[paul cotter (OP)]

A tenured professor of electrical engineering in  Germany applies ∇Χ∇Χ to the electric field, E and arrives at the following vector identity: grad div E -∇sqE. He then states that the term grad div E represents the "scalar wave" and proceeds to sell expensive but basic kits that supposedly demonstrate these "scalar waves". However div E=0 in a charge free zone( ie free space ) so grad0 is also 0. This individual also states that an ice can be run on water as fuel if ozone is added. I am dumbfounded. PS I apologise for alternating between the del operator and grad, div as I cannot get consistent use of symbols on this computer/operating system.

[Zer0]

It That Gentleman still in Business?
(Current Professor or long retired)

Are We referring to a considerably Old Senior Citizen?

[paul cotter (OP)]

ZerO, apologies, I missed your reply( I have been in my hibernation phase ). As far as I know he is still active, ie not an emeritus prof.

[Bored chemist]

Academia has to tolerate people who make absurd errors.
Sometimes they turn out to be right. :-)

[Eternal Student]

Hi.

He then states that the term grad div E represents the "scalar wave"

   Grad  (of a thing) is always a vector not a scalar.   So on the face of it I would be concerned about it being called the "scalar wave"  - but I haven't looked at exactly what this professor did.

PS I apologise for alternating between the del operator and grad, div as I cannot get consistent use of symbols on this computer/operating system.

   Obviously what you have done is OK anyway.    However, if you ever really wanted some mathematical notation then it can be done on any computer with any keyboard (e.g. a mobile phone)  if you use  LaTeX coding.   I'll put all of this under a pull-down spoiler, since it's not essential for the original post or reply.

Spoiler: show

You have probably noticed already that this forum software places something you want to appear in BOLD  inside  tags.   One very useful set of tags is the start and end     tex    tags because everything between those will be processed as LaTex.

This code produces  some usefull stuff:

Code: [Select]

"Del" or "nabla"  symbols are called with a "backslash" \  and the text "nabla" written straight after it   like this   [tex]  \nabla    [/tex]
Most special LaTex sybols are called with the backslash \ in front but note that a forward slash / MUST be used in the end tex tag.

Vectors with the arrow over the top   [tex] \vec{A}   [/tex].      Vectors as underlined characters    [tex] \underline{A}  [/tex]

The times symbol [tex] \times [/tex]  looks neater than using a letter  [tex] X [/tex]  for multiplication or vector cross products.

Write the curl of a vector like this  [tex] \nabla \times \vec{A}  [/tex]    but I prefer underlined vectors [tex] \nabla \times \underline{A} [/tex]

Exponentials can be done with the ^ character. So the Laplacian operator is written as   [tex] \nabla^2  [/tex]   
Just type that directly into the forum reply box and you will get this produced when you hit  "preview" or "post":

                - - - - - - - - - -
"Del" or "nabla"  symbols are called with a "backslash" \  and the text "nabla" written straight after it   like this   
Most special LaTex sybols are called with the backslash \ in front but note that a forward slash / MUST be used in the end tex tag.

Vectors with the arrow over the top   .      Vectors as underlined characters   

The times symbol   looks neater than using a letter    for multiplication or vector cross products.

Write the curl of a vector like this      but I prefer underlined vectors

Exponentials can be done with the ^ character. So the Laplacian operator is written as   
 - - - - - - -  - -  -

   Back to your original post:

   The identity         will hold for any sensible  vector  E.
   See half-way down the page here:   https://en.wikipedia.org/wiki/Vector_calculus_identities#Second_derivative_identities

By sensible vector, I mean it's smooth enough - all the derivatives you would want actually do exist.   You could have deliberately chosen a vector that had some discontinuity in some first derivatives if you wanted to invalidate that identity.
Note also that the operator ∇² on the right hand side is understood to be the vector Laplacian  (it acts on a vector to produce another vector).   Assuming E is the electric field and satisfies Maxwell's equations then you automatically have most of what you'll need to be confident the vector function is smooth enough for that identity to hold.   I haven't spent too long looking at it but it seems you would have to be deliberately trying hard to find a most unusual E field if you wanted to defeat that vector identity - so we'll just go along with the assumption the vector identity will hold.

   So nothing much is wrong with what that professor said to this point.   The only bit, as I said previously, that concerns me is the terminology "scalar wave".   That's not terminology I'm familiar with and the thing isn't a scalar, it would be a vector.

   Just from Maxwell's equations,  we have Grad(E) = 0 in free space without any charges exactly as you stated,  so yes  all of what he/she is calling the "scalar wave" would become a 0 vector there.    I'm going to assume the professor knows that and their  "scalar wave" idea is only interesting in regions where there are charges.   Overall impression  --->  I wouldn't be rushing off to find out what the professor was trying to say (or sell) based on what you have written.   

    As regards the fuel thing.   "An ice" can have a meaning other than the usual solid water ice.   Here's an example:
     In astrophysics and planetary science the term "ices" refers to volatile chemical compounds with freezing points above about 100 K, such as water, ammonia, or methane, with freezing points of 273 K (0°C), 195 K (−78°C), and 91 K (−182°C), respectively (see Volatiles).           [Extract from Wikipedia:     https://en.wikipedia.org/wiki/Ice_giant ]
     Without reading the full details,  maybe their ice thing could work.

Best Wishes.

[paul cotter (OP)]

Internal combustion engine=ice. I am sorry for any confusion, I should not be using abbreviations that may be misunderstood. PS, as explained to ZerO I haven't fully emerged from my annual hibernation phase.

[Zer0]

Academia has to tolerate people who make absurd errors.
Sometimes they turn out to be right. :-)

You got any fun or entertaining Evidences?

[paul cotter (OP)]

ZerO, check out dr Dolores Cahill, one of our own academics who fell down the rabbit hole and has not been able to extricate herself yet. 

[Zer0]

What if an Expert who suffered thru Serious Covid - 19 & never truly recovered from it's negative mental side effects goes onto make illogical statements...

Should people suffering thru Brain Fog be held accountable for what they say & do?

I'm observing something similar with Senior Citizens lately, they say absurd stuff n act crazy.
But undecided on whether i should view Them as Culprits or Victims?