I Gravitation and nucleons

[south]

TL;DR Summary

The quantum aspect of gravitation is of interest. We usually relate quantum behavior to particles. The question refers to this in the case of gravitation.

Could the gravitation between a body A and another body B correspond to the interaction of each nucleon of A with all the nucleons of B and vice versa?

 

[PeroK]

That's what you would expect. It's the precise nature of that interaction that is difficult to figure out.

 

[Ibix]

There has to be interaction with the electrons as well, and everything else, or the equivalence principle doesn't hold. It does hold - experiment has tested that to very high precision.

 

[south]

Thank you PeroK for helping me. If that is what we can expect, I am beginning to feel hope.

I would appreciate a little explanation of why we might expect the relationship between gravity and the interaction between nucleons of both bodies.

 

[south]

Thank you Ibix for helping me.

I understand that all particles are involved. I focused on nucleons because electrons perform larger and more chaotic motions than nuclear particles. I assumed that the resultant of electronic chaos would be small compared to the nuclear resultant.

 

[PeroK]

Thank you PeroK for helping me. If that is what we can expect, I am beginning to feel hope.

I would appreciate a little explanation of why we might expect the relationship between gravity and the interaction between nucleons of both bodies.

There are several potential theories of quantum gravity, but they are al highly mathematical. I'm not sure what material is around at the intermediate level.

Have you searched on line for quantum gravity?

 

[Ibix]

I would appreciate a little explanation of why we might expect the relationship between gravity and the interaction between nucleons of both bodies.

Are you asking if gravity is related to the strong force that binds nuclei together? Because @PeroK simply means that gravity is some interaction between particles but we can only model it in cases where quantum effects are negligible. Gravity has nothing to do with the strong force.

I understand that all particles are involved. I focused on nucleons because electrons perform larger and more chaotic motions than nuclear particles. I assumed that the resultant of electronic chaos would be small compared to the nuclear resultant.

I don't think you can really talk about particles and motions when you're hoping to study quantum gravity. You need quantum field theory which, to the very limited extent I understand it, does not really deal in discrete particles with well defined motion at all.

 

[south]

Are you asking if gravity is related to the strong force that binds nuclei together? Because @PeroK simply means that gravity is some interaction between particles but we can only model it in cases where quantum effects are negligible. Gravity has nothing to do with the strong force.

I don't think you can really talk about particles and motions when you're hoping to study quantum gravity. You need quantum field theory which, to the very limited extent I understand it, does not really deal in discrete particles with well defined motion at all.

Perhaps the idea of a particle is the skeletal simplification of what a field does. For my question, the idea of a particle is not necessary. It is enough that the energy density, the charge density, the linear and angular momentum densities, etc., are functions that exhibit a hump and that this hump moves, along which we suppose the particle moves. My question can be formulated in terms of a hump or a particle.

 

[PeroK]

Perhaps the idea of a particle is the skeletal simplification of what a field does. For my question, the idea of a particle is not necessary. It is enough that the energy density, the charge density, the linear and angular momentum densities, etc., are functions that exhibit a hump and that this hump moves, along which we suppose the particle moves. My question can be formulated in terms of a hump or a particle.

What has this to do with quantum gravity?

 

[south]

What has this to do with quantum gravity?

The question was formulated after briefly exploring, in a rudimentary way, the consequences of each nucleon of A interacting with all the nucleons of B and vice versa, assuming that each bond between a nucleon of A and one of B is of wave type with wave speed equal to C and with energy given by Planck's equation (law) $$ E= h \hspace{0.03 cm } \nu $$ .

 

[PeroK]

The question was formulated after briefly exploring, in a rudimentary way, the consequences of each nucleon of A interacting with all the nucleons of B and vice versa, assuming that each bond between a nucleon of A and one of B is of wave type with wave speed equal to C and with energy given by Planck's equation (law) $E= h \hspace{0.03 cm } \nu$ .

I'm not sure what your starting point is. Gravity is currently described by equating the curvature of spacetime to the total stress-energy - through the EFE (Einstein Field Equations). This is, however, formulated non-quantum-mechanically.

A theory of QG (Quantum Gravity) must find an alternative way to describe the equivalent of spacetime curvature using a QM formulation - perhaps through the interaction of quantum fields. There's nothing specific to nucleons here. The theory is expected to be a generic approach for all elementary particles and their quantum fields.

 

[south]

At no point did I attempt to get into the theory of quantum gravity, as it is beyond my scope. I only attempted to posit links between nucleons of A and nucleons of B. It is ridiculous to assume rigid links that do not vibrate. That is why I assumed links involving standing waves (without any pretense of specifying the kind of field that produces these waves). And I assumed that the energy of these exists in quantum portions. That was my whole intention.

 

[PeroK]

At no point did I attempt to get into the theory of quantum gravity, as it is beyond my scope.

If not quantum gravity, then what is this thread about?

I only attempted to posit links between nucleons of A and nucleons of B. It is ridiculous to assume rigid links that do not vibrate. That is why I assumed links involving standing waves (without any pretense of specifying the kind of field that produces these waves). And I assumed that the energy of these exists in quantum portions. That was my whole intention.

There are no links, rigid, vibrating or otherwise.

 

[south]

Ok. Thank you very much for answering my questions and clearing my doubts. Kind regards.

 

[south]

The masses of the proton and neutron differ slightly. Can I, accepting a slight error, propose an intermediate value $$m_i$$ and call it the mass of the nucleon? And can I, accepting another slight error, assume that all the mass of a body corresponds to nucleons? If these errors are allowed, it is possible to estimate without much error the number of nucleons in each body, in the following way.
$$ n_{_A} = \dfrac{m_{_A} }{m_i} $$
$$ n_{_B} = \dfrac{m_{_B} }{m_i}$$
$$m_i \ \rightarrow$$ mass of a nucleon

If each nucleon of body A interacts with all the nucleons of B and vice versa, then the total number of interactions is the product of both numbers of nucleons.
$$N = n_{_A} \ n_{_B}$$
That is:
$$ N = \dfrac{m_{_A} }{m_i} \ \dfrac{m_{_B} }{m_i} $$
$$ N = \dfrac{m_{_A} \ m_{_B} }{m_i^2} $$

The total number N of interactions is directly proportional to the product of the masses of both bodies.The gravitational force is directly proportional to N and, as a consequence, directly proportional to the product of the masses of bodies A and B, as in the Newtonian formula. This detail prompted my question.

Could the Newtonian formula have an error of the same proportion as the approximations mentioned above?

 

[jbriggs444]

Could the Newtonian formula have an error of the same proportion as the approximations mentioned above?

Are you willing to accept errors on the order of one percent?

The mass defect for iron is in that ballpark.

 

[Ibix]

Could the Newtonian formula have an error of the same proportion as the approximations mentioned above?

The difference between the Newtonian prediction of the perihelion precession of Mercury and the reality is about 43 seconds of arc per century. That is a vastly tighter bound (about one part in ten million) than all the stuff you neglect here.

 

[south]

Are you willing to accept errors on the order of one percent?

The mass defect for iron is in that ballpark.

My calculations had given about 0.04%, which is on the order of the differences found in the experiments of Eötvos and others like him between the Newtonian formula and the measurements. These experiments show a reasonably small dependence on the chemical composition of the bodies.

 

[PeterDonis]

I understand that all particles are involved. I focused on nucleons because electrons perform larger and more chaotic motions than nuclear particles. I assumed that the resultant of electronic chaos would be small compared to the nuclear resultant.

I have no idea why you would think this. The source of gravity is the stress-energy tensor. Having electrons "move more" in the center of mass frame of the object makes their gravitational effect larger, not smaller, since the electron's kinetic energy in the center of mass frame contributes to the object's overall gravitational mass.

 

[PeterDonis]

Could the Newtonian formula have an error of the same proportion as the approximations mentioned above?

Newtonian gravity is already known to be an approximation. We know its formula is not exact. In fact, in GR gravity is not even a force at all. So focusing on possible tiny errors in the Newtonian formula does not seem to me to be a fruitful way to look at the issue.

 

[PeterDonis]

assuming that each bond between a nucleon of A and one of B is of wave type with wave speed equal to C and with energy given by Planck's equation (law)

Where is this coming from? What does it have to do with gravity?

 

[south]

Are you willing to accept errors on the order of one percent?

The mass defect for iron is in that ballpark.

Agreed on that detail.
With the total number N of elementary interactions and with the hypothesis that the energy of each elementary interaction is quantized, the Newtonian formula appears as an immediate consequence.

 

[south]

I am not attempting to use General Relativity, as that is beyond my scope. I am simply curious to ask how gravity can be related to properties of matter, not spacetime. I am not attempting to involve General Relativity or the formulation of quantum theory here. Planck's law $$E = h \hspace{0.03 cm} \nu $$ is not itself a theoretical-body of the kind we understand as quantum theory. It is a law that first appeared in blackbody thermodynamic research. So I am not getting into either General Relativity or Quantum Theory, even though I assume that the energy of each elementary interaction is $$E = h \hspace{0.03 cm} \nu $$ .

 

[south]

Where is this coming from? What does it have to do with gravity?

I find it impossible to imagine a non-quantized interaction between two nucleon-type particles.

 

[berkeman]

Thread closed for Moderation.

 

[PeterDonis]

I find it impossible to imagine a non-quantized interaction between two nucleon-type particles.

Then, despite your protestations to the contrary, you're talking about quantum gravity. Which means that, instead of trying to make up your own personal theory, you need to go look at the literature on quantum gravity theories that already exists. Note that, while we do not have an accepted complete theory of quantum gravity, the handwaving you're doing is well within the scope of the massless spin-2 field effective theory that was developed in the 1960s and early 1970s. And you will find that effective theory tells you pretty much what you've already been told in this thread.

Thread will remain closed.