# Energy contained in the magnetic field

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16 minutes ago, beecee said:

More correctly and as is made clear, the magnetic field just like any other form of mass/energy warps the spacetime in its vicinity, and light follows geodesics in that curved spacetime.

Here's another verification quote from an expert.....

Q: Can a magnet bend light?

Kris Walker, BSc Adv. Physics & Astrophysics, Monash University (2021)

A; Yes, a magnetic field "has the capacity to bend spacetime and thus light". The Einstein field equations state that

Gμν=8πTμνGμν=8πTμν

If the energy-momentum tensor TμνTμν describes that of an electromagnetic field in free space then its value can be described by the Einstein-Maxwell equation for the electromagnetic stress-energy tensor

TEMμν=14π(F λμFνλ14FσλFσλgμν)TμνEM=14π(Fμ λFνλ−14FσλFσλgμν)

This value contributes to the final value TμνTμν. The curvature will be negligible for small magnetic fields but for very strong ones the contribution is significant. Like always, the light will appear to curve when travelling a respective geodesic in this warped spacetime.

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I don't see the relevance of that 'more correctly' bit, but certainly the above references agree with my earlier quoted comments. Point I was making was that your originally cited reference was poorly written. First stating a magnetic field has no effect on light. Then after the blah blah blah middle portion, introduced a caveat towards the end that contradicted the first stated position. Far less confusing and potentially misleading, would be to have presented the correct relevant picture at the outset.

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On 1/1/2019 at 7:58 PM, Danijel Gorupec said:

What is your hunch about the following...

If we could observe, from relative vicinity, a magnetar or some other neutron star that has a strong magnetic field - so that we are able to precisely track paths of compact objects closely encircling it or just making a close flyby - could we deduce, from paths of these object, whether the magnetic field curves the space or not (that is, if the magnetic field has mass-energy or not)?

I am imagining that path of an object entering deeply into magnetic field of a magnetar would look differently if there is mass-energy in magnetar's magnetic field than if all mass-energy is only within the compact body of the magnetar. (I think, this is analogue to how presence of dark mater changes paths of stars encircling galactic centers). I however don't have any hunch whether the effect would be observable.

And I am wondering if such an object that is entering magnetar's magnetic field could be a light beam - would it curvature differently if there is mass-energy in the magnetic field.

(Happy New Year)

With regards to your OP, I found the following which maybe of interest to you....

Just now, Q-reeus said:

I don't see the relevance of that 'more correctly' bit, but certainly the above references agree with my earlier quoted comments. Point I was making was that your originally cited reference was poorly written. First stating a magnetic field has no effect on light. Then after the blah blah blah middle portion, introduced a caveat towards the end that contradicted the first stated position. Far less confusing and potentially misleading, would be to have presented the correct relevant picture at the outset.

I see it as entirely relevant that mass/energy warps spacetime and that light follows geodesics in that spacetime. The magnetic field itself does not directly affect it as has been said. My apologies if you find that confusing, but I believe it is simply put and was understood by the author of the OP.

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26 minutes ago, beecee said:

I see it as entirely relevant that mass/energy warps spacetime and that light follows geodesics in that spacetime. The magnetic field itself does not directly affect it as has been said. My apologies if you find that confusing, but I believe it is simply put and was understood by the author of the OP.

You know perfectly well what my point was, and that I obviously have had no confusion whatsoever over the fact of a magnetic field contributing to gravitation thus to light deflection.
And btw your method of reproduction of maths in that Quora article has introduced various artifacts that make it look somewhat nonsensical. Best to have just provided the link.

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Posted (edited)
24 minutes ago, Q-reeus said:

You know perfectly well what my point was, and that I obviously have had no confusion whatsoever over the fact of a magnetic field contributing to gravitation thus to light deflection.

That's good and what I was pointing out to the author of the OP.

Quote

And btw your method of reproduction of maths in that Quora article has introduced various artifacts that make it look somewhat nonsensical. Best to have just provided the link.

Thank you for bring that to my attention.

On 1/2/2019 at 7:46 PM, Danijel Gorupec said:

Ok, I will interpret the answer from the Q+A site in favorable manner: magnetic field, by itself, should not affect light (but the answer, as I understand it, does not take in account light-bending due to mass-energy of the field). Although, the field strength of a magnetar is so high that I don't think any scientist would dare to guarantee that there won't be any unknown effect.

No, I don't care to bend light - I care to test the energy density formula for the magnetic field... I started to think about observational possibilities when I read on Wikipedia that energy density of magnetar's field can be thousand times that of lead.

A scientific paper that may be beneficial........

Magnetic field evolution in magnetar crusts through three-dimensional simulations:

## Significance:

The observed diversity of magnetars indicates that their magnetic topology is more complicated than a simple dipole. Current models of their radiative emission, based on axially symmetric simulations, require the presence of a concealed toroidal magnetic field having up to 100 times more energy than the observed dipole component, but the physical origin of such a field is unclear. Our fully 3D simulations of the crustal magnetic field demonstrate that magnetic instabilities operate under a range of plausible conditions and generate small-scale field structures that are an order of magnitude stronger than the large-scale field. The Maxwell stress and Ohmic heating from these structures can explain magnetar bursts and surface hotspots, using comparable poloidal and toroidal magnetic fields.

## Abstract:

Current models of magnetars require extremely strong magnetic fields to explain their observed quiescent and bursting emission, implying that the field strength within the star’s outer crust is orders of magnitude larger than the dipole component inferred from spin-down measurements. This presents a serious challenge to theories of magnetic field generation in a proto-neutron star. Here, we present detailed modeling of the evolution of the magnetic field in the crust of a neutron star through 3D simulations. We find that, in the plausible scenario of equipartition of energy between global-scale poloidal and toroidal magnetic components, magnetic instabilities transfer energy to nonaxisymmetric, kilometer-sized magnetic features, in which the local field strength can greatly exceed that of the global-scale field. These intense small-scale magnetic features can induce high-energy bursts through local crust yielding, and the localized enhancement of Ohmic heating can power the star’s persistent emission. Thus, the observed diversity in magnetar behavior can be explained with mixed poloidal−toroidal fields of comparable energies.

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Hope that helps somewhat in your research!

Edited by beecee

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On 1/5/2019 at 2:58 AM, swansont said:

The measured mass of any atom is smaller than the mass of its constituents. That difference is due to the “interaction energy” and includes nuclear and electrostatic terms.

Yes. So the electrostatic interaction has a mass, easily measured when considering the interacting particles together.

But when explaining the measured energy levels in hydrogen-like atoms, the mass of the nucleus-electron attraction can't be attributed to the electron. Not all, not one half, not even 1%. These figures are brutal.

That's why I disagree that the energy and the corresponding mass would be an attribute of the interacting particles. There is something fishy there.

On 1/6/2019 at 4:01 AM, beecee said:

Here's another verification quote from an expert
https://www.quora.com/Can-a-magnet-bend-light

[...]

There is exactly zero proof in that link. Said expert supposes that the energy of the magnetic field resides in the vacuum, and that light would respond to this energy like observation tells it responds to the mass of a galaxy.

But, sorry, we have observations for galaxies and our Sun only. Bending light with a kilogram of iron was never observed. We ignore what makes the mass of a galaxy, and gravitational lensing was observed where galaxies have no visible mass. Even claiming "only protons, neutrons and black matter bend light" would be consistent with our observations.

And we have observations that the Earth changes the pace of time. This is nicely consistent with light bent by other masses, but is not a proof.

The rest of the explanation by the "expert" is a mere consequence of his supposition, writing some Relativity equations as if bending by the magnetic field were sure.

Don't let some equations reproduced from a book impress you. There is absolutely nothing convincing in the link. It's a supposition with good-looking writing.

Don't misinterpret me: I make the same supposition.

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Posted (edited)
9 hours ago, Enthalpy said:

There is exactly zero proof in that link. Said expert supposes that the energy of the magnetic field resides in the vacuum, and that light would respond to this energy like observation tells it responds to the mass of a galaxy.

But, sorry, we have observations for galaxies and our Sun only. Bending light with a kilogram of iron was never observed. We ignore what makes the mass of a galaxy, and gravitational lensing was observed where galaxies have no visible mass. Even claiming "only protons, neutrons and black matter bend light" would be consistent with our observations.

And we have observations that the Earth changes the pace of time. This is nicely consistent with light bent by other masses, but is not a proof.

The rest of the explanation by the "expert" is a mere consequence of his supposition, writing some Relativity equations as if bending by the magnetic field were sure.

Don't let some equations reproduced from a book impress you. There is absolutely nothing convincing in the link. It's a supposition with good-looking writing.

Don't misinterpret me: I make the same supposition.

I don't let equations fool me, and my point was simply that mass/energy warps spacetime, that we recognise as gravity, and that light/EMR follows geodesics.

NB: Light/EMR will also warp spacetime due to its momentum, but very insignificantly and probably immeasurable as far as I know.

Of course Earth does not change the pace of time, the warpage that Earth causes in spacetime, sees time vary according to how high or low one is in it.

Edited by beecee

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11 hours ago, Enthalpy said:

Yes. So the electrostatic interaction has a mass, easily measured when considering the interacting particles together.

But when explaining the measured energy levels in hydrogen-like atoms, the mass of the nucleus-electron attraction can't be attributed to the electron. Not all, not one half, not even 1%. These figures are brutal.

1. You have provided no figures. But for H-1 it's -27.2 eV (13.6 eV is still there as KE, so the net energy is -13.6 eV). I don't see how that's "brutal"

2. You can't attribute the mass to any individual particle . The system has the energy, the system loses the energy when it becomes bound.

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We had already this discussion there, with the figures
http://www.scienceforums.net/topic/85377-relativistic-corrections-to-hydrogen-like-atoms/
The 27.2eV correction would be brutal. Twice as big as the relativistic mass, which is a much stronger correction than many others whose effect is quite visible.

"Not to individual particles" differs from your previous statement. But anyway, where is the energy?

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17 hours ago, Enthalpy said:

We had already this discussion there, with the figures
http://www.scienceforums.net/topic/85377-relativistic-corrections-to-hydrogen-like-atoms/
The 27.2eV correction would be brutal. Twice as big as the relativistic mass, which is a much stronger correction than many others whose effect is quite visible.

27.2 is the electrostatic energy term. The KE is 13.6eV. Neither of those are relativistic corrections (i.e. they are from Newtonian physics), and in any event neither is anywhere close to the mass (relativistic or not) of the electron. The net effect is 13.6 eV.

If you take the mass of H-1 and compare it with the mass of a proton and electron, that's what the difference is.

You seem to be claiming otherwise, and yet have provided no details or values to support your claim.

Quote

"Not to individual particles" differs from your previous statement.

Which statement? I referred to the system a while back, so that's not it.

Quote

But anyway, where is the energy?

It has been released from the system, probably in the form of a photon. It could be anywhere.

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Swansont, I'm sure you understand me far better than what you write here. Anyway:

13.6eV is the kinetic energy, which gives a relativistic correction to the electron's mass (or inertia, or call it however you want) in {1-v2/c2}-0.5. The electrostatic energy is twice as big and its effect on the atom's mass is easily measured, at least for the bigger repulsion energy between the protons.

This is already explained and detailed in the other thread
http://www.scienceforums.net/topic/85377-relativistic-corrections-to-hydrogen-like-atoms/

You stated there
https://www.scienceforums.net/topic/117589-energy-contained-in-the-magnetic-field/?do=findComment&comment=1087366
"whatever has the energy has the inertia"
and there, you computed an energy density of a field and compared it with the effect of a mass
https://www.scienceforums.net/topic/117589-energy-contained-in-the-magnetic-field/?do=findComment&comment=1087506
and I'm not pleased with a situation where the electron has no electrostatic energy, the electrostatic interaction has no inertia, but the electron+nucleus+interaction has a mass defect that results from the interaction. This is however what spectroscopy of hydrogenoids tells.

"Where is the energy" or its inertia: here the energy is attractive so it's a mass defect. If you prefer: where is the inertia of the interaction (negative) energy? OK, energy has gone elsewhere, it has increased the mass elsewhere, so the mass of the hydrogenoid at is smaller by the same amount. Where is it smaller? At the electron not, at the field not.

I also propose a different situation, without QM apparently, where the interaction energy is positive (repulsion) and must be accounted in for some purposes and not for others
http://www.scienceforums.net/topic/85377-relativistic-corrections-to-hydrogen-like-atoms/?do=findComment&comment=990276
not pleasant to me neither.

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11 hours ago, Enthalpy said:

Swansont, I'm sure you understand me far better than what you write here.

That would be a poor assumption.

11 hours ago, Enthalpy said:

Anyway:

13.6eV is the kinetic energy, which gives a relativistic correction to the electron's mass (or inertia, or call it however you want) in {1-v2/c2}-0.5. The electrostatic energy is twice as big and its effect on the atom's mass is easily measured, at least for the bigger repulsion energy between the protons.

And how big is it?  KE = (gamma-1)mc^2

The mass energy is 511 keV. Making gamma about 1.000027

The correction is very small. Brutally small, one might say, but I don't think that's what you meant.

11 hours ago, Enthalpy said:

This is already explained and detailed in the other thread
http://www.scienceforums.net/topic/85377-relativistic-corrections-to-hydrogen-like-atoms/

You might want to consider that whatever you presented, it was challenged. So saying "it was explained" is not really precise. You were wrong about some things.

11 hours ago, Enthalpy said:

Yes, and in that context I am correct. Energy is a property, not a substance. It does not exist on its own. If a particle has the energy, then it has the inertia.

11 hours ago, Enthalpy said:

and there, you computed an energy density of a field and compared it with the effect of a mass
https://www.scienceforums.net/topic/117589-energy-contained-in-the-magnetic-field/?do=findComment&comment=1087506

And again, context matters

11 hours ago, Enthalpy said:

and I'm not pleased with a situation where the electron has no electrostatic energy, the electrostatic interaction has no inertia, but the electron+nucleus+interaction has a mass defect that results from the interaction. This is however what spectroscopy of hydrogenoids tells.

I don't care if it pleases you, but I don't recall where anyone has claimed that the electron has no electrostatic energy. Interactions don't have inertia, as that is a property of the particles involved. Atoms and nuclei have mass defects because they release energy when you form them. You have to add energy to separate them (e.g. the 13.6 eV minimum you must add to ionize hydrogen, and the 13.6 eV of photons you will get when an electron becomes bound to a proton)

11 hours ago, Enthalpy said:

"Where is the energy" or its inertia: here the energy is attractive so it's a mass defect. If you prefer: where is the inertia of the interaction (negative) energy? OK, energy has gone elsewhere, it has increased the mass elsewhere, so the mass of the hydrogenoid at is smaller by the same amount. Where is it smaller? At the electron not, at the field not.

Energy is not attractive. The force (or interaction) is attractive.

Where is it smaller? You can't say. The particles are interacting. You can't assign the mass defect to a particular particle, since you don't have individual, isolated particles anymore.

11 hours ago, Enthalpy said:

I also propose a different situation, without QM apparently, where the interaction energy is positive (repulsion) and must be accounted in for some purposes and not for others
http://www.scienceforums.net/topic/85377-relativistic-corrections-to-hydrogen-like-atoms/?do=findComment&comment=990276
not pleasant to me neither.

Yes, you propose a new system. It is not mainstream physics, which is what we are discussing here.

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15 hours ago, Enthalpy said:

This is already explained and detailed in the other thread
http://www.scienceforums.net/topic/85377-relativistic-corrections-to-hydrogen-like-atoms/

!

Moderator Note

Please don't use arguments from speculative threads in mainstream topics. One unsupported claim isn't evidence for another.

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