Re: To Androcles and Henry: Ballistic Doppler Shift Equation

From: Henri Wilson (H_at_..(Henri)
Date: 01/16/05 

Date: Sun, 16 Jan 2005 21:34:46 GMT

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'.

>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?".

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)]).

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.

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

HW.
www.users.bigpond.com/hewn/index.htm

"If it's repeated often enough they'll eventually believe it" __Albert Bush