# Does Magnetism Curve Space and Time

#### gonegahgah

I am wondering if a magnetic force will deviate different mass amounts of the same material through the same path as each other just like gravity does to different mass amounts of any material?

Does anyone know? Has this been tested?

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#### Dr.Brain

Yes Magnetism curves the spacetime just like gravitational field does it, its just that you need special objects to detect them.Just like gravitational field can be felt by masses, magnetic field can be felt by charges.

BJ

#### robphy

Homework Helper
Gold Member
Magnetism curves spacetime via the electromagnetic field's contribution to the stress-energy tensor (the "matter side" of the Einstein equations). In GR, only matter and other non-gravitational forces contribute to the "matter side" of those equations. So, in GR, gravitation and magnetism are not on the same footing.

That "all masses fall the same way in a gravitational field" is based on the equality of gravitational mass and inertial mass.
Intuitively, a Newtonian argument for a point mass m in a gravitational field would run as follows:
ma = Fnet = Fgrav=GMm/r^2
where the first equal-sign is Newton's Second Law and the last equal-sign is the Newtonian Gravitational Force Law. (The "m" on the left is the inertial mass. The "m" on the right is the "gravitational mass".) The result is that a=GM/r^2, independent of the point mass m. The independence of m holds if you complicate the field with more "source masses" Mi arranged in space.

If we run though the corresponding argument for a charged particle in a magnetic field,
ma = Fnet = FLorentz=q(E+vxB). We find a=(q/m)(E+vxB).
Particles with the same charge-to-mass ratio would fall the same way. So, different masses of a homogeneous charged substance would fall the same way. However, if you had different materials [with different (q/m) ratios], they generally wouldn't.

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#### pervect

Staff Emeritus
gonegahgah said:
I am wondering if a magnetic force will deviate different mass amounts of the same material through the same path as each other just like gravity does to different mass amounts of any material?

Does anyone know? Has this been tested?
This should be approximately true as long as the moving material doesn't appreciably change the magnetic field, and as long as the size of the moving material is very small. First order variations or gradients of the magnetic field will averge out in the total force, but second order variations will not, so they must be kept small over the size of the moving material.

I don't know if this has been directly tested.

This is a different question than asking whether magnetism curves space-time (the answer to this question is also yes). Magnetism curving space-time means that a superconducting wire-loop carrying a current will weigh more than an identical wire-loop not carrying a current. You can view this increase in mass as being due to the fact that the magnetic field contains energy. The total mass should increase by L*I^2/2*c^2, which is the amount of energy stored in the magnetic field divided by c^2. However, I haven't done a detailed calculation to show that this is true.

#### gonegahgah

When space-time is curved don't all objects have no choice other than to follow those curves?

#### pervect

Staff Emeritus
An object will follow a geodesic in space-time when there is no other force acting on it. (Gravity is not a force in this context, we are modelling gravity as a curvature of space-time, so it would be incorrect to treat gravity as a force as well).

However, when an external force, such as an electric field acting on a charged particle, acts on a moving object, the object will not follow a geodesic through space-time.

It will follow some other path, which can be computed, but this path will be a different path than the geodesic path it would have followed if there were no force acting on the object.

#### gonegahgah

I don't know? That doesn't sound right.

I have a feeling that magnetism will cause objects to follow a geodesic through space-time and that whereas gravity has G as the constant, magnetism will have different constants for the different materials and compositions of the objects.

G is a constant isn't it?

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yes, but g is not.

#### pervect

Staff Emeritus
gonegahgah said:
I don't know? That doesn't sound right.

I have a feeling that magnetism will cause objects to follow a geodesic through space-time and that whereas gravity has G as the constant, magnetism will have different constants for the different materials and compositions of the objects.

G is a constant isn't it?
We are doing General Relativity here in the "General Relativity" forum, not Kaluza-Klein theory or M-theory, or some other theory. In GR, small test masses (I should add small test masses with no spin) that are subject only to gravitational forces follow geodesics in space-time. They do not follow geodesics when acted on by external forces, such as electric fields.

Other theories may have different formulations, but this is the formulation of Genreal Relativity.

#### gonegahgah

What is Kaluza-Klein theory or M-theory?

Why can't I ask about Magnetism in this forum if it behaves like General Relativity and would then have to be a part of general relativity?

Why do you say only small test masses?

Why can't we refer to gravity as a force when it must be the force of gravity that forces space and time to curve?

#### pervect

Staff Emeritus
Kaluza-Klein theory is a unification of electromagnetism and General Relativity. It treats both electromagnetism and gravity as being due to geometry.

http://en.wikipedia.org/wiki/Kaluza-Klein_theory

has more details. I'm afraid I don't know that much more about it than what's in the Wikipedia.

As the wikipedia mentions, KK theory has some difficulties, especially if you try to extend it to cover more forces than just gravity and electromagnetism.

You can certainly ask about magnetism and general relativity in this forum, but you should expect an answer from the standpoint of general relativity if you ask the question in the relativity forum.

You might try asking your question again in the "Strings Branes and LQG" forum if you want an M-theory perspective. M-theory is the latest incarnation of string theory.

http://en.wikipedia.org/wiki/M-theory

It is a "theory of everything" that tries to unify all forces in one theory.

If you have your own personal theories, you should be aware of the PF guidelines about overly speculative posts from the Theory Development forum.

Overly Speculative Posts:
Physicsforums.com strives to maintain high standards of academic integrity. There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. Posts or threads of an overly speculative nature will be moved to the Theory Development subforum without notice, where discussion may continue in quarantine. Forum staff may choose to lock threads in the Theory Development subform when they decide the topic has run its course. Advertisements of personal theories and unfounded challenges of mainstream science will not be tolerated anywhere on the site, including the Theory Development subforum. Users may not create threads in the Theory Development subforum.
Basically random speculative theories not based any sort of peer-reviewed scientific thought tend to get moved to the Theory Development forum by the moderators.

As far as test masses in GR go, large masses disturb the fabric of space-time. A small non-spinning test mass will follow a geodesic of the hypothetical space-time that would exist without the test mass being present. This statement can be made more rigorous, for instance MTW discuses it more on pg 1126, "Do the planets and suns really move on geodesics".

In the geometric theory of gravity, gravity is not treated as a force. The density of energy and momentum, given by the stress-energy-tensor, determines the curvature of space-time by the relation

G_uv = 8 Pi T_uv

where the left-hand side is a measure of how space curves, and the right side is the stress-energy tensor that describes how mass, energy, and momentum are distributed.

Treating gravity as a force is a hard habit to break, though. Fortunately, there are a few "bridges" between the geometric formulation of gravity, and the treatment of gravity as a force.

One good bridge is Cartan's reformulation of Newtonian gravity in the formalism of curved-space time. (The geodesic equation and the geodesic deviation equation are other useful "bridges" between gravity-as-a-force and gravity-as-geometry).

As you recall, small non-spinning test masses in GR move along geodesics. It is possible to use the formalism of curved space-time to describe a curved space-time that makes object move exactly as if they were subjected to a force of F = GmM/r^2. We have replaced the idea of forces totally, with the idea of objects following geodesics in a curved space-time. The physical behavior of the bodies remains the same.

This exercise does not introduce anything new, but it helps one to understand GR better. Strong gravity fields in GR actually warp space as well as space-time. (Example: just as clocks tick more slowly near a large mass, the meter is shorter. This gravitational length contraction is an illustration of how the geometry of space near a large mass cannot be flat). The warpage of space is very minor for "weak" fields such as the fields we have in our solar system, but it is important in explaining, for instance, the GR prediction that light from a distant star is bent twice the amount by the suns gravity that Newtonian theory would predict.

The formulation of gravity as curved-space time can naturally incorporate this warping of space into the theory, something that is not possible with the idea of "gravity-as-a-force".

#### gonegahgah

Hi Pervect,

You seem to know quite a bit about theories historically and I was wondering if you could possibly help me with something else that I am hoping to find.

I won't go into a theory I have because I realise this is not the place for any non-current theories but I am hoping that you might know if anything has ever been thought of in this respect.

Have any scientists ever considered a possibility of light being a helix (spiral, coil, vortex, etc) instead of a wave. I won't go into why because I know this forum is for educating on current accepted theories only. I'm just interested if you know whether this has ever been considered before and when and by whom?

Thanks if you can help me on this as with my other queries.

#### pervect

Staff Emeritus
I don't know if it will help you much, but there is a circular polarization of light in which the electric field traces out a helical pattern. This doesn't make light any less of a wave, though.

http://www.uwgb.edu/dutchs/petrolgy/genlight.htm [Broken]

Light can also be circularly polarized, with its electric field direction spiraling in a screw pattern.
The classical treatment of light is based on Maxwell's equations, which work very well to describe it, and circularly polarized light is one of the solutions to this set of equations.

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#### gonegahgah

Hi Pervect,

Thanks for trying for me. I've come across that one. It does look a lot like what I mean but does still consider light to just be a wave. If you do ever come across any historical scientific examinations of the possibility anywhere else or recall anything else like this I would love to hear it.

It was a very good try though.
The site you gave me is very thorough while remaining succint. Good site.
Thanks.

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#### Chronos

Gold Member
I like robphy's explanation. Aside from the stress energy contribution, magnetism has no effect on spacetime curvature. If a magnetic field somehow boosted or dampened gravity, a magnet in free fall would deviate from Newtons Laws. Such an effect would be particularly apparent in neutron stars [which have incredibly powerful magnetic fields]. No such effect is observed. All gravitational interactions are nicely accounted for by GR and Newtonian methods.

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