# Magnetic fields and gravitational waves. How far do they reach?

I read that magnetic fields perpendicular to a current shoot out and expand all the way to infinity.
Additionally a gravitational wave, no matter how small will also expand to infinity at the velocity of light.
Are these correct? If yes, why don't waves "lose" energy while "traveling"?

Update

I did not read this statement in a physics book. I read it in a "philosophical" book where the author tries to make a point taking this assertion for granted.
To be specific his exact example is:

We shall take a short piece of wire, connect both its ends to a battery through a switch and close the switch. Three things will happen:

1. That electrical current will run from one side of the battery to the other

2. A magnetic field perpendicular to the current will shoot out and expand all the way to infinity at the velocity of light

3. The wire will heat up slightly

So is this description correct only in a theoretical manner? In reality, due to other objects, will point 2 be invalid?

-
I remember a table in a Physics textbook where EM, gravity strong and weak force each had its maximum distance (range), though some ranges might have been $\infty$ –  raindrop Dec 23 '12 at 2:03
@Raindrop: If I understand correctly, if a force's gauge particle is massless then its extent is (maybe?) infinite but if its gauge particle has mass then its extent is bounded. I think the strong and weak forces have gauge particles with mass. –  yakiv Dec 23 '12 at 3:05
Sorry, I really don't know. –  raindrop Dec 23 '12 at 5:04
@yakiv That's basically it. Of course, all forces technically have infinite range. When people say "infinite range" they mean "strength decays asymptotically like a power of distance" and when they say "finite range $r_0$" they mean "strength decays asymptotically exponentially with characteristic length $r_0$" –  Chris White Dec 23 '12 at 6:31
@Jim, see my updated response below –  zhermes Dec 23 '12 at 22:13

In short, if there is nothing to interact with the wave, it can't lose energy. EM and gravity waves do not experience friction with vacuum, so they just keep going.

Of course, as they spread out, their energy becomes spread out as well. The power per unit area, or flux, is (somewhat trivially) inversely proportional to the area of the wavefront, so as long as this area is increasing, the wave's local "strength" decreases.

Edit: Taking the philosophical tack (which is certainly fair - physics was indistinguishable from philosophy for most of its history), I suggest analyzing things in a Leibnizian/Machian way. For both of them and their followers, all we have is measurements of how things move relative to one another, and any background "absolute space" (à la Newton) or "field" (à la Faraday) is just a mathematical invention that proves convenient for describing these relative motions.

When you turn on a current in a wire, the moving charges can make other charges at a distance move in response. The way in which these other charges respond is nicely described by first defining a magnetic field from the current, and then applying the appropriate force law for charges in a magnetic field. There is no distance beyond which the other charges are not influenced at all by the current, so the "magnetic field" (aka "influence of the current") extends to infinity. Furthermore, those distant charges won't "know" about the current until sufficient time has passed for the information about it to reach them, and hence the leading "edge" of the magnetic field moves outward at the speed of light.

-
Please see updated OP –  Jim Dec 23 '12 at 19:30

If the only thing in a(n infinite) universe was a current, it would produce an electromagnetic field (EMF) that propagated out towards infinity --- with an ever decreasing strength the further away it goes. Similarly for gravitational waves (GW), if the only thing was a properly accelerating mass.

In actuality the universe may or may not be infinite, and there are objects around that can absorb / dissipate the fields. For example, if the EMF encounters a conductor, or if the GW encounters enough mass --- they will be decreased in amplitude.

Presumably, once the fields are interacting with things, one would also need to think about them as quanta (i.e. photons and gravitons) at some point. In that case, there would eventually be a 'last' photon which is finally absorbed.

So I guess in summary, it depends on how deeply you want to look at it.

Most likely, whatever you were reading only wanted to emphasize the theoretical concept that in the absence of other factors the fields just kind of extend forever (and they didn't really want you to think about the details).

Edit (In response to OP's edits):

My same answer applies --- it just depends on what point the author is trying to get across. If its just the conceptual idea: yeah, sure, the fields fly out towards infinity at the speed of light. If you want to think about the more physical, detailed picture... then it gets a little more complicated.

Also, to clarify a little more on my previous points: in a realistic universe (but still assume an infinite one), a field will always be degraded by some finite (although perhaps outrageously large) distance. If nothing else, interacting with matter and with background light will eventually kill it.

By-the-way, kudos for not taking a philosopher's word for it on physics stuff.

-
"increasing" -> "decreasing" in first sentence? –  Chris White Dec 23 '12 at 1:58
even non interactive ones, spreading out radially will in the end have to be counted as single photons. Lubos in his blog has an interesting read on how single photons add up to a continuous field motls.blogspot.com/2011/11/… –  anna v Dec 23 '12 at 4:55
Please see updated OP –  Jim Dec 23 '12 at 19:29
The core point of this, is that he claims that an inisignificant action such as the current passing from the wire (from the batery) will have a side-effect which is "broadcasted" into a distance which is disproportionally larger than the action itself (just a small current from a battery). It seems correct in a "gross" way from your answer and of Cris –  Jim Dec 24 '12 at 0:03
That seems like a fair interpretation –  zhermes Dec 24 '12 at 0:50

In this thread one point was not discussed yet, as far as I read: That "wire" (which everybody will assume to be straight) is misleading. A wire with a battery makes a electric ciruit! "Circuit" has a original meaning: circular. So for any current "seen" from far away, you will see a current of the same strength but opposite direction close by. This is reason why magnetic fields diminish with a much higher power than inverse square. Another problem in this question is that the question of "reach" of some "transmitter" is not relevant. You always have to define the sensitivity of the detector used to receive the field, radiation etc when asking "how far".

-

The changing acceleration of the electrons explains the created negative electric field of the magnetic induction, the electromagnetic inertia, the changing relativistic mass and the Gravitational Force, giving a Unified Theory of the physical forces. Taking into account the Planck Distribution Law of the electromagnetic oscillators also, we can explain the electron/proton mass rate and the Weak and Strong Interactions.