# Electromagnetic force in 4D

1. Apr 2, 2004

### kuengb

I hope my question makes some sense; if not, just post an "evil smiley" and ignore it

So, my only "knowledge" about this is based on one of Hawking's books, wherein it is written: If space had four dimensions instead of three, gravitation would behave differently (I think it was $$1/{r^3}$$), so that there wouldn't be any stable planet orbits any more.

Now, what would happen to the electromagnetic force? My particular worry is the Lorentz force: If there is an analogon in four dimensions, what would it's direction be? Because, in 3D it is perpendicular to velocity and field vector, but in four dimensions this is ambiguous.

Would there possibly even be more than two aspects of the electromagnetic force? Hm?

2. Apr 3, 2004

### ranyart

Here is something for you to ponder?

In 3+1 dimensions (spacetime) the EM wave propergates along by Photons, which are visible as they bounce around in 3+1 spacetime.

In 2+1 dimensions (EM-Field) the Photon does not exist, or technically cannot be observed, but here lays the Force-Carrier replacing Photons.

In 1+1 dimensions (<->)(>-<) there is seperation of EM into base quantities, or SINGULAR Electro component and Magnetic component, with the corresponding energies being expansive or contractive..Negative and Positive.

Ive left out a little major detail!

Just as photons cannot be observed in lesser dimensional space, they can never transform into higher dimensional arena's, and still be called Photons?..for 3+1 spacetime..the buck stops with Photons.

3. Apr 3, 2004

### Janitor

In 3+1 spacetime, the Faraday tensor field for electromagnetism has (because it is rank-2 and antisymmetric) 3+2+1=6 independent components, which are numbers to be specified at each point in spacetime to characterize the e.m. field. Historically, before this tensor was conceived, physicists considered an e.m. field to be due to two fields, each with 3 components. The E field lived in 3D space and was a polar vector, while the B (or H) field also lived in 3D space and was an axial vector, or "pseudovector."

Presumably in a space with a different number N of space dimensions, intelligent beings would have needed to find the (N+1)x(N+1) tensor right off the bat, instead of limping by with a vector field plus a pseudovector field.

Last edited: Apr 3, 2004
4. Apr 3, 2004

Staff Emeritus
In our history, it was EM that drove relativity, and relativity that called up 3+1 geometry. But this is contingent, it might have been a different order. Parmenides and St. Augustine all but saw four dimensional reality, and we could make up an alternate history in which 3+1 geometry came to be, and drove physics, so EM was discovered in antiquity (they already knew both static electricity and magnetism).

5. Apr 3, 2004

### Janitor

Years ago I saw a semi-serious article somewhere, called "Could Newton have discovered relativity?"--and they meant Einstein/Lorentz relativity, not Galilean. I can't remember exactly what the author's point of view on it was, but he did quote some speculative parts of Newton's body of writing that at least suggested an anticipation of relativity of a sort, even though being written before electromagnetic theory was developed.

Ummm... This also brings to mind an article I read in an aviation magazine in my teens. It was on the topic of whether today's typical private pilot could have been an Ace in the first World War if he could travel back in time to that period with his Cessna 150, modified to carry a machine gun.

Last edited: Apr 3, 2004
6. Apr 4, 2004

Staff Emeritus
I wonder if the Cessna's modern engine could run on the crude gas of the time? I have no real idea, it was just the thought that came up.

I'm going to see if I can find that Newton relativity article.

7. Apr 4, 2004

### Janitor

We will let him carry a storage tank of avgas back in time as well. I believe the author concluded that the 150 would have been dominant early in the war, but it would have been in over its head by the end of the war.

The other item I mentioned may even have been a chapter in some book at the library, I'm not sure.