Re: Aberrations from the relativistic aberration of light

On May 22, 9:26 pm, shala...@xxxxxxxxx wrote:
On May 22, 2:24 pm, shala...@xxxxxxxxx wrote:



On May 22, 10:26 am, "Androcles" <Headmas...@xxxxxxxxxxxxxxxx> wrote:

<shala...@xxxxxxxxx> wrote in message

news:57c79e16-770f-48fc-b529-c5a83563bd40@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On May 21, 1:58 pm, "Androcles" <Headmas...@xxxxxxxxxxxxxxxx> wrote:

<shala...@xxxxxxxxx> wrote in message

news:74184524-b1b4-44ae-ab16-5dc0e2d951bd@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
|I always thought it worked like this:
|
| 1) The speed of light emitted by a source is c, regardless of its
| motion. That is, the photon does not move at a velocity of c with
| respect to some universal rest frame (how does one even begin to
| define such a frame anyway?).
|
| 2) Where an observer is moving at a relative velocity v \approx 0.5c
| directly away from the source, then a photon emitted directly toward
| the observer would approach it at relative velocity of v \approx 0.5c,
| increasing the observed wavelength by 2 (half the speed of light,
| twice the absorption time, twice the wavelength, half the frequency).
| This is where the 1 - cos(\phi) v/c term comes from.

Nope. \phi is simply the angle of incidence. When the light (or sound)
source is coming straight at you \phi is zero and cos(\phi) = 1.
If the light (or sound) source passes you by then \phi changes as it
does so. This is fairly obviously observed with the change in shift
of the sound of a passing car. The term is strictly Doppler's original.

| The remainder of
| the formula is just the kinematic time dilation of the observer.

No such animal exists.
http://www.androcles01.pwp.blueyonder.co.uk/Wave.xls
Feel free to check the equations or change the values in the yellow boxes.

|
| I take it you're not a fan of relativity.

You can take it I'm not a fan of stupidity, I take it you are not
a fan of reality.

--
Why did Einstein say
the speed of light from A to B is c-v,
the speed of light from B to A is c+v,
the "time" each way is the same?

Androcles

http://www.androcles01.pwp.blueyonder.co.uk/

Androcles,

| Like I said in this example, where the observer is moving directly
| AWAY from the source, and the photon is moving directly TOWARD the
| observer, it's implied that their direction vectors are identical, and
| so phi = 0, cos(phi) = 1, and thus 1 - cos(\phi) v/c = 0.5, resulting
| in a doubling of the wavelength.

1- cos(0) = 1-1 = 0 when I went to school. Maybe it has changed
since then.

--
Why did Einstein say
the speed of light from A to B is c-v,
the speed of light from B to A is c+v,
the "time" each way is the same?

Androcles

http://www.androcles01.pwp.blueyonder.co.uk/

Androcles, you forgot to include v/c in your calculation:

1 - cos(\phi) * v/c = 1 - 1 * 0.5 = 1 - 0.5 = 0.5

- Shawn

It also donned on me that this thread initially had nothing to do with
the relativistic Doppler effect. In that case, my apologies Albertito.

- Shawn

Don't worry, Shawn, Doppler effect, aberration of light
and addition of velocities are all related. This is the
simple equation that relates them all:

- c ln(z +1) = v + w,

where,
v and w are velocities of source and observer
in a given frame of reference,
c is the velocity of light, and
z is the Doppler shift.

Notice that c is velocity of light, not a speed, so it is a vector.
The above formula is true because c depends on the velocity
of the source, it is not an invariant.

So, |c ln(z +1)| is the magnitude, norm, of the sum v + w.
This formula can't be found in any textbook. If you love
SR, then replace the binary operator + by Einstein addition
of velocities. This will make c be invariant in magnitude,
but not in direction wrt observer. If you love Galilean relativity
then retain + as strictly an euclidean vector addition.

Let's evaluate the above equation for some cases
where velocity of the source is v = 0. Then

- c ln(z +1) = w

1) If z = -1, then |c| = oo, which means the observer
approched the source at infinite speed.
2) if z = e - 1, then c = - w, which means the observer
is receding from the source at speed |c|.
3) if z = 1/e - 1, then c = w, which means the observer
is approaching the source at speed |c|.
4) if z = 0, then w = 0, which means the observer
is at rest wrt the source.

If you analyze experimental data, no Doppler blueshift z < 0
less than -1 will be found, as measured directly from the
observed frequency f' and the original one f. Likewise, you
will find out there can be Doppler redshifts, z >0, with no
apparent upper bound. What does it mean?. It means
the equation - c ln(z +1) = v + w is true, and SR is wrong.

.

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