From: Koobee Wublee on
On Aug 5, 12:26 pm, "Paul B. Andersen" wrote:
> On 05.08.2010 01:16, Koobee Wublee wrote:

> > The second post by Professor Roberts has a wrong conclusion on
> > relativistic Doppler effect. The Lorentz transform actually leads to
> > a reverse Doppler effect. Where have the self-styled physicist been
> > in the past 100 years? See the following recent posts by yours truly
> > at:
>
> > http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en
>
> > http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en
>
> So can you please point out the error in the following derivation?
>
> A wave propagating in the positive x direction
> in the unprimed frame can be written:
> E cos(phi(t,x)) where phi(t,x) = wt - (w/c)x
>
> Let the primed frame be moving at v along the positive x-axis.
>
> The same wave transformed to the primed frame can be written:
> E' cos(phi'(t',x')) where phi'(t',x') = w't' - (w'/c)x'
>
> Applying the LT transform:
> t = g(t' + vx'/c^2)
> x = g(x' + vt')
> g = 1/sqrt(1-v^2/c^2)
> yields:
> wt - (w/c)x = wg((t' + vx'/c^2) - (w/c)g(x' + vt')
> = wg(1-v/c)t' - (w/c)g(1-v/c)x'
> = w't' - (w'/c)x'
>
> Thus:
> w' = wg(1-v/c) = w sqrt((1-v/c)/(1+v/c))
>
> The wave is red shifted in the primed frame.

First, you are stating the following which stands on no ground.

** w (t - x / c) = w' (t' - x' /c)

Secondly, you can easily write the result as the following instead,

** w = w' sqrt(1 + v / c) / sqrt(1 - v / c)

Where

** v = Speed of w' relative to w

And proudly claim w-w' moving away (v > 0) as Doppler blue shift.
Notice the classical Doppler effect for sound cannot be derived using
your method. This should be an alarm ringing in your head on your
part. Once again, your mistake is in the application of the Lorentz
transform.

The time transformation can generally be written as follows. You must
pay very close and crucial attention to the directions of these
vectors. The self-styled physicists have been hand-waving and spoon-
feeding this nonsense to their brain-washed pupils in the past 100
years.

** dt' = (dt - [v] * d[s] / c) / sqrt(1 - v^2 / c^2)

Where

** [v] = Velocity of dt' as observed by dt
** d[s]/dt = [c] = Velocity of light
** d[s]/dt * d[s]/dt = c^2

Since you are making the same mistake again, I shall not count this
one as a score of mine. Please study my posts below more carefully.
It is not that hard. <shrug>

http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en

http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en

Since you have brought up the wave equations for light, solutions to
Maxwell's equation in free space are:

SUM_n[[E_n] exp(a_n (w_n t + b_n [k_n] * [s]) + c_n)]

Where

** a_n = +/- 1 or +/- sqrt(-1)
** b_n = +/- 1
** [E_n] = Constant vector
** [k_n] = Direction vector
** [s] = Position vector
** k_n^2 = w_n^2 / c^2
** * = Dot product of two vectors

Filtering out solutions that do not allow propagation of waves, what
is left is the following representing one particular frequency of
interest.

E cos(w t - [k] * [s] + theta)

Where

** theta = Phase

You understand k^2 as 1 / wavelength^2. <shrug>

Should the Lorentz transform be applied to [k] and w?
From: Paul B. Andersen on
On 06.08.2010 08:48, Koobee Wublee wrote:
> On Aug 5, 12:26 pm, "Paul B. Andersen" wrote:
>> On 05.08.2010 01:16, Koobee Wublee wrote:
>
>>> The second post by Professor Roberts has a wrong conclusion on
>>> relativistic Doppler effect. The Lorentz transform actually leads to
>>> a reverse Doppler effect. Where have the self-styled physicist been
>>> in the past 100 years? See the following recent posts by yours truly
>>> at:
>>
>>> http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en
>>
>>> http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en
>>
>> So can you please point out the error in the following derivation?
>>
>> A wave propagating in the positive x direction
>> in the unprimed frame can be written:
>> E cos(phi(t,x)) where phi(t,x) = wt - (w/c)x
>>
>> Let the primed frame be moving at v along the positive x-axis.
>>
>> The same wave transformed to the primed frame can be written:
>> E' cos(phi'(t',x')) where phi'(t',x') = w't' - (w'/c)x'
>>
>> Applying the LT transform:
>> t = g(t' + vx'/c^2)
>> x = g(x' + vt')
>> g = 1/sqrt(1-v^2/c^2)
>> yields:
>> wt - (w/c)x = wg((t' + vx'/c^2) - (w/c)g(x' + vt')
>> = wg(1-v/c)t' - (w/c)g(1-v/c)x'
>> = w't' - (w'/c)x'
>>
>> Thus:
>> w' = wg(1-v/c) = w sqrt((1-v/c)/(1+v/c))
>>
>> The wave is red shifted in the primed frame.
>
> First, you are stating the following which stands on no ground.
>
> ** w (t - x / c) = w' (t' - x' /c)

It should be clear from the context that the event
with coordinates (t,x) in the unprimed frame
has the coordinates (t',x') in the primed frame.

The phase of the wave at a specific event is the same
in all frames of reference.
That is, phi(t,x) = phi'(t',x')
where (t,x) and (t',x') are the coordinates of the _same_ event.

You do know that the LT transforms the coordinates
of an event, don't you?
Or don't you? :-)

>
> Secondly, you can easily write the result as the following instead,
>
> ** w = w' sqrt(1 + v / c) / sqrt(1 - v / c)

Sure.
If the frequency of the wave in the primed frame is lower
than its frequency in the unprimed frame, then the frequency
of the wave in the unprimed frame is higher than its frequency
in the primed frame.

Do you find this obvious triviality remarkable? :-)

>
> Where
>
> ** v = Speed of w' relative to w
>
> And proudly claim w-w' moving away (v> 0) as Doppler blue shift.

Sure, what's wrong with that?
The wave is propagating in the positive x-direction!

------> wave

|----> x' ->v
|----> x

If the wave has the frequency w' in the primed frame,
an observer in the unprimed frame will measure the frequency
w = w' sqrt(1 + v / c) / sqrt(1 - v / c)
which is a blue shifted compared to w'.

> Notice the classical Doppler effect for sound cannot be derived using
> your method.

Why not?
"Classical Doppler" -> Galilean transform.

An acoustic wave propagating in the positive x direction
in the unprimed rest frame of the medium can be written:
A cos(phi(t,x)) where phi(t,x) = wt - (w/c)x
where c is the speed of the wave in the medium.

Let the primed frame be moving at v along the positive x-axis.

The same wave transformed to the primed frame can be written:
A' cos(phi'(t',x')) where phi'(t',x') = w't' - (w'/(c-v))x'
(The speed of sound in the prined frame is c-v)

Applying the Galilean transform:
t = t'
x = x' + vt'
yields:
wt - (w/c)x = wt' - (w/c)(x' + vt')
= w(1-v/c)t' - (w/c)x'
= w't' - (w/c)x'

Thus:
w' = w(1-v/c)
The wave is red shifted in the primed frame.
Note that k' = w/c = k
k' = k and thus lambda' = lambda
The wavelength is the same in all frames.


> This should be an alarm ringing in your head on your
> part. Once again, your mistake is in the application of the Lorentz
> transform.

There is no mistake.
You seem very confused about what Doppler shift is.

Try again to find an error? :-)

> The time transformation can generally be written as follows. You must
> pay very close and crucial attention to the directions of these
> vectors. The self-styled physicists have been hand-waving and spoon-
> feeding this nonsense to their brain-washed pupils in the past 100
> years.
>
> ** dt' = (dt - [v] * d[s] / c) / sqrt(1 - v^2 / c^2)
>
> Where
>
> ** [v] = Velocity of dt' as observed by dt
> ** d[s]/dt = [c] = Velocity of light
> ** d[s]/dt * d[s]/dt = c^2
>
> Since you are making the same mistake again, I shall not count this
> one as a score of mine. Please study my posts below more carefully.
> It is not that hard.<shrug>
>
> http://groups.google.com/group/sci.physics.relativity/msg/c06938d96ee7f84d?hl=en
>
> http://groups.google.com/group/sci.physics.relativity/msg/fddbda5c1bb76e80?hl=en
>
> Since you have brought up the wave equations for light, solutions to
> Maxwell's equation in free space are:
>
> SUM_n[[E_n] exp(a_n (w_n t + b_n [k_n] * [s]) + c_n)]
>
> Where
>
> ** a_n = +/- 1 or +/- sqrt(-1)
> ** b_n = +/- 1
> ** [E_n] = Constant vector
> ** [k_n] = Direction vector
> ** [s] = Position vector
> ** k_n^2 = w_n^2 / c^2
> ** * = Dot product of two vectors
>
> Filtering out solutions that do not allow propagation of waves, what
> is left is the following representing one particular frequency of
> interest.
>
> E cos(w t - [k] * [s] + theta)
>
> Where
>
> ** theta = Phase
>
> You understand k^2 as 1 / wavelength^2.<shrug>

No.

k^2 = 4*pi^2/wavelength^2
= w^2/c^2 for a non-dispersive wave

EM-waves in free space are non-dispersive.
And so are audible acoustic waves in air.

<shrug>

So setting the arbitrary constant theta = 0,
and letting the wave vector be parallel
to the x-axis, we are back to my equation above.

E cos(phi(t,x)) where phi(t,x) = wt - (w/c)x
or
E cos(wt - (w/c)x)

<shrug>

I took for granted that you knew that this is a solution
of Maxwell's wave equation.
(Or any wave equation, for that matter).

<shrug>

>
> Should the Lorentz transform be applied to [k] and w?


If you want to transform the wave to a different frame,
of course.

<shrug>

You can see above how k = w/c and w are transformed.
Note that k' = (w/c)sqrt((1-v/c)/(1+v/c))
That means that lambda' = lambda ((1+v/c)/(1-v/c))

<shrug>


--
Paul

http://home.c2i.net/pb_andersen/
From: BURT on
On Aug 6, 9:46 pm, artful <artful...(a)hotmail.com> wrote:
>
> > > > What does time do if not slow down from a fastest point?
>
> > > What a stupid question from a stupid person.  
>
> > There are Two Times that can slow down. One is from gravity. The other
> > is from mass in motion.
>
> Now you're just spouting nonsense.  Yours is a typical response from a
> troll .. can't say anything relevant and meaningful, so pout some
> nonsense assertion and try to divert the topic.

One time comes from Einstein's theory of gravity and the second comes
from his theory of motion. These are the Two times.

Mitch Raemsch
From: artful on
On Aug 7, 2:50 pm, BURT <macromi...(a)yahoo.com> wrote:
> On Aug 6, 9:46 pm, artful <artful...(a)hotmail.com> wrote:
>
>
>
> > > > > What does time do if not slow down from a fastest point?
>
> > > > What a stupid question from a stupid person.  
>
> > > There are Two Times that can slow down. One is from gravity. The other
> > > is from mass in motion.
>
> >
>
> One time comes from Einstein's theory of gravity and the second comes
> from his theory of motion. These are the Two times.

Now you're just spouting nonsense.  Yours is a typical response from a
troll .. can't say anything relevant and meaningful, so spout some
nonsense assertion and try to divert the topic.
From: Michael Moroney on
artful <artful_me(a)hotmail.com> writes:

>Now you're just spouting nonsense. =A0Yours is a typical response from a
>troll .. can't say anything relevant and meaningful, so spout some
>nonsense assertion and try to divert the topic.

This is Mitch/BURT you're arguing with. All he does is spout nonsense
from his own misunderstanding of physics, plus his own "physics by
proclamation". Don't expect anything more than arguing with the guy
sitting outside the bus station asking for quarters.