Fallacy of Relativistic Doppler Effect

On 25/03/11 14:04, PD wrote:
On Mar 25, 7:27 am, wrote:
On 24/03/11 22:34, PD wrote:









On Mar 24, 4:40 pm, wrote:
On 24/03/11 13:47, PD wrote:

On Mar 24, 7:40 am, wrote:
On 23/03/11 13:50, PD wrote:

On Mar 23, 5:39 am, wrote:
On 22/03/11 18:21, PD wrote:
I think Einstein confused himself thinking that clocks measure
time.

Yes, indeed. Time is what clocks measure.

You cannot have your cake and eat it either time is the reciprocal
of frequency or it is what a clock measures.

Time is not the reciprocal of frequency. Time is benchmarked by a
locally stationary reproducible process. See the NIST standards.

You are ducking the issue:

a/The frequency of a transverse moving clock is reduced.

Yes.

Why do you accept this statement yet query the one below?
Clearly in the context it is moving relative to you and you are
measuring it in your FoR

I shouldn't have, in retrospect. The frequency of the moving clock is
reduced relative to the frequency of ticks on a clock stationary in
this frame.

There is no reduction in any intrinsic frequency in the moving clock's
frame.




b/The time interval between ticks is increased (dilated means increased)

The time interval as measured by a clock at *rest* in this frame is
increased between the ticks of the clock that is moving in this frame,
yes.

I am clearly talking about the same clock as in a/

Then the statement makes no sense. The time interval between ticks on
the clock moving are *unchanged* in the frame in which that clock is
at rest.

So is the frequency "*unchanged* in the frame in which that clock is at
rest". You understood the first statement. The second statement relates
to the same scenario. Are you deliberately being bloody minded

I should have corrected the first statement as well.

No you are being bloody minded. What else does "the frequency of a
transverse moving clock" possibly mean other than it is moving relative
to you. In the frame in which the clock is at rest it isn't moving.



See the comment below about the absence of ethereal, standalone time.

c/ What the moving clock registers is reduced.

Reduced, relative to a clock at rest in this frame, yes.

Note that there is no ethereal, detached Time that is affected. What
you are *always* doing is comparing the time measured on one clock
between two events with the time measured on another clock between the
same two events.

I never said otherwise



Ignoring Doppler shift (How in practice I don't know but never mind) You
have a moving clock transmitting ticks and locally you have two clocks
one a normal clock counting locally generated ticks and a second
counting transmitted ticks.

You can measure how long the transmitted tick interval is. This is
"measuring the time between two events" as you describe it - the arrival
of one tick and the next. It is this "tick interval" (units seconds)
which dilates.

What is registered on the clock counting the received ticks is a "tick
count".

What time is, is what a clock locally at rest measures.

In note you say "measures" not "indicates".

" We may say of it the following three things:
Set I
(a) The journey occurred in time.
(b) The time of starting was 1 o'clock.
(c) The time occupied by the journey was 2 hours.

The same word, time, is used here in three quite different senses, as
may be seen by considering the corresponding statements about space:
Set II
(a) The journey occurred in space.
(b) The place of starting was London.
(c) The length of (or distance covered by) the journey was 60 miles.

Here we use three different words � space, place, length (or distance),
none of that could be substituted for either of the others without
depriving the sentence of meaning. The same distinctions, thus brought
to light, exist in the set I, but they are obscured by the use
of the same word, 'time', for three quite different ideas.

To distinguish the three meanings of 'time' I will re-express the set I
in the following not unnatural ways:
Set III
(a) The journey occurred in eternity.
(b) The instant of starting was 1 o'clock.
(c) The duration of the journey was 2 hours." Dingle

Note that only (c) has units of seconds. I think that part of the
problem is that we are all familiar with clocks# and think of them as
something which tells time in hours minutes and seconds. In scientific
terms we should perhaps not use the term clock but "duration meter" -
envisaging something with a digital reading which increments at some
interval 1/10^n seconds. The larger n then the better the resolution -
which is started by one detected event and stopped by another event.
Your statement:
"What time is, is what a clock locally at rest measures".
Becomes
What time is, is what a "duration meter" locally at rest measures.
In terms of my scenario the only interval which the duration meter can
measure is the interval between the ticks - the reciprocal of which is
the frequency of the ticks.

#If one is pedantic the strict definition of a "clock" is something
which chimes. If it doesn't chime the correct terminology is a "time-piece".

On 25/03/11 14:17, Daryl McCullough wrote:
Alfonso says...

To distinguish the three meanings of 'time' I will re-express the set I
in the following not unnatural ways:
Set III
(a) The journey occurred in eternity.
(b) The instant of starting was 1 o'clock.
(c) The duration of the journey was 2 hours." Dingle

Note that only (c) has units of seconds. I think that part of the
problem is that we are all familiar with clocks# and think of them as
something which tells time in hours minutes and seconds. In scientific
terms we should perhaps not use the term clock but "duration meter" -
envisaging something with a digital reading which increments at some
interval 1/10^n seconds. The larger n then the better the resolution -
which is started by one detected event and stopped by another event.
Your statement:
"What time is, is what a clock locally at rest measures".
Becomes
What time is, is what a "duration meter" locally at rest measures.
In terms of my scenario the only interval which the duration meter can
measure is the interval between the ticks - the reciprocal of which is
the frequency of the ticks.

Right. Time in the sense of (b), which is a way of assigning
labels to events, requires two things: (1) a clock for measuring
durations, and (2) an initial setting.

Under what circumstance would you consider an "initial setting" essential?



The Lorentz transformations involve both.

The Doppler shift involve only duration, though.
There are two events, e_1 and e_2 occurring at the
sender. There are two corresponding events, e_3 and e_4
occurring at the receiver, where e_3 = the event in which
the receiver gets the light signal from e_1, and
e_4 = the event in which the receiver gets the light
signal from e_2. The Doppler shift is about the ratio

T_r/T_s

where T_r = the time between e_3 and e_4, as measured
by the receiver's clock, and T_s = the time between
e_1 and e_2, as measured by the sender's clock.

--
Daryl McCullough
Ithaca, NY

Alfonso says...

On 25/03/11 14:17, Daryl McCullough wrote:
Alfonso says...

To distinguish the three meanings of 'time' I will re-express the set I
in the following not unnatural ways:
Set III
(a) The journey occurred in eternity.
(b) The instant of starting was 1 o'clock.
(c) The duration of the journey was 2 hours." Dingle

Note that only (c) has units of seconds. I think that part of the
problem is that we are all familiar with clocks# and think of them as
something which tells time in hours minutes and seconds. In scientific
terms we should perhaps not use the term clock but "duration meter" -
envisaging something with a digital reading which increments at some
interval 1/10^n seconds. The larger n then the better the resolution -
which is started by one detected event and stopped by another event.
Your statement:
"What time is, is what a clock locally at rest measures".
Becomes
What time is, is what a "duration meter" locally at rest measures.
In terms of my scenario the only interval which the duration meter can
measure is the interval between the ticks - the reciprocal of which is
the frequency of the ticks.

Right. Time in the sense of (b), which is a way of assigning
labels to events, requires two things: (1) a clock for measuring
durations, and (2) an initial setting.

Under what circumstance would you consider an "initial setting" essential?

To say that "It is now 1:00 p.m." requires not just a clock, but a
convention for when you set the clock to 12:00 a.m.

On the other hand, to say "It is 2 hours and 15 minutes since sunset"
does not require an initial setting.

--
Daryl McCullough
Ithaca, NY

On 25/03/11 12:56, Androcles wrote:

wrote in message
...
| On 24/03/11 22:34, PD wrote:
| On Mar 24, 4:40 pm, wrote:
| On 24/03/11 13:47, PD wrote:
|
|
|
|
|
|
|
|
|
| On Mar 24, 7:40 am, wrote:
| On 23/03/11 13:50, PD wrote:
|
| On Mar 23, 5:39 am, wrote:
| On 22/03/11 18:21, PD wrote:
| I think Einstein confused himself thinking that clocks measure
| time.
|
| Yes, indeed. Time is what clocks measure.
|
| You cannot have your cake and eat it either time is the reciprocal
| of frequency or it is what a clock measures.
|
| Time is not the reciprocal of frequency. Time is benchmarked by a
| locally stationary reproducible process. See the NIST standards.
|
| You are ducking the issue:
|
| a/The frequency of a transverse moving clock is reduced.
|
| Yes.
|
| Why do you accept this statement yet query the one below?
| Clearly in the context it is moving relative to you and you are
| measuring it in your FoR
|
|
| b/The time interval between ticks is increased (dilated means
increased)
|
| The time interval as measured by a clock at *rest* in this frame is
| increased between the ticks of the clock that is moving in this frame,
| yes.
|
| I am clearly talking about the same clock as in a/
|
| Then the statement makes no sense. The time interval between ticks on
| the clock moving are *unchanged* in the frame in which that clock is
| at rest.
|
| So is the frequency "*unchanged* in the frame in which that clock is at
| rest". You understood the first statement. The second statement relates
| to the same scenario. Are you deliberately being bloody minded
|
| See the comment below about the absence of ethereal, standalone time.
|
|
|
|
| c/ What the moving clock registers is reduced.
|
| Reduced, relative to a clock at rest in this frame, yes.
|
| Note that there is no ethereal, detached Time that is affected. What
| you are *always* doing is comparing the time measured on one clock
| between two events with the time measured on another clock between the
| same two events.
|
| I never said otherwise
|
|
| Ignoring Doppler shift (How in practice I don't know but never mind)
You
| have a moving clock transmitting ticks and locally you have two clocks
| one a normal clock counting locally generated ticks and a second
| counting transmitted ticks.
|
| You can measure how long the transmitted tick interval is. This is
| "measuring the time between two events" as you describe it - the
arrival
| of one tick and the next. It is this "tick interval" (units seconds)
| which dilates.
|
| What is registered on the clock counting the received ticks is a "tick
| count".
|
| What time is, is what a clock locally at rest measures.
|
| In note you say "measures" not "indicates".
|
| " We may say of it the following three things:
| Set I
| (a) The journey occurred in time.
| (b) The time of starting was 1 o'clock.
| (c) The time occupied by the journey was 2 hours.
|
| The same word, time, is used here in three quite different senses, as
| may be seen by considering the corresponding statements about space:
| Set II
| (a) The journey occurred in space.
| (b) The place of starting was London.
| (c) The length of (or distance covered by) the journey was 60 miles.
|
| Here we use three different words — space, place, length (or distance),
| none of that could be substituted for either of the others without
| depriving the sentence of meaning. The same distinctions, thus brought
| to light, exist in the set I, but they are obscured by the use
| of the same word, 'time', for three quite different ideas.
|
| To distinguish the three meanings of 'time' I will re-express the set I
| in the following not unnatural ways:
| Set III
| (a) The journey occurred in eternity.
| (b) The instant of starting was 1 o'clock.
| (c) The duration of the journey was 2 hours." Dingle
|
| Note that only (c) has units of seconds. I think that part of the
| problem is that we are all familiar with clocks# and think of them as
| something which tells time in hours minutes and seconds. In scientific
| terms we should perhaps not use the term clock but "duration meter" -
| envisaging something with a digital reading which increments at some
| interval 1/10^n seconds. The larger n then the better the resolution -
| which is started by one detected event and stopped by another event.
| Your statement:
| "What time is, is what a clock locally at rest measures".
| Becomes
| What time is, is what a "duration meter" locally at rest measures.
| In terms of my scenario the only interval which the duration meter can
| measure is the interval between the ticks - the reciprocal of which is
| the frequency of the ticks.
|
| #If one is pedantic the strict definition of a "clock" is something
| which chimes. If it doesn't chime the correct terminology is a
"time-piece".

The English "Clock" is derived from the German "Glocke" for "bell".
plural Glocken = bells. Glockenspiel = play bells.
Church towers had bells, then mechanical devices were added to ring
them once an hour.

Originally to call the monks to prayer. Originally with no dial.

Initially clocks only had an hour pointer,
the minute
hand was added later. The correct term is "chronometer."

Historically you may be correct but today the term "chronometer" is used
for a device with sufficient accuracy to be used for navigation.
Certainly in the antiques trade "timepiece" is used to describe a more
ordinary device which tells the time but doesn't chime.

On 23/03/11 13:54, PD wrote:
On Mar 23, 2:10 am, Koobee wrote:
On Mar 22, 11:58 am, Daryl McCullough wrote:

Alfonso says...

Einstein's 1905 paper was somewhat sloppy. He did not define whether v
was towards or away from the source.

That is not correct. Einstein very clearly specifies that we have two
frames of reference K and k, and that the spatial origin of the k system
is moving at speed v in the positive x-direction, as measured by system K.

Could you point out where exactly?

Yes, section 3, where it says, "Now to the origin of one of the two
systems (k) let a constant velocity v be imparted in the direction of
the increasing x of the other stationary system (K), and let this
velocity be communicated to the axes of the co-ordinates, the relevant
measuring-rod, and the clocks."


You are the same guy who claims in my post when I said:

a/The frequency of a transverse moving clock is reduced.

b/The time interval between ticks is increased (dilated means increased)

That it was not clear that b referred to the same clock as a/

When I pointed out that it did you stated:

"Then the statement makes no sense. The time interval between ticks on
the clock moving are *unchanged* in the frame in which that clock is
at rest".

Now to any sensible person "The frequency of a transverse moving clock
is reduced". means a clock moving w.r.t you - it wouldn't be moving in
its own FoR would it? So "b/ The time interval between ticks is
increased" is clearly referring to the same transverse moving clock as
in a/ but for some reason you need that explained to you ... yet when
Einstein says "if an observer is moving with velocity v relatively to an
infinitely distant source of light of frequency f" in section 7 you
consider it is perfectly clear from section 3 which is the direction of
v.

The mind boggles. I have come to the conclusion that in your posts you
deliberately go out of your way to misunderstand what is written, to
introduce red herrings and deliberately complicate things. If you like
playing silly games then don't bother to reply to my posts.




KW, it is now abundantly clear that you have never read the 1905
paper, probably cannot read it, and your entire history of whining
about your perception of SR is grounded entirely on stuff you've made
up out of your own head.


So v is positive means that an object at rest in system k is moving
in the positive x-direction, as measured in system K. v is negative
means that an object at rest in system k is moving in the negative
x-direction.

It depends on which side of the x-axis the observer is located. So,
what you are saying makes no mathematical sense without specifying
where the observer is located along the x-axis. A better way to
explain what v is is to describe it as a relative velocity of one
point as observed by another specific point.shrug

You are confusing Doppler shift with time dilation. They are not
the same thing.

This is exactly what yours truly has been telling you. That was why
yours truly asked you to make a movie with a certain bandwidth. Send
it after mixing with a carrier frequency, and demodulate it with an
almost identical carrier frequency. You will notice time dilation
does not reflect in the Doppler shift. So, yours truly has been
guiding your thoughts away from the dark side of science. Could you
at least show some appreciation?shrug Oh, divorcing time dilation
from Doppler effect will help you in demystification if you are smart
enough to realize so.shrug

I think Einstein confused himself thinking that
clocks measure time. They in fact count ticks.

I don't see any evidence that Einstein is confused about this.

That is because you cannot do anything else besides fudging the
mathematics to suit your belief.shrug

"Alfonso" wrote in message
...
| On 25/03/11 12:56, Androcles wrote:
|
| wrote in message
| ...
| | On 24/03/11 22:34, PD wrote:
| | On Mar 24, 4:40 pm, wrote:
| | On 24/03/11 13:47, PD wrote:
| |
| |
| |
| |
| |
| |
| |
| |
| |
| | On Mar 24, 7:40 am, wrote:
| | On 23/03/11 13:50, PD wrote:
| |
| | On Mar 23, 5:39 am, wrote:
| | On 22/03/11 18:21, PD wrote:
| | I think Einstein confused himself thinking that clocks
measure
| | time.
| |
| | Yes, indeed. Time is what clocks measure.
| |
| | You cannot have your cake and eat it either time is the
reciprocal
| | of frequency or it is what a clock measures.
| |
| | Time is not the reciprocal of frequency. Time is benchmarked by
a
| | locally stationary reproducible process. See the NIST standards.
| |
| | You are ducking the issue:
| |
| | a/The frequency of a transverse moving clock is reduced.
| |
| | Yes.
| |
| | Why do you accept this statement yet query the one below?
| | Clearly in the context it is moving relative to you and you are
| | measuring it in your FoR
| |
| |
| | b/The time interval between ticks is increased (dilated means
| increased)
| |
| | The time interval as measured by a clock at *rest* in this frame
is
| | increased between the ticks of the clock that is moving in this
frame,
| | yes.
| |
| | I am clearly talking about the same clock as in a/
| |
| | Then the statement makes no sense. The time interval between ticks
on
| | the clock moving are *unchanged* in the frame in which that clock is
| | at rest.
| |
| | So is the frequency "*unchanged* in the frame in which that clock is
at
| | rest". You understood the first statement. The second statement
relates
| | to the same scenario. Are you deliberately being bloody minded
| |
| | See the comment below about the absence of ethereal, standalone
time.
| |
| |
| |
| |
| | c/ What the moving clock registers is reduced.
| |
| | Reduced, relative to a clock at rest in this frame, yes.
| |
| | Note that there is no ethereal, detached Time that is affected.
What
| | you are *always* doing is comparing the time measured on one clock
| | between two events with the time measured on another clock between
the
| | same two events.
| |
| | I never said otherwise
| |
| |
| | Ignoring Doppler shift (How in practice I don't know but never
mind)
| You
| | have a moving clock transmitting ticks and locally you have two
clocks
| | one a normal clock counting locally generated ticks and a second
| | counting transmitted ticks.
| |
| | You can measure how long the transmitted tick interval is. This is
| | "measuring the time between two events" as you describe it - the
| arrival
| | of one tick and the next. It is this "tick interval" (units
seconds)
| | which dilates.
| |
| | What is registered on the clock counting the received ticks is a
"tick
| | count".
| |
| | What time is, is what a clock locally at rest measures.
| |
| | In note you say "measures" not "indicates".
| |
| | " We may say of it the following three things:
| | Set I
| | (a) The journey occurred in time.
| | (b) The time of starting was 1 o'clock.
| | (c) The time occupied by the journey was 2 hours.
| |
| | The same word, time, is used here in three quite different senses, as
| | may be seen by considering the corresponding statements about space:
| | Set II
| | (a) The journey occurred in space.
| | (b) The place of starting was London.
| | (c) The length of (or distance covered by) the journey was 60 miles.
| |
| | Here we use three different words — space, place, length (or
distance),
| | none of that could be substituted for either of the others without
| | depriving the sentence of meaning. The same distinctions, thus brought
| | to light, exist in the set I, but they are obscured by the use
| | of the same word, 'time', for three quite different ideas.
| |
| | To distinguish the three meanings of 'time' I will re-express the set
I
| | in the following not unnatural ways:
| | Set III
| | (a) The journey occurred in eternity.
| | (b) The instant of starting was 1 o'clock.
| | (c) The duration of the journey was 2 hours." Dingle
| |
| | Note that only (c) has units of seconds. I think that part of the
| | problem is that we are all familiar with clocks# and think of them as
| | something which tells time in hours minutes and seconds. In
scientific
| | terms we should perhaps not use the term clock but "duration meter" -
| | envisaging something with a digital reading which increments at some
| | interval 1/10^n seconds. The larger n then the better the resolution -
| | which is started by one detected event and stopped by another event.
| | Your statement:
| | "What time is, is what a clock locally at rest measures".
| | Becomes
| | What time is, is what a "duration meter" locally at rest measures.
| | In terms of my scenario the only interval which the duration meter can
| | measure is the interval between the ticks - the reciprocal of which is
| | the frequency of the ticks.
| |
| | #If one is pedantic the strict definition of a "clock" is something
| | which chimes. If it doesn't chime the correct terminology is a
| "time-piece".
|
| The English "Clock" is derived from the German "Glocke" for "bell".
| plural Glocken = bells. Glockenspiel = play bells.
| Church towers had bells, then mechanical devices were added to ring
| them once an hour.
|
| Originally to call the monks to prayer. Originally with no dial.
|
Originally to call everyone to prayer, and still done today in Islam.

| Initially clocks only had an hour pointer,
| the minute
| hand was added later. The correct term is "chronometer."
|
| Historically you may be correct but today the term "chronometer" is used
| for a device with sufficient accuracy to be used for navigation.

Historically you may be correct but today the term for a device with
sufficient accuracy to be used for navigation is "phone" or "cell phone"
or "mobile phone". It displays a chart which today is called a "map"
and utters "Enter roundabout","Take the second exit", "Recalculating";
"Make a U-turn", "Recalculating", to the annoyance of the bus driver
who knows where he's going when I tested my new toy. "Would you
mind turning that off, please, it is distracting".-- Bus driver.



| Certainly in the antiques trade "timepiece" is used to describe a more
| ordinary device which tells the time but doesn't chime.

Oh really? I've never been a knockoff imitation Rolex pedlar. Today
a timepiece is called a... err... phone. Yeah, that's it. Phone. Chimes
are called "ringtones".

Back to the issue -
t = 1/f where t is the period and f is the frequency.
tg = g/f

(unless one is a relativist incapable of understanding algebra, in which
case
tg = 1/fg where g = 1/sqrt(1-v^2/c^2)
Your student is insane, one cannot teach simple math to deranged imbeciles.
One should not mock the afflicted unless they ask for it, and Phuckwit
Duck certainly asks for it.

"A pulse is not DC electricity. Idiot. Bloody-faced idiot. Self-flagellating
bloody-faced idiot" -- Phuckwit Duck.
c = 1 and unitless in natural units." -- Phuckwit Duck
"(x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2 - (t1-t2)^2 is invariant" -- Mallard.
"It turns out that you can verify curvature of a space without
ever stepping away from the space to see it embedded in a
higher dimension." - Mallard.
"Requests for *proof* will be routinely ignored in science because
theories are not proven in science."-- Mallard.
"I'm pretty sure you believe only what you want to believe." -- Phuckwit
Duck.
"You can't even keep track of the lies you say." -- Mallard
[sitting in the duck blind, waiting with a shotgun for a duck to appear] --
Blind Phuckwit Duck

Alfonso says...

Now to any sensible person "The frequency of a transverse moving clock
is reduced". means a clock moving w.r.t you - it wouldn't be moving in
its own FoR would it? So "b/ The time interval between ticks is
increased" is clearly referring to the same transverse moving clock as
in a/ but for some reason you need that explained to you ... yet when
Einstein says "if an observer is moving with velocity v relatively to an
infinitely distant source of light of frequency f" in section 7 you
consider it is perfectly clear from section 3 which is the direction of
v.

The whole paper is explaining the derivation of and the implications of
the Lorentz transformations. He introduces the two frames K and k at
the beginning of the paper, and every section returns to these two
frames.

Section 7 starts off:
"In the system K, very far from the origin of co-ordinates, let
there be a source of electrodynamic waves..."

Then a few sentences later:
"We wish to know the constitution of these waves, when they are
examined by an observer at rest in the moving system k."

It's certainly possible that someone by this point has forgotten
the definitions of K and k, but that doesn't make it ambiguous.
If I'm reading Romeo and Juliet, I might forget whether
Benvolio is Romeo's cousin, or Juliet's cousin, but that
doesn't mean that it is ambiguous whose cousin he is. It's
right there in the play.

--
Daryl McCullough
Ithaca, NY

On Mar 24, 4:50 am, Daryl McCullough wrote:

Phi = kx - wt

To compute w' in a new coordinate
system, you rewrite x and t in terms
of x' and t':

x = gamma (x' + vt')
t = gamma (t' + v/c^2 x')

So in the frame F', we have:

Phi' = gamma k (x'+vt') - gamma w (t'+v/c^2 x')
= gamma (k-vw/c^2) x' - gamma (w-vk) t'

So
k' = gamma (k-vw/c^2)
w' = gamma (w-vk)

To get the nonrelativistic limit, you just
take the limit in which v/c is small, so
gamma is approximately 1, and v/c^2 is approximately
zero. This produces:

k' = k
w' = w-vk

In the Galilean case, there is no shift for *wave-length*
(k = 2pi/L, where L is the wavelength), but there is still
a shift for frequency (w is actually 2pi f, where f is
the frequency).

Yours truly was preparing to ruin a celebration, but the victory dance
never came. Why? So, here it is.

What is the transverse Doppler effect under relativity? According to
the energy transformation and also your derivation, it should predict
a blue shift while experiments time after time all have indicated
red. Oops! shrug

This disagreement of SR with experiments is serious and fatal, no?

checkmate

On Mar 26, 2:42*pm, Koobee Wublee wrote:
On Mar 24, 4:50 am, Daryl McCullough wrote:









Phi = kx - wt

To compute w' in a new coordinate
system, you rewrite x and t in terms
of x' and t':

x = gamma (x' + vt')
t = gamma (t' + v/c^2 x')

So in the frame F', we have:

Phi' = gamma k (x'+vt') - gamma w (t'+v/c^2 x')
= gamma (k-vw/c^2) x' - gamma (w-vk) t'

So
k' = gamma (k-vw/c^2)
w' = gamma (w-vk)

To get the nonrelativistic limit, you just
take the limit in which v/c is small, so
gamma is approximately 1, and v/c^2 is approximately
zero. This produces:

k' = k
w' = w-vk

In the Galilean case, there is no shift for *wave-length*
(k = 2pi/L, where L is the wavelength), but there is still
a shift for frequency (w is actually 2pi f, where f is
the frequency).

Yours truly was preparing to ruin a celebration, but the victory dance
never came. *Why? *So, here it is.

Between the constant talking about yourself in 3rd person [yours truly
this, yours truly that] and the constant shrugging I am beginning to
think you are mentally ill as well as stupid.

I'd say you are a narcissist but you refuse to post under your real
name. Which makes you just a coward.


What is the transverse Doppler effect under relativity? *According to
the energy transformation and also your derivation, it should predict
a blue shift while experiments time after time all have indicated
red. *Oops! *shrug

In what way are your arguments credible? It has already been
established that you were COMPLETELY WRONG when discussing your
strawman derivation of the relativistic Doppler effect. What are the
odds you are correct about the transverse Doppler effect?

You are probably making an idiotic error with how the coordinate
systems are arranged. Or something equally stupid, which is par for
the course for you.


This disagreement of SR with experiments is serious and fatal, no?

checkmate

Do you act this smug about things you don't understand in person, or
is this just an internet thing?

what is the big deal?...

doppler effect is strictly a matter of relative velocity,
between shouter & hearer, just as with sound,
whjere theior is also a characteristic speed,
which also depends upon an "index of rarefaction,"
to coin a term. some spaces are simply emptier than others.