[Physics] Magnetic fields and gravitational waves. How far do they reach

electromagnetic-radiationelectromagnetismexperimental-physicsgravitational-waves

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

After reading the answers:

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?

Best Answer

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.

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