Does electrical-magnetic fields curve spacetime?

[ensabah6]

Does electrical-magnetic fields curve spacetime? Is there time dilation effects in em fields on charged particles?

 

[HallsofIvy]

A non-charged, not-magnetic object is not affected by an electro-magnetic field and follows the same path as if there were no electro-magnetic field. If spacetime were curved by the field that would not be the case.

 

[DaTario]

To say that matter may be composed of non charged objects is a rather daring attitude. Quarks and etc will present allways some sort of reaction to an electro-magnetic field. The field will allways alter the internal field of these elementary particles, inducing forces. These force may of course cancel out inside the composite particle and generate a straight line as one of the possible behaviors.

We know that every energy density may cause some effect in space-time. My opinion is that concentration of electro-magnetic field lines produce effects on space time.

 

[MeJennifer]

Does electrical-magnetic fields curve spacetime?

Not just mass but also energy and pressure contribute to the curvature of spacetime. So the answer is yes.

A non-charged, not-magnetic object is not affected by an electro-magnetic field and follows the same path as if there were no electro-magnetic field. If spacetime were curved by the field that would not be the case.

I think that is incorrect.

Mass, energy and pressure all contribute to the curvature of spacetime. It is true that not all particles are influenced by electro-magnetism but all non-accelerating particles follow the curvature of spacetime and a spacetime containing an electro-magnetic field is obviously curved.

 

[Jonathan Scott]

Does electrical-magnetic fields curve spacetime? Is there time dilation effects in em fields on charged particles?

Electromagnetic fields do not affect space-time except indirectly by carrying tiny amounts of energy and momentum, which give rise to gravitational effects on space-time.

For example, since light beams carry momentum and are deflected by the gravity of a massive body, then conservation of momentum suggests that the light beams generate a tiny gravitational effect on the body, imparting an equal and opposite change in its momentum.

 

[gonegahgah]

If we were to talk about a communely shared space-time - one that everything shares consistently - then it would be difficult to integrate magnetism as it curves the path of some things and not other things.

Then again it even seems tricky to integrate more than one gravity source into a pictorisation of communely shared space-time. I don't know if it is impossible; my source only said it was tricky.

It is fairly easy to draw a 2D representation (in 3D) of a single gravity source with another separate object moving through its 2D plane. It is not easy at all to draw a 2D representation (in 3D) of two or more gravity sources acting on each other. Even overlapping the two individual space-time curvatures (like combining waves) creates a 2D space-time representation not consistent with observation. The greater mass creates a greater dip and the smaller mass creates a smaller dip. Combining the two creates a new landscape with different possibilities but not one that agrees with observation. In general it is difficult to create a 2D (in 3D) combined pictorial space-time landscape in which the larger mass will move towards the smaller mass as we observe (although slower then the smaller moves towards the larger of course).

So even though we have formulas in GR to represent the two body problem (I'm guessing we do) actually modelling these formulas pictorially into a common space-time landscape may be impossible.

If this is correct - and please correct me if I'm waffling nonsense as I would prefer not to - then it may be that a space-time landscape is a localised phenomena anyway. If so then each gravitational body must have its own private space-time surrounding it that other bodies travel through; as a common space-time landscape may not be achieveable.

Is that wrong? Can we represent n-body space-time pictorially? Is there a common space-time landscape through which everything travels; even the sources themselves?

 

[MeJennifer]

Can we represent n-body space-time pictorially? Is there a common space-time landscape through which everything travels; even the sources themselves?

No, GR is a background independent theory. Only the simplest spacetimes can be described with operations over a fixed background.

 

[gonegahgah]

Thanks Jennifer. That has cleared something up for me. In other words there are lot's of independent unconnected space-times; not just a single common space-time field that varies throughout. As to how I should apply that I'm not sure yet.

 

[MeJennifer]

In other words there are lot's of independent unconnected space-times; not just a single common space-time field that varies throughout. As to how I should apply that I'm not sure yet.

No, a universe contains only one particular spacetime.

 

[gonegahgah]

I'm confused now Jennifer.

If there is only one space-time then what is its shape?

From what I've seen a mass distorts space-time; and another mass distorts space-time; but it doesn't seem possible to simply combine their two distortions? If you could then you could create a space-time distortion map which all things would conform too; even the distorters themselves.

Or can we? No-one has said so yet.

 

[MeJennifer]

From what I've seen a mass distorts space-time; and another mass distorts space-time; but it doesn't seem possible to simply combine their two distortions?

It is true that, except for the simplest spacetimes, it is impossible to describe spacetimes by an analytical solution.

For instance, we have a vacuum solution for the spacetime of a point mass but we do not have a solution for a spacetime with three point masses. That does not mean such a spacetime is physically impossible, it only means that we cannot describe it mathematically by using an analytical solution. Numeric approximation or simulation is the best we have so far for those cases.

 

[Naty1]

If so then each gravitational body must have its own private space-time surrounding it that other bodies travel through; as a common space-time landscape may not be achieveable.

Each gravitational body affects a generic spacetime and curves it locally if you ignore smaller and smaller effects over greater distances. But spacetime is dynamic due to rotating planets, galaxies, asteroids and meteor's, exploding stars and vanishing black holes and an expanding universe.

No, a universe contains only one particular spacetime.

To me this means, one 'fabric" of spacetime stretching and deforming over time and distance as the mass, energy and pressures in the universe evolves.

 

[DrGreg]

gonegahgah, I think you were a little confused by MeJennifer talking about "spacetimes" in the plural.

The Universe we live in has only one spacetime, but when we analyse problems, we consider hypothetical spacetimes e.g. containing just one black hole and nothing else. So we can talk about "the spacetime of a non-rotating black hole", "the spacetime of a rotating black hole", "the flat spacetime of empty space" and lots of other spacetimes.

Each of these may locally approximate parts of the true spacetime of the Universe.

 

[granpa]

do electrical-magnetic fields curve spacetime or are electro-magnetic fields the curvature of spacetime? the latter can only be true if there is more than one spacetime manifold. perhaps our 3 dimensional manifol exists in a 4 dimensional manifold which exists in a 5 dimensional manifold and so on. one manifold for each long range force. one for the electrci field. one for the magnetic field. one for gravity. and one for the strong force.

 

[Sjorris]

I'm no GR guru, frankly I have no experience in the field, but I'm wondering, is there something as a 'force' in GR, or does all matter follow the geometry of spacetime? Differently charged particles take on different paths in the vicinity of electric and/or magnetic fields, or so it seems to me and also it follows from Maxwell's equations, so I'm guessing that there actually is 'force' in GR, then the situation seems pretty simple to me. Neutrally charged non-magnetic particles follow the geometry of spacetime, other particles find forces exerted on them which make them divert from the path neutrally charged non-magnetic particles would take.

 

[xantox]

Does electrical-magnetic fields curve spacetime?

Yes. The stress-energy tensor, which is the source of the gravitational field in general relativity, has portions from the electromagnetic field (as well as, in principle, from any other field).

 

[Dale]

Yes. The stress-energy tensor, which is the source of the gravitational field in general relativity, has portions from the electromagnetic field (as well as, in principle, from any other field).

To expand on this: http://en.wikipedia.org/wiki/Electromagnetic_stress-energy_tensor"

 

[gonegahgah]

It is a little confusing. Naty you talk of generic local spacetimes & of still only one space-time fabric in the same post. How do you have many but one?

As an example, if you have two separated same size masses and plonk something in between it will be weightless and won't move towards either. Move the thing in the centre either way then it will begin to drift, accelerating towards the mass it is closer to. So the object in the middle must be on top of a space-time hill. But if it is on top of a space-time hill then how do the two main masses also drift towards each other - as they do - defying the hill? So obviously the object in the middle sees a different landscape to the two masses. It sees a hill top where the two masses don't see that hill top and instead see a down-hill slope all the way towards each other; in defiance of each other's downhills.

Masses generate space-time valleys but have to ignore their own valley otherwise they would not move anywhere. So obviously every mass in the universe has to draw its own space-time landscape that does not match the space-time landscape of any other mass for the same corresponding spaces.

So there may be a common space-time mathematics but their does not seem to be a common single space-time landscape that everything observes.

How then can it be said to be a single fabric if the fabric must have many simultaneous shapes? Is it another quantum phenomena like particle-wave duality?

 

[Dale]

I like the hill and valley analogy, but it is probably more appropriately used to understand Newtonian gravity than GR. In Newtonian gravity the "altitude" of a given location would represent the gravitational potential at that location. In your scenario, one large mass by itself rests at the bottom of a deep valley, but when you add a second large mass then the "sum" of the two valleys results in each mass being slightly off of the deepest point in the valley. They therefore go downhill towards each other despite the fact that between them there is always a "saddle-ridge".

The difference with GR and Newtonian gravity is that with Newton the solution of the two masses is simply the sum of the solutions for each individual mass, but the same is not true for GR.

 

[gonegahgah]

Thanks Dale. I'm not sure the hill and valley analogy fits either Newtonian gravity or GR gravity. Both would struggle with hills in the middle that are somehow defied. GR gravity incorporates velocity and speed of light considerations which Newtonian gravity doesn't. That's probably a simplification but I noticed this in particular.

I can appreciate GR gravity from a mathematical perspective, and I have seen it posited in only this respect on some sites, but for it to generate something physically tangible as space-time seems to me to create problems with n-body situations. Space-time is either only a mathematical match to observation for each one to many calculation or a physical and tangible entity itself. If it is tangible then it must have a polyality (poly-duality) nature; as no two respondents agree on its landscape.

 

[Dale]

Both would struggle with hills in the middle that are somehow defied.

No, this is not a problem. Didn't you see my explanation above:

when you add a second large mass then the "sum" of the two valleys results in each mass being slightly off of the deepest point in the valley. They therefore go downhill towards each other despite the fact that between them there is always a "saddle-ridge".

 

[gonegahgah]

Sorry Dale, what's a saddle-ridge?

 

[granpa]

how do the two main masses also drift towards each other - as they do - defying the hill? So obviously the object in the middle sees a different landscape to the two masses. It sees a hill top where the two masses don't see that hill top and instead see a down-hill slope all the way towards each other; in defiance of each other's downhills.

2 masses on a rubber sheet won't drift toward one another because of the ridge between them?

 

[Dale]

Sorry Dale, what's a saddle-ridge?

It is a local maximum in one direction (the line from one mass to the other) and a local minimum in the other direction (the perpendicular bisector of the first line).

 

[gonegahgah]

Can you provide me with a picture Dale? I don't understand.

 

[jtbell]

Imagine a pass between two mountains that are next to each other. You can cross the pass by coming up from the lowlands on one side and then going down into the lowlands on the other side, in which case the pass is a local maximum. Or you can cross the pass by coming down from one mountain and then going up the other one, in which case the pass is a local minimum.

 

[Dale]

Can you provide me with a picture Dale? I don't understand.

Here is a picture of a http://en.wikipedia.org/wiki/Image:Saddle_point.png"

 

[Naty1]

Naty you talk of generic local spacetimes & of still only one space-time fabric in the same post.

My post #12 was explained, I believe, using different words in post # 13. I meant nothing more than that...one common/generic coordinate grid of spacetime with different shapes in different locations...blackhole vicinities look very different than "empty" space for example...they would at first appear to just sit still...

In your post "It's a little confusing"... I don't think your picture of the two distant masses is accurate because, equivalently, we could say the rubber sheet analogy is weak...the rubber sheet analogy goes only so far...it doesn't work so well for two distant masses of equal size.

when you mention two bowling balls...think of them instead first as very close together...they will still be in their own troughs...but the peak between them is lower the closer the balls...the peak between them is lower than the level to the outer sides...so the balls would drift together, or should be envisoned to do so, even though their individual local trough is lower than the peak in the middle...when these masses are distant from each other, you'd never notice the slight depression in the trough...the low gravitational attraction...so they might appear to sit still when we know there is attraction...

 

[gonegahgah]

Thanks for the picture Dale. Good explanation of saddle-ridges too jt.

I can also understand your explanation now Dale. As you said, for two masses the summation of the two overlapping dips produces an alteration to the valleys produced by the masses so that centre of the valleys are slightly away from where the centre of the masses are in the direction towards each other. And the amount of alteration to a respondent's valley is equivalent, no matter the respondent's mass, because the source's effect at each radii is independent of the respondent.

Crystal clear now, thanks Dale.
It is possible to draw a point-in-time space-time landscape that all objects conform to (in 2D slices drawn in 3D).
Very good.

 

[Dale]

Excellent! Glad that helped.