Re: [SR] Dismaying intellectual desert?

Den 01.04.2024 22:23, skrev Richard Hachel:

Le 01/04/2024 à 21:59, "Paul B. Andersen" a écrit :

measure any speed.
>
But when it is approaching you at an angle, you can measure the
angular velocity, and when the distance is known, you can calculate
the apparent transversal velocity, which indeed may be higher than c.

 But NO!

You are quoting a correct statement out of context, and crying NO!
Why?

 Vapp=v/(1+cosµ.v/c)
If v=c and cos=0 (tranversal move), Vapp=c.

Let's stay in the real world.
The only objects moving at "relativistic speeds" we
can visually observe, are astronomical objects, like
the matter in the jets from some galaxies (from their
central black hole).
The only motion we can visually observe, is transversal motion.
So if the jet is coming right at us, we will see the matter
at exactly the same point at the centre of the galaxy, the apparent speed of the matter is zero.
But when it is approaching you at an angle, you can measure the
angular velocity, and when the distance is known, you can calculate
the apparent transversal velocity, which indeed may be higher than c.
My explanation frm a post written back in 2003:
===============================================
About "superluminal jets":
--------------------------
an example of which you can see here:
http://spiff.rit.edu/classes/phys200/lectures/superlum/m87jet_hst_big.jpg
The "basic effect" is simple:
An object is moving with a speed v straight towards the observer O.
  O ------------------------------B--------A
                                  |<- L  ->|
The time interval between the observation of light emitted from
A and B will be the time interval between the emissions minus
the time the light uses to go from A to B:
t_o = L/v - L/c
The "apparent speed" will be the distance between A and B divided by
the observed time interval:
v_app = L/t_o = v/(1-v/c)
Note that v_app > c when v > c/2.
However, the above is not possible to observe in the real world,
of the obvious reason that you will have no way of observing the
distance L.
So what is observed?
Matter in the jets are moving at high speed.
As this matter ploughs through the intergalactic medium (very thin gas),
radiation - mostly at radio frequencies - is emitted. It is this
radiation and not the matter itself that is observed.
The stream of matter is however not very steady. It may be "blobs" of
matter in the jets which will be visible in the observed radiation.
These "blobs" are observed to move, and it is supposed that the matter
in the jets move with the same speed as the observed "blobs".
So what really is observed is the angular speed of these blobs,
from which you can calculate the transversal speed assuming you know
the distance to the source.
So let's redo the calculations above on a more realistic case:
  O                                                  * galaxy
                            angle of jet from       A
                            line of sight = a      /
                                                  / jet
                                                 /
                                                B
The observed time interval between reception of light emitted from A
and B (distance L) will be:
t_o = L/v - L*cos(a)/c
The apparent _transversal_ speed will be the apparent _transversal_
distance divided by this time interval:
v_app = L*sin(a)/t_o = v*sin(a)/(1 - (v/c)*cos(a))
Note that v_app > c when v > c/(sin(a)+cos(a))
Note also that since (sin(a)+cos(a)) > 1 for any a < pi/2, v_app can
as long as the jet is moving against the observer be > c if v is
sufficiently close to c.
For example, if a = pi/4 the apparent transversal speed is superluminal
if v > ca. 0.7*c
--
Paul
https://paulba.no/