Here you demonstrate:
- You don't know that Φ is the phase of the wave.
Or rather: you don't know what the phase of a wave is.
- You don't understand that (t,x,y,z) are the coordinates
of an event.
- You don't understand that the phase is a function
Φ(t,x,y,z) of these coordinates. Φ = ω{t-(lx + my + nz)/c}
And this is despite the fact that I (an probably several others)
have explained this to you before:
|03.04.2021 Paul B. Andersen wrote:
|> Look at this:
|>
https://paulba.no/pdf/AberrationDoppler.pdf
|>
|> I am not expecting you to understand anything of it,
|> the point is that equation (1) and (2) are the equations
|> for the electric field in an EM wave moving in the positive
|> z direction. Equation (2) is the phase of the wave.
|> Equation (6) is the same equation as:
|> Φ = ω{t − (lx+my+nz)/c}
|> with the slight difference that this is the phase
|> of a wave propagating in a general direction.
|>
|> Anybody with the slightest knowledge of physics
|> will immediately recognize these equations, and will know
|> that the wavelength is 2πc/ω. (λ = c/f)
|06.04.2021 Paul B. Andersen wrote:
|> Thomas, in all elementary physics books you will find
|> a chapter with the name "Wave motion" or similar.
|>
|> I looked in the first physic book I ever read,
|> Margenau et al: Physics, from 1953.
|> Here I find as the equation for a wave (any wave):
|>
|> y = A⋅sin(2π(t/P-x/λ))
|>
|> where P is the period, P = 1/f, and λ is the wavelength
|>
|> The argument of a sinus is always a phase,(an angle in radians), so:
|> Φ(t,x) = 2π(t/P-x/λ)
|>
|> This equation can be written on several equivalent forms:
|>
|> Einstein's equation was:
|> Φ = ω{t − (lx+my+nz)/c}
|> In the case where the wave is moving along the x-axis,
|> the direction cosines are l = 1, m = 0 and n = 0,
|> and the equation for the phase can be written:
|> Φ(t,x) = ω(t - x/c) = (ω⋅t - (ω/c)⋅x)
|>
|> inserting ω = 2πf yields:
|> Φ(t,x) = (2πf⋅t − (2πf/c)⋅x) = 2π(f⋅t - (f/c)⋅x)
|>
|> inserting λ = c/f yields:
|> Φ(t,x) = 2π(f⋅t − (1/λ)⋅x)
|>
|> You don't have to be a physicist to know this,
|> it is _very_ elementary physics, and it was
|> known as such _long_ before 1905.
If you don't understand these equations, you are not
competent to read the paper where the equations occur.
>>
>> What he writes here is incredibly naive, this is high school wave motion
>> stuff here he is trying to discuss.
You said you were "forced to understand every single word in the text"
But you keep demonstrating that you understand nothing of the text:
>
> Actually not.
>
> I think mainly like a programmer, who writes a code-review or something
> similar.
> I read a text and find a symbol like 'x', for instance.
>
> Now x is not a variable and much less a physical quantity. Thaat 'x' is
> simply a short text, which consists from a single ACII character 'x'.
>
> That is is taken as the name of a variable.
>
> Variables store something. The 'x' is a 'handle' by which that storage
> is addressed.
>
> Now I ask the question, what shall be stored at that storage.
>
> So, I scimmed the text for possible meanings of 'x'.
>
> The first occurance of 'x' denotes a scalar part of a postition vector
> in coordinate system K.
>
> So, ok, 'x' stores scalars, which mean a number, by which the unit
> vector of that coordinate system shall be multiplied.
>
> All together they build a vector (x,y,z), which belongs to system K.
>
> That is nice and no problem at all.
>
> But any further occurances of 'x' are therefore meant as scalar part of
> position vector (x,y,z) from system K.
This reminds me of a Dilbert story.
I can't find the cartoon, but the story goes like this:
Teacher solving equations on the blackboard, saying:
" .. and then x = 5"
Dilbert raising his hand, saying:
"Wait a darn minute! Yesterday you said x = 3!"
>
> Similar with l, m, and n, which also occur in that equation.
>
> These are 'direction cosines' and belong to angles of the incoming ray
> at the position of the observer.
>
> This is also nice and no problem at all.
>
> But what does the author want to say with this equation, if the
> position in K is not defined and the postion of the observer or a ray
> arriving there were not under consideration?
This is defined:
The equation is in the beginning of
§ 7. Theory of Doppler’s Principle and of Aberration
If you read on, you will find:
".. an observer is moving with velocity v relatively to
an infinitely distant source of light of frequency ν (nu),
in such a way that the connecting line “source-observer”
makes the angle φ with the velocity of the observer referred
to a system of co-ordinates which is at rest relatively to
the source of light,.."
You demonstrate that you do not understand what this means
in your "annotation".
"To define velocity in respect to infinity would be a very
bad idea, because ‘Infinitely distant' is remaining infinitely
distant, even if you move in respect to infinity. Velocity
is defined as v=dx/dt. And because that 'x' in dx is not
changing (stays always 'infinity'), v will remain zero, however
you move. Therefore, your velocity in respect to infinity is always
zero."
This is nonsense!
The source is stationary in K at infinity.
The observer is moving at the velocity v⃗ in K, in such a way
that the connecting line “source-observer” makes the angle φ with
the velocity.
Look.
A star with parallax - say < 1"- can be considered to be
infinitely far away, and stationary in the solar frame.(K)
And you are saying that the velocity of the Earth in the solar
frame is always zero because the star is so far away! :-D
https://paulba.no/pdf/Stellar_aberration.pdf
>
>
> I complained here about missing definitions of used variables and about
> inconsisted or impossible interpretations of variables names already
> used otherwise.
>
> A computer programm would quit at that time with a general error message.
>
> I wrote, that I do not understand, what the variables are supposed to
> express.
The reason is simple. You are ignorant of elementary physics,
and you are not competent to read Einstein's paper.papaer
>
> My guess was, that phase angles were actually meant, but cannot read the
> author's mind.
The problem is rather that you cannot read a text about physics.
--
Paul
https://paulba.no/