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I came across these two, conflicting conclusions information sources comparing at the quantum-scale distances (e.g. distance between two protons) the strength of Gravity Vs. Electromagnetism.

I understand that at macro-scale and even microscopic distances most of the matter in the universe is charge neutral (i.e. opposite charges inside matter cancel out) which however is not true for gravity in matter which is omnipresent and cannot be cancelled out and therefore for macroscopic distances it is the dominant force in our universe.

However, at the quantum scale of sizes, matter seems to be fundamentally dominated more by charge and mass and gravity becomes negligible thus the hierarchy problem. Actually according to this article of the two 36 orders of magnitude weaker than electromagnetism.

However, according to this article here, this is a myth! Is this explanation just a kind of a formalism artifact non-physical interpretation or is this actually true?

Are there quantum LHC experiments to measure gravity at the quantum scale or is this only theoretically derived?

I am confused, and ask for a canonical answer?

Markoul11
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    https://en.wikipedia.org/wiki/Planck_units#Significance – Connor Behan Mar 13 '23 at 09:04
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    See https://physics.stackexchange.com/q/582842/226902, https://physics.stackexchange.com/a/570443/226902 and https://physics.stackexchange.com/q/144908/226902 – Quillo Mar 13 '23 at 09:18
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    In the given article the conclusion seems to be different than the one stated in OP. The last sentence is: "In short, it makes no sense to even ask what is the relative strength of gravity and electromagnetism" – AlmostClueless Mar 13 '23 at 09:27
  • Well, it actually also says inside "If you define the dimensionless strength of gravity using the Planck mass you get exactly $1$. In the case, gravity is 137 times stronger than electromagnetism." – Markoul11 Mar 13 '23 at 09:39
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    @ConnorBehan Still, the force in Newtons of the electrostatic repulsion force between two protons is much much larger than their gravitational attraction. IMHO, it is the level of coherency that is the resolution to the hierarchy problem. EM dipole forces are much more coherent forces than gravity. – Markoul11 Mar 13 '23 at 10:07
  • This always strikes me as an apples and oranges thing. – StephenG - Help Ukraine Mar 13 '23 at 12:38
  • Actually everything is duplicate in PSE :) – Markoul11 Mar 13 '23 at 19:46
  • What is a “coherent” force, and how does one quantify that coherence to show that “EM dipole forces are much more coherent forces than gravity”? – Ghoster Apr 08 '23 at 21:55

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