Does an electric charge curve spacetime ?

[Gonzolo]

Does an electric charge "curve spacetime"?

If theorists (starting with A. E.) can make a theory about spacetime curvature caused by mass (GR), couldn't there be a similar theory where some spacetime curvature is caused by electric charges? Both are $$F = k/r^2$$ in elementary physics.

A postulate could be that an electron in an elevator (made of electons, or a negatively charged inside surface) cannot tell the difference whether :

1. the elevator is stopped and that there is a large + charge underneath or :

2. the elevator is accelerating upwards

Where does this lead? What happens if you take magnetism into account?

 

[Garth]

Mass and energy cause curvature. Einstein spent much of the rest of his life after developing GR to try and include E-M theory as well, a unified field theory, but was unsuccessful; probably because he didn't know about the strong and the weak nuclear forces at the time, which have to be included as well.

However this question may be the opportunity to consider the following, "According to the EEP a stationary electron on a laboratory bench is accelerating w.r.t. the local Lorentzian freely falling inertial frame of reference. According to Maxwell’s theory of electromagnetism an accelerating electric charge, such as an electron, radiates. So why doesn’t it? Or, if it is thought that such an electron actually does radiate, what is the source of such radiated energy?"
Garth

 

[Gonzolo]

I don't know what EEP and w.r.t. stand for.

That's interesting but it's not unification that I want to talk about. I am wondering whether a theory similar to GR can be developped from the two postulates of my first post (or similar ones), instead of the familiar ones with gravity and mass.

Based on the premise that charge and mass are equally important, why does mass curve spacetime, but not charges? "What happens if we replace m by q in GR's equations" and consider attractions and repulsions?" I believe that if mass can curve spacetime, then so should + and - charges. So a GR-like theory should be able to be developped talking about charges instead of mass (whether its useful or not).

Perhaps this thread belongs in the theory developped section. I let GR specialists out there be the judges.

 

[jcsd]

It's a fair question. The reason is that gravity affects all particles in the same way; charge doesn't. Accelration due to gravity is independentof the particular properties of the particle whereas acceleration due to the electromagnetic force depends on it's mass to charge ratio.

There was an attempt to include the electromagnetic force as the curvature of spacetime - Kaluza-Klein theory, which needed the additon of an extra spacetime dimension. Later some of the ideas of Kaluza-Klein theory were used in string theory.

 

[Garth]

I don't know what EEP and w.r.t. stand for.

EEP = Einstein Equivalence Principle :w.r.t = with respect to.

That's interesting but it's not unification that I want to talk about. I am wondering whether a theory similar to GR can be developped from the two postulates of my first post (or similar ones), instead of the familiar ones with gravity and mass.

Einstein had a go and couldn't develop one, but perhaps you will succeed!

Garth

 

[humanino]

Based on the premise that charge and mass are equally important, why does mass curve spacetime, but not charges? "What happens if we replace m by q in GR's equations" and consider attractions and repulsions?" I believe that if mass can curve spacetime, then so should + and - charges. So a GR-like theory should be able to be developped talking about charges instead of mass (whether its useful or not).

The problem is that a spin 2 field, like the supposedly graviton, always causes attraction. It cannot yield to repulsion.

This requires negative energy. You will get time travel and loose causality.

 

[Gonzolo]

I believe that spins and gravitons were un-thought of when A. E. developped GR and am not aware that they are considered in GR today. The theory I have in mind should be able to be developped from nothing else than classical physics, as GR was.

I'm living in 1916 for this thread and telling Einstein that there is a (perhaps parallel) spacetime associated with charges (mass not considered). I'm asking him to prove to me that a very strong electric field cannot curve a light beam as would a massive star. And am suggesting that electric forces can be explained with differential geometry.

 

[Dburghoff]

Now, I'm not a physicist (just a first-year engineering student), but I'd like to venture a guess why. I've actually thought of something like this, Gonzolo, but I came up with an explanation which satisfies me, and I think will satisfy you as well.

The whole premise behind GR is that it is impossible to distinguish between gravity and acceleration. That is, if you stood in an elevator in space which was accelerating at 9.8 m/s² without access to the outside world, there is no experiment that you could do to determine that you are not on Earth (assuming that on Earth, slight fluctuations in g near the surface are impossible to measure). Essentially, gravity and acceleration are the same thing. Now, everything else in GR is based on this premise, including the curved space around massive objects.

However, the same cannot be said of a electric fields. Let's go back to our closed elevator scenario. It's incredibly easy to determine the difference between electromagnetism and "regular" acceleration. All you have to do is place an electron on one side of you and a proton on the other. If both fall to the floor of the elevator, you know that you're both "regularly" accelerating. If one falls to the floor and the other rises towards the ceiling, you know that you're under the influence of a charged object. Therefore, the basic premise of GR is false when considering EM, and nothing else can be derived from it.

Hope I helped!

 

[pervect]

If theorists (starting with A. E.) can make a theory about spacetime curvature caused by mass (GR), couldn't there be a similar theory where some spacetime curvature is caused by electric charges? Both are $$F = k/r^2$$ in elementary physics.

So far, this sounds like Kaluza-Klein theory, which is an attempt to get electromagnetism from a geometrical theory. It didn't work out on its own, but it helped inspire string theory

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

However, elevators and equivalence principles are not involved in Kaluza-Klein theory. Instead, one contemplates a 5-d spacetime, and eventually one concludes that one of the dimensions may be small and "curled up". One gets gravity and electromagnetism and a scalar field (which hasn't been observed) out of such a theory. You'll see some of the ideas in Kaluza-Klein theory which are later used by string theory (the extra spatial dimensions and the way they are handled).

BTW, magnetism and electrostatic forces are unified by special relativity - a magnetic field is basically just the consequence of an electric field as seen by a moving observer.

 

[Gonzolo]

The whole premise behind GR is that it is impossible to distinguish between gravity and acceleration. That is, if you stood in an elevator in space which was accelerating at 9.8 m/s² without access to the outside world, there is no experiment that you could do to determine that you are not on Earth (assuming that on Earth, slight fluctuations in g near the surface are impossible to measure). Essentially, gravity and acceleration are the same thing. Now, everything else in GR is based on this premise, including the curved space around massive objects.

Yup, I pretty much agree with that.

However, the same cannot be said of a electric fields. Let's go back to our closed elevator scenario. It's incredibly easy to determine the difference between electromagnetism and "regular" acceleration. All you have to do is place an electron on one side of you and a proton on the other. If both fall to the floor of the elevator, you know that you're both "regularly" accelerating. If one falls to the floor and the other rises towards the ceiling, you know that you're under the influence of a charged object. Therefore, the basic premise of GR is false when considering EM, and nothing else can be derived from it.

That is true. But if you only have an electron, how can you tell? Couldn't one recreate GR with this case? And then another GR for the proton case? Perhaps that by then mixing the 2 "new" GR theories, we would arrive to the same conclusions than by having both charge in the elevator. I do not know.

pervect, Kaluza-Klein theory may be what I'm trying to talk about, I am not sure. I would try to avoid mass and gravity to begin with, to see where it goes. Perhaps KK did that, and eventually added mass to complete the theory. Honestly, I would need rigourous GR and KK introductions. I am wondering where the premise of my first post would lead if I gave it to A. E. or knew how to demonstrate his equations.

 

[hellfire]

However this question may be the opportunity to consider the following, "According to the EEP a stationary electron on a laboratory bench is accelerating w.r.t. the local Lorentzian freely falling inertial frame of reference. According to Maxwell’s theory of electromagnetism an accelerating electric charge, such as an electron, radiates. So why doesn’t it? Or, if it is thought that such an electron actually does radiate, what is the source of such radiated energy?"

Radiation is due to a reconfiguration of the electric field lines due to a change in the motion of the charge (the new field lines emerging from the charge do not match with the old ones). Inside a gravitational field the field lines are static and thus there is no radiation. May be this explanation is too simple and I am missing something...?

 

[da_willem]

That is true. But if you only have an electron, how can you tell? Couldn't one recreate GR with this case? And then another GR for the proton case? Perhaps that by then mixing the 2 "new" GR theories, we would arrive to the same conclusions than by having both charge in the elevator. I do not know.

all particles fall at the same rate in a gravitational field because both inertia and the gravitational attraction are proportional to the mass of the falling object: F=ma=GMm/r^2. So the acceleration a=Gm/r^2 is independent of the mass of the object.

For an electric charge this is different: F=ma=CqQ/r^2 so a=CqQ/mr^2. So it depends both on the mass and the charge of the object. So there is no equivalence principle like that of GR.

 

[pervect]

all particles fall at the same rate in a gravitational field because both inertia and the gravitational attraction are proportional to the mass of the falling object: F=ma=GMm/r^2. So the acceleration a=Gm/r^2 is independent of the mass of the object.

For an electric charge this is different: F=ma=CqQ/r^2 so a=CqQ/mr^2. So it depends both on the mass and the charge of the object. So there is no equivalence principle like that of GR.

Yes, this is what makes the geometrical interpretation very "natural" for gravity. Since all particles behave the same way because of the equivalence principle, it's easy to describe the motion of a particle geometrically by making the natural motion of a particle a geodesic.

However, the geometrical POV can be used to handle forces as well, as Kaluza-Klein theory shows. The mechanism for doing so is a little "tricky" (extra spatial dimensions, often rolled up into a small curve).

 

[Garth]

Inside a gravitational field the field lines are static and thus there is no radiation.

Define "static" - static in the laboratory non-inertial frame, or static in the freely falling, inertial Lorentzian frame?

Which should the electron not radiate in?

-Garth

 

[Gonzolo]

all particles fall at the same rate in a gravitational field because both inertia and the gravitational attraction are proportional to the mass of the falling object: F=ma=GMm/r^2. So the acceleration a=Gm/r^2 is independent of the mass of the object.

For an electric charge this is different: F=ma=CqQ/r^2 so a=CqQ/mr^2. So it depends both on the mass and the charge of the object. So there is no equivalence principle like that of GR.

That makes sense (with a = GM/r^2 instead). I understand better. The ratio q/m suggests why Kaluza-Klein unifies gravity and EM. KK is probably the simplest complete geodesic EM theory.

Now this may be an insult to Newton (and to myself), but mathematically, we could use F = qE instead of F = ma. This gives rise to E playing the role of a. But E = d?/dt = F/q = (m/q)*(dx^2/dt^2) = (m/q)*a... the same ratio. The ratio q/m might suggests why Kaluza-Klein unifies gravity and EM.

For the sake of exploring what happens if I consciously look away from inertia, mass and gravity, I'll keep going :

What about if I shove m into the C (or use m = 1 for simplicity)? The electron in our EM elevator is alone and has constant mass anyway. We then got a = CqQ/r^2, just like gravity. C's units have changed though, so this may start controversy. I may be departing physics.

 

[da_willem]

Now this may be an insult to Newton (and to myself), but mathematically, we could use F = qE instead of F = ma. This gives rise to E playing the role of a

Physically (not only mathematically) they are both true but have a very different meaning! F=ma is an incomplete law that describes how an object responds to a force. F=ma is incomplete in the sense that it needs the input of a force to tell you something about the movement of he object. F=qE is an example of such a force, but is not an equation of motion like Newtons second law, and thus has (with all the other formulas describing all other forces) an entirely different status...

 

[hellfire]

Define "static" - static in the laboratory non-inertial frame, or static in the freely falling, inertial Lorentzian frame?

Which should the electron not radiate in?

-Garth

I would say the field lines are static in the laboratory frame in which the electron is at rest. Does this mean the electron should radiate in a free falling frame? I have to admit that my first post was only a guess, but I really don't know. May be you could elaborate a little bit.

 

[Garth]

I would say the field lines are static in the laboratory frame in which the electron is at rest. Does this mean the electron should radiate in a free falling frame? I have to admit that my first post was only a guess, but I really don't know. May be you could elaborate a little bit.

According to the equivalence principle of GR the natural inertial Lorentzian frame is the freely falling one. The table-top is being accelerated upwards wrt this frame by the force pushing on it by the floor. The electron itself on the lab table is therefore accelerating upwards wrt this inertial frame, being 'pushed upwards' by the table and according to Maxwell ought to be radiating.

I have had the opinion expressed in a university physics community that in fact such electrons do radiate, but at such a low power that it has not been detected. In which case the second part of my question comes into play, if so, where does this energy of radiation come from? The electron is just sitting there minding its own business!

In my view this question is tied up with the problem that energy is not locally conserved in GR, and there has been some discussion about that on these forums.
- Garth

 

[selfAdjoint]

I understood it perfectly, but a newby might have thought you were supporting absolute motion, which we both know isn't so.

 

[Garth]

I understood it perfectly, but a newby might have thought you were supporting absolute motion, which we both know isn't so.

Understood. However, and here may be the beginning of a new thread, I quote pensively "you were supporting absolute motion, which we both know isn't so" ??

My questioning ?? about a preferred (absolute is too strong a term) frame is the question of Mach's Principle.

SR is rightly configured for empty space, we have space-time and a set of test particles that define that space and time by their interactions, yet do not perturb it. In such an empty space the principle of relativity, i.e. no preferred frames, holds its own. This is codified in the conservation of energy-momentum, or 'rest energy', or mass defined by the equation of 4-momentum.

We now introduce matter and their associated gravitational fields, which are interpreted in GR as a curvature of that space-time and carry forward the SR principle of no-preferred frames, the conservation of energy-momentum.

However if we now introduce Mach's Principle, which suggests the phenomenon of inertia ought to arise from accelerations with respect to the general mass distribution of the entire universe, then we might indeed choose a particular or preferred frame when masses are introduced, that which is the Centre of Mass frame of the system under investigation.

Cosmologically this will be that in which the CMB is globally isotropic, co-moving with the surface of last emission, and in the laboratory this will be the Centre of Mass of the Earth.

The interesting observation here is that the electron sitting on a lab table might be accelerating wrt to the freely falling frame preferred by GR as the Lorentzian inertial frame, but it is at rest wrt to the Earth preferred by Mach's Principle as the Centre of Mass frame.

Hence if both Maxwell and Mach are correct the electron should not be radiating and there is no problem over where the energy of any such radiation might come from!

Just food for thought.

- Garth

 

[selfAdjoint]

Well, I don't believe in Mach's principle, because GR has had such success that it seems to rule it out. To reintroduce it now at this late date is to say that GR is insufficient among classical theories, and what would lead you to think that?

 

[juju]

Hi all,

It might be possible to form a curvature theory of electromagnetics if you start with the idea that each pair of charges is the source of the curvature rather than single particles.

juju

 

[pervect]

I have had the opinion expressed in a university physics community that in fact such electrons do radiate, but at such a low power that it has not been detected. In which case the second part of my question comes into play, if so, where does this energy of radiation come from? The electron is just sitting there minding its own business!

I'm surprised this issue hasn't been resolved. It seems to me that the static nature of the charge relative to the observer at infinity means that it should not radiate from the viewpoint of the observer at infinity.

 

[Entropy]

Mass and energy cause curvature. Einstein spent much of the rest of his life after developing GR to try and include E-M theory as well, a unified field theory, but was unsuccessful; probably because he didn't know about the strong and the weak nuclear forces at the time, which have to be included as well.

Did you quote that from Brian Green's book: The Fabric of The Cosmos? Heh, I was just reading that today and I notice that there's a passage where he says the exact same thing you said. Good book.

 

[Garth]

Did you quote that from Brian Green's book: The Fabric of The Cosmos? Heh, I was just reading that today and I notice that there's a passage where he says the exact same thing you said. Good book.

No I didn't - a case of "great minds think alike, fools seldom differ" I guess!
Garth

 

[Garth]

I'm surprised this issue hasn't been resolved. It seems to me that the static nature of the charge relative to the observer at infinity means that it should not radiate from the viewpoint of the observer at infinity.

So your observer at inifinity is co-moving with the Earth is she? A case for Aristotelian relativity?

Garth

 

[Garth]

Well, I don't believe in Mach's principle, because GR has had such success that it seems to rule it out. To reintroduce it now at this late date is to say that GR is insufficient among classical theories, and what would lead you to think that?

So your electron on a lab table is accelerating, and radiating I presume (if you still believe in Maxwell), so where do you think its energy of radiation is coming from?

Garth

 

[selfAdjoint]

So your electron on a lab table is accelerating, and radiating I presume (if you still believe in Maxwell), so where do you think its energy of radiation is coming from?

Garth

The downward force of gravity on the electron is balanced by the upward force of the table, so the net acceleration of the electron is zero, and it doesn't radiate.

In general the Standard model accounts for electromagnetic radiation and conserves energy. Wherever the electrical energy "comes from", it can't be Mach's principle because that, in denying GR, contradicts experiment.

 

[Garth]

The downward force of gravity on the electron is balanced by the upward force of the table, so the net acceleration of the electron is zero, and it doesn't radiate.

hmmm.. Should not the frame of reference in which the electron is not accelerating be the locally Lorentzian freely falling one? The one in which physics is simple when analyzed locally? [MTW pg 4]

In general the Standard model accounts for electromagnetic radiation and conserves energy. Wherever the electrical energy "comes from", it can't be Mach's principle because that, in denying GR, contradicts experiment.

Unless that is there is another gravitational theory that fully includes Mach's Principle, which does not contradict experiment. May I commend Self Creation Cosmology which claims to be such a theory? [See posts/threads about it on these Forums]

 

[Garth]

It might be possible to form a curvature theory of electromagnetics if you start with the idea that each pair of charges is the source of the curvature rather than single particles.

Hi juju;
The Earth is full of charges and we would be either completely squashed by them or propelled into space, the electromagnetic force is so much stronger (~10^40) than the gravitational force. However we are not squashed/launched into space because the like and unlike charges cancel each other out. So I guess that a pair of charges probably wouldn't be a source of curvature because the nett 'force' or curvature would be zero.
Garth

 

[pervect]

So your observer at inifinity is co-moving with the Earth is she? A case for Aristotelian relativity?

Garth

I'm not sure if you are saying that there will be some radiation due to the Earth's acceleration due to it's orbit around the sun (probably true, IMO, I wasn't being sufficiently nit picky when I responded) or whether you are talking about the relative velocity between the observer at infinity and the earth. The relative velocity shouldn't matter as far as the radiation issue goes - an electron moving at a constant velocity shouldn't radiate.

 

[pervect]

hmmm.. Should not the frame of reference in which the electron is not accelerating be the locally Lorentzian freely falling one? The one in which physics is simple when analyzed locally? [MTW pg 4]

Whether or not radiation exists depends on the coordinates, it's not a physical invariant. Photon number is conserved by the Lorentz boost, but not by arbitrary coordinate changes. It's possible for the observer accelerating and co-moving with the electron not to see any radiation, while another observer accelerating with respect to it will see radiation.

 

[Garth]

I'm not sure if you are saying that there will be some radiation due to the Earth's acceleration due to it's orbit around the sun (probably true, IMO, I wasn't being sufficiently nit picky when I responded) or whether you are talking about the relative velocity between the observer at infinity and the earth. The relative velocity shouldn't matter as far as the radiation issue goes - an electron moving at a constant velocity shouldn't radiate.

Thank you - however it is the relative acceleration that is important.

I don't think you can solve the issue by taking the r -> infinity limit, unless that is that boundary is co-moving with the Earth and thus make the Earth the centre of the universe in some sense!

Whether or not radiation exists depends on the coordinates, it's not a physical invariant. Photon number is conserved by the Lorentz boost, but not by arbitrary coordinate changes. It's possible for the observer accelerating and co-moving with the electron not to see any radiation, while another observer accelerating with respect to it will see radiation.

Two questions: 1. "Has the latter been demonstrated experimentally?"

I am thinking here of a situation in which the mutual acceleration is not gravitational (that is an added complication) but caused by the observer physically being boosted by a force.

and 2. "What is the source of the energy of such radiation?"

When you accelerate an electric charge you are doing work on it and some of that re-appears as radiation, however when the acceleration is "passive" either because it is the observer who accelerates, or because it is sitting passively and stationary in a gravitational field on a laboratory bench, then I question the source of such energy.

Garth

 

[pervect]

I don't think you can solve the issue by taking the r -> infinity limit, unless that is that boundary is co-moving with the Earth and thus make the Earth the centre of the universe in some sense!

We are on different wavelengths here.

I'm a bit surprised you don't see why I've been talking about the observer at infinity.

Let me jog your memory a bit

In which case the second part of my question comes into play, if so, where does this energy of radiation come from?

The reason I brought up the observer at infinity was to answer the second part of your question. Do I really need to go through the whole spiel on asymptotic flatness and energy in GR again? I will if it serves some useful purpose - If I recall correctly you have your own theory with it's own view on energy conservation, but I'd hope you'd be interested in understanding the mainstream view. I believe I'm presenting the mainstream view reasonably fairly, but I'm not, alas, infallible. Anyway, if you want me to clarify this or talk about it more I will, but I'm hoping that pointing out my previous remarks on this topic will be enough.

Oh, yes, I guess I haven't mentioned what I see as "the solution". The main solution is that the detection or non-detection of radiation is observer dependent, it's not a physical invariant. It's also not strictly speaking a local pheomenon at all. Google finds (amusingly enough) pmb's webpage with a wide variety of quotes from the literature pointing out the observer dependent nature of the existence of radiation

http://www.geocities.com/physics_world/falling_charge.htm

Two questions: 1. "Has the latter been demonstrated experimentally?"

Not as far as I know. I believe there were some experiments proposed to measure Unruh radiation, but I don't think they have been carried out, they will be very difficult. Unruh radiation is also a digression from the topic, the mechanism is different, but it illustrates the main point that the existence or non-existence of radiation is observer dependent.

I am thinking here of a situation in which the mutual acceleration is not gravitational (that is an added complication) but caused by the observer physically being boosted by a force.

I *think* that such an observer should see fields that look like radiation, but since the problem is notoriously tricky, and since I haven't actually carried out any calculations, take this with a grain of salt.

and 2. "What is the source of the energy of such radiation?"

When you accelerate an electric charge you are doing work on it and some of that re-appears as radiation, however when the acceleration is "passive" either because it is the observer who accelerates, or because it is sitting passively and stationary in a gravitational field on a laboratory bench, then I question the source of such energy.

Garth

Well, let me jog your memory again here. Just to be sure we're communicating, do you recall what I think is a necessary and sufficient condition for energy to be conserved in GR? (You don't have to wade through all my posts, just this one, to answer this question).

 

[juju]

Hi Garth,

I was thinking of a situation where each pair of charges only curved the space between the charges. Thus, in the aggregate these would cancel, but still exist locally.

juju