Scalar waves

[ivica]

Scalar waves, how much do we know about them ?
Do you have something about it, of a value, to share with us?
 
https://en.wikipedia.org/wiki/Wave_equation
https://en.wikipedia.org/wiki/Scalar_field
https://en.wikipedia.org/wiki/Scalar_field_theory
http://rationalwiki.org/wiki/Scalar_wave
   

Kids, be afraid, !

[ivica]

[sidd]

Definitions:

1) A wave is a solution of the wave equation, which states that the second spatial derivative of a field times the square of the wave velocity is equal to the second time derivative of that field.

2) The field can be a scalar. Then you have, for example, sound waves, where the field is the gas pressure.

what would you like to know ?

[ivica]

Sidd, thanks for your question,
I'd like to know what we do not know .

[sidd]

"I'd like to know what we do not know ."

Why, so woud I ...

Here is something we do not know. The solutions to the wave equation  are often written f(x-ct) where f is an arbitrary function, x and t and the space and time co-ordinates, and c is the wave velocity. This trivially satisfies the wave equation and is called the "retarded" solution. But the function f(x+ct) is an equally good "advanced" solution, which is (usually) rejected on the grounds of causality, since it represents a wave travelling backward in time. Wheeler and Feynman actually worked out the case where both solutions were considered for electromagnetism.

https://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory

There is a story that Einstein was present when this was presented, enquired if it woud generalize to gravity, and was told that it was a work in progress. Thereupon the big E remarked that Wheeler would not be successful in the generalization.

Which he wasnt.