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A physicist responds
I am an experimental physicist and process theologian and I would like to clarify a few things about the Higgs boson, or "God" particle.

1.  NO ELEMENTARY PARTICLE HAS EVER BEEN "SEEN".  This is because not all of them interact with the electromagnetic field and, those that do, are much, much smaller then the wavelength of visible light.  We have only seen photons that suggest the existence of elementary particles.

2.  What has been observed is changes in systems (atomic or sub-atomic) measured through interactions with devices that we believe that we understand.  WHAT HAS BEEN OBSERVED IS EVIDENCE THAT SOME OF WHAT WE THINK ARE ELEMENTARY PARTICLES HAVE MASS AND OTHERS DO NOT.  Also, the existence of particles, their collisions and creation, seem to suggest that the property called mass is grainy.  It is not continuously distributed, but rather comes in distinct jumps and changes in magnitude.

3.  THESE OBSERVATIONS ARE A PUZZLE OR PROBLEM BECAUSE THEY ARE NOT WHAT WE HAD EXPECTED FROM OUR THEORIES.  Here is a related example:  by looking at particle collisions, physicists have observed the incoming and outgoing particles of these collisions that suggest that particles we call baryons and mesons (like protons and neutrons), are composed of fractionally charged particles that have been called, amusingly, “quarks”.  According to the theory embraced currently by most physicists, a single quark CANNOT be observed; all that can be observed is reactions that make the most sense if we posit the existence of quarks.  Quarks have never been seen and, possibly, can never be seen; but some experimental evidence is most easily explained by positing their existence. 

4.  THE SOLUTION TO THIS PUZZLE IS EXPLAINED BY THE INVENTION OF A THEORY THAT POSITS UNSEEN PARTICLES OR INTERACTIONS. Therefore the solution of the question “[w]here did the thought of the Higgs boson come from?” is the statement taken from the Wikipedia article on them that states “the Higgs Boson is an elementary particle initially theorized in 1964 and TENTATIVELY confirmed to exist on 14 March 2013.”

So, having explained all this, I believe that it is fair to state that the Higgs boson WOULD NOT have existed without our first thinking of it.  The effect of the Higgs particles did, of course, exist for many millennia before humans walked upright; but the concept of the Higgs boson did not exist until the mid 60s.  This is all that the Higgs boson is:  it is a concept that helps us explain observations that we have made.  It helps us build a conceptual framework that we can use to explain our observations of the universe around us. 

Like all elementary particles, the Higgs boson exists in our minds as a convenient tool that we posit to help us make sense of what we observe.  We can’t manipulate these particles by our thoughts, though we might find the need to append our thoughts slightly if doing so will help us make sense of further observations.