Gauge invariance confusions: symmetry vs redundancy, active vs passive

[MathematicalPhysicist]

Well, this well-known saying by Einstein is disproven by himself. From the moment on he left his solid foundation in phenomenology, he didn't achieve much more of his miraculous insights he had between 1901-1920.

Yeah I know, every genius makes mistakes.
I know I had my fair share of mistakes... :-(

 

[MathematicalPhysicist]

But I keep on trying!

 

[PeterDonis]

Yeah I know, every genius makes mistakes.
I know I had my fair share of mistakes... :-(

Unfortunately, "being a genius" -> "making mistakes" is not logically equivalent to "making mistakes" -> "being a genius". Otherwise every single person on the planet would qualify as a genius.

 

[MathematicalPhysicist]

Unfortunately, "being a genius" -> "making mistakes" is not logically equivalent to "making mistakes" -> "being a genius". Otherwise every single person on the planet would qualify as a genius.

Obviously.
But who defines who is a "genius" in the first place?

 

[Fra]

So?

A taste of the dark age roots of probability theory, when appeal to authority was the major ranking factor.

/Fredrik

 

[Fra]

I think for a relativistic physicist the idea of locality is very natural. I'm not aware of any successful non-local formulation of relativistic physics. The natural language for relativistic dynamics is field theory, i.e., the locality of interactions. So to make a global symmetry local is a pretty obvious heuristic step.

Perhaps you understand something I don't, but while I agree there one can argue from a priori naturalness (and I am with you on a heuristic level) the a priori freedom needs to be tamed by a selection principle, otherwise one could argue that there should be all kinds of crazy symmetries (that is never observed). I seek explanatory clues beyond the heuristics.

I can even embrace the naturalness of an a priori ultimate total freedom for an interacting inside agents to both freely permute the event index(~ pre-spacetime), and recode their microstructure (~ pre-fields) - from which their actions follows as guiding stochastics. And obviously once you allow that, you "trade" crazy transformations of the microstructure, for crazy dynamics. The ultimatey naturaless gives you the ultimate dualities between.

But the question is why "settles" with a specific subset of possible symmetries, that are manifested as interactions?

I think it's when different representations like above are put together - allowed to interact / in terms of interacting subsystems or interacting agents - that we have the clue for the logic of selecting the right interactions and groups. Somehow, it seems to me it takes nothing less than a full unification to understand this. There are gaps in the constructing princuiples, where we have heuristics only.

String theory has the same mess, leading to landscapes. Without understanding how things interact, there is not selection principle and not explanatory power. The only way string theory every made any partial sense to me, it is to view the string as an agent, that interacts with other strings. The problem is that the description is still from the point of an externa observer.

/Fredrik

 

[Demystifier]

But who defines who is a "genius" in the first place?

Community, by consensus.

 

[MathematicalPhysicist]

Community, by consensus.

Keep up the jokes Demystifier!
You are quite hilarious...

 

[Demystifier]

Keep up the jokes Demystifier!
You are quite hilarious...

Do you know any other method for genius detection?

 

[andrew s 1905]

Do you know any other method for genius detection?

I think the modern PC approach is self identification!

 

[Demystifier]

I think the modern PC approach is self identification!

I used to be conceited, now I'm perfect.

 

[Fra]

I think the modern PC approach is self identification!

With that method, beware the commong differential diagnosis is just madness.

I prefer Demystifiers method of external observers. Of course, its has its own pitfalls: Its possible that the all external observers are wrong, because the ingenuity is hidden only to the solipsist genius. This does not violate bells theorem because the external still TREATS you like a 50% idiot. Its the determinism premise that is wrong.

/Fredrik

 

[MathematicalPhysicist]

Do you know any other method for genius detection?

I don't believe in using this word, only idiots use it to describe someone who they want their appraisal.

I never thought I was a genius or humble, I am just really curious and love the subject more than everything else and that's enough for me to keep on trying and learning...

Cheers, mates!

 

[Demystifier]

This does not violate bells theorem

This is particularly obvious when one describes it with the g-potential (with g standing either for genius or gauge), so the act of genius is local when his B-factor (or her B-factor, to avoid sexism accusations, with B standing either for brain or magnetic field) is vanishing at the place of action. This genius-gauge duality shows that any act of genius is invariant under passive transformations and hence redundant.

 

[iuvalclejan]

Gauge transformations can be both active and passive. Active gauge transformations are principal fiber bundle automorphisms, whereas passive gauge transformations are changes of local trivializations. And there is also a passive version of diffeomorphisms: Coordinate changes. The physical relevance comes from the active versions, because requiring invariance under them restricts theory space.

After having skimmed the paper, I wouldn't say it clarifies anything. Why not just teach the fiber bundle formalism? Then everything becomes quite obvious.

Ultimately, the only thing that matters for symmetry is whether the Lagrangian (or more accurately the action) remains invariant under some transformation. Whether the invariance comes from an active or passive transformation doesn't matter. The Noether currents are the same.

 

[Demystifier]

Ultimately, the only thing that matters for symmetry is whether the Lagrangian (or more accurately the action) remains invariant under some transformation. Whether the invariance comes from an active or passive transformation doesn't matter. The Noether currents are the same.

That's true for global transformations. But local (gauge) transformations are different.

 

[CelHolo]

The way I always learned it was gauge redundancy comes from using local fields to describe massless states, since the DOF count differs. Any global symmetry of the massless states then becomes a gauge symmetry of the local fields.

 

[vanhees71]

Ultimately, the only thing that matters for symmetry is whether the Lagrangian (or more accurately the action) remains invariant under some transformation. Whether the invariance comes from an active or passive transformation doesn't matter. The Noether currents are the same.

For local gauge symmetries it doesn't make sense to distinguish between "active" and "passive" transformations, because a priori gauge symmetries are just due to redundancies in the description (e.g., describing the same electromagnetic situation either with Lorenz or with Coulomb-gauge four-potentials).

For real symmetries of nature you have the choice to interpret the transformations either passively, i.e., the independence of the description of a given situation on the choice, e.g., of the Cartesian basis in Newtonian or special relativistic physics (invariance under rotations, isotropy of space) or actively, i.e., stating that when reorienting a specific setup of an experiment its results don't change, i.e., there is no way to specify a preferred direction in space by any physical observation.