Re: [Phys-l] EM, is it energy

[John Denker <jsd@av8n.com>]

On 11/29/2007 09:45 PM, carmelo@pacific.net.sg asked:

>  Poynting Vector gives the direction of flow of  
> "abstract concept"?

Yes.

> Ironically, many physicists prefer to consider energy as an "abstract  
> concept", yet explain the flow of energy through Poynting vector as if  
> it is a material being.

I don't see anything ironic about it ... unless you 
insist on misstating the idea and then putting an 
absurd emphasis on the verb "is" in that sentence.

There is an abstract notion of conservative flow that 
is /approximately/ realized by flowing water and very 
very /precisely/ realized by energy.  As previously 
explained, we don't say the flow of water "is" the 
flow of energy, but certainly the flow of water is 
_like_ the flow of energy.  No analogy is perfect, 
but this analogy has tremendous conceptual and 
pedagogical power.

To drive home the point, consider passing an electrical
current through aqueous sulfuric acid, as in an electro-
chemical battery or in an electrolysis setup.

So, what is flowing here?  Well, for starters there are 
some solvated H(+) ions flowing left-to-right, and to a 
first approximation there are some solvated electrons 
flowing right-to-left.

But that's not all,   There is /charge/ flowing from 
left to right.  Charge is an abstraction.  Sometimes
non-experts refer to electrons as negative "charges" 
but that is just wrong, as this example makes clear.  
The flow of charge differs in magnitude from the flow 
of electrons, even after you have duly accounted for 
the signs.

It is also wrong to think of the negative "charges" as
being lighter than the positive "charges".  In this
case, the vast bulk of the negative carriers are
bisulfate ions, HSO4(-), which are dramatically heavier 
than the negative ions.

One good way to keep track of it is in terms of baryon 
number, which is conserved in such processes.
 -- There is a certain flow of baryon number (protons
  and neutrons).
 -- There is a certain flow of lepton number (electrons).
 -- There is a certain flow of charge.
 -- There is a certain flow of energy.
 -- Of the six different pairwise combinations of the
  previous items, none of them are equal.  
 -- Indeed there is a significant component of energy
  flow _perpendicular_ to the electrical current, as the
  current causes Joule heating and the heat flows out
  of the current-carrying region.
 -- There are other conserved quantities, not least
  momentum, whose flow can be considered.
 -- All of these flows are considerably more abstract 
  than the usal third-grade-level notion of the "flow 
  of water".
 -- Being abstract doesn't make them any less real or 
   any less useful.  Abstract is the opposite of concrete 
   and tangible.  Abstract is not the opposite of real.


These points are discussed in greater detail at
  http://www.av8n.com/physics/reality-reductionism.htm

The smart way to formalize the idea of conservative flow 
is:
  http://www.av8n.com/physics/conservative-flow.htm

Tangentially related is
  http://www.av8n.com/physics/one-kind-of-charge.htm