Re: Scalar waves

Am Mittwoch000001, 01.05.2024 um 09:46 schrieb J. J. Lodder:

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The dimensional analysis of course is the attachment of a mathematical
model to a physical model at all, then with regards to usual
"dimensions" being quantitative and geometrical.
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The dimensionless really does have any number of "balanced implicits"
in it. Any sort of "1 unit/unit" is a thing, and as well in the
quantities, "1 goes-to-1-from-the-left/goes-to-1-from-the-right",
sort of arrives at the same thing.

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Well, in reality 1 means a natural dimensionless number.

 Nonsense. That 'dimensionless' doesn't belong there.
And 1 being a natural number doesn't have a meaning.
It is, by the mathematical definition of natural number.
 

Having no units says, that c is unitless and has only the numerical value 1.

 Your misunderstandings in a nushell.
All it says is that 'length' and 'time' are measured in the same unit.
(apart from an inconvenient numerical factor)
 This is precisely what all working physicists have been doing
ever since the abolition of the meter as an independent unit
at the 17th CIPM, 1983.
 

The symbol '1' has a meaning: it is meant as numerical value 'one'.
Since it is a number only, it contains no units or dimensions of whatever kind.
This is the meaning of the term 'number'.
Physical quantities are never numbers only, because any quantity is composed of a numerical value and a definition, to what that number belongs.
Since c=1 means 'the speed of light in vacuum is always one', the dimensions 'length' and 'time' in c=~ ckm/s' must have somehow vanished (mysteriously).
In our usual world you cannot cancel km and seconds, hence in the realm of light-speed space and time must be of the same dimension (otherwise they could not be canceled).
The number 300.000 is no big deal, of course, and we could use lightseconds and seconds instead of km and seconds.
BUT: still lightsecond is a unit of length, which you must not cancel with seconds.
TH