Are neutrinos traveling through our bodies what really make us attracted to the Earth?
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1See also: http://physics.stackexchange.com/q/21477/ and http://physics.stackexchange.com/q/23429/ – dmckee --- ex-moderator kitten Sep 30 '13 at 16:29
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1Possible duplicate of Could we prove that neutrinos have mass by measuring their gravitational signature? – ZeroTheHero Apr 17 '17 at 23:11
3 Answers
The neutrinos traveling through your body are not in anyway attached to you: if they did stick to you in some sense they wouldn't go through so freely.
So, while the neutrinos are subject to gravity, they don't contribute to your weight, even by the incredibly tiny amount of mass that they constitute.
Are neutrinos traveling through our bodies
Unless we are near a reactor neutrinos traveling through our bodies come either from the earth where radioactive materials decay, or from the space around us where stars, including the sun emit them in the interactions that keep them hot and shining.There will also exist primordial neutrinos which like the cosmic background radiation permeate everything.
Neutrinos are weakly interacting and pass through matter very fast without interacting as their mass is very small and their velocity close to the velocity of light.
what really make us attracted to the earth?
What attracts us to the earth is the gravitational force . In the elementary particle framework the carriers of force are specific for each interaction, gluons for the nuclear strong force, Z and Ws for the weak force, photons for the electromagnetic and gravitons , are hypothesized to be the carriers of the gravitational force.
So no, neutrinos have nothing to do with the apples falling. The gravitons are the culprits.

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I would add that it's easy to see why the neutrino can never be responsible for gravity, since it's a fermion and force carriers are always bosonic. – Wouter Sep 30 '13 at 17:08
I suppose the question refers to the scenario that there is an isotropic radiation of neutrinos in universe and that the part of this radiation that passes through earth before it penetrate our bodies is somewhat weaker than the corresponding radiation from above and that this difference give rise to a presumable tiny force downward, that is a (tiny) part of the "real gravity" but not of the theoretical gravity.

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"and that the part of this radiation that passes through earth before it penetrate our bodies is somewhat weaker than the corresponding radiation from above" Have you actually calculated the difference? It is instructive to do so. Remember that the elevator speech version of the cross-section is 'a typical solar neutrino only has a 50% chance of interacting in s light-year of lead shielding'. – dmckee --- ex-moderator kitten Jul 19 '15 at 00:29
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I can't calculate that. I toke a one year course in physics at university for forty years ago and I was not that successful and have forgotten most of it. A calculation would be interesting, even if I'm sure that it is a very tiny force. But that is the way I interpreted the question. – Lehs Jul 19 '15 at 00:46
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Here is an example calculation I did for solar neutrinos passing through Venus. The short version is that you can safely treat neutrinos as not even noticing planets unless you have a very sensitive detection system indeed. Super-K (a 30,000 ton detector) sees a difference in upward and downward neutrino fluxes due to oscillation but is insufficiently sensitive to notice the difference due to scattering and absorption. – dmckee --- ex-moderator kitten Jul 19 '15 at 02:00