Why Are Yang-Mills Fields Crucial to the Standard Model?

[kurious]

What in simple terms is a Yang-Mills field?
What has it got to do with the standard model of particle physics
and why are all particles in the standard model massless - is this something
to do with getting the standard model to be consistent with the Higgs field?
Do we need the standard model given that it doesn't go well with gravity,
when in reality gravity fits in quite naturally with the rest of the world?
Does the math of modern physics have to be so difficult or is this just
a sign that modern physics is going wrong?Why is perturbation theory needed in quantum field theories - what probem does it solve - what problems does it cause?

 

[Epsilon Pi]

What is going wrong with GTR?

Too many questions kurious,

Should we not better ask why the General Theory of Relativity doesn't go well with the standard model?
Why QM and GTR do not talk to each other?
What is going wrong with GTR?
Does it have to do with the fact Einstein used Tensor Analysis for it?
Does it have to do with the fact QM start with the complex Schrodinger wave equation?
Must not complexity be taken to a minimum - such as a basic unit system based on Euler relation- if we want to overcome such an incommesurability(as T.S.K put it) problem in our interpretation of the physical world?

Regards

EP

Do we need the standard model given that it doesn't go well with gravity,
when in reality gravity fits in quite naturally with the rest of the world?
Does the math of modern physics have to be so difficult or is this just
a sign that modern physics is going wrong?

 

[marlon]

What in simple terms is a Yang-Mills field?
What has it got to do with the standard model of particle physics
and why are all particles in the standard model massless - is this something
to do with getting the standard model to be consistent with the Higgs field?
Do we need the standard model given that it doesn't go well with gravity,
when in reality gravity fits in quite naturally with the rest of the world?
Does the math of modern physics have to be so difficult or is this just
a sign that modern physics is going wrong?Why is perturbation theory needed in quantum field theories - what probem does it solve - what problems does it cause?

Yang-Mills fields are the fields of the Yang-Mills-theory, that's logic. Now this theory can be viewed as the general model according which QFT works. It describes the behaviour of all elementary particles like electrons or messengers like fotons or gluons. Basically one starts from a lagrangian like in the Hamilton-Lagrangre-mechanics.In this lagrangian one finds the fields describing the elemantary particles, together with kinetic and potential energy. Then you look for global symmetries (global = independent of position and time) which correspond to a conserved quantity (like electric charge for EM-interactions). This is called the theorem of Noether. Then you make these global symmetries local. In order to maintain covariance under Lorentztransformations, extra fields will have to be introduced. These extra fields will describe the messenger particles like fotons. The exact way interactions between particles via the messengers, will evolve is determend by the conserverd quantity. This quantity should be seen as the referee, determing what interactions are valid and what not.


Tensors are needed because of the "limitations of the human mind". We always want to make are reference frame lorentzian in our near perimetre, because that is the way we are used to look at things. One says that are metric is locally lorentzian. Because of this demand tensors are used and Lorentzcovariance is needed. In general relativity there is no preferred reference frame, so every quantity has to behave in the exact same way in every frame. We can go from frame to frame via parallel transport of vectors.
If we have info in frame one and we go to frame two via parallel transport, this info in frame two must behave in the same way as in frame one. This is covariance.

All elementary particles are massless before the spontanious breakdown of symmetry. They are massless because mass mixes the left and right handed chiralities of particles. The chirality is a quantity that describes the relation between spindirection and direction of momentum.Same direction is right-handed chirality and opposite direction of spin and momentum is left-handed-chirality. Different chirality corresponds to fundamentally diffrent particles because the two chiralities do not couple in the same way to elektroweak interactions.

Perturbationtheory is needed in order to get fysical (usefull) results out of the model. When an interaction between particles must be described , one takes the corresponding potential energy multiplied by the coupling constant and puts this in the lagrangian of the model. Now if the coupling constant is not too big one can calculate stuff by performing some kind of Taylor-expansion in function of the coupling constant. The first term in this expansion always is the socaled free theory. This means a theory without the interaction taken into account. Then one by one one adds the different terms of the expansion into the model in order to bring in the effects of the actual particle-interaction which is described by the potential energy. The coupling constant describes the strength of the interaction.

Note that this constant does not always is a constant. It can vary on the speed of the interacting particles, like in QCD...Problems arise when the coupling constant is big, then expansion is invalid just as with taylor. In order to solve this one can make some kind of duality-transformation to a model that describes the same situation but with very low coupling constant.

There are threads that i wrote which give such an example like quarkconfinement.



black, out of inspiration

i hope this clarifies some of your questions

marlon

 

[marlon]

addendum

No gravity in QFT. One of the mean reasons. In QFT you have Heisenbergs-principle. So a particle's position is never exact. This does not count for general relativity.

Gravity is not implemented in the Standard Model because its effects are very very small, they can be ignored at this scale (up to 10^-15meters)

 

[Epsilon Pi]

Are not there other ways of representing gravitational fields?

Kurious was confused in the first place about the way QM is in conflict with the prevailing representation(GTR) of gravitational fields.
Tensors is the tool used by Einstein to develope his ideas about the "generally covariant laws" of nature, but are you sure there are not other ways to develope the laws of gravitational fields that are not in conflict with QM representation?
Are you sure there is not a tool that by definition includes uncertainty in its representation? If it is, then we have a language or tool that is not so complicated as the ones we have today, not accesible for the "normal minds", which I think was the feeling kurious expressed in his question:
"Does the math of modern physics have to be so difficult or is this just a sign that modern physics is going wrong?"

Regards

EP

Tensors are needed because of the "limitations of the human mind". We always want to make are reference frame lorentzian in our near perimetre, because that is the way we are used to look at things. One says that are metric is locally lorentzian. Because of this demand tensors are used and Lorentzcovariance is needed. In general relativity there is no preferred reference frame, so every quantity has to behave in the exact same way in every frame. We can go from frame to frame via parallel transport of vectors.
If we have info in frame one and we go to frame two via parallel transport, this info in frame two must behave in the same way as in frame one. This is covariance.
marlon

 

[marlon]

ok, that is a very interesting question. I don't have the answer whether there is a better mathematical language to describe things without them nasty tensors.

I think the biggest problem to overcome, in order to achieve this goal is a very spectacular one : WE HAVE TO GET RID OF THE CONCEPT OF DISTANCE !

Remember that tensors are born in the geometry of Riemann. One can calulate the Riemanntensor on a locally flat space (like we right now) and yet still be able to conclude he or she is on a global curved space. i think this intrinsic property of differentialgeometry is marvelous.

But to give you my view : I think some twisted mind could develop a theory without a distance in it. But the problem that remains is, what is the use ? We would not be able to interprete such a theory, right ?

Tensors and a of this calculation-horror comes directly from the fact that we always want to measure are local - lorentzian-space ...

 

[Lonewolf]

It's nothing to do with the fact GR uses tensors. Tensors are also used quantum field theory.

 

[marlon]

I think these difficulties in calculation or not a sign of fysics going wrong. They are the sound of brain - inevitability !

There is no other option for our limited minds !

WE SHALL MEASURE AND OVERCOME

 

[Epsilon Pi]

Two different languages in conflict?

Evidently you are using two different languages that do not talk to each other, that of QM and that of GTR. What has prevailed since QM is a dual concept of wave-particle, and this concept is impossible to be expressed by GTR, which is then, in certain sense, a classic representation of physical reality, classic in the sense it cannot rationalize duality. This is what is wrong in modern physics.

Regards

EP

addendum

No gravity in QFT. One of the mean reasons. In QFT you have Heisenbergs-principle. So a particle's position is never exact. This does not count for general relativity.

Gravity is not implemented in the Standard Model because its effects are very very small, they can be ignored at this scale (up to 10^-15meters)

 

[marlon]

It's nothing to do with the fact GR uses tensors. Tensors are also used quantum field theory.

Yep, yep

tensors are widely used. Even the engineers use them to express the directional dependence of some quantities like pressure or mass. or to express anisotropic properties of cristals

 

[Epsilon Pi]

Tensor not an ideal too for covariant laws of nature

Nobody is talking about tensors are not widely used. My central point is that they are not the better tool for representing the covariant laws of nature, as with them as I put it before, we cannot represent a concept such as wave-particle concept

Regards

EP

Yep, yep

tensors are widely used. Even the engineers use them to express the directional dependence of some quantities like pressure or mass. or to express anisotropic properties of cristals

 

[marlon]

Evidently you are using two different languages that do not talk to each other, that of QM and that of GTR. What has prevailed since QM is a dual concept of wave-particle, and this concept is impossible to be expressed by GTR, which is then, in certain sense, a classic representation of physical reality, classic in the sense it cannot rationalize duality. This is what is wrong in modern physics.



EP

Ehh, so what ?

Why would we want to do that ?

What is the advantage ?

The concept of dualities is very well known in QFT.

But this is not the case for GRT, right... so ?
Are you saying they cannot be unified ? I think not ... what about strings...

greetz marlon,

 

[marlon]

Nobody is talking about tensors are not widely used. My central point is that they are not the better tool for representing the covariant laws of nature, as with them as I put it before, we cannot represent a concept such as wave-particle concept

Regards

EP

What wave - particle concept ? You mean in general relativity??

What about the fields-particle relation ?

 

[Epsilon Pi]

getting rid of a fundamental concept?

No, why should we have to get rid of such a fundamental concept?
Why we think that Riemann geometries have to be used for representing physical reality? because Einstein used it with Tensor Analysis?
Why don't we use sort of complex differential geometry in which duality is rationalized?

Regards

EP

I think the biggest problem to overcome, in order to achieve this goal is a very spectacular one : WE HAVE TO GET RID OF THE CONCEPT OF DISTANCE !

 

[Epsilon Pi]

no they cannot be unified

No, QM and GRT cannot be unified, they talk different languages...strings is a noble intent, let us wait what it gives us

Regards

EP

Ehh, so what ?

Why would we want to do that ?

What is the advantage ?

The concept of dualities is very well known in QFT.

But this is not the case for GRT, right... so ?
Are you saying they cannot be unified ? I think not ... what about strings...

greetz marlon,

 

[marlon]

No, QM and GRT cannot be unified, they talk different languages...strings is a noble intent, let us wait what it gives us

Regards

EP

Different languages, but they both use tensors, so they can not be the cause of problems.

Indeed strings are not yet a certainty
But we are forgetting one fine concept of from topology. What about compactification and wrapped up dimensions? Maybe this is taking us to far.

Don't just say they talk different languages just because of the difficulties we have in unifying them. Both models use tensors extensively because of the same reason. It has nothing to do with the fact that one uses fields and the other uses curvature of spacetime

 

[kurious]

Some great answers to my original question.Thanks a lot.
Why is the uncertainty in a particle's position not used in General relativity -
couldn't we just say that a particle has a probability of being at a given
point in a distance range and a certain probability for its momentum in a small range of momenta and work out a relativity theory that has a stress energy tensor that reflects this i.e a theory that yields a stress energy tensor that has a certain probability of existing with a certain numerical value?
Noether's theorem relates symmetry laws to conserved physical quantities.
are any physical quantities conserved together: for example is the conservation of electric charge conjugate with the conservation of
spin?

 

[Lonewolf]

Some great answers to my original question.Thanks a lot.
Why is the uncertainty in a particle's position not used in General relativity

The main reason is that general relativity is a classical theory, not a quantum theory. There have been attempts to develop a gravitational uncertainty principle. You may be interested in http://arXiv.org/abs/gr-qc/9904026

It's worth noting that inside the infinite density singularity inside the event horizon of a black hole, we are uncertain of even the uncertainty principle

 

[Epsilon Pi]

Something very, very wrong in modern physics?

Hi Lonewolf and everybody,

Thank you! At last we find an akin point of view of the way I see physical reality.
In the first place what is needed, IMHO, is not just necessarely to develop a "gravitational uncertainty principle", but to use a tool such as complex numbers that permits us to rationalize that duality of time and space, wave and particle, ect.

And your important second point about black holes is not again one of those great contradictions that result by using the wrong tool?
Not only with it is violated a fundamental law of nature such the conservation of energy-matter but additionally as you have pointed out "we are uncertain of even the uncertainty principle". Why at atomic levels the system cannot collapse but it can at large?
Definitively as I have insisted, there is something very, very wrong with modern physics.

Regards

EP

The main reason is that general relativity is a classical theory, not a quantum theory. There have been attempts to develop a gravitational uncertainty principle. You may be interested in http://arXiv.org/abs/gr-qc/9904026

It's worth noting that inside the infinite density singularity inside the event horizon of a black hole, we are uncertain of even the uncertainty principle

 

[marlon]

What if we were able to perform an analogon of the Wick-rotation to some sort of complex time or distance-coordinate ?

Shouldn't we be able to incorporated compex numbers.

Besides I think the solution is to be found in the search for dualities between models with uncertainty and those that do not incorporate such a consept.

 

[Epsilon Pi]

to invent again what is already?

Euler relation is in fact sort of rotation vector in the complex plane; that plane which is, as it were, the background of physical reality or sort of canvas where it is possible to represent the dynamic complexity of the real.
Furthermore for representing physical reality we must use a mathematical symbolic representation that has proved already its usefulness; in fact complex numbers not only have been used sucessfully in IE, but in QM.

Why do we have to invent again what is already invented?

Regards

EP

What if we were able to perform an analogon of the Wick-rotation to some sort of complex time or distance-coordinate ?

Shouldn't we be able to incorporated compex numbers.

Besides I think the solution is to be found in the search for dualities between models with uncertainty and those that do not incorporate such a consept.

 

[kurious]

Lonewolf:
The main reason is that general relativity is a classical theory, not a quantum theory. There have been attempts to develop a gravitational uncertainty principle. You may
be interested in http://arXiv.org/abs/gr-qc/9904026

Kurious:

This gravitational uncertainty principle is for a rough Newtonian approximation:

x = h/p + ( p/ h) L^2

where p is uncertainty in momentum x is uncertainty in distance and L is the Planck length.

 

[kurious]

In order to maintain covariance under Lorentztransformations, extra fields will have to be introduced.

If we have info in frame one and we go to frame two via parallel transport, this info in frame two must behave in the same way as in frame one. This is covariance.

All elementary particles are massless before the spontanious breakdown of symmetry. They are massless because mass mixes the left and right handed chiralities of particles. The chirality is a quantity that describes the relation between spindirection and direction of momentum.Same direction is right-handed chirality and opposite direction of spin and momentum is left-handed-chirality. Different chirality corresponds to fundamentally diffrent particles because the two chiralities do not couple in the same way to elektroweak interactions.

marlon

Kurious:
How do we know for sure that the physical world
is exactly Lorentz covariant.If it is only approximately covariant
would there be any need to add extra fields?

Are particles that are massless a mixture of left and right chirality?
A quark has a different chirality compared to an electron?

 

[Epsilon Pi]

where is duality?

Interesting Kurious, but where is the duality of wave-particle included in that representation?

Regards

EP

Lonewolf:
Kurious:

This gravitational uncertainty principle is for a rough Newtonian approximation:

x = h/p + ( p/ h) L^2

where p is uncertainty in momentum x is uncertainty in distance and L is the Planck length.

 

[kurious]

This gravitational uncertainty principle is for a rough Newtonian approximation:

x = h/p + ( p/ h) L^2

This principle comes from the paper Lonewolf listed.

 

[Epsilon Pi]

Unfortunatly because of some problems in my PC, I have not been able to read that paper, that's why I asked where was the rationalization of duality in that interpretation.
In spite of what Antonio Lao wrote down about Plank, I think it was with him that started non-classical physics, but history plays an essential role in its evolution, so it was just in 1926, when Schrodinger postulated his well-known complex wave equation when that duality was rationalized in a complex differential equation for the first time, and this equation does not have anything to do with gravitational fields, right?

Regards

EP

This gravitational uncertainty principle is for a rough Newtonian approximation:

x = h/p + ( p/ h) L^2

This principle comes from the paper Lonewolf listed.

 

[marlon]

Kurious:
How do we know for sure that the physical world
is exactly Lorentz covariant.If it is only approximately covariant
would there be any need to add extra fields?

Are particles that are massless a mixture of left and right chirality?
A quark has a different chirality compared to an electron?

The concept of Lorentz covariance is the fundamental rule of GTR but also of QFT. If we want to make sure there is not a preferred reference frame every fysical law must behave in the exact same way in every frame. In order to be sure if that Lorentz covariance is needed. The question whether our fysical universe is Lorentz covariant would be the same as asking if GFT has any fysical relevance ?? I think the answer to that is clear...

Those extra fields are needed to describe the messenger bosons. Approximate covariance is useless, it even does not exist. Even if it were to exist then them extra fields would offcourse still be necessary.


No massless particles are a mixture of the two chiralities. This is impossible because each chirality corresponds to a fundamental different particle. By this, I mean that the four interactions behave differently for each chirality. An electron can be left handed and also reght handed, but not the two at once ...(then it would have restmass)

 

[Epsilon Pi]

Not that the physical world is exactly Lorentz covariant(as a matter of fact should it not be Einstein covariant?), it is our interpretations of physical reality that have pretended to be exact or precise.
If we have an interpretation with both duality rationalized and uncertainty included why we have to complicate matters more than they already are by the introduction of additional theoretical fields, with no corresponding physical basis? Are not they just interpretations, or paradigm-determined?. Is not this part of the great crisis our physics is living?

Regards

EP
PD: "I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of a science, whatever the matter may be." Lord Kelvin 1883.

Kurious:
How do we know for sure that the physical world
is exactly Lorentz covariant.If it is only approximately covariant
would there be any need to add extra fields?
?

 

[kurious]

Kurious:
How do we know for sure that the physical world
is exactly Lorentz covariant.If it is only approximately covariant


Kurious:

What I meant by this is what if the Lorentz transforms are mathematically
inaccurate so that (1-v^2/c^2)^1/2 could be for example (1-v^2/c^2 + 10^-19)^1/2
Experimental results at todays accuracies would agree with (1-v^2/c^2)^1/2 but the reality would be (1-v^2/c^2 + 10^-19)^2.
This can give a new kind of covariance - Tab equals Tba still,and the four-momentum of a photon is still zero under this transformation.And a proton of radius 10^-15 metres falling into a black hole and reaching the speed of light at the singularity will have a radius at the singularity of 10^-19 x 10^-15 = 10^-34 metres.The singularity is removed!
I don't believe in waves - I think waves are just a mathematical description of a large number of particles,just like a wave at sea is derived from the movements of millions of water molecules.
I favour the Bohm interpretation of quantum mechanics over standard copenhagen QM.In Bohm's theory there can be cause and effect although
the pilot wave can change instantaneously along its length which to me suggests Bohm's theory needs modifying.

 

[Epsilon Pi]

well, well, well you certainly are free to believe whatever you want and I can't argue about it. Evidently we are talking about different paradigms and there we have, by all odds, an incommensurability problem.

My best regards

EP

Kurious:
How do we know for sure that the physical world
is exactly Lorentz covariant.If it is only approximately covariant


Kurious:

I don't believe in waves - I think waves are just a mathematical description of a large number of particles, just like a wave at sea is derived from the movements of millions of water molecules.

 

[Epsilon Pi]

problems with the tool?

My apologies Marlon, for not answering your point. As I have pointed out in other post, the main problem with QM and GTR is that they have an incommesurability problem, in part for the different paradigms from which they start that has to do with two different languages that do not talk to each other, I mean Tensor Analysis and Complex numbers, as in the latter it is possible to rationalize duality what cannot be done in the former. The tool as a tool can be used anywhere, but would you not as an engineer use a tool that fit better for the problem in question?

Regards

EP

Different languages, but they both use tensors, so they can not be the cause of problems.

Indeed strings are not yet a certainty
But we are forgetting one fine concept of from topology. What about compactification and wrapped up dimensions? Maybe this is taking us to far.

Don't just say they talk different languages just because of the difficulties we have in unifying them. Both models use tensors extensively because of the same reason. It has nothing to do with the fact that one uses fields and the other uses curvature of spacetime

 

[marlon]

ok, got your point and I agree.

But complex numbers can be used in GTR right ?

Besides why would we need to introduce the particle-wave-duality in GTR ?

I think this can be done by fields which are also used in GTR just as in the same way that they are used in QFT

regards
marlon

 

[Epsilon Pi]

using complex numbers in GTR?

Hi Marlon,

How would you use complex numbers in GTR? by using Complex Tensors? did Einstein try that?

No, we cannot introduce the wave-particle duality in GTR, at least, in what we undertand by it according to Einstein

Regards

EP

ok, got your point and I agree.

But complex numbers can be used in GTR right ?

Besides why would we need to introduce the particle-wave-duality in GTR ?

regards
marlon

 

[Epsilon Pi]

Now I have been able to read the paper, but let me please repeat here what I posted somewhere else

Cannot those dualities be rationalized, as it were, in a complex mathematical description, i.e., a basic unit system which is not anymore an inequality?, but an equation in which the equal sign is not precisely a symbol JUST to reduce the one to the other? a symbol that permits us to include both, yes-or-no, and complementarity?
Will not be this complex mathematical symbolism nearer to QM? Don't we need a symbolism with which the main fundamental equations of physics, such as those of the Lorentz transformation group, the Schrodinger wave equation, those of gravitational fields, both Newtonian and einsteinian, and additionally those laws of the pendulum that as was pointed out by T.S.K
"How else are we to account for Galileo's discovery that the bob's period is entirely independent of amplitude, a discovery that the normal science stemming from Galileo had to radicate and that we are quite unable to document today?"

can be expressed, not as some kind of TOE, but as a mathematical procedure or language that permits to include them all?... but is really modern physics interested in such an endeavor?

Just some repetitive thoughts in my mind

EP

Lonewolf:
The main reason is that general relativity is a classical theory, not a quantum theory. There have been attempts to develop a gravitational uncertainty principle. You may
be interested in http://arXiv.org/abs/gr-qc/9904026

Kurious:

This gravitational uncertainty principle is for a rough Newtonian approximation:

x = h/p + ( p/ h) L^2

where p is uncertainty in momentum x is uncertainty in distance and L is the Planck length.