4 ms·

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

by kmm 14y ago

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 http://en.wikipedia.org/wiki/Fourier_series [2]: http://en.wikipedia.org/wiki/Plane_wave http://en.wikipedia.org/wiki/Plane_wave [3]: http://upload.wikimedia.org/wikipedia/commons/b/b0/Wave_packet_%28dispersion%29.gif http://upload.wikimedia.org/wikipedia/commons/b/b0/Wave_pack...

Diederich 14y ago
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.
mcrider 14y ago
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?
- kmm 14y ago
  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.
- Variance 14y ago
  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.
colanderman 14y ago
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.)
- nilaykumar 14y ago
  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_the_Standard_Model_Lagrangian 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.
  - colanderman 14y ago
    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?
- kmm 14y ago
  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.
deleted 14y ago
[deleted]
Keyframe 14y ago
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?

by kmm 14y ago

Diederich 14y ago

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.

mcrider 14y ago

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?

kmm 14y ago
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.
Variance 14y ago
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.

colanderman 14y ago

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.)

nilaykumar 14y ago
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_the_Standard_Model_Lagrangian 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.
- colanderman 14y ago
  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?
kmm 14y ago
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.

deleted 14y ago

[deleted]

Keyframe 14y ago

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?