What is Local U(1) Gauge-Invariance and its role in electromagnetism?

[sudhirking]

Can someone please explain to me this internal symmetry...

Also please do take mind that i don't have strong mathematical knowledge, YET...
but can u state out the conceptual, non-mathematical, principles in local U(1) Guage -Invariance and how it reasons for virtual phton exchange which causes electro-magnetism.

 

[malawi_glenn]

I already answered that question.

If you don't know mathematics on the levels of complex phases and partial derivatives, then I don't think that is much to do. But I try.

The thing is that you start with a free lagrangian (which is kinetic minus potential energy) , free means no potential! I.e no interatctions, just free particles flowing in space.

Then you impose a symmetry, which changes the functions in the lagrangian describing this free particle, by a phase. An example of phase change is sin(x) -> sin(x + pi/3).
The phase is unobservable, i.e. there is no experiment which can measure this phase. Hence, each observer may choose his/her own value on that phase, it should NOT change the physics (the Lagrangian).

So by imposing such criterion, that the phase should be a function of time and position, you MUST introduce a potential, to make the Lagrangian unchanged (invariant) when imposing such symmetry.

So the result is that by starting from a lagrangian for a free particle, imposing a symmetry that depends on space and time, one ends up with a lagrangian with a potential, i.e. particles interacting.

Now virtual particle exchange is something else. Virtual particle exchange comes when you calculate contractions etc. and is purely mathematical.

 

[sudhirking]

Thank you for your helpful description, and I 'm sorry that i could not comprehend your previous post which answers this question due to lack of sofisticated math. I also thank you for helping me understand Langrangian, though wouldn't the L value be qual to a negative value as kinetic energy POTENTIAL is included in the potential energy and taht the potential energy holds more values including thermal, etc? Also, what does Langragian aim for, what does it try to say about a body's system? Due to some ambiquity in classical concepts, i cannot seem to understand the reason of this system's importance. Please help me in grasping these princicles and thank you for your answer!

 

[sudhirking]

Also, i do not understand why you must introduce a potential just because of the usage of function representing space and time coordinates because the physics of the Langragian system should never change!

 

[malawi_glenn]

but thermal energy is kinetic energy.. you are mixing concepts here.

The Lagrangian is just Kinetic Energy minus Potential Energy.

When you know more math (and physics) you will be able to derive the Euler-Lagrange equation, so that the equation of motion becomes almost trivial to find.

If you look at the mathematical description I showed you in the other thread, you will see why the potential must be there.But since you don't know math, you must wait a couple of years til you can understand it ;-)

Sorry kid, but eventually you must learn to walk before you can run, it is just the way it is.

 

[sudhirking]

Thx for all your help and cooperation with my insatiable curiosity. unfortunately, i can't wait for the math to come as i am currently learning pre cal on many respurces. in fact, i am not even supposed to be in pre cal, school wise, till around sophmore year. i have yet to wait till some high school year till i ge there. Then, i think its the year after chemistry, physics, but that is what, a good 3-4 years away! I DEFIENENTLY CANNOT WAIT! i gues i must learn how to walk faster then usual. Do u know any good basics on mathematics in physics- like some good textbook name that i can buy??

 

[sudhirking]

Back to science, when you say that virtual particle exchange is purely amthematica, there has to be some concepts that logically arise due to math. Can u pls explain how the virtual particle exchange waorks, like answering question why do they exchange virtual photons and give a brief explanation how??

 

[malawi_glenn]

You can learn calculus, one dimensional and several dimensional. And linear algebra such as vectors and matricies.

The mathematics behind virtual particle exchange is quite complicated and you would not understand a thing if i wrote something. And "why photons" has to do with basic facts of electrodynamics. You must know basic physics before even try to get what modern quantum physics is dealing with.

 

[sudhirking]

Ok, i will ask simpler ohysics wuestions later before repraoching to quantum... *sigh*

BUT, is it possible, for the proton exchange to be cause by a repulsive, and/or regular attractive gravity?

 

[malawi_glenn]

You are asking nonsense stupid questions since you don't know anything about the realm which are asking about. You seem to be desperate, also you are not following our advices.

 

[sudhirking]

I relaize and that was why i was just asking... and btw i am going to follow ure advive but i sent that post above yours before looking at what you said on wat math and science i should learn. It's just taht i always had an idea, or a poorly developed hypothesis that the application of negative matter to gravity would have considerable quantum effects. SIghhh... i give up hope for my ideas...Well..this is the last physics forums you will see from me, and as happy as u may be for that, i will go on buying textbooks and try to develop my hypothesis into the thepry of everything...Maybe when I'm 70 or 80 i will come up with something, but for now, i must move on to calculusm and then get a physics textbook... then one on GRand another on EM and later QCD. Then i wil continue by learning the strong force and weak force and all before, i will learn QM to understand's elemetnary particles...siighh
But hey, the truth is fascinating and I'm sure this negative matter leads to negative curvature though deep within it, it promotes an idea that violates the simple laws of violation of conservation of mass, but as shown by GUT and other physicist, that mass decay would extend over or close to the universe's lifetime! well.. i want to know the truth.. So I'm going to ask my parents for these textbooks, and I knopw they are going to say no as it does interfere with school... sigh..


WELL GOOD BYE PHYSICS FORUMS

 

[malawi_glenn]

Define "negative matter"

Define "truth"