Energy contained in the magnetic field

[Danijel Gorupec]

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)

[beecee]

11 hours ago, 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)

And a happy new year to you also. Photons/light due to there momentum curve/warp the spacetime they are traversing, albeit ever so very slightly. So, yes magnetic fields would also curve/warp spacetime.  

I would doubt though that any path of light would be directly affected by the magnetic field/s, but I'm fairly sure there are others here that can answer that more positively.

Edited January 1, 2019 by beecee

[Enthalpy]

Every energy has an inertia, and attracts massive objects, and is attracted my massive objects, so at least conceptually, the magnetic field would change the path of nearby stars, of light, and so on.

One banal example, but with the electrostatic field, is the mass of heavy elements. As more nucleons compose a nucleus, from hydrogen to iron and beyond, the strong force releases attraction energy, and iron is lighter than expected from a sum of protons, electrons and neutrons. But as more protons (and neutrons) are added beyond iron, the electrostatic repulsion between the protons increases, and atoms get not-so-light per nucleon as iron. This mass resulting from the electrostatic field is commonly measured on decent scales, or by electromagnetic deflection.

Still very obscure to me: the inertia of the interaction energy doesn't count when we compute the acceleration of the particles due to that interaction. So this mass depends on the observer and possibly on the use he wants to make of it.

There would probably be practical difficulties to an observation using the magnetar, as our knowledge of its mass "without the magnetic field" is supposedly too imprecise to check if the magnetic energy makes a difference.

Besides gravitational effects, strong magnetic fields might act on light by other means. Experiments on Earth, with limited human technology, have shown none, to my limited knowledge.

[swansont]

21 minutes ago, Enthalpy said:

Every energy has an inertia, and attracts massive objects, and is attracted my massive objects, so at least conceptually, the magnetic field would change the path of nearby stars, of light, and so on.

Energy isn’ a substance. It is a property. Whatever has the energy is the thing that has inertia.

21 minutes ago, Enthalpy said:

Still very obscure to me: the inertia of the interaction energy doesn't count when we compute the acceleration of the particles due to that interaction. So this mass depends on the observer and possibly on the use he wants to make of it

The inertia of the interaction energy? What you have called interaction energy has been released, so it’s not part of the system.

 

 

[Danijel Gorupec]

1 hour ago, Enthalpy said:

There would probably be practical difficulties to an observation using the magnetar, as our knowledge of its mass "without the magnetic field" is supposedly too imprecise to check if the magnetic energy makes a difference.

Besides gravitational effects, strong magnetic fields might act on light by other means. Experiments on Earth, with limited human technology, have shown none, to my limited knowledge.

Thanks. My thinking is that even with our current knowledge some rough estimates could be made on what percentage of magnetar's mass is contained in its magnetic field outside of its compact body. Probably then someone could estimate how much a light beam (passing close to magnetar compact body) would deflect - that is, what is the difference in this deflection depending on the mass distribution (all mass within the compact body versus some mass outside of the compact body)...  My math knowledge is probably way too limited to make such an estimation.

The general idea is to have observational confirmation that mass-energy really is spread in the field. But i cannot estimate if such observation is only a distant dream or something that is achievable.

Absolutely agree that there is a fear that such strong magnetic fields might act on light by other means than by space-curving (causing too much 'noise' for precise measurement).

One thing  that I am just thinking about - if the magnetic field of a magnetar quickly wobbles somehow (as that of a pulsar), the path of a light beam could wobble at the same frequency. Maybe this wobbling could help us with our measurements (it is sometimes easier to measure some oscillatory signal).

[beecee]

1 hour ago, Danijel Gorupec said:

Thanks. My thinking is that even with our current knowledge some rough estimates could be made on what percentage of magnetar's mass is contained in its magnetic field outside of its compact body. Probably then someone could estimate how much a light beam (passing close to magnetar compact body) would deflect - that is, what is the difference in this deflection depending on the mass distribution (all mass within the compact body versus some mass outside of the compact body)...  My math knowledge is probably way too limited to make such an estimation

 

4 hours ago, beecee said:

I would doubt though that any path of light would be directly affected by the magnetic field/s, but I'm fairly sure there are others here that can answer that more positively.

OK some research and I found this Q+A site....

https://van.physics.illinois.edu/qa/listing.php?id=2009&t=light-and-magnets...-and-gravity

:Q:"How far can a magnetic field bend light? Could it be bent enough so that it goes around a three dimensional object and comes out (after going 180 degrees, I guess) the other side, being bent by the magnet, therefore making it seem as though the object had the light bass through it completely, and it does not appear to the human eye? Here is the best example I can give: -->=light, O=Object, *=mag. field, / or \=light bent. ___ |***| If this can be done, please tell --->/*O*\---> me how, and what would be needed to perform such a thing. Thank you. (PS - This would need to be done in a round sense, as in all around the 3-d object, not in just one line, so please keep that in consideration. Also, if you know any other way to get the desired effect please inform me.)"

:A: "Nice try. Unfortunately, the path light takes is not affected by the presence of a magnetic field. Light itself is composed of an oscillating electric and magnetic field, and one very important property of electric and magnetic fields is what we call "linearity." That is, if you have two sources of electric and/or magnetic fields, you can predict what the combined field is just by adding the two source fields together. The two fields don’t change each other at all. So if you add the field of a light ray to any other field we can imagine, the light ray will continue as before and the extra field will just stay the same, adding to it in places where the extra field is strong, but having no effect beyond the reach of the extra field. So there is no way that a magnetic field can bend light. 

Although magnetic fields might not do the trick for you, there is quite a bit more about light that can be taken advantage of. For instance, if the object is very small (small compared to the wavelength of the light), the light will simply diffract around the object and be invisible or nearly so anyway. Please see our . 

Also, even though a magnetic field won’t do anything for the light, a gravitational field, sufficiently strong, will in fact bend light. This was observed early in the 20th century confirming Einstein’s General Theory of Relativity in which light from the planet Mercury was bent by a very tiny amount by the enormous gravitational field of the sun. Unfortunately they needed a total solar eclipse to block out the bright sun’s rays so they could see the feeble light from Mercury on the other side of the sun passing close by where the effect was big enough to be measured. 

One of the more spectacular demonstrations of bending light by a gravitational field is "gravitational lensing" of light from very faraway bright objects whose light passes close by another distant object with plenty of mass. Here is a description, along with some *very* nice pictures: 

. 

The problem with making an object invisible in this way is that the light cannot be bent any way desired -- what you get is just lensing, and you get multiple images of the object in back of the object doing the light-bending. An object like this will attract quite a lot of attention! These galaxies sure attracted our attention. And you need a galaxy-sized gravitational field to do the trick. 

To make a gravitational "invisibility cloak" requires quite a strong gravitational field. Maybe the best way to do it is to have such a strong field that the light just gets sucked into the object and cannot come out. Then you have a black hole. Not invisible because you can tell that your light is gone, but interesting nonetheless. Here’s a tutorial on black holes: 



Now the disclaimers back on your original question: If your magnetic field is strong enough over a large enough distance, you can have enough energy stored in it to do gravitational lensing, and then refer to the above answer on gravitational lensing. This however is a very difficult way of getting a strong gravitational field. It is much easier just to collect a galaxy’s worth of matter than to collect the equivalent energy in a magnetic field (neither is particularly easy, I admit!) 

The second disclaimer is that there is a small expected deviation from linearity of electric and magnetic fields due to quantum mechanics and the ability of electrons to pop out and go away on microscopic time scales. This only becomes noticeable for very very high frequency light colliding with other very very high-frequency light (it wouldn’t be noticeable and may even have exactly zero effect for a static magnetic field and visible light -- I haven’t done any calculations). There are plans to make such a light-light collider, but it requires a many-mile electron accelerator to get the energy of the light high enough. 

If you are really interested in getting light to go around a solid object so that it looks like it went through, the low-tech solution might be the easiest. Magicians use mirrors for this purpose all the time!" 

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[Danijel Gorupec]

7 hours ago, beecee said:

 

OK some research and I found this Q+A site....

...

:A: "Nice try. Unfortunately, the path light takes is not affected by the presence of a magnetic field. Light itself is composed of an oscillating electric and magnetic field, and one very important property of electric and magnetic fields is what we call "linearity." That is, if you have two sources of electric and/or magnetic fields, you can predict what the combined field is just by adding the two source fields together. The two fields don’t change each other at all. So if you add the field of a light ray to any other field we can imagine, the light ray will continue as before and the extra field will just stay the same, adding to it in places where the extra field is strong, but having no effect beyond the reach of the extra field. So there is no way that a magnetic field can bend light. 

...

If you are really interested in getting light to go around a solid object so that it looks like it went through, the low-tech solution might be the easiest. Magicians use mirrors for this purpose all the time!" 

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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.

[swansont]

3 hours ago, 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.

How big is it?

 

[Q-reeus]

4 hours ago, 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.

You were quite right to question validity of that earlier quote-mined passage claiming a magnetic field has *no* effect on a light trajectory. In GR any source of stress-energy-momentum density is a source of gravitation. And a magnetic field is at least a source of energy density and stress (Maxwell stresses). So it for sure will contribute to bending of a light trajectory. At 'normal' terrestrially available magnetic energy densities, the effect is minuscule. What that quote-mined passage was evidently implying was there is no appreciable *electromagnetic* coupling between a magnetic field and EM radiation. Even there, at extremely high magnetic field energy densities, QED nonlinearities come into play and there is actually a non-zero coupling - 'vacuum birefringence' e.g. https://cds.cern.ch/record/357780/files/9806417.pdf

 

[Danijel Gorupec]

3 hours ago, swansont said:

How big is it?

 

Wikipedia claims some 10^10 tesla.

[swansont]

2 hours ago, Danijel Gorupec said:

Wikipedia claims some 10^10 tesla.

the energy density of a magnetic field is B^2/2u      u (mu) is the permeability

That's about 10^26 J/m^3, or a density equivalent of 10^9 kg/m^3  

 

Neutron stars have a density of about 10^17 kg/m^3

IOW, the energy contained in the magnetic field is small compared to the mass of the star

 

 

 

 

[Danijel Gorupec]

35 minutes ago, swansont said:

IOW, the energy contained in the magnetic field is small compared to the mass of the star

Yes, I need to accept that it would be too difficult to detect light-beam path deviation due to field mass. Thanks.

[Enthalpy]

On 1/1/2019 at 10:49 PM, swansont said:

Energy isn’t a substance. It is a property. Whatever has the energy is the thing that has inertia.

No, that's wrong. The energy of an electron in a hydrogen-like atom (1 electron, many protons) is properly computed with the relativistic mass correction and without the mass correction of the electrostatic attraction. This correction would be much bigger than the experimental accuracy, so the electron and the nucleus don't bear the interaction mass. We had already this discussion.

Problem is, I ignore where the interaction's mass is. Or worse, it exist for some observations but not for some others, even for one single observer if I grasp it properly.

On 1/1/2019 at 11:52 PM, Danijel Gorupec said:

One thing  that I am just thinking about - if the magnetic field of a magnetar quickly wobbles somehow (as that of a pulsar), the path of a light beam could wobble at the same frequency. Maybe this wobbling could help us with our measurements (it is sometimes easier to measure some oscillatory signal).

That would be fantastic. Swansont computed the magnetic energy to me much smaller than the neutronium's mass, but the magnetic field has a very strong pattern, shrinking to zero at some positions. If the distribution of the neutronium's mass is even enough, or has a distinct shape, maybe the effect of the magnetic field can be distinguished.

With (how much?) chance, a magnetar exists that bends light from two farther sources passing very close and less close to it. Then the comparison of the wobbles would tell if all the mass-energy that bends the light is below the surface... except that we probably don't have the necessary accuracy.

[swansont]

33 minutes ago, Enthalpy said:

No, that's wrong. The energy of an electron in a hydrogen-like atom (1 electron, many protons) is properly computed with the relativistic mass correction and without the mass correction of the electrostatic attraction. This correction would be much bigger than the experimental accuracy, so the electron and the nucleus don't bear the interaction mass. We had already this discussion.

Problem is, I ignore where the interaction's mass is. Or worse, it exist for some observations but not for some others, even for one single observer if I grasp it properly.

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.

[Danijel Gorupec]

9 hours ago, Enthalpy said:

With (how much?) chance, a magnetar exists that bends light from two farther sources passing very close and less close to it. Then the comparison of the wobbles would tell if all the mass-energy that bends the light is below the surface... except that we probably don't have the necessary accuracy.

I understand the method, great! In fact, it occurs to me that even one single light source, passing slowly through the magnetic field, can be used - its light should, if conditions are preferable, display larger wobbling amplitude as it approaches the magnetar's surface. This actually could provide some mass-energy distribution information.

Edit: I still think, however, that our instruments cannot do it - eight orders of magnitude, calculated by Swansont, seems as a too large obstacle.

Edited January 5, 2019 by Danijel Gorupec

[Q-reeus]

54 minutes ago, Danijel Gorupec said:

I understand the method, great! In fact, it occurs to me that even one single light source, passing slowly through the magnetic field, can be used - its light should, if conditions are preferable, display larger wobbling amplitude as it approaches the magnetar's surface. This actually could provide some mass-energy distribution information.

Edit: I still think, however, that our instruments cannot do it - eight orders of magnitude, calculated by Swansont, seems as a too large obstacle.

But maximum magnetic field can be according to the Wiki article 'greater than 10^11 Tesla'. That bumps up the field energy density by more than two orders of magnitude.
But only over a relatively short time frame given field decay is in theory fairly rapid.

[Danijel Gorupec]

4 minutes ago, Q-reeus said:

But maximum magnetic field can be according to the Wiki article 'greater than 10^11 Tesla'. That bumps up the field energy density by more than two orders of magnitude.
But only over a relatively short time frame given field decay is in theory fairly rapid.

Yes, but I don't know how much is this 10^11 estimation reliable. Also, it might be the density figure within the magnetar's body (wikipedia is not clear about it). It is also very unlikely that our magnetar will be perfectly aligned to make optimal conditions for our measurements. That's why I opted for the more conservative 10^10 value.

Another obstacle, I think, is that the physical size of the field is way too small - several tens of kilometers in diamter. How much would an occultation from such a small object last - a fraction of a second? I guess it is too small to make measurement, but I actually don't know.

[Q-reeus]

1 hour ago, Danijel Gorupec said:

Yes, but I don't know how much is this 10^11 estimation reliable. Also, it might be the density figure within the magnetar's body (wikipedia is not clear about it). It is also very unlikely that our magnetar will be perfectly aligned to make optimal conditions for our measurements. That's why I opted for the more conservative 10^10 value.

Another obstacle, I think, is that the physical size of the field is way too small - several tens of kilometers in diamter. How much would an occultation from such a small object last - a fraction of a second? I guess it is too small to make measurement, but I actually don't know.

And even then best to consult a specialist astrophysicist who could guess well enough if the general environment would be clean enough for a magnetic field gravitationally induced deflection to be extracted. For instance the mass quadrupole moment of magnatar might well dominate as a first order correction to spherical mass approximation. And maybe geodetic effect too (just guessing here). It's the specialist's job to try and account for all such things but such headaches I happily leave to them.

[swansont]

3 hours ago, Q-reeus said:

For instance the mass quadrupole moment of magnatar might well dominate as a first order correction to spherical mass approximation.

Even if this were the case, why would it matter? 

[Q-reeus]

6 hours ago, swansont said:

Even if this were the case, why would it matter? 

Because a quantitative evaluation of one influence has to be somehow extracted from that of existent competing ones. Even the very spatial form of a given magnatar magnetic field might evolve drastically over time and be very different at a given time to the naive expectation of a simple dipolar distribution.

[swansont]

33 minutes ago, Q-reeus said:

Because a quantitative evaluation of one influence has to be somehow extracted from that of existent competing ones. Even the very spatial form of a given magnatar magnetic field might evolve drastically over time and be very different at a given time to the naive expectation of a simple dipolar distribution.

But you were talking about the correction, of a higher-order mass distribution term. How big is that correction?

[Q-reeus]

19 minutes ago, swansont said:

But you were talking about the correction, of a higher-order mass distribution term. How big is that correction?

I'm not that specialist astrophysicist that would have a good handle on the answer. Just the quadrupole moment itself would depend on such specifics as spin rate and mass and detailed EOS for starters. All I pointed out was perturbing influences other than an ab initio assumed dipolar form magnetic field will be present and need to be considered. Any disagreement there?

Edited January 6, 2019 by Q-reeus

[swansont]

39 minutes ago, Q-reeus said:

I'm not that specialist astrophysicist that would have a good handle on the answer. Just the quadrupole moment itself would depend on such specifics as spin rate and mass and detailed EOS for starters. All I pointed out was perturbing influences other than an ab initio assumed dipolar form magnetic field will be present and need to be considered. Any disagreement there?

If the quadrupole mass term is small, then it won’t matter if the magnatic contribution is similar. In order for it to matter, the magnetic term needs to be appreciable, as compared to the mass. Do you have any evidence that it is?

[Q-reeus]

20 minutes ago, swansont said:

If the quadrupole mass term is small, then it won’t matter if the magnatic contribution is similar. In order for it to matter, the magnetic term needs to be appreciable, as compared to the mass. Do you have any evidence that it is?

Of course not. I'm not the one here proposing a possible optical test of gravitational deflection by a magnatar magnetic field. Everyone agrees it would be tiny compared to the primary gravitational influence namely magnatar mass. Just how small and how much other competing factors will potentially mask it is - to keep repeating - subject to many specifics, all in the realm of specialist astophysicists! I'm not a specialist astrophysicist.

[beecee]

On 1/3/2019 at 12:29 AM, Q-reeus said:

You were quite right to question validity of that earlier quote-mined passage claiming a magnetic field has *no* effect on a light trajectory. In GR any source of stress-energy-momentum density is a source of gravitation. And a magnetic field is at least a source of energy density and stress (Maxwell stresses). So it for sure will contribute to bending of a light trajectory. At 'normal' terrestrially available magnetic energy densities, the effect is minuscule. What that quote-mined passage was evidently implying was there is no appreciable *electromagnetic* coupling between a magnetic field and EM radiation. Even there, at extremely high magnetic field energy densities, QED nonlinearities come into play and there is actually a non-zero coupling - 'vacuum birefringence' e.g. https://cds.cern.ch/record/357780/files/9806417.pdf

 

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.....

https://www.quora.com/Can-a-magnet-bend-light

Q: Can a magnet bend light?

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

Answered Sep 27, 2017

 

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 λμFνλ−14FσλFσλgμν)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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A probable lesser know fact is that light/photons themselves also ever so very slightly, warp spacetime due to their momentum....

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.

Yep, that's all I'm saying in relation to spacetime curvature and the geodesic path of light, and I believe important. 

Edited January 6, 2019 by beecee