Re: To Androcles and Henry: Ballistic Doppler Shift Equation

From: Thomas Wong (nonfunctional_email_at_comcast.net)
Date: 01/17/05 

Date: 16 Jan 2005 16:08:25 -0800

Henri Wilson wrote:
> On 11 Jan 2005 05:14:51 -0800, "Thomas Wong"
<nonfunctional_email@comcast.net>
> wrote:
>
> >Hi, Everybody!
> >
> >I'm in my ultrafast spaceship traveling with my buddies Androcles
and
> >Henri on a tourist trip to Uranus. It will take us only a few hours
to
> >reach our destination, because our ship is capable of reaching NAFAL
> >(nearly-as-fast-as-light) velocities.
>
> Velocities are always relative. I gather you mean 'wrt Earth'.

Yes. The spaceship is heading directly outwards with no tangential
velocity.

> >We're in no real hurry though,
> >and we don't want to waste our supply of antimatter fuel, so right
now
> >the speedometer says that we're driving slowly at only 35,940 km/s
away
> >from Earth.
> >
> >The driver gets to choose the radio station. I'm in the driver's
seat
> >so I tune the radio to my favorite Houston oldies radio station
KLDE-FM
> >(107.5).
> >
> >Unfortunately, what is coming out of the speakers is COUNTRY!
> >
> >Ahah, I know what is going on! Doppler shift!
> >
> >Out of curiosity, I want to find out what station I'm listening to.
> >
> >The relativistic Doppler shift equation is
> >f/f_0 = sqrt((1-v/c)/(1+v/c))
> >and when I plug the spaceship velocity into the equation, it tells
me
> >that I'm tuned to KHYT (95.3).
> >
> >Androcles looks at me sort of funny.
> >
> >Henri screws his mouth up.
> >
> >"Uh, Tom," says Androcles. "The relativistic Doppler shift equation
is
> >wrong. Light travels ballistically."
> >
> >To Androcles and Henri:
> >
> >1) What is the Ballistic Doppler Shift equation for this case?
> >2) What is the speed of light from the radio stations relative to
me?
> >3) What frequency on Earth am I tuned to?
> >4) What is the wavelength of the radio waves that I am receiving?
> >5) What station am I listening to?
> >
> >Finally,
> >Instead of driving away from the Earth in my spaceship, I attach a
huge
> >Bergenholm drive to the Earth and PUSH Earth away from my stationary
> >spaceship at a speed of 34,840 km/s.
> >1') What is the Ballistic Doppler Shift equation for this case?
> >2') What is the speed of light from the radio stations relative to
me?
> >3') What frequency on Earth am I tuned to?
> >4') What is the wavelength of the radio waves that I am receiving?
> >5') What station am I listening to?
> >
> >Thanks, buddies.
> >
> >Tom
>
> Sorry, I'm coming in a bit late here.
> I gather you have noticed my queries about the possible differences
between
> diffraction gratings and prisms. The question is, " for light, what
do
> wavelength and frequency mean?".

Yes, I did notice. Which is why I framed my question in terms of
generated radio waves, where, as you point out below, there is no doubt
about the meanings of frequency and wavelength, since frequency and
wavelength are both directly measureable.

Sorry about my initial reversal about what is happening to the radio
dial. We're all human, after all.

> The answer is straightforward in the case of a generated EM signal.
It leaves
> the source at c with a known frequency, fo. Its 'wavelength' is
simply the
> distance between points of equal phase as they radiate away.
>
> The time interval between wavecrest emission, at the source, is
t=L/c, where L
> is the wavelength there. The time interval between wavecrest arrival
at an
> observer, moving at v towards the source, is L/(c+v). Thus,
wavecrests arrive
> at a relatively moving observer at the rate fo(c+v)/c. (This is
different from
> the equation for sound in a gas [fo(vo/(vo-v)]).

Actually, the Doppler equation for sound in a gas depends on whether
the source is moving or the observer is moving. For sound, these are
two distinctly different cases.

Your equation should be identical to observer moving situation, but
instead, you've written the source moving equation.

The two situations for Doppler shift of sound are unifiable into a
single equation. May I use u for source velocity and v for the observer
velocity?

In which case, the generalized Doppler equation for sound, using your
nomenclature, is f = fo(vo+v)/(vo-u)

The identity of the ballistic Doppler equation with the observer moving
situation should be evident.

> Note: both source and observer clocks agree on these times, assuming
they were
> identical and presynched. Clocks and rods are not physically affected
by
> velocity changes.
>
> As to wavelength, as you pointed out it doesn't change. A one metre
wavelength
> in the source frame will remain 1 metre in the moving observer frame.
That
> means successive wave crests will simultaneously lie adjacent to the
ends of a
> 1 metre rod in both frames.
>
> So, in both frames, the wavecrests of the same light passing over
identical
> gratings, at grazing angle, would have a similar relationship with
the lines on
> the grating. It would appear that a grating should NOT reveal doppler
shift
> according to the ballistic theory. However, when you consider light
coming onto
> the grating at an oblique angle, you will see that this angle itself
changes in
> the moving observer frame.

...and I was very careful to deal only with the incident light normal
with the grating situation.

> I have not resolved the difference between this problem and that of a
prism
> which I believe is 'frequency sensitive'.

When you figure this out, let me know. Newton had a similar problem
with his version of ballistic theory.

> We have no idea what frequency means, when applied to single photons
(if such
> exist)
> I think that by looking at this whole subject from the ballistic
point of view,
> we might actually discover something important.

I'm hoping you will eventually discover that there is no way to resolve
this from the ballistic point of view.

Tom

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