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Comment by runn1ng | Hacker News Reader

I still don't get it.

I still don't get how they jumped from "We have this Higgs field" to "and hey, the field is a particle."

Don't worry, don't worry. This one of the most complicated theories in physics (apart from string theory) to grasp intuitively. I'm a physicist and I could try to help you.

Think of an excitation of the field. One of the "axioms" of quantum field theory is that the energy of an excitation is related to the inverse square of the wavelength. Don't ask me why, it's just like that. Think of UV radiation or X-rays, which are just light with a higher frequency and you know those radiation is more damaging to the human body than for example radio waves.

Now, are you familiar with Fourier decomposition?[1] It's the idea that all functions are the sum of a waves (sines and cosines). We do the same thing in quantum field theory, we have our quantum field and we write it as the sum of our elementary wavefunctions, which are called plane waves[2]. When you look at a wave packet[3], you can't really say what its wavelength is. Wavelength is not a local concept, as for example the height of the wave, but the wave differs from place to place, so it's impossible to give it just one wavelength! We don't have that problem with plane waves. Because they're the same all over the universe, they have a clear wavelength and thus a well-defined, unique energy. This concept, an excitation of a field with a well-defined energy (and thus a well-defined mass!) is what particle physicists call "a particle".

When a collision happens in a collider, we're actually preparing two plane waves and pointing them in the same direction. As they collide, the wavefunctions of the various fields become incredibly complex. We humans can only "see" excitations with a well-defined mass, or better yet, our detectors can only detect excitations with a well-defined mass. And thus instead of a complicated field, we see a mess of particles going in different directions and having different masses, energies and speeds.

Does that make it any clearer?

[1]: http://en.wikipedia.org/wiki/Fourier_series [2]: http://en.wikipedia.org/wiki/Plane_wave [3]: http://upload.wikimedia.org/wikipedia/commons/b/b0/Wave_pack...

Yes, somewhat. Thank you very much.

I've enjoyed pondering this stuff since the 70s when I was a child. How much I've 'gotten' it has varied over the years, but it's never been very deep.

Your description, I think, deepened my understanding a good bit.

I'm still not clear on the value of finding the Higgs Boson or why its so exciting -- If I understand correctly, not finding it (or disproving it exists? Is that logically possible?) will force us to rewrite certain aspects of physics. But what effect will finding it have to either theoretical or applied science?

If we find no Higgs boson right now, there's still other options: multiple Higgs bosons, composite Higgs bosons, etc. We're only looking for the most simple configuration right now. If does do not exists (and it will take many many years to prove that), we're having a bit of a problem as this invalidates the central tenet of quantum field theory.

All of quantum field theory is based on the principle of local gauge symmetry. This means that by demanding the field be invariant under the transformations of a certain mathematical framework, the interactions appear automatically (don't worry if you don't understand that, that would take more than one HN post). This is all very beautiful but the problem is that this only works for massless fields. The Higgs mechanism solves this by instead of postulating mass as an intrinsic property of a field, it supplies mass as an extrinsic property.

Technically speaking all fields are still massless, yet due to their interaction with the Higgs field, they behave as if they had mass! This is good, because we can keep our precious gauge symmetries and particles can have mass which is a very basic experimental fact. (I'm ignoring some important parts here, like symmetry breaking, but this post is already getting too long).

If no Higgs is found, either some brilliant mind must find another solution to preserve the principle of local gauge symmetries, or we must leave field theories behind and look for another solution.

I personally hope no Higgs is found, as Higgsless theories look more appealing to me. Obviously, Nature shouldn't conform to my personal aesthetic views, so if proof for Higgs is found, I will have to accept that.

More or less the happy sense of being proved right. Since the Higgs is well-modeled and well-understood in theory, other than the value of its mass, we already have a rudimentary scientific understanding of what it does and how it works. But it's critically important that these theories, like the Standard Model that predicts the Higgs, be experimentally confirmed--though you are right that it would be far more earthshaking if it didn't appear.

It's just a model - finding higgs will add validity to that model as a useful tool. not finding it - invalidating that theory puts us back to the drawing board and/or focuses people on other theories. It's not the end or beginning of anything, just another step.

I want my time travel and anti-gravity and FTL drive, at consumer prices. I want to see dinosaurs and travel around the universe in the blink of an eye. Keep working science people.

This was a very good explanation, thank you. One question: the Standard Model describes a finite number of "fundamental" particles/waveforms, correct? What makes them "fundamental"? Presumably they are orthogonal (or at least span a complete vector space), but there must be some restriction on the (otherwise infinite) domain? (e.g. "waveforms with total energy = 1" and "wavelength is kX where k < 4" or some such.)

Fundamental particles enter the Standard Model through the Lagrangian. Each particle is given its own field in the action: [http://en.wikipedia.org/wiki/Standard_Model#Construction_of_...].

I'm not quite sure what you mean by "orthogonal" as the mathematics involved is not simply linear algebra.

kmm stated that "we have our quantum field and we write it as the sum of our elementary wavefunctions", so I assumed that any quantum field can be described by a superposition of the elementary wavefunctions convolved with some sort of particle-position function P(p, x) (where, roughly, P(p, x) = E if particle p exists at position x with energy E, otherwise P(p, x) = 0). Am I wrong to assume this?

Edit: from what I can understand about the formation of the Standard Model from the Lagrangian, the domain restriction which makes the elementary wavefunctions elementary is wavefunctions which evolve over time (according to EM theory) such that when viewed as particles, their motion is compatible with QM (or relativity?), and that there are only a finite number of distinct wavefunctions which are needed to span this space. Is this roughly correct?

Are you under the impression that all particles live in one All-Embracing Majesty? That is not true, although all particles of the same type are excitations of a single field, different types of particles have their own fields. For example, the electron and the tau have two separate fields. The weak interaction makes for some mixing, but that is not really important.

If you're wondering why there's exactly 12 (+ 1 for the Higgs?) fields, I cannot answer that question and it's one of the open questions in current theoretical physics.

I understand that there are different fields. More so my question is, why are there a finite (as opposed to infinite) number of fundamental waveforms for any given field? My intuition is that this is because the domain of "candidate" waveforms is restricted to those which exhibit particle-like behavior (i.e. compatible with a particle physics). I'm not sure if this intuition is correct however.

We chose our basis because it is convenient. It's called a Fock space[1]. You can choose any basis you want, the equations of motion derived from the Lagrangian will tell you how any wavefunction evolves, independently from your choice of basis.

The number of waveforms isn't finite by the way. There's a fundamental waveform for every momentum (which can be any real number) and for every number of particles (which must be a positive integer).

[1]: http://en.wikipedia.org/wiki/Fock_space

Yes, I realized by "finite number of waveforms" I actually meant "finite number of waveform-generating functions parameterized over momentum/energy and number of particles". But I think you and lmm have answered my question, thanks!

There are an infinite number of possible waveforms; pretty much any waveform in the electron field is a valid one. What we see as a single electron is simply a "spike" waveform localised in a particular position. There's no reason you couldn't have a more smeared-out waveform that was "an electron somewhere in the universe", though entanglement comes into play at some point.

When we have particular constraints (e.g. known energy) that constrains the space of possible waveforms. E.g. when we talk about there being an electron in an orbital around an atomic nucleus, what we actually mean is there's a waveform. of a particular shape around the nucleus.

Are you asking why we only ever see waveforms corresponding to whole numbers of electrons? That's the "quantum" part of quantum mechanics; certain values are quantized (e.g. electric charged). I don't have a good intuition for why that's so though, except to observe that the time evolution of a system preserves this quantization, so there's no way to ever go from having one electron to having half an electron (for example).

At some point "why" becomes impossible - everything just becomes a set of relationships between things that we can define and predict. The only real answer to "why", from a scientific point of view, is ultimately "because that's how it is"

Most good science comes of asking "why" - if you took "because that's how it is" as the answer to "why did the apple fall" science wouldn't have got as far as it has. Whenever a theory has some seemingly arbitrary property it's worth asking "why"; sometimes the answer is "we don't know yet", but that doesn't mean it's not worth asking the question.

Couldn't agree more - I wasn't thinking about how that might be interpreted when I wrote it..... Absolutely we ask "why" - and look for explanations. I meant nothing with regards to being defeatist and not looking at things - only that, as far as I can see, even though we'll keep going deeper and deeper and discovering more and more, we'll never get to a final answer (other than perhaps getting to a point where we can't research further without blowing up the universe? I read too much sci-fi.

A final answer would be boring..... WHY is a fantastic question - it's just not something pure science can answer with finality, only layers until we get to an unknown.

This all makes sense to an extent, but I'm still having a hard time grasping what is field... a field of what? I get that particles are basically excited field manifesting a value, a particle... but what constitutes a field?

One page explanations written by physicists: http://www.fsc.ufsc.br/~marilena/higgs.htm

edit: As the links are down, here they are from the Wayback Machine:

http://web.archive.org/web/20080209000844/http://www.phy.uct...

http://web.archive.org/web/20110724100137/http://www.phy.uct...

http://web.archive.org/web/20110724100208/http://www.phy.uct...

http://web.archive.org/web/20100202022203/http://www.phy.uct...

http://web.archive.org/web/20100323013823/http://www.phy.uct...

The links don't lead anywhere.

edit: Web archive to the rescue. Thank you.

Quantum theory is based on the concept of wave-particle duality. Think of the ocean. The water as a whole is pretty wave-y and non-localized (i.e. it's not in one place). But the crests of the waves (the "excitations") can be thought of as particles because they're localized fairly well.

So really all a Higgs boson is, is an excitation of the Higgs field.

This is called Quantum Field Theory. See http://en.wikipedia.org/wiki/Quantum_field_theory.

This explains it well http://simple.m.wikipedia.org/wiki/Higgs_Boson

wave-particle duality. All fields have an associated particle: e.g em field - the photon.

o....k. So, there is one Higgs field in the world which belongs to one Higgs Bosson, and there are no more Higgs bossons in the world?

Or does it mean that there are more Higgs fields in the world (and, thus, every particle can have a different mass depending on in which field it is) and there are therefore more Higgs bossons?

There is a single Higgs field. But the Higgs field can be excited in many different places! Same for anything else, like an electron - that's why we say that two electrons are indistinguishable from each other. Fundamentally, they're made of the same "stuff": the electron field that permeates the universe.

Particles get mass by "coupling" to the Higgs field. I.e. the excitations of the electron fields - electrons - interact with the excitations of the Higgs field - Higgs bosons. This, through a complicated process described by quantum field theory (that I don't admit to fully understand), gives the particle what we call mass. Different particles couple to the Higgs with different strengths, yielding various particle masses. The Higgs even couples to itself (rather incestuously), which is why it has mass!

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