# Does an electric charge curve spacetime ?

1. Sep 21, 2004

### 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?

2. Sep 21, 2004

### 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

3. Sep 21, 2004

### 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.

Last edited by a moderator: Sep 21, 2004
4. Sep 21, 2004

### 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 thoery were used in string theory.

5. Sep 21, 2004

### Garth

EEP = Einstein Equivalence Principle :w.r.t = with respect to.
Einstein had a go and couldn't develop one, but perhaps you will succeed!

Garth

6. Sep 21, 2004

### humanino

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.

7. Sep 21, 2004

### 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.

8. Sep 21, 2004

### 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!

9. Sep 21, 2004

### pervect

Staff Emeritus
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.

10. Sep 22, 2004

### Gonzolo

Yup, I pretty much agree with that.

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.

11. Sep 22, 2004

### hellfire

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...?

12. Sep 22, 2004

### da_willem

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.

13. Sep 22, 2004

### pervect

Staff Emeritus
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).

14. Sep 22, 2004

### Garth

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

15. Sep 22, 2004

### Gonzolo

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.

Last edited by a moderator: Sep 22, 2004
16. Sep 22, 2004

### da_willem

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...

17. Sep 22, 2004

### hellfire

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 dont know. May be you could elaborate a little bit.

18. Sep 22, 2004

### Garth

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

19. Sep 22, 2004

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

20. Sep 23, 2004

### Garth

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

Last edited: Sep 23, 2004