In the last few days, I have been discussing with Ed Dellian the notion of causality, in relation to electromagnetics.

Here are some interesting issues from this discussion.

An important question is what we call “Causality”, the “cause-effect” relation. Can we call causality a relation between events happening without involvement of matter (or mass), or a relation that is only between events involving material objects. The latter seems to follow from Newtonian physics and so called “geometric proportionality”.

So, let me define two forms of what seem to be in the realm of causal relationship. Here ExH is the Poynting vector (cross-product of two vectors – E electric field and H magnetic field).

(Form 1)

– an event on ExH (say, step from 0V to 4V) taking place at point A of the transmission line – Cause;

– an event on ExH (step from 0V to 4V) taking place 200 picoseconds later at point B of the transmission line – Effect

(Form 2)

– an event on ExH (say, step from 0V to 4V) taking place at some point X of the transmission line – Cause;

– a move (change in motion) of a particle with finite mass next to point X – Effect.

I think this is an important question. It concerns two forms of transfer of energy:

(1) at the level of energy current between a change in energy current (force) and  another change in energy current (force) – this does not involve matter

(2) at the level between a change in energy current (force outside moving matter) and motion (change of motion).

So, far the view from physical philosophers like Ed Delian is dismissive of Form 1, and sort of partially aligning with Form 2.

This is what he wrote to my question about these forms:

The requirement of causality is to distinguish between cause (A) and effect (B) being quantities of physical entities (A, B)  differing in kind (lat. genus) like apples and pears. Whether physical entities differ in kind can be found by analyzing their dimensions. Cause A (dimension A) and effect B (dimension B) are entities with different dimensions (different entities). Consequently a mathematical law of causality (generation of effect B by a generating cause A) cannot read B = A. The only reasonable mathematical relation between such different quantities (if there is any) is a geometric proportionality according to A/B = C = constant. The dimensions of the constant C accordingly will be given [A/B].

So your “form 1” where you deal with two “events” of a same kind has nothing to do with causality.

What about “form 2”? There is at point X what you call an “event on ExH”, and there is, as you say, “a move of a particle next to point X”. Now, should the “move” of the particle be lawfully related to the “event”, for example, to the event being symbolized by E, and should p be proportional to E according to E/p = c = constant, this would describe a causal relation between E and p.

But how to apply this example to the problem of “energy current” in a transmission line? As I see things, the observable – the “effect” – is not a “move” of something material from A to B at the transmission line. By analogy I would say, the effect at X is a transfer of “momentum” p from one particle, or pendulum bob, to the other, or, as in a billiard game, from one ball to the other, caused by a “force” impressed on the particle, which “force” some call “energy”. Consequently, there is no moving “energy current”; rather the cause  “energy” must already be “there” at every point of the transmission line, so that it can locally generate the effect of “transfer of momentum from particle to particle” according to the law E/p = c = constant as soon as the switch is turned to light the lamp. So I would say, the impression of “energy current” is only due to (1) confusing the effect with the cause, and (2) confusing the scalar “velocity c” of generation of an effect in space and time with a vector velocity v of “current”, that is, material transport from A to B. I think the billiard ball example is striking: You can observe the velocity v of the rolling ball A, and you can observe that the momentum of A is “immediately” transferred to the ball B in the collision. The generation of the momentum of B takes place at the “velocity of generation” c, which has nothing to do with the velocity v of the rolling balls. Analogously may happen the generation of momentum p as an effect of cause E at every point of a transmission line, which, as the generated momentum p “propagates” through the line (propagating in one direction since the cause E is a vector!),  only apparently indicates a “current” (move from A to B) at “velocity c”. 

To which I replied (quoting him first):

The requirement of causality is to distinguish between cause (A) and effect (B) being quantities of physical entities (A, B)  differing in kind (lat. genus) like apples and pears. Whether physical entities differ in kind can be found by analyzing their dimensions. Cause A (dimension A) and effect B (dimension B) are entities with different dimensions (different entities). Consequently a mathematical law of causality (generation of effect B by a generating cause A) cannot read B = A. The only reasonable mathematical relation between such different quantities (if there is any) is a geometric proportionality according to A/B = C = constant. The dimensions of the constant C accordingly will be given [A/B].

What about causality of the same kind (species) – parent to child?

So your “form 1” where you deal with two “events” of a same kind has nothing to do with causality.

So, what is this? Clearly the event B that is further from the source of the step – it cannot happen before A. In fact it can only happen after event A, and moreover this “after” happens L/c  time units later – where L is the distance between points A and B in the transmission line.

And we can’t deny this effect because this is what we see in the experiments.

I can interpret this as geometric proportionality with coefficient k, which is dimensionless in your terms.

But, incidentally, who said that geometric proportionality should be defined by the algebraic division operator?

Physical world can suggest us other forms of proportionality – for example, we can define proportionality in the form of a time-shift operator?

Please not that I am not dismissing your definition of causality as being limited. I am just looking for a form of expressing the event precedence effect in transmission line, which is what we see in our experiments. Ivor’s theory underpins it with the notion of “Heaviside signal” (aka “energy current”).

The search for truth on causality continues ….