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Electromagnetic repulsion is inversely related to the square of the distance between both objects. Shouldn't this mean that the integral of the force between two protons is infinite if the distance becomes zero? If so, how can protons fuse? Or does proton fusing occur while there is space between the protons?

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    $\begingroup$ See physics.stackexchange.com/q/93600, physics.stackexchange.com/q/23797 and links therein. $\endgroup$ – HDE 226868 Nov 8 '15 at 23:24
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    $\begingroup$ The distance doesn't have to be exactly zero for them to collide because they occupy a volume in space. $\endgroup$ – ja72 Nov 9 '15 at 0:21
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    $\begingroup$ It is your conception of "collide", in this context, that must be refined. $\endgroup$ – Alfred Centauri Nov 9 '15 at 1:11
  • $\begingroup$ Tow plastic balls 1 cm in diameter, charged with +q each, collide quite well. $\endgroup$ – Energizer777 Nov 9 '15 at 4:27
  • $\begingroup$ Simple explanation here. en.wikipedia.org/wiki/Coulomb_barrier Proton fusion happens when the protons are "Close enough for the strong interaction to take place". $\endgroup$ – userLTK Nov 9 '15 at 5:03
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Shouldn't this mean that the integral of the force between two protons is infinite if the distance becomes zero?

Physics developed quantum mechanics to model nature, as it became obvious that the infinities described by classical 1/r potentials would never build up atoms and build up the world we know. The attraction of the electrostatic potential would absorb the electrons into the nucleus and a hydrogen atom would never exist, nor chemical bonds.

As spectroscopic data from experiments showed the electron of the hydrogen atom , instead of spiraling down on the proton radiating continuously, generated a spectral series which was fitted with the Balmer etc series. The Bohr model was born which led to the complete theory of Quantum mechanics.

In quantum mechanics, a proton impinging on a proton feels a repulsion and scatters off, the crossection of the scattering can be accurately calculated as a function of the energy of the projectile. The experiment showed that when the energy became large enough the electrostatic potential no longer repelled all the projectiles, but some of the impact "enters" the proton itself and scatters off hard cores within the proton. The original experiments probing the constituents of the proton were with electrons, but the theory is the same. That is how quarks were discovered.

Edit after comment by OP

Deep inelastic scattering is represented in Feynman diagrams as:

deepinelastic

From left to right the incoming projectile interacts by exchanging a transfer of energy and momentum represented by the wiggly line as a virtual particle to the target proton, represented as a ball, and it interacts directly with a constituent. (The projectile can be another ball as the icon for the target proton) For this diagram the energy is high enough so that the individual constituents of the target proton have a probability to interact directly, instead of as a whole, and their behavior can be studied.

In proton proton scattering at low energies the exchanged virtual particle is electromagnetic, and the scattering crossection will show the repulsive force between two same charges. As the energy grows, the strong force between the constituents takes over, and virtual gluons are exchanged, overcoming any effect from the virtual photons which reflect the repulsion of like charges.

Or does proton fusing occur while there is space between the protons?

In proton proton scattering as a function of the energy, at center of mass energies close to the binding energy of the Deuteron, below two MeV, the weak interaction also plays a role in addition to the electromagnetic: there is a probability of fusion into a deuteron with a positron and an electron neutrino taking up the energy, momentum and quantum number balance. Due to the weakness of the weak interaction this is practically not measurable in the lab and mainly theoretical calculations are used. This process is important for astrophysical calculations of star evolution, where densities and temperatures are high enough to generate the reaction.

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  • $\begingroup$ I am confused by your statement "but some of the impact 'enter' the the proton itself and scatters off hard cores within the proton" $\endgroup$ – Oscar Laird Nov 10 '15 at 2:24
  • $\begingroup$ At the level of elementary particles, momentum and energy are transferred to the target by the exchange of virtual particles which are an icon for carrying the impact of energy and momentum. I will expand $\endgroup$ – anna v Nov 10 '15 at 4:20
  • $\begingroup$ @OscarLaird I have complained about the duplicate label here meta.physics.stackexchange.com/questions/7212/… . You could edit your question and explain that you are not talking about touching in the sense of the duplicate links. $\endgroup$ – anna v Nov 10 '15 at 6:00

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