# How would magnetic fields/electromagnetism interact with a wormhole?

e.g. let's say you have something like this:

<--M<-- A|   O   |B

where A| and |B are the two ends of a wormhole, pointed in the direction of the pipes, and the arrows represent the polarity of the magnet (or something. I may have futzed up the terminology a little). Take your pick of what kind of wormhole, but it has to be traversable.

How would objects that would be noticeably affected by the magnetic field of M ('O') behave if they were placed between the two mouths A and B?

Additionally, what if there was some sort of tube enclosing the wormhole so that an object could not travel 'outside of the wormhole' (e.g. go around A.)

• Is this similar to what you are asking ? uab.cat/web/newsroom/news-detail/… – Mihai B. Jan 1 '17 at 16:09
• No. It's not. That's an interesting concept, but the wormhole I'm talking about is the kind that connects points in space. – Stackstuck Jan 3 '17 at 17:12
• If objects A and B are two entangled electrons captured in two different orbitals of two different atoms, and this atoms are then separated across thousands of KM apart, after which the only one atom is subjected to very strong magnetic field causing the electron to switch it's spin from up to down then immediately it's counterpart entangled electron will switch it's spin from down to up. This in the light of ER=EPR (aka "wormhole=entanglement") is an answer and a clarification to your first question, I hope. – Mihai B. Jan 3 '17 at 17:41
• A and B are not objects, they're sides. Of a full-on, you go in one end, you come out the other, spacetimey wormhole. Other than that, I'm not quite sure I understand what you mean. – Stackstuck Jan 3 '17 at 17:44
• It's outside, as I tried to make clear on the diagram. – Stackstuck Jan 3 '17 at 18:03

If the wormhole is field traversable (most wormholes are $field$ traversable, traversable is referred rather about particles and quanta being able to pass through or not) then the problem reduces to solving how magnetic field acts on the object, which depends on the following parameters:

• the $area$ of the mouth of the wormhole
• the distance between the field source and the wormhole
• the distance between the wormhole and the affected object
• in case we study a non-static situation we need the retarded positions, and in that case we also need to know the length of the wormhole or rather the length of the $geodesic$ that connects the 2 space-time "sheets"

As for the case you mentioned above it depends on the nature of the object $O$.

If for example the object is a permanent magnet and the distance between the object and each wormhole mouth is small and the area of the mouth is big enough then the north pole of the magnet will be attracted to one side of the wormhole and the south pole to the other side of the wormhole (the force $F$ will depend on $A$ and $l$). The magnet will "levitate" between the 2 mouth of the wormhole (under the above specified constraints).
The greater the distance the smaller the effect; the greater the area the more field can pass through.

One can easily apply classical formulas like in the force between magnets, as long as the wormhole does not distort field lines directions, as long as it can be approximated to an "open door" between space-time sheets.

Otherwise a more complex situation needs to be solved using General Relativity, with the metric $g_{\mu\nu}$ of our wormhole, integrating electromagnetism in the energy tensor of matter $T^{\mu\nu}$ and solving Einstein's field equations.

• What if O isn't a magnet, but instead a chunk of iron or similar? – Stackstuck Jan 13 '17 at 17:50
• If it's an electric solenoid through which current passes then according to Ampere's model it can be thought as a permanent magnet, so it will be affected "exactly" like a permanent magnet. If it's just a piece of iron previously magnetized then until the magnetization's lost, it's similar to previous examples. Perhaps what you are looking for is to see if there's going to be some kind of perpetuum self excitation? If that's the case I have to disappoint you. Field lines exiting the wormhole will spread in other directions too causing loss in time. And last case- if no magnetization: no effect – Mihai B. Jan 13 '17 at 19:50
• images.sciencedaily.com/2015/09/150903081506_1_540x360.jpg – Mihai B. Jan 13 '17 at 19:56
• I think I lost you somewhere along the line, and then you lost me somewhere along the line. Probably around when you said 'perpetuum self excitation'. Also: The diagram is roughly to scale. I say roughly because it's hard to do scale with ASCII art, but it's roughly to scale. The object would fit through the wormhole, in other words. What would the magnetic field generated by M look like, if there's just nothing there but the wormhole? – Stackstuck Jan 14 '17 at 4:16