the way Max Tegmark does.  

 

Moller has an interesting view on 'Flat' geometry.

The usual method of defining flat is to say there is no (zero) curvature

ie

the Tensor R_iklm = 0.

Moller says

Quote

A flat space is a space in which it is possible to introduce a system of coordinates which is geodesic at every point.

The two are, of course, equivalent.

I interpret which is geodesic at every point to mean every point lies on a geodesic.

 

Markus also makes the point that spacetime is a fundamental common to different descriptions.

16 hours ago, Markus Hanke said:

This is just my current view on this matter, which may evolve and change as I continue learning and pondering. I do not claim that it absolutely can’t be read any other way. One notable problem with this view of mine is that there is at least one computational device that is shared by all formalisms which I am aware of - space-time. Does that mean that space-time is ontologically real, even if it can’t be observed? Is it possible to formulate GR without recourse to any concept of space-time? And what about things like the Ahoronov-Bohm effect? What are the implications?

Have you ever heard of overdetermined systems ?

Consider a set of 'spacetime points'.
Now the structure for this set will be determined by the (set of) relations between the points.
The 'formalisms' Marcus speaks of can be thought of different sets of relations.
Each different set of relations will generate slightly different 'spacetimes'.
That is they will make the mathematical structure of the spacetime set of points different.
Useful ones must contain many similarlities or even congruences, if they are to reproduce observed spacetime behaviour.

Now introducing a coordinate system into spacetime is not a minimum set.
The spacetime is overdetermined.

That is a coordinate system introduces information on structure which is not in the minimal relation set.

To find the minimal  set we can take frame invariants and deduce their relations.

In flat geometry the interval is the frame invariant quantity.

The minimal spacetime becomes a network of spacetime points, linked by invariant intervals.
Such a network does not offer the unused property of orientation that arises from the use of a coordinate system.

 

[Markus Hanke]

11 hours ago, beecee said:

Their observed polarization characteristics shy locations are consistent with Einstein's GR but not with Mead's G4v.  Nice try, Carver.

This is why I previously mentioned the fact that no vector model can ever capture all degrees of freedom involved in gravity, on fundamental grounds. You need at a minimum a rank-2 tensor. This has been known for a long time (it is even mentioned in some old texts such as MTW), so I don’t know why people still try, and then argue about it.

10 hours ago, studiot said:

Now introducing a coordinate system into spacetime is not a minimum set.
The spacetime is overdetermined.

That is a coordinate system introduces information on structure which is not in the minimal relation set.

Good point!

10 hours ago, studiot said:

The minimal spacetime becomes a network of spacetime points, linked by invariant intervals.
Such a network does not offer the unused property of orientation that arises from the use of a coordinate system.

I have been pondering lately (being a monk has its advantages - I have time on my hands!) if it might not be possible to formulate GR in terms of Graph Theory, which ties in nicely with what you said above.  Rough idea being to see what happens when you treat GR as a finite and initially discrete graph/network of events with given relations - without any recourse to geometry or manifolds, at least at first. I’m wondering how applying local constraints would affect the global structure of such a graph; and what happens if one lets the number of nodes increase. Ultimately I’m wondering if a sufficiently fine-grained graph/network with the right structure can approach some semblance of the 4D differential geometry machinery we are ordinarily using for GR. Hope this makes some sort of sense.

This is only an idea, haven’t begun any work on it - don’t know if it’s worth pursuing, or even if this makes sense. I’d need to teach myself graph theory first, so sorry for brutalising terminology. But I hope you get the drift - fundamentally I’m interested in whether the structures encapsulated in GR can arise from something other than geometric and topological considerations. To see if there’s another level to it behind the obvious. No such formalism seems to exist yet (at least I couldn’t find anything) - which probably means I’m missing something, and doesn’t bode well.

How do you as a mathematician feel about such an idea?

Edited September 7, 2021 by Markus Hanke

[geordief]

47 minutes ago, Markus Hanke said:

I have been pondering lately (being a monk has its advantages - I have time on my hands!) if it might not be possible to formulate GR in terms of Graph Theory

https://theconversation.com/a-new-kind-of-physics-stephen-wolfram-has-a-radical-plan-to-build-the-universe-from-dots-and-lines-136830

 

Along those lines?

Edited September 7, 2021 by geordief

[joigus]

2 hours ago, Markus Hanke said:

[...]

I have been pondering lately (being a monk has its advantages - I have time on my hands!) if it might not be possible to formulate GR in terms of Graph Theory, which ties in nicely with what you said above.  Rough idea being to see what happens when you treat GR as a finite and initially discrete graph/network of events with given relations - without any recourse to geometry or manifolds, at least at first. I’m wondering how applying local constraints would affect the global structure of such a graph; and what happens if one lets the number of nodes increase. Ultimately I’m wondering if a sufficiently fine-grained graph/network with the right structure can approach some semblance of the 4D differential geometry machinery we are ordinarily using for GR. Hope this makes some sort of sense.

[...]

(My emphasis)

Interesting. But what are you going to do with all those diffeomorphisms? Differentiability is hard-wired into GR.

[studiot]

4 hours ago, Markus Hanke said:

I have been pondering lately (being a monk has its advantages - I have time on my hands!) if it might not be possible to formulate GR in terms of Graph Theory, which ties in nicely with what you said above.  Rough idea being to see what happens when you treat GR as a finite and initially discrete graph/network of events with given relations - without any recourse to geometry or manifolds, at least at first. I’m wondering how applying local constraints would affect the global structure of such a graph; and what happens if one lets the number of nodes increase. Ultimately I’m wondering if a sufficiently fine-grained graph/network with the right structure can approach some semblance of the 4D differential geometry machinery we are ordinarily using for GR. Hope this makes some sort of sense.

This is only an idea, haven’t begun any work on it - don’t know if it’s worth pursuing, or even if this makes sense. I’d need to teach myself graph theory first, so sorry for brutalising terminology. But I hope you get the drift - fundamentally I’m interested in whether the structures encapsulated in GR can arise from something other than geometric and topological considerations. To see if there’s another level to it behind the obvious. No such formalism seems to exist yet (at least I couldn’t find anything) - which probably means I’m missing something, and doesn’t bode well.

How do you as a mathematician feel about such an idea?

Graph theory is a geometric way of representing relations.

The most basic is the elementary relation is the connection. eg A is connected to B, but A is not connected to C etc.

Much of elementary graph theory  - the travelling salesman, konigsburg bridges etc is devoted to solving simple networks possessing only the connectivity relation. When programmed as matrices for computing this use what is called the incidence matrix.

This is not much use for spacetime however.

The next up is the weighted connection and we can use the invariants as weights, noting the in spacetime every point is connected to every other point.

'Graphs' were developed for solving sets of simultaneous equations by geometric reduction proceedures.
These (not to be confused with schoolboy xy plots as graphs) have been called flow graphs and set of quite sophisticated equations can be solved this way both linear and non linear including self regenerative equations.

I have speculated before (though not here) that these would hold out much hope for incorporating the more complicated relations inherent in say GR.
They have been used to do this with the stress tensor, that Mordred was so fond of.

A pity he is also not with us for this discussion.

 

[Intoscience]

So far this has been a very interesting, informative and often over my head discussion! Some great posts from the resident experts and our honoured guest!

Being a Layman (or at best a novice) I have limited understanding of the subjects I enjoy, space-time, gravity and the speed of light.

Reading through the posts, the discussion has often diverted off track from the original post. One of the diverts was the semantics of terms and phrases. One which I commented on way back in the discussion as a sort of dismissal.

Since then I have come to realise that in fact the importance of the usage, meaning and context of some terms and phrases used have a profound effect on my preconceived understanding.

In pondering the original post - "Is gravity a force?" and the phrase so often used - "the force of gravity"  I started to consider the meanings behind both.

The force of gravity:

• The interaction between 2 or more objects resulting in a mutual attraction - Newtonian
• The curvature of space-time - GR (Einstein - preferred model)

These 2 descriptions appeared to me to be conflicting. Then I had the idea to split the phrase into 2 terms - gravity & gravity force.

• Gravity - space-time curvature
• Gravity force - the interaction between mass, space and time 

From this I realised that we are dealing with 2 separate, but related entities - cause (gravity force- interaction) and effect (gravity - spacetime curvature)

So, based on this premise, going  back to the original question - Is gravity a force?, makes no sense, rather the question should be - what is the gravity force? or, to stick with the often used phrase, - what is the force of gravity?

WARNING! wild speculation and imagination alert!!! -

So considering gravity within this new context, I had no problem imagining a consolidation between GR & QM model's of gravity. In my imagination I consider the "force of gravity" to be a quantifiable interaction between space- time and mass where the interaction is.. , maybe using force carrying particles (gravitons) similar to the other kwon forces within the standard model.       In GR the math describes the possibility of singularities forming at the extreme small scales and high densities.   In my imagination, at such scales the force carriers become intensely active, however are unable to operate below the Planck scales. Such that this tiny region of space is just too small for force carrying particles to operate in. Therefore the curvature of space-time ("mutual attraction") ceases to operate at Planck distances, resulting in the impossibility of singularities forming. So I can image at the centre of BH's for example an object extremely dense, extremely small but larger than a Planck volume.  

Edited September 8, 2021 by Intoscience
spelling

[studiot]

34 minutes ago, Intoscience said:

So far this has been a very interesting, informative and often over my head discussion! Some great posts from the resident experts and our honoured guest!

Being a Layman (or at best a novice) I have limited understanding of the subjects I enjoy, space-time, gravity and the speed of light.

Reading through the posts, the discussion has often diverted off track from the original post. One of the diverts was the semantics of terms and phrases. One which I commented on way back in the discussion as a sort of dismissal.

Since then I have come to realise that in fact the importance of the usage, meaning and context of some terms and phrases used have a profound effect on my preconceived understanding.

In pondering the original post - "Is gravity a force?" and the phrase so often used - "the force of gravity"  I started to consider the meanings behind both.

The force of gravity:

• The interaction between 2 or more objects resulting in a mutual attraction - Newtonian
• The curvature of space-time - GR (Einstein - preferred model)

These 2 descriptions appeared to me to be conflicting. Then I had the idea to split the phrase into 2 terms - gravity & gravity force.

• Gravity - space-time curvature
• Gravity force - the interaction between mass, space and time 

From this I realised that we are dealing with 2 separate, but related entities - cause (gravity force- interaction) and effect (gravity - spacetime curvature)

So, based on this premise, going  back to the original question - Is gravity a force?, makes no sense, rather the question should be - what is the gravity force? or, to stick with the often used phrase, - what is the force of gravity?

WARNING! wild speculation and imagination alert!!! -

So considering gravity within this new context, I had no problem imagining a consolidation between GR & QM model's of gravity. In my imagination I consider the "force of gravity" to be a quantifiable interaction between space- time and mass where the interaction is.. , maybe using force carrying particles (gravitons) similar to the other kwon forces within the standard model.       In GR the math describes the possibility of singularities forming at the extreme small scales and high densities.   In my imagination, at such scales the force carriers become intensely active, however are unable to operate below the Planck scales. Such that this tiny region of space is just too small for force carrying particles to operate in. Therefore the curvature of space-time ("mutual attraction") ceases to operate at Planck distances, resulting in the impossibility of singularities forming. So I can image at the centre of BH's for example an object extremely dense, extremely small but larger than a Planck volume.  

Yay, you have gained something from the thread +1

So Gravity (or gravitation as the posh word) is a phenomenon that can exert a Newtonian force but it also has other properties.

In particular it can affect time, which as far as we know, other Newtonian forces cannot do.

 

 

[Markus Hanke]

On 9/7/2021 at 6:35 PM, joigus said:

Interesting. But what are you going to do with all those diffeomorphisms? Differentiability is hard-wired into GR.

Yes, good point. I don’t know the answer. I’m hoping that smoothness and continuity might somehow arise naturally for proper choice of relations. But of course I can’t know this.

On 9/7/2021 at 8:41 PM, studiot said:

I have speculated before (though not here) that these would hold out much hope for incorporating the more complicated relations inherent in say GR.
They have been used to do this with the stress tensor, that Mordred was so fond of.

So perhaps the idea isn’t completely worthless after all...thanks, studiot.

14 hours ago, Intoscience said:

maybe using force carrying particles (gravitons) similar to the other kwon forces within the standard model.

This is the most obvious approach towards a model of quantum gravity. In fact, it is actually straightforward(-ish) to formulate such a model. The problem is that the result turns out to be physically meaningless, so unfortunately this does not work.

[Intoscience]

14 hours ago, studiot said:

Yay, you have gained something from the thread +1

So Gravity (or gravitation as the posh word) is a phenomenon that can exert a Newtonian force but it also has other properties.

In particular it can affect time, which as far as we know, other Newtonian forces cannot do.

 

 

Yes, I always enjoy threads that teach me lots of new things, so thanks folks for your much appreciated inputs!

Regarding time, I mentioned earlier in the thread about maybe focussing more on what space-time is, rather than what gravity is, which may yield the answers we are looking for. 

I think, for me at least, if space time can be curved, warped... then it must "be" something physical in a sense. Or perhaps rather, space itself is physical, since time can be deemed a coordinate much like the 3 dimensions of space. So in my mind it's space that is warped not time, per say. So, the coordinates of time like the other dimensions change due to the warping of space. So, its the physical interaction between mass and space that causes the warping thus producing the gravity. I'm sure I'm way off with this line of thinking, but maybe I can learn from it.  

Edited September 9, 2021 by Intoscience
spelling