Why is gravity a weak force at the atomic scale?

[Arend]

TL;DR

Following the classical mech. g=-GM/R^2, for quantum distances the gravity force would be strong. What are the quantum mechanisms that cause the effects of gravity to vanish?

Hi. Following the classical mech. g=-GM/R^2, for quantum distances the gravity force would be strong. What are the quantum mechanisms that cause the effects of gravity to vanish? The position uncertainty or the probabilistic wave function can be a justification for suppressing strong gravitational coupling?
Thank you,
Arend

 

[PeroK]

TL;DR Summary: Following the classical mech. g=-GM/R^2, for quantum distances the gravity force would be strong. What are the quantum mechanisms that cause the effects of gravity to vanish?

Hi. Following the classical mech. g=-GM/R^2, for quantum distances the gravity force would be strong. What are the quantum mechanisms that cause the effects of gravity to vanish? The position uncertainty or the probabilistic wave function can be a justification for suppressing strong gravitational coupling?
Thank you,
Arend

Do the mathematics. The gravitational force between two electrons, say, is very weak compared to the electrostatic force.

 

[Arend]

Do the mathematics. The gravitational force between two electrons, say, is very weak compared to the electrostatic force.

Sorry, incomplete question. For example, applying the classical gravitational force between two electrons at Planck distance results in a strong force (~1.35 x 10^20 N). I know, that the "size" of the electron is bigger, but could be the case for other scenario. The point is, the classical expression allows infinite gravitational field for a "point". tks

 

[PeroK]

Sorry, incomplete question. For example, applying the classical gravitational force between two electrons at Planck distance results in a strong force (~1.35 x 10^20 N). I know, that the "size" of the electron is bigger, but could be the case for other scenario. The point is, the classical expression allows infinite gravitational field for a "point". tks

It allows an unbounded gravitational force, but also an unbounded electrostatic force, which is always much greater.

The electrostatic force between two electrons is much greater than the gravitational force. Do the maths!

 

[Arend]

It allows an unbounded gravitational force, but also an unbounded electrostatic force, which is always much greater.

The electrostatic force between two electrons is much greater than the gravitational force. Do the maths!

For example, a not charged particle, such as a neutrino, even a very small mass would generate a huge gravitational field closer to such "point" mass. Changing the question, would the gravitational field have a limitation due to the quantum environment?

 

[PeroK]

For example, a not charged particle, such as a neutrino, even a very small mass would generate a huge gravitational field closer to such "point" mass. Changing the question, would the gravitational field have a limitation due to the quantum environment?

Newton's law of gravity isn't a fundamental law. No one knows what is the fundamental law of quantum gravity.

Nevertheless, one problem is that the gravitational force is so much weaker than the electrostatic force for elementary particles.

Someone got a Nobel Prize simply for detecting a neutrino. Doing a gravitational experiment with neutrinos would be great - but the practical difficulties are immense.

 

[Arend]

Understood. tks!

 

[PeterDonis]

What are the quantum mechanisms that cause the effects of gravity to vanish?

We don't know that they do. All we know is, as @PeroK said, the effects of gravity are many, many orders of magnitude smaller than the effects of any other interaction.

strong gravitational coupling?

The gravitational coupling, as far as quantum field theory is concerned, is not strong. It's weak--much weaker than any of the other fundamental interactions.

Note that this is a quantum question you're asking, so the Newtonian gravitational force formula is irrelevant. We don't have a good comprehensive quantum theory of gravity, but in the 1960s and early 1970s, the quantum field theory of a massless spin-2 field was investigated, and it was found that its classical limit is General Relativity, so that QFT is at least a plausible effective theory of gravity's quantum properties. The coupling in that theory is weak, much weaker than any of the other couplings in the Standard Model.

 

[DaveC426913]

As others are telling you, the gravitational effect does not "vanish" at subatomic scale. What makes you think it does?

It certainly is overwhelmed by larger forces, but gravity is still there. In principle, the gravity of every subatomic particle affects every other particle in the universe, across vast distances.