Non-geometric approach to gravity impossible?

In summary: However, this seems like a more difficult task than modeling it without invoking curvature in space-time.
  • #1
waterfall
381
1
Is it really impossible that gravity can be modeled non-geometrically?


I read the following in Weinberg paper Gravity:

"An alternative way to conceive of gravity would of course be to follow the lead of other theories, and regard the gravitational field as simply a distribution of properties (the field strenghts) in flat spacetime. What ultimately makes this unattractive
is that the distinctive properties of this spacetime would be completely unobservable,
because all matter and fields gravitate. In particular, light rays would not lie on the "light
cone" in a flat spacetime, once one incorporated the influence of gravity. It was ultimately the
unobservability of the inertial structure of Minkowski space that led Einstein to eliminate it
from his theory of gravitation and embrace the geometric approach."

I'd like to know:

1. Is gravity in flat spacetime means the same as force based gravity or is force based gravity another method where there is no spacetime but fixed space and time? If so, this means gravity in flat spacetime is fields based gravity in contrast to force based gravity?

2. How come light rays won't lie on the "light cone" in a flat spacetime gravity theory?


3. What is meant by the "unobservability of the inertial structure of Minkowski" that makes impossible gravity based on flat spacetime?


4. Is it totally impossible to model gravity that is not based on spacetime curvature? Maybe there is another way or is Gravity Geometry forever?

Thanks.
 
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  • #2
It might be helpful to read Einstein's description of rulers on a heated slab

http://www.bartleby.com/173/24.html

Einstein points out that being able to tile a surface with squares that don't overlap at all is possible only on a plane.Einstein doesn't specifically mention the surface of a sphere as a counterexample, but you can imagine trying to do it, and realize that it won't work - for instance, the circumference of the Earth at the equator (0 degrees lattitude) won't equal the circumference of the Earth a short distance above it (say 1 minute of an arc above the equator).

The point is that with the actual rulers we use, observable rulers, the geometry of space-time is measurably curved - at least according to General Relativity (and light bending experiments agree with this prediction).

We can't tile space with perfect cubes that fit perfectly together, nor can we tile space-time with perfect hypercubes. This happens because space-time isn't flat (and spatial slices of consant Schwarzschild time aren't flat either).

It turns out you can make such a "heated ruler" theory to describe gravity. You wind up with imaginary rulers and clocks that perfectly cover an unobservable flat background space-time with squares, like the marble slab, and real rulers that expand and contract and clocks that speed up and slow down due to "extra fields" that affect all matter uniformly (like the heated rulers), so that actual rulers can't tile the geometry (with hypercubes for the example of space-time).

Note that in a space-time geometry, clocks play the role of rulers, in that they measure "distances in time".

More formally, one actually uses the Lorentz interval of special relativity than the usual concept of distance, but it probably won't be too confusing to gloss over this point.

There are some limits to this approach, that Weinberg didn't mention. For instance, you can't make a flat background spacetime have wormholes, because the topology isn't the same. You also tend to run into problems trying to model black holes (a black hole, fully extended with the Kruskal extentions, is equivalent to a wormhole, so the topology is basically different).
 
  • #3
1) What do you mean by "force" based gravity? If you mean "forces" as conceived by Newton, then that is untenable due to special relativity. Forces (conceived thusly) are instantaneous and SR tells us no information can travel faster than the speed of light. This is the reason we use field theories. The "forces" are mediated by fields and so one can have non-instantaneous transmission of "forces".

2) If we assumed all space-time is flat, then the gravitational effect would have to be modeled non-geometrically. We know from observation; however, that light rays bend in the presence of matter. In this sense, light wouldn't follow the straight-line geodesics which define a light cone in flat space-time.

3) Because all matter (massless or massive) are affected by gravity, there is no way to "shield" the effects of gravity. This means that even if you used light, you cannot grid out the straight line grids of a flat space-time in any way, because the light rays themselves would bend. There is no way to "map out" a flat grid when you are in the presence of matter, and therefore, you can't "see" this flat background space-time whenever you have matter around (which is always, since no matter = no interactions=no observations).

4) I don't think it's "totally impossible". One certainly can come up with different models for gravity, but the appeal of a geometric approach, as Weinberg points out, is that it gets rid of a lot of unnecessary assumptions like some flat background space-time which we can never observe experimentally.
 
  • #4
Matterwave said:
1) What do you mean by "force" based gravity? If you mean "forces" as conceived by Newton, then that is untenable due to special relativity. Forces (conceived thusly) are instantaneous and SR tells us no information can travel faster than the speed of light. This is the reason we use field theories. The "forces" are mediated by fields and so one can have non-instantaneous transmission of "forces".

2) If we assumed all space-time is flat, then the gravitational effect would have to be modeled non-geometrically. We know from observation; however, that light rays bend in the presence of matter. In this sense, light wouldn't follow the straight-line geodesics which define a light cone in flat space-time.

3) Because all matter (massless or massive) are affected by gravity, there is no way to "shield" the effects of gravity. This means that even if you used light, you cannot grid out the straight line grids of a flat space-time in any way, because the light rays themselves would bend. There is no way to "map out" a flat grid when you are in the presence of matter, and therefore, you can't "see" this flat background space-time whenever you have matter around (which is always, since no matter = no interactions=no observations).

4) I don't think it's "totally impossible". One certainly can come up with different models for gravity, but the appeal of a geometric approach, as Weinberg points out, is that it gets rid of a lot of unnecessary assumptions like some flat background space-time which we can never observe experimentally.

Because of the symmetry in the theory. One can model gravity as physical field or mathematical spacetime geometry and curvature. I know our physics now is such that we only accept models and accept the map for the territory. From symmetry, the following is so:

Gravity as physical field
Gravity as spacetime geometry and curvature

They are equivalent by symmetry. But are they totally equivalent? No. It's like asking this.

A car as a physical object
A car as modeled as curve and geometry in the graphics program

Are they equivalent? Maybe by symmetry, but not or instead of selling you an actual car, I may as well sell you the software for the autocad graphics program.

Bottom line is. If one models gravity as a physical field. There may be a way to shield gravity. In General Relativity, there is no way to shield it. So there is the limitation of GR. When we focus too much on GR, we would become limited by what is possible and beyond.
 
  • #5
I stated "there is no way to 'shield' the effects of gravity" not based off the theory but based off experiment.

If you can show some experiment that shows a potential of "gravitational shielding", then please share.

A theory is not "limited" just because it prohibits something. A theory is only "limited" if it is unpredictive or experimentally unfalsifiable or overly narrow in its application.
 
  • #6
Matterwave said:
I stated "there is no way to 'shield' the effects of gravity" not based off the theory but based off experiment.

If you can show some experiment that shows a potential of "gravitational shielding", then please share.

Perhaps this can happen 100 years later or if done kept hidden from public (Black Project) to avoid loss of revenue of expensive jet fuel and profit.

A theory is not "limited" just because it prohibits something. A theory is only "limited" if it is unpredictive or experimentally unfalsifiable or overly narrow in its application.

What I'm saying is that there is no mechanism in General Relativity to shield gravity while in gravity as field based, it is possible. So GR is limiting. In fact, so limiting that it makes physicists sure no shielding can occur.. but note GR is just a model that we mustn't mistake for the territory.
 
  • #7
waterfall said:
GR is just a model that we mustn't mistake for the territory.

You left out the bit where it says "GR is just an experimentally well verified model (...)".
 
  • #8
Here are my 2cts:
waterfall said:
Is it really impossible that gravity can be modeled non-geometrically?
As such models have been published, evidently this is not impossible.
[..] I'd like to know:
[..] 2. How come light rays won't lie on the "light cone" in a flat spacetime gravity theory?
I suspect that this is more a matter of notation than a fundamental difference: in "flat spacetime", light rays bend around the Sun.
[..] 4. Is it totally impossible to model gravity that is not based on spacetime curvature? Maybe there is another way or is Gravity Geometry forever?
Thanks.
Some people have attempted a different description; I don't know how successful these attempts were/are. If I can find back a recent one, I'll add it as illustration. :smile:
 
  • #9
harrylin said:
Here are my 2cts:

As such models have been published, evidently this is not impossible.

What models? pls mention them. Anyway I wrote this thread about 2 weeks ago. I learned that string theory as a theory of quantum gravity can pull off the non-geometric thing even explain the dynamics of black holes.. all without curved spacetime.. but as spin-2 field on flat spacetime below the Planck scale and quantum gravity near the Planck scale or black hole (I assume black hole is tied up to Planck scale.. isn't it.. or is it because of the unique geometry that's why it can't be described in flat spacetime?).

I suspect that this is more a matter of notation than a fundamental difference: in "flat spacetime", light rays bend around the Sun.

But the sun has mass, won't it be enough to attract the photons classically? I think the argument is that it has no mass. But they say this can be modeled on flat spacetime. So what makes massless light bend around the sun in flat spacetime (what argument do proponents of this use?)?

Some people have attempted a different description; I don't know how successful these attempts were/are. If I can find back a recent one, I'll add it as illustration. :smile:

A field based approach is more logical. The geometry thing may be due simply to certain symmetry inherent in it and doesn't mean gravity is geometry. It's like saying my car can be modeled in graphics program.. hence my car is geometry. So please share all field based models. Thanks.
 
  • #11
robphy said:
Here's something with essentially no spacetime: Geroch's "Einstein Algebras"
projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.cmp/1103858122&page=record

Interesting, but pls explain first how light can be bent by the sun if it has no mass.. unless there is an unmeasured third polarization and light has a tiny mass like neutrinos? If not. What is the reason massless light can be bent by the sun if one won't take the geometric approach to gravity as a priori?
 
  • #12
waterfall said:
Interesting, but pls explain first how light can be bent by the sun if it has no mass.. unless there is an unmeasured third polarization and light has a tiny mass like neutrinos? If not. What is the reason massless light can be bent by the sun if one won't take the geometric approach to gravity as a priori?
Even in Newtonian gravity light can be bent by the sun. The Newtonian gravitational force on a massless object is 0, but "bending" is not force, and it does not require force to accelerate massless objects in Newtonian mechanics. Bending is acceleration, and [itex]a=GM/r^2[/itex] regardless of m.

However, the fact that a is independent of m is precisely the feature that allows you to express gravity geometrically.
 
  • #13
DaleSpam said:
Even in Newtonian gravity light can be bent by the sun. The force is 0, but "bending" is not force, it is acceleration, and [itex]a=GM/r^2[/itex] regardless of m.

Then why did they announce in 1919 that the bending of the light by the sun is proof that General Relativity was right when they could just announce Newton was right?!
 
  • #14
waterfall said:
Then why did they announce in 1919 that the bending of the light by the sun is proof that General Relativity was right when they could just announce Newton was right?!
Because they predicted different amounts of bending, by a factor of 2.
 
  • #15
DaleSpam said:
Because they predicted different amounts of bending, by a factor of 2.

So using spin-2 field on flat spacetime (which is equivalent to GR covered by harmonic coordinates as convinced to me by atyy and other people in other threads). How does one explain this extra factor of 2 thing (without using the geometry of General Relativity as a priori)?
 
  • #16
I have no motivation to even attempt that (try to derive a GR result without using GR). It sounds like a very difficult task for little or no benefit.
 
  • #17
This paper summarizes (in a biased way) field theory gravity (FTG).

http://arxiv.org/abs/gr-qc/9912003

There is a Lagrangian and the interaction term is

[tex]
\Phi^{\mu\nu}T_{\mu\nu}
[/tex]

which predicts spin 2 and spin 0 interactions.
 
  • #18
waterfall said:
What models? pls mention them.
Sorry, must search...
But the sun has mass, won't it be enough to attract the photons classically? I think the argument is that it has no mass. But they say this can be modeled on flat spacetime. So what makes massless light bend around the sun in flat spacetime (what argument do proponents of this use?)?
As a matter of fact, Einstein first reduced GR to a flat spacetime approximation and then used the Huygens construction for the calculation. His argument was thus what also is called "gravitational lensing". You can read it here (not far from the end, starting with p.198 in the English translation):
http://www.Alberteinstein.info/gallery/gtext3.html [Broken]
A field based approach is more logical. The geometry thing may be due simply to certain symmetry inherent in it and doesn't mean gravity is geometry. It's like saying my car can be modeled in graphics program.. hence my car is geometry. So please share all field based models. Thanks.
You may be surprised to read in the above-mentioned overview that Einstein regarded GR as a field theory; the geometry was for him a mathematical toolbox.
 
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  • #19
waterfall said:
Bottom line is. If one models gravity as a physical field. There may be a way to shield gravity. In General Relativity, there is no way to shield it. So there is the limitation of GR. When we focus too much on GR, we would become limited by what is possible and beyond.

No, classical gravity as a field in flat spacetime is the same as classical gravity as curved spacetime geometry restricted to harmonic coordinates. If it is impossible in one framework, it is impossible in the other framework.
 
  • #20
atyy said:
No, classical gravity as a field in flat spacetime is the same as classical gravity as curved spacetime geometry restricted to harmonic coordinates. If it is impossible in one framework, it is impossible in the other framework.

So in flat spacetime, how does light bend around the sun... via the Huygen's path Harrylin mentions? How else?

Harmonic coordinates mean near the singularities as you mentioned. Does this mean inside the event horizon (say 10 light years across) or most inner part of it near the center (near Planck scale)? Whatever, in quantum gravity which goes beyond the Planck scale, it can address the issues inside the event horizon or just near the singularities? This is because it is not possible to address black holes in flat spacetime. Then would quantum gravity of spin-2 field in flat spacetime be able to address black holes whose event horizon (say 10 light years across) is still much below the Planck scale size? How? Note it is only near the singularity that Planck scale physics address. Hope you get what I'm asking or I'd have to rewords this again. Thanks.
 
  • #21
Gravity is described by a second rank tensor, hence the spin 2 designation. Electromagnetism is described by a first rank tensor.
 
  • #22
waterfall said:
What I'm saying is that there is no mechanism in General Relativity to shield gravity while in gravity as field based, it is possible. So GR is limiting. In fact, so limiting that it makes physicists sure no shielding can occur.. but note GR is just a model that we mustn't mistake for the territory.

What makes physicists so sure that gravity cannot be shielded, is that if it was possible, perpetual motion of the kind that provides free energy would be possible. Long before GR was formulated it has long been recognised that energy cannot be created or destroyed and that law (conservation of energy) is unlikely to change in a hundred years or even a thousand years.

waterfall said:
But the sun has mass, won't it be enough to attract the photons classically? I think the argument is that it has no mass. But they say this can be modeled on flat spacetime. So what makes massless light bend around the sun in flat spacetime (what argument do proponents of this use?)?

Galileo discovered over 400 years ago that the rate that objects fall is independent of their mass, so it is reasonable to assume that even light which has no mass will fall at the same rate as everything else (although this requires we drop the concept of gravity being a force). This meant that bending of light by the Sun by an amount equal to that predicted by Newtonian acceleration was not convincing proof of GR, but the fact that light bends twice as much (due to the curvature of space as predicted by Einstein) was much more convincing.
 
  • #23
yuiop said:
Galileo discovered over 400 years ago that the rate that objects fall is independent of their mass
Yes but just as an aside that is not exactly true.

For an object to fall it takes two objects, both fall towards each other and the more mass is involved the faster it will be.
 
  • #24
pervect said:
It might be helpful to read Einstein's description of rulers on a heated slab

http://www.bartleby.com/173/24.html

Einstein points out that being able to tile a surface with squares that don't overlap at all is possible only on a plane.


Einstein doesn't specifically mention the surface of a sphere as a counterexample, but you can imagine trying to do it, and realize that it won't work - for instance, the circumference of the Earth at the equator (0 degrees lattitude) won't equal the circumference of the Earth a short distance above it (say 1 minute of an arc above the equator).

The point is that with the actual rulers we use, observable rulers, the geometry of space-time is measurably curved - at least according to General Relativity (and light bending experiments agree with this prediction).

We can't tile space with perfect cubes that fit perfectly together, nor can we tile space-time with perfect hypercubes. This happens because space-time isn't flat (and spatial slices of consant Schwarzschild time aren't flat either).

It turns out you can make such a "heated ruler" theory to describe gravity. You wind up with imaginary rulers and clocks that perfectly cover an unobservable flat background space-time with squares, like the marble slab, and real rulers that expand and contract and clocks that speed up and slow down due to "extra fields" that affect all matter uniformly (like the heated rulers), so that actual rulers can't tile the geometry (with hypercubes for the example of space-time).

Note that in a space-time geometry, clocks play the role of rulers, in that they measure "distances in time".

More formally, one actually uses the Lorentz interval of special relativity than the usual concept of distance, but it probably won't be too confusing to gloss over this point.

There are some limits to this approach, that Weinberg didn't mention. For instance, you can't make a flat background spacetime have wormholes, because the topology isn't the same. You also tend to run into problems trying to model black holes (a black hole, fully extended with the Kruskal extentions, is equivalent to a wormhole, so the topology is basically different).

When you say flat spacetime can't have black holes. Is it because flat spacetime can't model the Planck scale or is it because right at the start of the event horizon, flat spacetime can't model say the 10 light years event horizon down to near the Planck scale? If so, then why do people like atyy say spin-2 field in flat spacetime is equal to general relativity in spacetime covered by harmonic coordintes (near Planck scale). It is not equivalent when you can't even model the 10 light year event horizon down to near the Planck scale.
 
  • #25
Passionflower said:
Yes but just as an aside that is not exactly true.

For an object to fall it takes two objects, both fall towards each other and the more mass is involved the faster it will be.

Yes, I once made the joke that if Galileo dropped Jupiter it would 'fall' (move towards Earth's surface) a lot faster than a canonball.
 
  • #26
waterfall said:
What models? pls mention them. [..]
A recent one that I found back is by Ilja Schmelzer (just Google for it). He also published a related paper in Foundations of Physics, but his Arxiv papers and website are more to the point. I also found this:
https://www.physicsforums.com/showthread.php?t=14258 :smile:
 
  • #27
Passionflower said:
Yes but just as an aside that is not exactly true.

For an object to fall it takes two objects, both fall towards each other and the more mass is involved the faster it will be.

PAllen said:
Yes, I once made the joke that if Galileo dropped Jupiter it would 'fall' (move towards Earth's surface) a lot faster than a canonball.


if you were at a midpoint between Jupiter and the Earth (and not falling) then the rate that Jupiter falls towards the Earth would be the same as the rate that a canonball falls towards the Earth. What is different is the rate that the Earth accelerates towards Jupiter or the cannonball. So even a massless object could fall towards the Earth at the same rate as any other object, but the Earth would not accelerate towards the massless object.
 
  • #28
yuiop said:
if you were at a midpoint between Jupiter and the Earth (and not falling) then the rate that Jupiter falls towards the Earth would be the same as the rate that a canonball falls towards the Earth. What is different is the rate that the Earth accelerates towards Jupiter or the cannonball. So even a massless object could fall towards the Earth at the same rate as any other object, but the Earth would not accelerate towards the massless object.

That's true, but doesn't get at the issue of sloppy wording. Someone standing on the ground would see a Jupiter mass black hole dropped from a tower fall faster than cananball dropped earlier. That is a fact, period. The principle intended is that rate of fall is independent of composition, and is essentially independent of mass over many orders of magnitude (atom to mountain), but not exactly independent of mass.

Midpoint is also incorrect - you mean center of mass.

Also, in GR, the mass dependence of 'free fall' has another component - gravitational radiation, which is a nonlinear phenomenon.
 
  • #29
yuiop said:
What makes physicists so sure that gravity cannot be shielded, is that if it was possible, perpetual motion of the kind that provides free energy would be possible. Long before GR was formulated it has long been recognised that energy cannot be created or destroyed and that law (conservation of energy) is unlikely to change in a hundred years or even a thousand years.

There is contradictory views about this (even from experts).
Precisely GR is formulated in a way that doen't assure energy conservation, or as Hilbert put it: General relativity has improper energy theorems instead of proper energy theorems.
We have a FAQ in the cosmology subforum that deals with this and asserts that energy is not conserved in the cosmological models based on GR.
That would lead me to think that according to GR it is not so sure that gravity cannot be shielded, in a way it could (see "relative energy of a black hole" thread, especially peterdonis posts). It would seem the gravitational energy is shielded, in the sense that it is not a source of curvature (meaning it is not part of the stress-energy tensor as explained by peter donis in the abovementioned thread).
 
  • #30
I need to know something about this spin-2 field in flat spacetime = curved spacetime.

1. What is the reason for the Equivalence Principle in this Spin-2 field in Flat Spacetime Field Theory of Gravitation?

2. A larger ball with more mass should suppose to fall faster because the gravitational field between the Earth and the object is more (in this spin-2 flat spacetime version). Yet Galileo showed they fell at the same rate. Is there a version of asympototic freedom in flat spacetime where larger mass would have fewer emitted gravitons to match the smaller sized object hence they falling at the same rate?
 
  • #31
yuiop said:
if you were at a midpoint between Jupiter and the Earth (and not falling) then the rate that Jupiter falls towards the Earth would be the same as the rate that a canonball falls towards the Earth.
In order to keep that midpoint one would have to accelerate and the acceleration would not be constant.

So in that case what do you think your measurements would actually prove?
 
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  • #32
waterfall said:
1. What is the reason for the Equivalence Principle in this Spin-2 field in Flat Spacetime Field Theory of Gravitation?

http://arxiv.org/abs/1105.3735
"Asking for consistent self interactions leads essentially uniquely to GR and full general coordinate invariance [4, 5, 6, 7, 8, 9, 10] (see also chapter 13 of [2], which shows how helicity 2 implies the equivalence principle)."

http://arxiv.org/abs/1007.0435
"As argued by Weinberg [38], the equivalence principle can be recovered as the spin-two case of his low energy theorem. ... In other words, massless particles of spin-two must couple in the same way to all particles at low energies."
 
  • #33
Thanks. I need to understand 2 basic things:

1. Say in the future gravitons were finally detected. Does it mean spin-2 fields actually existed and they occur in the backdrop of flat spacetime. Or do gravitons imply spacetime curvature is a priori? But in what sense is there spacetime curvature and at the same time gravitons existing when the two are more of a dual much like photons and electromagnetic wave (these are dual descriptions)? Unless you mean detection of gravitons don't tell us whether spacetime is really curved or dynamics just occurring in flat spacetime by spin-2 fields?

2. Can Loop Quantum Gravity be formulated as spin-2 field in flat spacetime? Or does LQG stay valid only if spacetime is actually curved?
 
  • #34
waterfall said:
But in what sense is there spacetime curvature and at the same time gravitons existing when the two are more of a dual much like photons and electromagnetic wave (these are dual descriptions)?

The classical electromagnetic wave is a coherent state of photons on flat spacetime. Similarly, classical curved spacetime (that can be covered by harmonic coordinates) is a coherent state of gravitons on flat spacetime.

Within string theory, gravitons are only approximate degrees of freedom, and strings are more primary. So in the string theory picture, curved spacetime is a coherent state of strings on flat spacetime. In the AdS/CFT picture, strings and space are both emergent, and neither are primary.
 
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  • #35
PAllen said:
Midpoint is also incorrect - you mean center of mass.

Yes, that is what I meant, more precisely I should of said for an observer at rest in the centre of mass frame.

PAllen said:
That's true, but doesn't get at the issue of sloppy wording. Someone standing on the ground would see a Jupiter mass black hole dropped from a tower fall faster than cananball dropped earlier. That is a fact, period. The principle intended is that rate of fall is independent of composition, and is essentially independent of mass over many orders of magnitude (atom to mountain), but not exactly independent of mass.

I agree that it is true that in the rest frame of the the Earth that more massive objects fall faster than less massive objects (as long as they are not dropped at the same time) but the point that I was making (and I am sure you understood what I was getting at) in the rest frame of centre of mass of the Earth and falling object, the acceleration of the falling object is independent of its mass in Newtonian physics. Agree?

Put it another way. In the rest frame of the Earth the acceleration of a falling object is proportional to G(M+m) where M is the mass of the Earth and m is the mass of the falling object. It is easy to see that if m goes to zero, that the acceleration does not go to zero.
 
<h2>1. What is the non-geometric approach to gravity?</h2><p>The non-geometric approach to gravity is a theoretical framework that attempts to explain gravity without relying on the concept of space-time curvature, as proposed by Einstein's theory of general relativity. It suggests that gravity is not a fundamental force, but rather an emergent phenomenon arising from the interactions of other fundamental particles.</p><h2>2. Why is the non-geometric approach considered impossible?</h2><p>The non-geometric approach to gravity is considered impossible because it goes against the well-established and experimentally verified theory of general relativity. It also lacks supporting evidence and has not been able to make accurate predictions about gravitational phenomena.</p><h2>3. What are the main criticisms of the non-geometric approach to gravity?</h2><p>One of the main criticisms of the non-geometric approach is that it fails to explain the observed bending of light around massive objects, known as gravitational lensing. It also does not account for the effects of gravity on the flow of time, as predicted by general relativity.</p><h2>4. Are there any ongoing research efforts towards the non-geometric approach to gravity?</h2><p>While the non-geometric approach to gravity is not widely accepted in the scientific community, there are ongoing research efforts to explore alternative theories of gravity. Some scientists are investigating modified versions of general relativity that do not rely on the concept of space-time curvature.</p><h2>5. What are the potential implications of the non-geometric approach to gravity being proven impossible?</h2><p>If the non-geometric approach to gravity is proven impossible, it would reinforce the validity of general relativity as the most accurate theory of gravity to date. It would also highlight the importance of experimental evidence and the rigorous testing of scientific theories. Additionally, it could lead to further advancements and refinements in our understanding of gravity and the universe.</p>

1. What is the non-geometric approach to gravity?

The non-geometric approach to gravity is a theoretical framework that attempts to explain gravity without relying on the concept of space-time curvature, as proposed by Einstein's theory of general relativity. It suggests that gravity is not a fundamental force, but rather an emergent phenomenon arising from the interactions of other fundamental particles.

2. Why is the non-geometric approach considered impossible?

The non-geometric approach to gravity is considered impossible because it goes against the well-established and experimentally verified theory of general relativity. It also lacks supporting evidence and has not been able to make accurate predictions about gravitational phenomena.

3. What are the main criticisms of the non-geometric approach to gravity?

One of the main criticisms of the non-geometric approach is that it fails to explain the observed bending of light around massive objects, known as gravitational lensing. It also does not account for the effects of gravity on the flow of time, as predicted by general relativity.

4. Are there any ongoing research efforts towards the non-geometric approach to gravity?

While the non-geometric approach to gravity is not widely accepted in the scientific community, there are ongoing research efforts to explore alternative theories of gravity. Some scientists are investigating modified versions of general relativity that do not rely on the concept of space-time curvature.

5. What are the potential implications of the non-geometric approach to gravity being proven impossible?

If the non-geometric approach to gravity is proven impossible, it would reinforce the validity of general relativity as the most accurate theory of gravity to date. It would also highlight the importance of experimental evidence and the rigorous testing of scientific theories. Additionally, it could lead to further advancements and refinements in our understanding of gravity and the universe.

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