Gotcha. Thanks.
Killer explanation. Thanks.
Could you elaborate, using your superb metaphors, about the complex disturbed distortions you mentioned (I forgot your wording) in the post about the “vibrations” in the field that you said are responsible/can be be related to (acceptable post-hoc-ergo propter hoc avoidance fudge?) virtual particles? Your post implied, to me at least, that the field “vibrations” are clear as a bell for non-virtuals. But the whole point of a Higgs boson is that it is virtual. The math is all tied up with a ribbon now for that ripple in the field, the ripple that is weird and complex relative to the other ones?
Undoubtedly in my ridiculous sans-math conceptualization of this my questions are a bunch of non-sequiturs.
Finally, if I may, as your guidance counselor, I reccomend you take the physics AP tests in Physics, Chemistry, Biology, and Mathematics, pursue further studies in the sciences, and don’t spend so much time in the AV Club. Plus you’ll get more girls.
The Higgs bosons associated with the field at low energy are all virtual, since there’s not enough energy available for them to be real. But what the LHC is attempting to produce (or possibly, has already produced) is a real Higgs. This is only difficult because the Higgs has such a high mass, which means you need a lot of energy to make a real one.
The “whole point” of the Higgs boson is that it gives mass to particles by interacting with them. Interactions are messy! Real particles are “clear as a bell” vibrations that aren’t so messy; we can calculate exactly what the ripples in the field look like if there are no interactions. But any interaction, whether it is between a particle and the Higgs boson, or between two electrons, or even between a particle and itself, is messy. It is just as messy in QED (the quantum version of electromagnetism) as it is for the Higgs. In both cases it is so messy that we can’t get exact answers for most things. The calculation framework we use to find approximations involves summing as much as we can of an infinite series of mathematical terms that look like ripples. So if you want you can think of the interaction as a sum of ripples (it’s like a Taylor or Fourier series, if you know a little Calculus). We call these ripples “virtual particles.” In reality the interaction is just one big messy jiggling field, and it is kind of silly to try to think of that big jiggly mess as a bunch “particles” on top of each other. But because of the approximation framework, it is mathematically convenient to decompose that mess into a sum of ripples which behave similarly to real particles, and call them “virtual particles.”
So all this talk of “virtual Higgs” is just shorthand for saying:
“We have a way of calculating the interaction between particles and the Higgs field. Our method of calculation is approximate. But we can make predictions, and give error bars on our predictions.”
This is no different from QED, or any other good physical theory, really. All forces are described using virtual particles in our mathematical framework, even ones that are considered mathematically “tied up with a ribbon.” They have to be if you think about it. Can you think of how an attractive force could be described by real particles going back and forth? They would push the particles away from each other! The only way to describe it in terms of “particles”, if you must insist, is with “virtual particles” that don’t behave like normal particles.
So all forces must be described by virtual particles (if we annoyingly insist on describing the force using fictional particles) within our mathematical framework. And all forces are messy, because they represent interactions between ripples. A ripple might be a nice “clear as a bell” vibration on an infinite unmolested drumhead, but if you put your fingers on the drumhead the vibrations aren’t so clear anymore near your fingers. When two particles get near each other, it’s like two fingers on a drumhead, and the equations for the ripples are not so simple anymore near your fingers. But after the particles interact and go their separate ways, the fingers are far apart on the drumhead, and the drumhead vibrates normally again. It may be a bit complicated to calculate the vibrations between the fingers, but we can do it!
That was a bit rambling, but hopefully some part of it helped.
I am not Batman.
To be clear, we can only deal with QED using approximations, but we can make those approximations as good as we like, by taking the expansion out to enough terms. So if you want an answer that’s correct out to, say, a dozen decimal places, you can get that (though of course it’s more work to get more decimal places). And once you have an answer that’s correct out to a dozen decimal places, you don’t generally much care whether your method is exact or only an approximation (and indeed, even the “exact” methods will still involve approximations in getting the final answer).
Why the italics around “describing”? I’m missing something important, I think.
Who said you were?
A force is just a force. A force is a force is a force…
A force/interaction is not “caused by” particles. It is just a force/interaction. We can describe the effect of the force/interaction using “virtual particles”, but that is just one mathematically convenient way of describing what happens. Another way of describing what happens is just to say that we have fields with ripples in them, and the fields couple non-linearly with other fields, so that when two ripples get close to one-another, there are wibbly-wobbly-sloshes and ripply-resonances and spiky-vibrations between them, and then after the turbulence dies down the ripples are far apart again.
And the fact that the Higgs boson decomposes instantaneously, so it’s not like you can hold it and examine it and show it to your friends. You just look at the “stuff” that goes in and the “stuff” that comes out.