# A causes B – what does it mean?

There is a debatable issue that concerns the presence of causality in the interpretation of some physical relationships, such as those involved in electromagnetism. For example, “the dynamic change in magnetic field H causes the emergence of electric field E”. This is a common interpretation of one of the key Maxwell’s equations (originating in Faraday’s law). What does this “causes” mean? Is the meaning purely mathematical or is it more fundamental, or physical?

First of all, any man-made statements about real world phenomena are not strictly speaking physical, because they are formulated by humans within their perceptions, or, whether we want it or not, models, of the real world. So, even if we use English to express our perceptions we already depart from the “real physics”. Mathematics is just a man-made form of expression that is underpinned by some mathematical rigour.

Now let’s get back to the interpretation of the “causes” (or causality) relations. It is often synonymized  with the “gives rise” relation. Such relations present a lot of confusion if they originate from the interpretation of mathematical equations. For example, Faraday’s law in mathematical form, curl (E) = – dB/dt,  does not say anything about the RHS causing or giving rise to the LHS. (Recall that B is proportional to H with the permeability of the medium being the coefficient of proportionality.)

The interpretation problem, when taken outside pure mathematics leads to the question, for example, of HOW QUICKLY the RHS causes the LHS? And, here we have no firm answer. The question of “how quickly does the cause have an effect” is very much physical (yet neither Faraday nor Maxwell state anything about it!), because we are used to think that if A causes B, then we imply some temporal precedence between the event associated with A and the event associated with B. We also know that it is unlikely that this ‘causal precedence’ will effect faster than the speed of light (we haven’t seen any other evidence of information signalling acting faster than the speed of light!). Hence, the causality with the speed of light is something that may be the result of our causal interpretation. But, then this is probably wrong to assume that Faraday or Maxwell gave this sort of interpretation to the above relationship.

Worth thinking about causality, isn’t it?

I have no clear answer, but in my opinion, reading the original materials on electromagnetic theory, such as Heaviside’s volumes, rather than modern textbooks would be a good recipe!

I recommend anyone interested in this debatable matter check out Ivor Catt’s view on it:

http://www.ivorcatt.co.uk/x18j73.pdf

http://www.ivorcatt.co.uk/x18j184.pdf

To the best of my knowledge, Catt was the first to have noticed and wrote about the fact that modern texts on electromagnetism actively use the ’causes’ interpretation of Maxwell’s equations. He also claims that such equations are “obvious truisms about any body or material moving in space”.  The debatable matter may then start to move from the question of the legitimacy of the causal interpretation of these equations towards the question of how useful these equations are for actual understanding of electromagnetism …