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EDIT - I have included the context of the quote I am interested in, as people seem to be as baffled by Einstein's quote as I am:

In a 1920 address Einstein says this:

Think of waves on the surface of water. Here we can describe two entirely different things. Either we may observe how the undulatory surface forming the boundary between water and air alters in the course of time; or else-with the help of small floats, for instance - we can observe how the position of the separate particles of water alters in the course of time. If the existence of such floats for tracking the motion of the particles of a fluid were a fundamental impossibility in physics - if, in fact nothing else whatever were observable than the shape of the space occupied by the water as it varies in time, we should have no ground for the assumption that water consists of movable particles. But all the same we could characterise it as a medium.

We have something like this in the electromagnetic field. For we may picture the field to ourselves as consisting of lines of force. If we wish to interpret these lines of force to ourselves as something material in the ordinary sense, we are tempted to interpret the dynamic processes as motions of these lines of force, such that each separate line of force is tracked through the course of time. It is well known, however, that this way of regarding the electromagnetic field leads to contradictions.

Generalising we must say this:- There may be supposed to be extended physical objects to which the idea of motion cannot be applied. They may not be thought of as consisting of particles which allow themselves to be separately tracked through time. In Minkowski's idiom this is expressed as follows:- Not every extended conformation in the four-dimensional world can be regarded as composed of world-threads. The special theory of relativity forbids us to assume the ether to consist of particles observable through time, but the hypothesis of ether in itself is not in conflict with the special theory of relativity. Only we must be on our guard against ascribing a state of motion to the ether. (http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html)

I have seen a lot of animations doing exactly this, depicting the lines of force as changing through time. For example: https://www.youtube.com/watch?v=VdoL8IOwJw0 (go to the very end of the video, or look at minutes 1:53-2:08 , 7:31-7:48)

What are the contradictions that Einstein is talking about here?

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  • $\begingroup$ I guess it something about radiation. In the video I did not see lines of force, could you point the precise minute. $\endgroup$
    – jinawee
    Apr 14, 2014 at 17:43
  • $\begingroup$ Hi @jinawee I added minutes to look at. $\endgroup$
    – Wapiti
    Apr 14, 2014 at 17:50
  • $\begingroup$ Well, in those cases there is no acceleration. Hence, no radiation. $\endgroup$
    – jinawee
    Apr 14, 2014 at 19:55
  • $\begingroup$ I don't know what you mean. Are you saying that when we think of the EM field as lines of force traveling through time, there is no acceleration? Or are you saying there is no acceleration in the video I gave as a toy example? $\endgroup$
    – Wapiti
    Apr 14, 2014 at 19:58
  • $\begingroup$ I'm saying that the video shows current going through a wire. That means constant speed → no acceleration → no radiation. I think (not sure) that if there was radiation (electromagnetic waves), lines of force would be inacurrate. $\endgroup$
    – jinawee
    Apr 14, 2014 at 20:02

1 Answer 1

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It's because magnetic and electric fields transform into one another depending on your intertial frame, and therefore field lines aren't an invariant intrinsic property of space.

In one frame, you could have a region where there's only a uniform magnetic field $\vec B$, so that any stationary charge remains classically at rest. Yet viewed from a frame moving normal to the direction of this magnetic field, the fields now become:

$$\vec {E'} = \gamma\vec V\times \vec B, \quad \vec {B'} = \gamma\vec{B} $$

In this frame, a stationary charge will now be accelerated by the electric field $E'$.

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  • $\begingroup$ +1 for the answer, but can we be sure that it is this simple: I mean, this is a history question, so do you have any other quotes from Einstein supporting this answer? Reading further here (the OP's quote is at the bottom of p8) it would seem that your answer is likely to be what he means. $\endgroup$
    – Selene Routley
    Apr 14, 2014 at 23:56
  • $\begingroup$ @WetSavannaAnimalakaRodVance I can remember reading Feynman somewhere giving a similar argument: The model of magnetic field lines as being gears and cogs, stresses etc in the medium in one frame, but then disappearing in another frame. $\endgroup$
    – John McAndrew
    Apr 15, 2014 at 11:07
  • $\begingroup$ John, thanks - interesting. I though it might be as you said but then a tensor field, as a geometric object whose "shape" varies with position in spacetime, doesn't seem that much different in character to me from field lines, but then we do look at these things nearly one hundred years after the fact. $\endgroup$
    – Selene Routley
    Apr 15, 2014 at 11:44
  • $\begingroup$ Yes, I am sure this is the answer. It is very clear in retrospect. Einstein talked about these difficulties in his 1905 paper, in particular the moving magnet and conductor problem (en.wikipedia.org/wiki/Moving_magnet_and_conductor_problem). So the 'well-known contradictions' are one the primary drivers for his original theory. I have also seen Feynman saying something similar, about how the fields disappear and reappear. Thanks for clearing that up! $\endgroup$
    – Wapiti
    Apr 15, 2014 at 16:34

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