Does gravity field really exist?

In summary, in GR gravity is associated with the curvature of space caused by the presence of massive bodies. Along with GR, there is an approach in which the gravitational field is a real physical field, whose properties can be described by equations, similar to the Maxwell equations for electromagnetic field. These equations include a differential equation for the gravitational field, which describes its sources as a combination of common substance, electromagnetic field, and gravitational field strength. The resulting formula for the energy density of the gravitational field is negative, indicating that the energy of gravitational interaction is also negative. In addition, a formula for refined Newton's law takes into account the gravitational field as a source of gravitation, which may explain the observed deceleration of the space station "P
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The discussion remembers me something I read in a lecture note of general relativity so I want to mention it here both because it may be useful and also because to find out the connection I feel! But I can't give a reference because its actually a lecture note in my own language.
In that lecture note, at first it is argued that gravity should be a massless spin2 field. Then the free Fierz-Pauli Lagrangian is given:
[itex]
L=\frac 1 2 (h_{\mu \ ,\lambda}^\lambda h^{\mu \nu}_{\ \ ,\nu}-h_{\mu \lambda}^{\ \ ,\mu}h^{,\lambda})+\frac 1 4(h_{,\mu}h^{,\mu}-h_{\mu\nu}^{\ \ ,\lambda} h^{\mu\nu}_{\ \ ,\lambda})
[/itex]
(There may be some typing errors in the lecture notes so maybe this isn't right completely!)
Anyway, the EL equations coming from that Lagrangian are [itex] D^{\alpha \beta}_{\mu\nu} h_{\alpha \beta}=0 [/itex], where [itex] D^{\alpha\beta}_{\mu \nu}=(\eta_{\mu}^{\alpha}\eta_{\nu}^{\beta}-\eta_{\mu\nu}\eta^{\alpha \beta})\partial^\rho \partial_\rho+\eta_{\mu\nu}\partial^{\alpha}\partial^\beta+\eta^{\alpha \beta}\partial_\mu \partial_\nu-\eta_{\mu}^{\beta}\partial^\alpha \partial_\nu-\eta_{\nu}^{\alpha}\partial^\beta \partial_\mu[/itex], which satisfies [itex] \partial^\mu D^{\alpha \beta}_{\mu\nu}=0[/itex].
But when we put the stress-energy tensor of matter in the RHS, we'll have [itex] D^{\alpha \beta}_{\mu\nu} h_{\alpha \beta}=T_{\mu\nu} [/itex] which gives [itex] \partial^\mu T_{\mu\nu}=0 [/itex]. But this is an inconsistency because its not the stress-energy tensor of the matter alone that should be conserved but the total stress-energy tensor. So to solve this inconsistency, people started to add higher order terms to the LHS but it turns out that continuing to no finite order is enough and so an infinite series pops out. Now its Ogievetsky and Polubarinov that sum up this infinite series and show that it actually gives Einstein's Field Equations(1965,Ann.Phys. ,35, 107).
Then, as an easier solution, its proposed to vary the action [itex] S_0=\int [\phi^{\mu\nu}(\partial_\alpha\Gamma_{\mu\nu}^{\alpha}-\partial_\nu\Gamma_{\alpha\mu}^{\alpha})+\eta^{\mu\nu}(\Gamma_{\mu\nu}^{\alpha}\Gamma_{\rho\alpha}^{\rho}-\Gamma_{\beta\mu}^{\alpha}\Gamma_{\alpha\nu}^{\beta})] d^4x [/itex] w.r.t. [itex] \Gamma_{\mu\nu}^{\alpha} [/itex] and [itex] \phi^{\mu\nu} [/itex] which gives an equivalent theory to the mentioned Fierz-Pauli action. Then the Minkowski metric is replaced by a dynamical metric and the variation of the new action w.r.t. the dynamical metric is taken as the stress-energy tensor of gravity. After modifying the action farther for getting a consistent theory, the action takes the form of the Einstein-Hilbert action and so we're led to GR.(This is mentioned as Deser's method!)
I said this because I failed to see the connection between this procedure and the discussion here, so maybe someone can clarify or give some references explaining this procedure farther.(For example in calculating that infinite series, I'm really interested in seeing it but I couldn't find the paper.)
(Here's a link to the lecture note, at least you can see the equations! The things I said start at page 20)
 
<h2>1. What is gravity field?</h2><p>The gravity field is a region in space around a massive object where the force of gravity is exerted. It is responsible for the attraction between objects and is what keeps celestial bodies in orbit.</p><h2>2. How do we know that gravity field exists?</h2><p>We know that gravity field exists because of its observable effects on objects. For example, objects fall towards the ground due to the pull of gravity. Additionally, the orbits of planets and moons around larger objects, such as the Earth and the Sun, are evidence of the existence of gravity field.</p><h2>3. Can gravity field be measured?</h2><p>Yes, gravity field can be measured using specialized equipment, such as a gravimeter. This device measures the strength of the gravitational pull at a particular location and can also be used to map the variations in gravity field across the surface of the Earth.</p><h2>4. Does the strength of gravity field vary on different planets?</h2><p>Yes, the strength of gravity field can vary on different planets depending on their mass and size. For example, the gravity field on Earth is stronger than that on the Moon because Earth is larger and has more mass.</p><h2>5. Can gravity field be manipulated or controlled?</h2><p>No, gravity field cannot be manipulated or controlled. It is a fundamental force of nature that is always present and cannot be altered by humans. However, we can use technology, such as rockets, to overcome the pull of gravity and travel in space.</p>

FAQ: Does gravity field really exist?

1. What is gravity field?

The gravity field is a region in space around a massive object where the force of gravity is exerted. It is responsible for the attraction between objects and is what keeps celestial bodies in orbit.

2. How do we know that gravity field exists?

We know that gravity field exists because of its observable effects on objects. For example, objects fall towards the ground due to the pull of gravity. Additionally, the orbits of planets and moons around larger objects, such as the Earth and the Sun, are evidence of the existence of gravity field.

3. Can gravity field be measured?

Yes, gravity field can be measured using specialized equipment, such as a gravimeter. This device measures the strength of the gravitational pull at a particular location and can also be used to map the variations in gravity field across the surface of the Earth.

4. Does the strength of gravity field vary on different planets?

Yes, the strength of gravity field can vary on different planets depending on their mass and size. For example, the gravity field on Earth is stronger than that on the Moon because Earth is larger and has more mass.

5. Can gravity field be manipulated or controlled?

No, gravity field cannot be manipulated or controlled. It is a fundamental force of nature that is always present and cannot be altered by humans. However, we can use technology, such as rockets, to overcome the pull of gravity and travel in space.

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