Does an electric charge curve spacetime ?

[Antonio Lao]

I'm afraid I can't make any sense of Antonio's second post, I'm not sure what he's trying to say.

what i mean, without going into a lot of mathematical jargons, is that infinite mass of GR leads to a singularity but infinite spacetime curvatures of positive and negative structures from polarization of localized gauge fields (hence structures for electric charge, weak charge, and color charge) lead to a viable theory of quantum gravity.

Note:

GR deals with only one singularity but a workable quantum theory of gravity will have to deal with two singularities for both positive and negative curvature.

 

[selfAdjoint]

AFAIK ther's no infinite mass in GR. The singularity inside a black hole is a finite mass confined in zero volume; infinite density.

 

[Antonio Lao]

selfAdjoint,

Thanks for your clarification.

 

[Gonzolo]

"This means that _uncharged_ particles, following a geodesic, will not follow the same path near a charged black hole as they will near an uncharged one with the same mass."

This is interesting. Are these charges necessarily paired up as dipoles? Or does it include the case of a net charge (+ or -)? This would apply no only to black holes, but also to a body with finite and measurable volume (i.e. a balloon or static-charged balloon), wouldn't it?

 

[pervect]

"This means that _uncharged_ particles, following a geodesic, will not follow the same path near a charged black hole as they will near an uncharged one with the same mass."

This is interesting. Are these charges necessarily paired up as dipoles? Or does it include the case of a net charge (+ or -)? This would apply no only to black holes, but also to a body with finite and measurable volume (i.e. a balloon or static-charged balloon), wouldn't it?

The metric I gave the URL for (Reisner-Nordstrom, abbreviated as R-N from here on) describes a charged black hole, a black hole with a net charge. Physically, if the BH has a positive charge, the negative charges would have to be located somewhere. Such charges are _not_ included in the metric I gave, however.

You would use the R-N metric to describe the external gravitational field of a highly charged spherically symmetric body, just as you would use the Schwarzschild metric to describe the gravitational field of an uncharged spherically symmetric body.

You'd model the electric field of such a black hole as Q/r^2, (just like the columb field) in the R-N coordinates.

This is a purely classical solution - it doesn't include quantum effects, such as particle pair production from intense electric fields (the Schwinger critical field limit).

 

[Gonzolo]

Thanks, this is just about my level of talk when it comes to GR.

(although, I would tend to believe it is in great part because I haven't chosen to completely dive into it yet...the 1916 paper is the only formal litterature I have, and I can confirm that it is not the best for an introduction to the subject...)

 

[pervect]

what i mean, without going into a lot of mathematical jargons, is that infinite mass of GR leads to a singularity but infinite spacetime curvatures of positive and negative structures from polarization of localized gauge fields (hence structures for electric charge, weak charge, and color charge) lead to a viable theory of quantum gravity.

This looks like a case where the mathematical jargon might be more comprehensible than the English :-).

From what I can make out you are not doing an analysis based on General Relativity. Exactly what it's based on isn't too clear at this point - here's an opportunity for a simple description, such as - string theory, M theory, loop quantum gravity, or none of the above.

 

[Antonio Lao]

pervect,

Can You help me visualize the various intersections of a surface of positive curvature and a surface of negative curvature?

 

[pervect]

I'll assume that the answer is "other theory" until I hear different.

The usual visual aid/3d representation for/of a negative curvature is a saddle surface, for a positive curvature a sphere. So I guess you'd have to visualze a sphere intersecting a saddle surface, though I"m not sure why or what you are visualizing.

 

[Antonio Lao]

pervect,

Since both the saddle and sphere are both described by some sort of parametric equations of differential geometry (a subject of which I have little knowledge of), their intersections can become simultaneous solutions of their interactions when the parameters are quantitified as time, mass, force, or energy functions. Can I take this for granted? I am looking for some minimum geodesics. Perhaps, a geodesic that is equivalent to the Planck length?

 

[raodhananjay]

I am a statistician, I wanted to know whether light is a wave or a particle ? And what is light in string theory ?

 

[selfAdjoint]

I am a statistician, I wanted to know whether light is a wave or a particle ? And what is light in string theory ?

Short answers. Yes. and The Same.

Longer answer, since early in the twentieth century light has been viewed as having both particle and wave properties. Which property you see depends on what experiment you do; if your experiment concerns, say, frequency or interference you will detect waves, and if you do an experiment based on momentum, you will detect particles. This idea actually came out of experiments, not theory, and it was only later includied in the growing theory of quantum mechanics.

String theory builds particles at the wave level out of string vibrations, so it basically supports this wave/particle duality.

 

[juju]

This means that _uncharged_ particles, following a geodesic, will not follow the same path near a charged black hole as they will near an uncharged one with the same mass.

This should, in theory, be testable using neutral particles in a large electric field. If it is true for black holes it should be true everywhere.

Here's another thought.

The curvatures (positive and negative) do not need to be thought of as being in the same direction as the gravitational curvature. They can be looked at as being orthogonal to it.

They can also be looked as a twisting of space/time, rather than a curvature.

juju

 

[gptejms]

I have a question:-from the little bit that I know,any physical field except the gravitational is a part of T_{mu,nu} and causes curvature.Has any experiment
ever been done which shows that the electromagnetic field causes space-time
curvature?Are static fields from charges also included in T_{mu,nu}?

 

[raodhananjay]

Thanks for the reply. Sorry I would love fire in some more so please ...
In the duality priniciple , how does it explain an energy dissipation ?

Another question is as how does Light travel continously for an infinitely long distance (say sun to Earth )?

Atmosphere starts at some good distance above Earth's surface then in absence of vacuum , shouldn't the light get decayed ?
If you answer that its too powerful so it reaches us then shouldn't be too bright and hot above Earth atmosphere.

 

[Nereid]

Welcome to Physics Forums raodhananjay!

A suggestion if I may: your questions are good ones, but are not related to relativity, or to whether (and to what extent) electric charges curve spacetime - perhaps you could start a thread with these questions, in Quantum Mechanics?

In the duality priniciple , how does it explain an energy dissipation ?

It doesn't, directly; dissipation involves absorption (and, maybe, re-emission).

Another question is as how does Light travel continously for an infinitely long distance (say sun to Earth )?

As far as we can tell, there is no limit to how far light can travel. The furthest we've seen - and indeed, the further we can ever see - is the surface of last scattering, approx 13 billion light-years.

Atmosphere starts at some good distance above Earth's surface then in absence of vacuum , shouldn't the light get decayed ?

Some of the photons incident on the top of the Earth's atmosphere are indeed absorbed or scattered; astronomers measuring the apparent magnitude of a star include a correction - called 'air mass' - in their data reductions.

 

[pervect]

I have a question:-from the little bit that I know,any physical field except the gravitational is a part of T_{mu,nu} and causes curvature.Has any experiment
ever been done which shows that the electromagnetic field causes space-time
curvature?Are static fields from charges also included in T_{mu,nu}?

T_{mu,nu} = T_{\mu \nu} is the stress energy tensor, and as was previously mentioned, yes, the static electric field generates terms in the stress-energy tensor. As was also mentioned, the contribution is a trace-free one. This means that Baez's ball of perfectly electrical neutral coffee grounds

http://math.ucr.edu/home/baez/gr/outline2.html

don't change in volume (gravitate together) because of the electric field, as the trace of the stress-energy tensor determines R₀₀. However, the presence of the electric field does curve space-time.

 

[gptejms]

pervect,thanks for your answer.I repeat the second part of my question:-has any experiment ever been done which shows that the electromagnetic field causes space-time curvature?

 

[Nereid]

pervect,thanks for your answer.I repeat the second part of my question:-has any experiment ever been done which shows that the electromagnetic field causes space-time curvature?

If you don't mind, I'd like to ask a slightly different question ... with our current experimental capabilities, *could* we do an experiment which would show that an 'electromagnetic field causes space-time curvature'? In principle, what would an experiment to test the idea look like?

 

[gptejms]

Your question 'suggests' to me that with our present capabilities,we can't produce such high intensity electromagnetic fields---enough to cause any significant spacetime curvature.Can you give an order of magnitude calculation to give us an idea?An experiment to test the idea could look like this---if light bends in region of such a high intensity electromag. field(perhaps we could concentrate on just the magnetic field and try producing extraordinarily strong magnets)then we would know that the curvature has been produced.But I am sure there must be better ways around.

 

[pervect]

There are some relevant experimental tests, but they may not be very satisfying. For instance, Eotvos type tests comparing aluminum and gold.

Columb energy, (i.e. the energy in the electrostatic field), which is proportional to [nuclear charge]^2, amounts in a gold nucleus to .4 percent of the mass, but only .1 percent of the mass in an aluminum nucleus. Very sensitive experiments have been done to detect any differences in gravitational forces on aluminium and gold, (testing the principle of equivalence), but none have been found.

 

[Nereid]

Your question 'suggests' to me that with our present capabilities,we can't produce such high intensity electromagnetic fields---enough to cause any significant spacetime curvature.Can you give an order of magnitude calculation to give us an idea?An experiment to test the idea could look like this---if light bends in region of such a high intensity electromag. field(perhaps we could concentrate on just the magnetic field and try producing extraordinarily strong magnets)then we would know that the curvature has been produced.But I am sure there must be better ways around.

Let's think about this from the PoV of what the most intense EM fields and greatest spacetime curvature is, in the present universe, and later we'll examine whether any of these are amenable to tests - even in principle - of well-formed hypotheses. OK?

First, the most intense magnetic fields, in the present universe, are likely to be http://solomon.as.utexas.edu/~duncan/magnetar.html , whose fields are likely to be as many OOM stronger than the strongest we can generate here on Earth is greater than the Earth's own field.

Next, the most energetic gammas may well have a comparable 'curvature effect' to objects whose gravity we can measure. For example, we have 'seen' TeV gammas from the Crab pulsar (or nebula), and expect that GRBs emit PeV or higher gammas (such energetic gammas probably cannot propagate clear across the universe, but as we've 'seen' a couple of nearby AGN in TeV, perhaps a nearby GRB might be 'visible' in PeV gammas). Homework question: if a TeV gamma were converted (magically) into a lump of baryons (yes, it would be magic!), what would the mass of that lump be?

Next (2), it may be that a 'long duration' GRB results in the formation of black hole whose mass is several times that of the Sun. If the progenator star had a magnetic field, it may be that, in the last few microseconds before the BH formed, that field reached an intensity which makes a magnetar's field look like a fridge magnet. Too, the spacetime curvature would be far more extreme than that around the Sun (which has provided the most sensitive tests of some aspects of GR to date).

Finally, as the two neutron stars in a binary merge/collide (they lose energy as gravitational waves; without some external event, a collision is certain), many kinds of extreme environments will likely be created.

Closer to home, you might like to read the reports of the Fundamental Physics Working Group (it's in the middle of the page), from the recent ESA Cosmic Visions workshop. Do you feel that any of the proposed (local) experiments would test a hypothesis related to spacetime curvature resulting from EM?

 

[Gonzolo]

You lost me with GRB and AGN.

But surely, one could calculate the deviation of a beam of light due to an earth-built electric or magnetic field, even if the deviation is in order of femtometers or less.

I finally received my first book on tensors. GR is next. Hopefully, I'll see what the difficulty resides.

 

[Nereid]

You lost me with GRB and AGN.

Gamma ray burst, active galaxy nuclei (http://www.ulo.ucl.ac.uk/~diploma/year_one/heasarc.gsfc.nasa.gov/docs/objects/agn/agntext.html ).

But surely, one could calculate the deviation of a beam of light due to an earth-built electric or magnetic field, even if the deviation is in order of femtometers or less.

You mean, for example, moving a strong permanent magnet close to and away from a LIGO arm?

 

[raodhananjay]

Thanks NEREID . Sorry , you are right , I guess should be asking related questions. Let's start now, I had been inspired by one of the posts , hence I started my queries here. Otherwise although the header " electric .. " of this thread made me curious , I am kind of lost here. Ok Is Somebody ready to do small revision or introduction of things you do here. PLEASE somebody do that for me.

 

[Gonzolo]

Gamma ray burst, active galaxy nuclei (http://www.ulo.ucl.ac.uk/~diploma/year_one/heasarc.gsfc.nasa.gov/docs/objects/agn/agntext.html ).You mean, for example, moving a strong permanent magnet close to and away from a LIGO arm?

Exactly, but perhaps an electrically-generated magnet instead (MRI systems etc.). I would think that superconducting AC would generate the strongest human-made B-fields possible.

 

[Nereid]

Re-reading some of the posts near the start of this thread gave me the idea that perhaps we should be a little more precise about what any experiment is trying to test.

Gonzolo started this thread with a question about whether electric charge could 'curve spacetime', and in the last few posts we've been discussing whether a magnetic field can 'deflect' a beam of light. Would someone please be kind enough to explain why a non-null result in the latter would lead one to conclude 'yes, it can' for the former?

 

[Gonzolo]

I assume that in free space, all that can deflect a beam of light is space-time curvature. So whether the electric charge is moving (B-field) or not (E-field) can be seen as a detail (although certainly not for calculations). The question is for EM in general.

 

[juju]

Hi,

If EM fields curve space/time then time dilation effects should be seen. These would manifest in the changing of particle decay rates.

juju

 

[Calculex]

Re-reading some of the posts near the start of this thread gave me the idea that perhaps we should be a little more precise about what any experiment is trying to test.

Gonzolo started this thread with a question about whether electric charge could 'curve spacetime', and in the last few posts we've been discussing whether a magnetic field can 'deflect' a beam of light. Would someone please be kind enough to explain why a non-null result in the latter would lead one to conclude 'yes, it can' for the former?

I have a similar problem with the question. Curvature of space-time necessarily means that the frames of reference of all inertial observers would we affected. Since only charged masses would be affected by the presence of another electric charge, electrically neutral masses would measure time and space without being affected. How can this be a curvature of space-time?

Besides, Maxwell's equations state that the speed of propagation of an electromagnetic wave depends only on the values for \epsilon_0 and \mu_0 (the permittivity and permeability constants for space). These are experimentally derived and and neither of these constants depend on the magnitude of the respective electric or magnetic fields.

Calculex