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The Higgs Boson as a field of snow

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#26 derangedhermit

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Posted 08 October 2013 - 10:34 PM

humans cannot apply math to political (or, by extension, other "emotionally invested") issues

recent study proving it

#27 PeterR280

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Posted 08 October 2013 - 10:43 PM

There are two issues here:

1) quantum mechanics is counter-intuitive. You can't come up with quantum mechanics just by thinking about physical events. The mathematics gave results about reality at the atomic level that were shocking.

2) quantum and classical physics, even theories that are intuitive cannot be completely explained by spoken language alone. One needs to understand the mathematic to truly understand the concepts.

#28 GregLee1

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Posted 08 October 2013 - 11:20 PM

2) quantum and classical physics, even theories that are intuitive cannot be completely explained by spoken language alone. One needs to understand the mathematic to truly understand the concepts.

Yes, you need to understand the mathematics to understand the concept. That's obvious. So if you don't understand the mathematics, we don't have to appeal to some issue with spoken language to explain why you won't understand the concept. No maths -- no get it.

Now, what does spoken language have to do with it? Do you mean to be saying that even if you do understand the mathematics, you will still not be able to understand the concept unless you can see a mathematical form written down? A spoken explanation will not work. That's what you seem to be saying.

#29 PeterR280

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Posted 08 October 2013 - 11:32 PM

In the case of quantum mechanics, even though you understand the mathematics, what the equations tell you does not make sense.

#30 deSitter

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Posted 09 October 2013 - 05:09 AM

There are two issues here:

1) quantum mechanics is counter-intuitive. You can't come up with quantum mechanics just by thinking about physical events. The mathematics gave results about reality at the atomic level that were shocking.

2) quantum and classical physics, even theories that are intuitive cannot be completely explained by spoken language alone. One needs to understand the mathematic to truly understand the concepts.


The ideas behind the Higgs mechanism and the requisite particle state are neither counter-intuitive nor unspeakable. I just spoke about them as clearly as I possibly could, in a way that cannot be misunderstood. Here it is again as numerated statements:

1) Conservation laws and interactions between pieces of matter are not optional. They are the fundamental building blocks of our picture of physical reality.

2) Distant action is not possible. All interaction is caused by local fields that propagate according to the laws of special relativity.

3 There is one and only one way to ensure that conservation laws are always satisfied in any given interaction in a way that is compatible with locality and relativity - they must be described by gauge fields having certain fixed mathematical properties (they must structured by Lie groups, in technical language).

4) Gauge fields are, by their very nature, long-range in action. There is no gauge invariant field that is not long-range. Any restriction to its range must originate in a separate type of interaction, mediated by a "guest" field that is not part of the original interaction schemata.

5) The weak interaction is, observationally, short-range. It does not operate from galaxy to galaxy, or from star to star, or from wall to wall, or from hair to hair. It operates from nucleon to nucleon.

6) Thus, there MUST be a additional participant in the interaction, whose only purpose is to shorten the range of the interaction through a mechanism that itself is not part of the original idea of conservation laws supported by gauge invariance.

7) That participant is the Higgs field, the mechanism is called the Higgs mechanism, and the overall idea is known as "spontaneous symmetry breaking". The prototype for this sort of scheme is the expelling of the magnetic field from a superconductor, which phenomenologically, amounts to the photon acquiring a mass inside the superconductor, and so becoming effectively short-range. The missing, expelled magnetic field is the physical consequence of the now-short-range photon.

If one wishes to make an analogy, then the proper one is - the vacuum itself behaves in many ways as does a superconductor.

The Higgs field itself is, in a well-defined sense, a quasi-particle. It has no independent existence outside its role in symmetry breaking. There are other quasi-particles that show up all the time in physics and have real, measurable effects - the most common being the phonons of condensed matter physics. "Quasi" does not mean unreal. It means the idea of "particle" itself is reaching the limit of its expressive and explanatory content.

It is unfortunate that mystics and obfuscators have encouraged everyone to hide behind blanket statements such as "no one understands quantum mechanics" or "relativity and quantum theory are unintuitive". To Ogg in the year 1, a falling apple described by Newton's law would be unintuitive. A thing becomes intuitive when you learn how to use it. A bicycle is not intuitive until one learns how not to fall off it. None of what is involved in the Higgs mechanism and the field theory it is a part of is unintuitive. If anything, it is TOO intuitive, and encourages people to think in terms of macroscopic pictures that are simply not valid on the small level.

-drl

#31 PeterR280

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Posted 09 October 2013 - 05:47 AM

I'd be curious if any person without any knowledge of physics understood what the Higgs Field is from what you said above,

#32 Charlie B

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Posted 09 October 2013 - 10:01 AM

Nice Danny!

Charlie B

#33 AstroGabe

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Posted 09 October 2013 - 12:09 PM

Good summary Danny. I have minor exception with one thing though - that there is no gauge invariant field that is not long range. The electroweak gauge bosons (W and Z) still satisfy the U(1)_EM gauge invariance since that gauge symmetry still persists. I would ammend it to say that gauge bosons that are responsible for short range forces still satisfy gauge invariance as long as those gauge symmetries are not broken.

Also, the Higgs field does have existence outside the role of symmetry breaking. It existed before symmetry breaking in the early universe and its behavior before and after symmetry breaking can explain the baryon asymmetry of the universe (why there are more particles than anti-particles in the present day).

Gabe

#34 deSitter

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Posted 09 October 2013 - 12:16 PM

Gauge invariance is absolutely, fundamentally long range. Said otherwise, any Yang-Mills field in necessarily massless. And no, the Higgs field does not exist in any context at all outside symmetry breaking. We don't live in the early universe, we live now, and phenomenological ideas cannot be pushed into realms where they cannot be expected to operate.

-drl

#35 AstroGabe

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Posted 09 October 2013 - 12:29 PM

I see your point on the gauge invariance. I think it was a misunderstanding of what you meant on my part.

But you can expect the description to operate just as well in the early universe at temperatures of O(100 GeV) or so. That's what is being probed directly at the LHC, and what we find is well described.

Gabe

#36 Otto Piechowski

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Posted 09 October 2013 - 12:35 PM

Thank you, each and everyone of your for talking physics and the math behind the physics here. Please continue doing so on this topic on which you are now engaged.

Please allow me to encourage you to focus your attention, also, on the opening article to which I referred in the NYT. I would, very much like to hear and appreciate hearing, your response to these questions about that article and its contents:

Does the Higgs Boson article using a snow covered field as an analogy for describing the nature and function of the Higgs Boson in a manner in which readers who know no or little physics and math...
1. Is this article accurate in what it says?
2. Does the article address the central aspects of what the Higgs Boson is?
3. Does the article allow the reader to better understand what the Higgs Boson is?

Thank you.

Otto

#37 deSitter

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Posted 09 October 2013 - 12:53 PM

I see your point on the gauge invariance. I think it was a misunderstanding of what you meant on my part.

But you can expect the description to operate just as well in the early universe at temperatures of O(100 GeV) or so. That's what is being probed directly at the LHC, and what we find is well described.

Gabe


I don't expect that. In fact when energy density is high enough, ALL interactions have the same range, and mix together, even in our limited phenomenological view. That range is hard to define, because the entire world becomes a teeming maelstrom of things changing into each other in a roiling soup. In such a world, the Higgs mechanism is irrelevant, and the Higgs field would sit glumly on the bench like a klutzy infielder whose presence on the team is mandated by nepotism.

But in fact it is almost certain that the tidy picture of strict conservation laws mediated by gauge fields on a flat spacetime background is wildly inapplicable in such situations. What we have works in our calm modern universe, where most of spacetime is empty, and the action is confined to the interior of stars and the centers of galaxies.

Attempts to bring Higgs machinery into cosmology are, in my opinion, rather pathetic.

-drl

#38 PeterR280

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Posted 09 October 2013 - 01:32 PM

How would you reconcile it with General Relativity and the principle of equivalence?

#39 deSitter

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Posted 09 October 2013 - 03:35 PM

I wouldn't - such a program is hopeless for reasons on both sides of the fence. New ideas are needed.

=drl

#40 PeterR280

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Posted 09 October 2013 - 04:02 PM

You would think the same mechanism is at play giving rise to the metric.

#41 deSitter

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Posted 09 October 2013 - 05:46 PM

Why would you think that?

-drl

#42 PeterR280

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Posted 09 October 2013 - 06:01 PM

To be consistent with relativity

#43 llanitedave

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Posted 09 October 2013 - 09:01 PM

In such a world, the Higgs mechanism is irrelevant, and the Higgs field would sit glumly on the bench like a klutzy infielder whose presence on the team is mandated by nepotism.


Now, THAT's an analogy!

#44 shawnhar

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Posted 10 October 2013 - 08:28 AM

I'd be curious if any person without any knowledge of physics understood what the Higgs Field is from what you said above,

I have a limited knowledge of physics and thought it was the most clear explanation I have seen so far.

I took from it that the Higgs field propogates out and allows the weak force to operate at a distance that would otherwise violate conservation. - Is that a valid understanding?

#45 deSitter

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Posted 10 October 2013 - 10:48 AM

The best analogy for the role of the Higgs interaction comes from classical mechanics! It is this. A typical problem tackled by the physics student in his first full-blown physics course, is to solve the problem of a ball bearing in a gravitational field, rolling on the inside of a spherical surface. The ball bearing wants to fall, but is "constrained" by the spherical bowl and must remain on that bowl. So its trajectory is not straight down, rather, a more or less complex motion on the sphere itself. We are taught a method for dealing with problems that involve constraints like this - "Lagrangian mechanics". The free motion of a falling object is described by a "Lagrangian function". To this function is added another term with an undetermined "Lagrange multiplier" to take account of the sphere. Once the equations are solved this way, you can determine the value of the undetermined Lagrange multiplier. It turns out that it gives just the required normal force of the sphere on the ball to ensure that it does not leave the sphere. So you can look at things from two points of view - you have the motion of a ball constrained to a sphere, or you can ignore the sphere altogether and add in a mysterious "sphere force" that causes the ball to deviate from its normal course of falling straight down.

Now, what if you had a ball bearing that was moving on a sphere which was invisible? You'd be perplexed and wonder, why isn't this ball bearing falling down to the floor like the other ones? And you try things and eventually hit on the idea of this sphere force. The sphere force is not pre-determined, it is just what it needs to be to resist motion off the sphere.

That is pretty much what happens with the Higgs field. The gauge bosons are by their nature massless and so long-range, but they behave as if they were not. So you throw into the Lagrangian function that describes the various fields and their interactions in the massless case, this mysterious "Higgs field" which always provides just what is needed to make the gauge bosons appear massive.

The Higgs field thus describes, not an actual state of matter alone, but matter in relation to the background in which it moves. It is more a property of the vacuum of particle physics itself, than an independent entity.

It is very likely that the Higgs boson story is not over. A tight argument says that it must be composite in some way, perhaps made of actual matter in some sort of bound state. This also has an analogy in superconductivity. The ultimate cause for (normal) superconductivity is the pairing of electrons that takes place when you put them in cold metal lattice. They interact not just with each other, but also the lattice in which they move. So, even though they repel each other electromagnetically, they are also attracted to each other because of some magic that happens when they are inside a cold atomic lattice other than free space. The attraction can be strong enough to overcome the electromagnetic repulsion and they form bound pairs (Cooper pairs). These pairs are bosons and can now pile into the same quantum state. The result is the supercurrent. The long-range electromagnetic interaction, or at least, part of it, has been hidden by interaction with the background atomic lattice. The Higgs field in this scenario is then to be thought of as excitations of this lattice that result in the net attractive force. The lattice behaves just as it has to, to ensure pairing of electrons and formation of the supercurrent. Once the current is established, you can forget about the background lattice and treat the supercurrent alone. When the energy is high enough, the temperature of the lattice goes up, it begins to vibrate out of its normal orderly pattern that allows the quantum collective state to form, the interactions of electrons via the lattice breaks down, the supercurrent disappears, and the normal state of unscreened, long-range electromagnetic interaction returns.

Without the theory of superconductivity as developed by London and London, Landau and Ginzburg, and finally Bardeen, Cooper, and Schrieffer, none of the modern model of spontaneously broken gauge symmetry as a fundamental theory would exist. This illustrates in dramatic terms, that this model - broken gauge symmetry - is *entirely* phenomenological, and will eventually be replaced by a complete theoretical model involving new ideas.

-drl

#46 Otto Piechowski

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Posted 10 October 2013 - 11:40 AM

Danny,

I wish I would have had you as a physics teacher in high school.

Another issue: You wrote, "The Higgs field thus describes, not an actual state of matter alone, but matter in relation to the background in which it moves. It is more a property of the vacuum of particle physics itself, than an independent entity."

Do you remember many months ago when I asked you/this forum about the idea of uneducated "savant" I knew name Lawrence who suggested that space was the cause of motion. Is your statement which I just quoted, consistent with, similar to his idea?

His reasoning was that, according to Einstein, energy is a type of matter, and according to Newton a thing cannot overcome its own inertial movement; therefore, matter cannot move itself, nor can various forms of energy (forces) move matter because that would be a case of matter moving itself. The only thing, left, Lawrence reasoned was space and therefore he suggested space is what causes motion.

Otto

#47 GregLee1

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Posted 10 October 2013 - 11:57 AM

... and according to Newton a thing cannot overcome its own inertial movement;

Did they have Roman candles in Newton's day?

#48 deSitter

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Posted 10 October 2013 - 12:27 PM

Danny,

I wish I would have had you as a physics teacher in high school.

Another issue: You wrote, "The Higgs field thus describes, not an actual state of matter alone, but matter in relation to the background in which it moves. It is more a property of the vacuum of particle physics itself, than an independent entity."

Do you remember many months ago when I asked you/this forum about the idea of uneducated "savant" I knew name Lawrence who suggested that space was the cause of motion. Is your statement which I just quoted, consistent with, similar to his idea?

His reasoning was that, according to Einstein, energy is a type of matter, and according to Newton a thing cannot overcome its own inertial movement; therefore, matter cannot move itself, nor can various forms of energy (forces) move matter because that would be a case of matter moving itself. The only thing, left, Lawrence reasoned was space and therefore he suggested space is what causes motion.

Otto


No, that's a trivial oversimplification. It may be possible to have a new more inclusive space in which matter shows up as aspects of that space. That's an idea very close to my heart. But spacetime, the 4d sort that lives under field theory, is not a form of matter, and the Higgs field is not coextensive with it. The Higgs field is an aspect of field theory and its vacuum, which presumes flat, continuous spacetime as a stage.

-drl

#49 Otto Piechowski

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Posted 10 October 2013 - 12:38 PM

Thank you Danny.

Your words "matter shows up as aspects of that space. That's an idea very close to my heart" sound interesting.

Otto

#50 dvb

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Posted 10 October 2013 - 12:48 PM

I applaud the science writers who attempt to explain physics to laypeople.

The exercise will necessarily be imperfect, and the laypeople know that, but I also applaud the laypeople who are curious about these things, and who hope to understand them as best they can.

And, I applaud those of you who are in a position to critique those attempts to explain to laypeople, and who can find the right balance between comprehensibility and accuracy.

:applause:

But, please, may be all be saved from the worst such efforts, such as references to a "God Particle".

:tonofbricks:






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