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 Why the Higgs boson is so important!

WHY THE HIGGS PARTICLE IS SO IMPORTANT!

1. WHY THE HIGGS PARTICLE?

To make clear why the Higgs particle is so important, we need to explain why the introduction of the Higgs particle in physics was inevitable. As brief as possible it boils down to this:

The electric and magnetic forces between elementary particles can be described as if they are transmitted via the exchange of massless light-particles or in other words by exchanging light:

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In first instance, calculations of this electromagnetic force between elementary particles didn't result in ordinary numbers, that can be compared to what is found in experiments, but infinitely large numbers. By using a trick, these infinitely large numbers can be turned into ordinary numbers.
This trick only works if all the infinities can be put into the parameters of the theory that have to be determined by experiment anyway, like the masses of the particles and the strengths of the forces. By setting the parameters equal to the experimentally determined values, the infinities are removed and one is left with a theory that exactly agrees with experiment (up to 10 or more decimal places). However, this shows that such a theory has its intrinsic limitations: masses of particles and the strengths of forces cannot be predicted and have to be measured experimentally.
In the electromagnetic theory, the Higgs field was not needed to give elementary particles their mass. The experimentally measured masses of the particles could be added directly via mass-terms to the equations.

Another force, the weak force, is responsible for a certain kind of radioactivity but is also essential to make our Sun shine. The weak force is only effective over a very short range because it is not transmitted by massless light-particles but by light-particles with mass. There are two types of these massive light-particles, an electrically charged massive light-particle (W particle) and an electrically neutral light-particle (Z particle):

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In the theory of these massive light-particles the infinities could no longer be absorbed into the parameters of the theory, an infinite number of these parameters would be necessary.
So the question arises how mass could be given to light-particles with mass.

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