1. We all know that, a current carrying conductor produces a magnetic field around it. So, how does Electric current or charges in motion able to create a magnetic field around themselves? I mean what special phenomena is occurring in charges that are in motion but is not occurring in charges at rest? How does flowing current produce magnetic field????

2.

3. Originally Posted by Nerdvvt
We all know that, a current carrying conductor produces a magnetic field around it. So, how does Electric current or charges in motion able to create a magnetic field around themselves? I mean what special phenomena is occurring in charges that are in motion but is not occurring in charges at rest? How does flowing current produce magnetic field????

4. Electric and magnetic fields are not separate phenomena, but just two aspects of the same underlying entity - the electromagnetic field. What combination of these two aspects you see depends on your state of relative motion to the source - if you are at relative rest to the charge you can see only electric fields, if there is relative motion you will have a magnetic aspect as well. However, it is the electromagnetic field itself which is the more fundamental entity, and that never changes ( provided the source remains the same ). The vector formulation of Maxwell's equations doesn't make that very clear, but if you formulate them in terms of differential forms, then this relationship becomes very obvious.

5. Oh well, That's absolutely right......It's very well understood that Electric and magnetic fields are two aspects of the same entity but my question is how does this dependence arise?? how does relative motion lead to the creation of magnetic field?? you wrote "if you are at relative rest to the charge you can see only electric fields, if there is relative motion you will have a magnetic aspect as well." but why?? please specify the reason for this relationship !

6. Originally Posted by Nerdvvt
please specify the reason for this relationship !
To be honest I am not really certain what you are getting at. The electromagnetic field ( represented here by the Faraday tensor F ) manifests as a relation between the 4-force which a particle experiences when it moves through a region containing such a field, and the particle's own 4-velocity, in the following way :

This is an empirical law, and asking why this law is the way it is cannot really be answered by physics. We can only investigate the properties of how such a field behaves, and how it influences its surroundings; to do so we define the so-called electromagnetic 2-form as

and find that this differential form ( which is really just an antisymmetric rank-2 tensor ) satisfies the relations

meaning that the surfaces which represents this form do not end or meet, and

meaning that the amount flux tubes which represent the dual of that form ( called the Maxwell form ), and which end within an elementary volume, is equal to the amount of charge enclosed in that volume. Both of these are very intuitive notions, and if you put these together with the original definition of the electromagnetic field tensor you obtain precisely Maxwell's equations in the usual form.

but my question is how does this dependence arise??
Considering the above, the question now becomes why the surfaces of Faraday never end or meet, and why the amount of Maxwell flux tubes equals the amount of source points. The latter question has a mathematical answer - it can be understood as a direct result of the generalised Stokes theorem. The former question does not have any deeper answer that I am aware of ( anyone, please correct me if I am wrong on this ); it is an empirically found relation which physically means quite simply that there are no elementary magnetic monopoles. So, the only answer I can really give you here is that the relations between electric and magnetic fields arise from Stokes theorem, coupled with the empirical observation that there no elementary magnetic monopoles - the rest is just mathematics.

7. Originally Posted by Nerdvvt
please specify the reason for this relationship !
If you are looking for a more "intuitive" explanation this one seems reasonably good:
Q: What is a magnetic field? | Ask a Mathematician / Ask a Physicist
(scroll down to the "Now consider two parallel, current carrying wires" bit)

I think that this simple explanation in terms of length contraction only works in simple cases like two parallel wires (for more complex cases you may need the formalism Markus describes).

8. No No........I was asking about the phenomena at the microscopic level............What exactly is happening ? At the the quantum level??

9. Originally Posted by Nerdvvt
No No........I was asking about the phenomena at the microscopic level............What exactly is happening ? At the the quantum level??
That is exactly what the link I posted explains: how it is perceived from the perspective of individual electrons and protons. It basically comes down to a change in the apparent density of charge when a current flows (due to relativistic effects) which means there is an attractive force.

10. Thanks a lot #strange.......................The bit of information you shared was really good!!...........As it was written in the text

Classical physics: A when a charge moves in some direction it creates a magnetic field that wraps around it.
I'm just questioning this concept, like why, When a charge moves it creates a magnetic field around it what's the quantum concept involved??????

11. Originally Posted by Nerdvvt
Thanks a lot #strange.......................The bit of information you shared was really good!!...........As it was written in the text

Classical physics: A when a charge moves in some direction it creates a magnetic field that wraps around it.
I'm just questioning this concept, like why, When a charge moves it creates a magnetic field around it what's the quantum concept involved??????
I don't think I can explain it any better than the diagrams in that page. What part of that are you struggling with? The magnetic field is just the electric field seen from another frame of reference.

If you need more detail then you need to understand the math that Markus presented.

This is an intermediate description, that takes the informal diagrams and develops the math that explains it: Magnetism, Radiation, and Relativity

12. Originally Posted by Nerdvvt
Thanks a lot #strange.......................The bit of information you shared was really good!!...........As it was written in the text

Classical physics: A when a charge moves in some direction it creates a magnetic field that wraps around it.
I'm just questioning this concept, like why, When a charge moves it creates a magnetic field around it what's the quantum concept involved??????
I can't beat Strange's explanation. It's an effect of relativity, not a quantum effect.That's why it arises between charges in relative motion.

The mathematical formalism that everyone uses implicitly assumes this, but without needing to refer to it explicitly. Historically, this formalism arose from empirical studies of the relations between magnetism and electricity, i.e. it was all well developed before relativity came along. This may be why the relativistic origin of the effect often seems to be only mentioned as a sort of interesting footnote.

13. But producing a unified explanation was, I believe, one of Einstein's motivations for developing the theory of relativity.

14. Originally Posted by Strange
But producing a unified explanation was, I believe, one of Einstein's motivations for developing the theory of relativity.
Now that I didn't know. How very interesting. So he was, in effect, asking himself a similar question to our poster, being - presumably - dissatisfied with adopting a mere mathematical formalism without an underlying explanatory mechanism.

I like that, actually. I am often frustrated by "explanations" of phenomena which just tell you the mathematics they obey, without a physical picture behind it.

I suppose the irony would be that with General Relativity, one has a mathematical description of gravity, in terms of distortion of spacetime by mass, but which does not really give a picture of why mass does this.

15. Originally Posted by exchemist
I suppose the irony would be that with General Relativity, one has a mathematical description of gravity, in terms of distortion of spacetime by mass, but which does not really give a picture of why mass does this.
Actually, the underlying reason is to be found in my signature; there is a geometric quantity called the "Cartan moment of rotation", and this quantity turns out to be automatically conserved through the topological principle that the boundary of a boundary always vanishes. At the same time we know that energy-momentum is locally also conserved, so what GR does is simply associate these two conserved quantities. The result is the Einstein field equations, and everything that follows from them. Of course one can go on and ask why these quantities should be associated, but then that is when we leave the realm of physics and enter metaphysics and philosophy.

16. You can think of it in another way too. Consider a pretzel, and imagine you place it on a table, kneel down, and look at it sideways; what do you see ? You will see only a solid and flat piece of dough. Now stand up and look at the pretzel top-down. What do you see now ? You will see an intricately shaped object with three "holes" in it. The full complexity of the pretzel becomes visible only once you change your relation in space to the pretzel in just the right way. Same with electromagnetic fields - both the "electric" and "magnetic" parts are always there, but which one you see depends on your state of relative motion, i.e. on the geometric relation between yourself and the field. It's like looking at the same thing from different perspectives, which is of course precisely what Einstein realised once he fully understood the implications of Lorentz transformations.

17. Originally Posted by Markus Hanke
Originally Posted by exchemist
I suppose the irony would be that with General Relativity, one has a mathematical description of gravity, in terms of distortion of spacetime by mass, but which does not really give a picture of why mass does this.
Actually, the underlying reason is to be found in my signature; there is a geometric quantity called the "Cartan moment of rotation", and this quantity turns out to be automatically conserved through the topological principle that the boundary of a boundary always vanishes. At the same time we know that energy-momentum is locally also conserved, so what GR does is simply associate these two conserved quantities. The result is the Einstein field equations, and everything that follows from them. Of course one can go on and ask why these quantities should be associated, but then that is when we leave the realm of physics and enter metaphysics and philosophy.
Thanks Markus, I'll need to do some reading to get my head round this - if indeed I'm capable of grasping it at all. Welcome back by the way and I hope your mountain excursion reinvigorated you.

18. Originally Posted by exchemist
Thanks Markus, I'll need to do some reading to get my head round this - if indeed I'm capable of grasping it at all. Welcome back by the way and I hope your mountain excursion reinvigorated you.
Thank you, and yes, it did
This is pretty advanced stuff, and not so easy to get your head around; Misner/Thorne/Wheeler dedicate an entire chapter to this in Gravitation, a textbook well worth getting if you have the money, and the only source I know of that explains this in a manner which is actually understandable for someone who isn't a mathematician. The key concepts here are the topological principle that "the boundary of a boundary is zero", the so-called Bianchi identities, and the curvature 2-form. I will not link to the respective Wiki pages, as I find them to be basically incomprehensible ( is it just me ?? ).

The basic idea is to associate two quantities which are conserved - energy-momentum on one side, and the geometric quantity "Cartan moment of rotation" on the other side. The former is conserved through Noether's theorem and the laws of thermodynamics, the latter is conserved due to the Bianchi identities and the aforementioned topological considerations. The entire theory of relativity follows from associating these.

19. Originally Posted by Markus Hanke
The basic idea is to associate two quantities which are conserved - energy-momentum on one side, and the geometric quantity "Cartan moment of rotation" on the other side.
Is there any "arbitrariness" in that choice? Are there other conserved quantities that could be chosen? If so, is this choice the only one that produces useful results?

20. Originally Posted by Strange
Is there any "arbitrariness" in that choice? Are there other conserved quantities that could be chosen? If so, is this choice the only one that produces useful results?
Very good question, Strange. The answer is no, it is not unique, unless one imposes further demands as follows on our quantity G :

1. G must be a Riemann tensor, and must be a function of the metric ( this is trivial, but important )
2. G shall be linear in the first derivatives of the metric, and quadratic in the second derivatives
3. G must have the same symmetries and the same conservation laws as the stress-energy tensor
4. G must reduce to the Newtonian case for weak, stationary fields

Given these conditions, it can be shown that the Einstein tensor ( and thus the Cartan moment of rotation ) is the only possible choice. Without these conditions, the choice is not unique, and you could obtain a variety of other field equations, such as Einstein-Cartan theory for example.

EDIT : Condition (2) should read - G shall be linear in the second derivative of the metric, and quadratic in the first derivative. Apologies for the mistake above.

21. Originally Posted by Markus Hanke
2. G shall be linear in the first derivatives of the metric, and quadratic in the second derivatives
What is the physical significance of this one (if any)?

[The others either make some sense or I am aware they will not make any sense to me! I'm not sure which category to put this one in...]

22. Originally Posted by Strange
What is the physical significance of this one (if any)?

[The others either make some sense or I am aware they will not make any sense to me! I'm not sure which category to put this one in...]
Also a good question, which I never really thought about - all GR textbooks I have read simply state this as a basic requirement for the tensor, since its covariant derivate must vanish identically ( just as the covariant derivative of the stress-energy tensor must vanish ). I don't know if there is any physical significance to this requirement over and above the mathematical implications ( I don't think you could get its covariant derivative to vanish if the tensor contains any other combinations of derivatives of the metric, in a coordinate basis ). Perhaps KJW could comment on this if he is reading the thread...?

23. Originally Posted by Markus Hanke
( I don't think you could get its covariant derivative to vanish if the tensor contains any other combinations of derivatives of the metric, in a coordinate basis ). Perhaps KJW could comment on this if he is reading the thread...?
Actually, it can be shown that for every scalar that is a function of the metric tensor and its partial derivatives to any order, there is a conserved second-order tensor. In the case of the Einstein tensor, the scalar is the Ricci scalar. The constraint is that the function of the metric tensor and its partial derivatives to any order must transform as a scalar (which won't be true for just any function of the metric tensor and its partial derivatives to any order).

24. Originally Posted by Nerdvvt
I'm just questioning this concept, like why, When a charge moves it creates a magnetic field around it what's the quantum concept involved??????
In terms of quantum theory, electromagnetism is a U(1) gauge theory.

25. Originally Posted by Markus Hanke
2. G shall be linear in the first derivatives of the metric, and quadratic in the second derivatives
*whisper* it's the other way round *whisper*

26. Originally Posted by KJW
Originally Posted by Markus Hanke
2. G shall be linear in the first derivatives of the metric, and quadratic in the second derivatives
*whisper* it's the other way round *whisper*
Holy crap ! You are right, my apologies...didn't pay attention here
Corrected.

In the case of the Einstein tensor, the scalar is the Ricci scalar. The constraint is that the function of the metric tensor and its partial derivatives to any order must transform as a scalar
Thank you, that's what I was looking for

27. Originally Posted by Nerdvvt
We all know that, a current carrying conductor produces a magnetic field around it. So, how does Electric current or charges in motion able to create a magnetic field around themselves? I mean what special phenomena is occurring in charges that are in motion but is not occurring in charges at rest? How does flowing current produce magnetic field????
Feynman had a crack at a quantum mechanical description when he was working on Quantum Electrodynamics (QED). One of the important byproducts of his work in the many different formulations used to describe QED such as path integral approaches was that it was easy to combine together what was back then treated independently as logitudinal and transverse fields which then clearly demonstrated the relativistic invariance of QED.

"The electromagnetic field was split into two parts, the longitudinal part (for electric field) and the other (for magnetic field) mediated by photons, or transverse waves. The longitudinal part was described by the Coulomb potential acting instaneously in the Schrodinger equation, whereas the transverse part had an entirely different description in terms of quantization of the transverse waves. The seperation depended on the relativistic tilt of your axes in spacetime. People moving at different velocities would seperate the same field into longitudinal and transverse fields in a different way. Somebody else in a different coordinate system would calculate the succession of events in terms of wave functions on differently cut slices of spacetime and with a different seperation of longitudinal and transverse parts. The Hamiltonian theory did not look relativistically invariant, but of course it was. You could actually see the relativistic invariance straight away - or as Schwinger would say - the covariance was manifest."

More detail and a great read. It also gets into Wheeler-Feynman absorber theory which Feynman found was a satisfying conclusion. This theory was a foundation upon which Cramer developed the popular Transactional Interpretation of QM:-))

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