How does Higgs field relate to Aether theories? I am an amateur learning about the Higgs because I was interested in what the LHC's purpose is.
I read that as a particle passes through space, it is actually passing through a Higgs field and there are little Higgs particles that accumulate on the moving particle, which is where mass and momentum come from.
But that's where my main question comes from:
This all sounds similar to a "medium"; and mediums usually impart resistance on particles moving through them so the particles would slow down even in space.  As far as I know, this is the reason why aether/ether theories don't work.
Please let me know.
 A: The Higgs ether does not pick out a preferred velocity--- it is the same in all reference frames. Because of this, it can't impart a resistance to velocity, since any velocity is symmetric with any other. There is no Higgs drag. But it can impart a resistance to change in velocity, and this is a change mass. The most important thing is that it allows different helcities of fermions, which would be necessarily massless, to join up in pairs to make massive fermions.
A: 
I read that s a particle passes through space, it is actually passing through a Higgs field and there are little Higgs particles that accumulate on the moving particle, which is where mass and momentum come from.

That's one way that people try to describe the Higgs mechanism to non-specialists, but it doesn't really work like that. The Higgs boson is more like a side effect of the mechanism by which particles gain mass, not the thing that actually gives the particles mass. There aren't really little Higgs bosons latching on to particles and slowing them down.
You're right about that causing problems for physics, if that were the way it worked. It wouldn't break relativity, but it would prompt us to wonder why we haven't noticed the effect of this "cloud" of Higgs bosons. This is very similar to what people were thinking in the late 1800s, when they were wondering why they didn't notice the effect of the electromagnetic aether.
A: I think you are confusing the Higgs field with the so-called Dirac sea.
The both things give some mass to the particles.
But it is Dirac sea that has pairs of virtual particles that lake dipoles accumulate on a charged particle and increase its mass.
It is the Dirac sea that behaves more like Aether, not the Higgs field.
