Hi all,

In recent threads I was trying to show velocities
do not add as Einstein's addition formula states,
but strictly as euclidean vectors,

w = u + v,

and the correct Doppler formula for that sum is

f' = Exp( - w/c) f.

So, this Doppler formula is telling us there is a relative
anisotropy of light for moving bodies, and we avoid
time dilation and length contraction.

Let's see this interesting issue. Rapidity r is defined as
a hyperbolic angle, r = arctanh(v/c). Under SR, c is
regarded as universal constant, so the beta is always
in the range 0 v/c 1. This means, we can write

r = arctanh(v/c) = ln( sqrt( ( 1 + v/c)/(1 - v/c) ) )
so,
Exp( - r) = sqrt( ( 1 - v/c)/(1 + v/c) ),

which is the relativistic Doppler factor. I was wondering why
the relativistic Doppler factor was implicitly hidden into the
rapidity, but that's only a feature of the function arctanh. SR
can predict a relativistic Doppler effect, for speed w, as

f'' = sqrt( ( 1 - w/c)/(1 + w/c) ) f

IOW, under S we can add rapidities as being euclidean,
and express the relativistic Doppler in function of the sum
of rapidities,

r_w = r_u + r_v ,
f'' = Exp( - r_w/c) f

These two equations form a system that is isomorphic to the
system I've provided

w = u + v,
f' = Exp( - w/c) f

Now, we can clearly guess where is the trick SR uses to hide
the relative anisotropy of light. The sum rapidity r_w can be
rescale to yield w, as w = c_w r_w, for real c_w. So we can
write

f'' = Exp( - w/c_w) f, but now c_w is not neccesarily equal
to the constant c.

Likewise, we can rescale to u = c_u r_u and v = c_v r_v,
for reals c_u and c_v. We get the system of equations

w/c_w = u/c_u + v/c_v,
f'' = Exp( - w/c_w) f.

We can show this system of equations is physically meaningless,
because there are two different physical phenomena involved in
it. Firstly, there is the real phenomenon of the relative motion of
bodies, regardless they emit or reflect off light. Secondly, there
is
the real phenomenon of emission of light, regardless the bodies
are at rest or in relative motion. In this rationale, it is assumed
three
inertial bodies move along the same straight line. Now, we can
split both phenomena into different equations, as

w = u + v, [1]

c_w' = (c_u' c_v')/c, [2]
with
c_w' = c Exp(-w/c), [3]
c_u' = c Exp(-u/c), [4]
c_v' = c Exp(-v/c) [5]

So, the former equation [1] describes the relative motion
of bodies, regardless the propagation of light, and the latter
ones [2][3][4][5] describe anisotropic propagations of light.
This means the relative motion of bodies is independent of
the light they may emit, but the propagation of light they emit
is dependent of their relative motion. Under SR, we find the
opposite view, propagation of light is independent on the
relative motion, but relative motion is dependent on propagation
of light. So, are both views equivalent for describing the same
relativistic effects? The short answer is NO, they aren't.

summarizing, under SR we have the system of equations

w/c_w = u/c_u + v/c_v,
f'' = Exp( - w/c_w) f,

and in my model, we get the simpler system

w = u + v,
f' = Exp( - w/c) f

Both systems only match (f'' = f') for the case

c_w = c_u = c_v = c,

it is saying they only match when rapidities equals
their respective betas,

w/c = r_w , u/c = r_u, v/c = r_v

So, where is the trick used by SR? Under SR, we add
velocities of inertial bodies through the addition of their
respective rapidities. But, a rapidity has embeded the
anisotropic propagation of light. For example, w/c_w, is
a rapidity for the beta w/c, it is saying arctanh(w/c) = w/c_w.
Once that addition of rapidities is performed, SR replaces
the constant c in the Doppler formula by the anisotropic
velocity c_w to compound another rapidity. In conclusion,
the relative anisotropy that SR is hidden is

c' = w / arctanh(w/c)

This means SR is equivalent to Galilean relativity equipped
with that rule for the relative anisotropy of light. The limit of
that c' when w tends to c or to -c is, of course, c' = 0, which
can be interpreted as an infinite time dilation. In my model,
the relative anisotropy has a different form, it is

c' = c Exp( -w/c)

The limit of c', in this model, when w -oo is c' = 0, and
c' = oo for w - -oo. In this model, the relative anisotropy
can yields values that may be interpreted as time dilations
or even as time contractions, depending on the sign of w.
If that speed is an approaching speed (w0), then c' is
superluminal, and c' is subluminal if it is a recessional
speed (w 0).

Regards

Albertito skrev:
Hi all,

In recent threads I was trying to show velocities
do not add as Einstein's addition formula states,
but strictly as euclidean vectors,

w = u + v,

Have you done the one thing that can prove
Einstein's formula wrong?

If you have, why don't you tell us about
the experiment that falsified Einstein's formula?

[..]


--
Paul

http://home.c2i.net/pb_andersen/

On May 6, 8:11 pm, "Paul B. Andersen"
wrote:
Albertito skrev:

Hi all,

In recent threads I was trying to show velocities
do not add as Einstein's addition formula states,
but strictly as euclidean vectors,

w = u + v,

Have you done the one thing that can prove
Einstein's formula wrong?

If you have, why don't you tell us about
the experiment that falsified Einstein's formula?

[..]

--
Paul

http://home.c2i.net/pb_andersen/

Someone has already pointed out to you that the
Pioneer anomaly may be very well a experiment that
can falsify Einstein's formula.

On Wed, 07 May 2008 12:52:09 +0200, "Paul B. Andersen"
wrote:

Albertito wrote:
On May 6, 8:11 pm, "Paul B. Andersen"
wrote:
Albertito skrev:

Hi all,
In recent threads I was trying to show velocities
do not add as Einstein's addition formula states,
but strictly as euclidean vectors,
w = u + v,
Have you done the one thing that can prove
Einstein's formula wrong?

If you have, why don't you tell us about
the experiment that falsified Einstein's formula?

[..]

--
Paul

http://home.c2i.net/pb_andersen/

Someone has already pointed out to you that the
Pioneer anomaly may be very well a experiment that
can falsify Einstein's formula.

Not really.
There are too may open questions to do that.

But you said you have tried to show that velocities
do not add as Einstein's addition formula states,
but strictly as euclidean vectors w = u + v

Don't you know of any experiments testing how
velocities transform?
How did Einstein's velocity transform and
the Galilean velocity transform do in those tests?
Were any of them falsified?

I think that one of the problems with discussing velocity addition
under SR vs "older models", and then talking about experimental
verification, is that people tend to forget that lots of the older
models could also generate their own velocity-addition formulae.

Any model that assumes that the velocity of light is somehow mangled
by the motion of objects tends to generate these sorts of formulae.
The //status// of velocity-addition under SR is unusual, but the
associated phenomenology isn't especially new. The significance of the
match between Fizeau's experiment and SR sometimes gets exaggerated, I
don't think the match was supposed to be any better than the match
between Fizeau and Fresnel's old aether-dragging model (which Fizeau's
experiment was seemingly meant to test).

If we're sticking to strictly optical effects, we find that quite a
few theories have "non-Galiean" relationships when composite shifts
are involved.
For instance, with ancient emission theory, the Doppler shift law for
a recedign object was f'/f = (c-v)/c , so if you watched an object
receding at half the speed of light, it's frequency would be halved.

If there was then a second object beyond it, also receding, at half
lightspeed wrt /it/, then you'd normally tend to say that that second
object was receding from you at exactly the speed of light ... but it
wouldn' t be receding at the speed of //its own// light.

For a signal passed from the more distant object, to the intermediate
object, to you, the frequency of the light (according to old emission
theory) would be freqOriginal×0.5×0.5 , so you'd expect to see the
furthest object's signals, relayed vie the intermediate object, to
have one quarter of their original frequency, as we'd expect under
emission theory if we'd observed it directly while it was only
receding at 0.75c, rather than c.
The "effective" recession velocity calcualtion for the
indirectly-observed object under emission theory would then be
0.5c+0.5c = 0.75c


Similar "non-Galilean" patterns show up under other models where
lightspeed is variable, and can be justified by pointing out that a
relative "velocity", defined as a fraction of the speed of light, can
end up being assigned a different nominal value when the speed of the
light-signal that's being used as a reference changes.


Obviously, a lot of the old models were pretty stinky in places, but
we have to remember that the main advantage of the Galiean transforms
isn't perhaps so much their historical relavance, as their narrative
value in explaining the thought-processes that take us from (a)
assuming that the speed of light is globally fixed in the laboratory
frame (fixed stationary absolute aether), to (b) arriving at a
"relativised" version of that global-c description, provided by
special relativity.

If we're going to try to make a fair comparison, the Galilean
transforms themselves arguably don't correspond to the relationships
that appear in all pre-SR theories, or even to all the //major//
pre-SR theories.


SR does (however) seem to depart from older models in how its
velocity-addition formula is applied and interpreted:
In older theories, the appearance of a "special" v.a.f. would
typically have been taken as solid evidence that the motion of bodies
was altering the propagation of light (but that no single body's state
of motion could be used to absolutely dictate the speed of all light
in an experiment).
Under special relativity, the motion of nearby bodies is assumed to
have no effect on the propagation of light "in vacuo", so instead of a
v.a.f. documenting local lightspeed variations caused by the relative
velocities between intermediate objects in the signal path, the //SR//
v.a.f. applies even when no physical bodies corresponding to those
intermediate stages are present, and has to be taken instead as as a
structural quality inherent to spacetime itself.

=Erk= (Eric Baird)
www.relativitybook.com

Eric Baird wrote in message
...
| On Wed, 07 May 2008 12:52:09 +0200, "Paul B. Andersen"
| wrote:
|
| Albertito wrote:
| On May 6, 8:11 pm, "Paul B. Andersen"
| wrote:
| Albertito skrev:
|
| Hi all,
| In recent threads I was trying to show velocities
| do not add as Einstein's addition formula states,
| but strictly as euclidean vectors,
| w = u + v,
| Have you done the one thing that can prove
| Einstein's formula wrong?
|
| If you have, why don't you tell us about
| the experiment that falsified Einstein's formula?
|
| [..]
|
| --
| Paul
|
| http://home.c2i.net/pb_andersen/
|
| Someone has already pointed out to you that the
| Pioneer anomaly may be very well a experiment that
| can falsify Einstein's formula.
|
| Not really.
| There are too may open questions to do that.
|
| But you said you have tried to show that velocities
| do not add as Einstein's addition formula states,
| but strictly as euclidean vectors w = u + v
|
| Don't you know of any experiments testing how
| velocities transform?
| How did Einstein's velocity transform and
| the Galilean velocity transform do in those tests?
| Were any of them falsified?
|
| I think that one of the problems with discussing velocity addition
| under SR vs "older models", and then talking about experimental
| verification, is that people tend to forget that lots of the older
| models could also generate their own velocity-addition formulae.
|
| Any model that assumes that the velocity of light is somehow mangled
| by the motion of objects tends to generate these sorts of formulae.
| The //status// of velocity-addition under SR is unusual, but the
| associated phenomenology isn't especially new. The significance of the
| match between Fizeau's experiment and SR sometimes gets exaggerated, I
| don't think the match was supposed to be any better than the match
| between Fizeau and Fresnel's old aether-dragging model (which Fizeau's
| experiment was seemingly meant to test).
|
| If we're sticking to strictly optical effects, we find that quite a
| few theories have "non-Galiean" relationships when composite shifts
| are involved.
| For instance, with ancient emission theory, the Doppler shift law for
| a recedign object was f'/f = (c-v)/c , so if you watched an object
| receding at half the speed of light, it's frequency would be halved.
|
| If there was then a second object beyond it, also receding, at half
| lightspeed wrt /it/, then you'd normally tend to say that that second
| object was receding from you at exactly the speed of light ... but it
| wouldn' t be receding at the speed of //its own// light.

You'd still have zero frequency - if you could observe it.
|
| For a signal passed from the more distant object, to the intermediate
| object, to you, the frequency of the light (according to old emission
| theory) would be freqOriginal×0.5×0.5 ,

It would be (and still is) f'/f = (c-v-u)/c = 0.


| so you'd expect to see the
| furthest object's signals, relayed vie the intermediate object, to
| have one quarter of their original frequency, as we'd expect under
| emission theory if we'd observed it directly while it was only
| receding at 0.75c, rather than c.

No I would not. I'd expect (and get) zero. Nor does the second
emitter have to be "more distant", it can quite easily be catching up to
and passing the first emitter. The light it emits is INDEPENDENT of
the first emitter.


| The "effective" recession velocity calcualtion for the
| indirectly-observed object under emission theory would then be
| 0.5c+0.5c = 0.75c

Wrong. 0.5c +0.5c = 1.0c.
You are playing games with Xeno's paradox.

| Similar "non-Galilean" patterns show up under other models where
| lightspeed is variable, and can be justified by pointing out that a
| relative "velocity", defined as a fraction of the speed of light, can
| end up being assigned a different nominal value when the speed of the
| light-signal that's being used as a reference changes.
|
|
| Obviously, a lot of the old models were pretty stinky in places, but
| we have to remember that the main advantage of the Galiean transforms
| isn't perhaps so much their historical relavance, as their narrative
| value in explaining the thought-processes that take us from (a)
| assuming that the speed of light is globally fixed in the laboratory
| frame (fixed stationary absolute aether), to (b) arriving at a
| "relativised" version of that global-c description, provided by
| special relativity.

Einstein said:
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.

That's the garbage relativity is built on.


|
| If we're going to try to make a fair comparison,

Fair comparison?
There is NO comparison between sense and nonsense, Eric.

On May 8, 8:45 pm, "Androcles" wrote:
Einstein said:
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.

That's the garbage relativity is built on.


Einstein said:
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.

Albertito says:
the speed of light from A to B is c' = c*Exp(-v/c),
the speed of light from B to A is c''= c*Exp( v/c),
the "time" each way is not the same, for the same
distance r = AB = BA,

t' = r/c' = r*Exp(v/c)/c
t''= r/c'' = r*Exp(-v/c)/c

Eric Baird wrote in message
...
| On Thu, 8 May 2008 20:45:15 +0100, "Androcles"
| wrote:
|
|
| Eric Baird wrote in message
| .. .
| | On Wed, 07 May 2008 12:52:09 +0200, "Paul B. Andersen"
| | wrote:
| |
| | Albertito wrote:
| | On May 6, 8:11 pm, "Paul B. Andersen"
| | wrote:
| | Albertito skrev:
| |
| | Hi all,
| | In recent threads I was trying to show velocities
| | do not add as Einstein's addition formula states,
| | but strictly as euclidean vectors,
| | w = u + v,
| | Have you done the one thing that can prove
| | Einstein's formula wrong?
| |
| | If you have, why don't you tell us about
| | the experiment that falsified Einstein's formula?
| |
| | [..]
| |
| | --
| | Paul
| |
| | http://home.c2i.net/pb_andersen/
| |
| | Someone has already pointed out to you that the
| | Pioneer anomaly may be very well a experiment that
| | can falsify Einstein's formula.
| |
| | Not really.
| | There are too may open questions to do that.
| |
| | But you said you have tried to show that velocities
| | do not add as Einstein's addition formula states,
| | but strictly as euclidean vectors w = u + v
| |
| | Don't you know of any experiments testing how
| | velocities transform?
| | How did Einstein's velocity transform and
| | the Galilean velocity transform do in those tests?
| | Were any of them falsified?
| |
| | I think that one of the problems with discussing velocity addition
| | under SR vs "older models", and then talking about experimental
| | verification, is that people tend to forget that lots of the older
| | models could also generate their own velocity-addition formulae.
| |
| | Any model that assumes that the velocity of light is somehow mangled
| | by the motion of objects tends to generate these sorts of formulae.
| | The //status// of velocity-addition under SR is unusual, but the
| | associated phenomenology isn't especially new. The significance of the
| | match between Fizeau's experiment and SR sometimes gets exaggerated, I
| | don't think the match was supposed to be any better than the match
| | between Fizeau and Fresnel's old aether-dragging model (which Fizeau's
| | experiment was seemingly meant to test).
| |
| | If we're sticking to strictly optical effects, we find that quite a
| | few theories have "non-Galiean" relationships when composite shifts
| | are involved.
| | For instance, with ancient emission theory, the Doppler shift law for
| | a recedign object was f'/f = (c-v)/c , so if you watched an object
| | receding at half the speed of light, it's frequency would be halved.
| |
| | If there was then a second object beyond it, also receding, at half
| | lightspeed wrt /it/, then you'd normally tend to say that that second
| | object was receding from you at exactly the speed of light ... but it
| | wouldn' t be receding at the speed of //its own// light.
|
| You'd still have zero frequency - if you could observe it.
|
| If you had an observer and two objects, all-in-a-line, with each
| receding from its immediate neighbour at half lightspeed:
|
| : A ............... B ............... O
| : 0.5c 0.5c
|
| .., then, under Emission Theory, light passed //directly// from A to O
| would indeed arrive with a "frequency" of zero.

Emission Fact, Eric. It's not a theory at all, only non-facts are theories.

|
| But Emission Theory would predict a different frequency-shift if the
| light was passed from A to O //indirectly//, via B. B in this case
| acts as a sort of "stepping-stone", velocity-wise.


Maybe by your emission theory, but emission fact doesn't need to
make prophecies. Some of us are not in the horoscope business.

Xeno's paradox:
An arrow is loosed toward a target but first it has to reach halfway
and then it has to reach half of that, ad infinitum. No matter what it's
position it will always half the remaining distance to travel first,
and so it never reaches the target.



| Emission Theory would say that since B sees A with its frequency
| halved, and O sees B with //its// frequency halved, then if B points a
| TV camera at A, registers a halved frequency, displays that halved
| frequency on a screen, and O then watches that screen, ad sees the
| frequency halved again ...

Eric Baird's emission theory isn't Emission Fact. Eric Baird is imitating
Xeno
and doesn't fool Androcles.

| ... Then B sees the image of A on the screen, with one quarter the
| orignal frequency. Ditto if the camera and sceeen is replaced by a
| phase-locked electronic transponder that takes in A's signal and
| rebroadcasts it to O. The transponder will register A's signal as
| halved, and will rebroadcast it "as-is" with that same halved
| frequency. O will then receive that rebroadcast and find a further
| halving of frequency.
| You can then try replacing the transponder with a simple sheet of
| glass.
|
| So, under Emission Theory, the physical presence of B in the signal
| path affects the propagation of light, and makes A visible to O, and
| if we really want to, we can apply a velocity addition formula to
| generate a new "effective velocity" that can be used with ET's shift
| formula to generate the shift prediction for the //indirectly-passed//
| signal in one stage. If I have this right, the corresponging v.a.f.
| for emission theory would then probably be something like
|
| : W = u + v - uv/c
|
You do not have it right.

| , or, if all velocities are experessed as fractions of the speed of
| light,
|
| : W = u + v - uv
|
|
|
| : =CONSEQUENCES=

Not worth bothering with. Your emission theory isn't anything plausible,
I still rely on FACT.



|
| The modification of the original shift relationships when radiation is
| passed indirectly allows Emission Theory (and some other old theories)
| to generate a version of Hawking radiation.
|
| Fr'instance, if we took an old Newtonian "Dark Star" whose radius was
| just under the critical r=2M limit, then as distant observers we
| wouldn't be able to see any light from the body's surface directly ...
| r=2M woudl be the absolute limit at which the surface escape velocity
| would equal lightspeed, and at which plugging that "c" terminal
| velocity into the ET shift equations to get the gravitaitonal shift
| would give a gravitationally redshifted frequency of zero.
| Any light generated any lower than r=2M would be described (under ET)
| as not being visible to us.
|
| But under Emission theory, that light still passes outward through
| r=2M a little way before being pulled back into the star by gravity,
| and if it interacts with other material while outside the horizon, it
| can be deflected or accelerated free from the pull of the star.
| So the partial dependency of the final frequency shift (in some non-SR
| models) on the motion of any bodies in the signal path, which can be
| described by a velocity-addition formula, can also be used to explain
| Hawking radiaiton (and "Unruh radiation"/"acceleration radiation"
| effects) in non-SR contexts.
|
|
| : =GENERALITY=

Not worth bothering with.

1 = 1/2 + 1/2^2 + 1/2^3 + 1/2^k for k = 4 to infinity.
Your emission theory is not my emission fact.




| In general, velocity-addition formulae tend to be a feature of any
| theory in which the frequency-shift result after two shift
| transitions,
|
| : "Shift(u) × Shift(v)"
|
| isn't the same as the result you'd get by writing
|
| : "Shift(u+v)"
|
|
|
| : =SPECIAL RELATIVITY=

Not worth bothering with.
|
| The big difference with SR is that //it's// velocity-addition formula
| doesn't depend on the physical existence of any intermediate objects
| with a specified state of motion.
|
| Under SR, our two individual recession redshifts of v=0.5c would each
| have given a frequency-shift of
|
| : f'/f = SQRT[ (c-v) / ( c+v) ] = SQRT[0.5/1.5] = SQRT[1/3]
|
| , so our total shift after two of these stages would be
|
| : f'/f = SQRT[1/3] × SQRT[1/3] = 1/3 = 0.333'
|
| Instead of calculating this composite velocity-shift in two stages, we
| can apply SR's velocity-addition law to calculate a combined velocity
| W
|
| : W = (u+v) / (1+uv/cc) = [ 1 / (1+0.25) ] = 4/5 c = 0.8c
|
| and then use "0.8c" with the usual SR shift formula
|
| : f'/f = SQRT[ (c-v) / (c+v)] = SQRT[0.2/1.8] = SQRT[1/9] =1/3 = 0.3333'
|
| , to get the same answer as before.
|
| Where SR differs from other theories is that the SR calculation
| doesn't depend on the physical existence of any //real// object "B".
|
| If we set up our our A-B-O example under other theories with a v.a.f,
| and then remove object B, then the signal, which is now moving
| directly from A to O, will tend to arrive with a different shift value
| depending on whether B is in the signal path or not.
|
| But under special relativity, if we take away B, the observed
| frequency in our example is still exactly "one third" regardless of
| whether B exists or not. The SR v.a.f. applies to the relationships
| between notional inertial frames, irrespective of whether or not there
| are any objects or observers in those frames. So under SR, "W" isn't
| an "artificial" or "invented" velocity, or an "effective" velocity,
| it's the genuine article.
|
| That's where the difference is.
|
| : =LANGUAGE TRAPS=

Not worth bothering with.

| There's also a subtle but important difference between the way that we
| treat the algebra of "v" and "c" under these different types of model.
| Under emission theory or a total dragged-aether model, we'd tend to
| say that
|
| : c v
|
| , in other words, "v" is our starting reference, and "c" is always
| larger (a moving object's forward-emitted light always leaves it
| faster than the object itself moves).
|
| Under special relativity, we'd instead tend to say
|
| : v c
|
| Although the two statements may look equivalent, in a sequential
| language, the second statement usually carries a slightly different
| meaning -- it implies that "c" is our initial known reference, and
| that the velocity of an object is always compelled to be smaller than
| this.
|
| So, under SR-based physics, we can't have classical indirect radiation
| through a gravitational horizon. By using the second statement,
| SR-based physics presumes that the motion of matter doesn't affect the
| speed of light, and the gravitational event horizon at r=2M becomes
| inescapable. The "pre-SR" velocity-addition trick doesn't work under
| SR/GR1915, because the horizon is fixed, and that leads us to model
| the horizon using a metric in which the inescapability of the horizon
| surface means that light never passes outwards through the surface at
| all. Where emission theory allows a dark star to be surrounded by a
| ghostly haze of particles that were only indirectly observable, under
| GR1915, the exterior region of an isolated black hole is described as
| being totally empty. The way that SR's v.a.f. applies to gravitational
| problems is the opposite way around to how things tended to work under
| older models: instead of the v.a.f describing how the effective
| horizon could contract behind a particle when it was bumped free of a
| dark star, under GR1915, a v.a.f illustrates how, no matter how many
| times a particle is accelerated outwards by any velocity less than c,
| it can never achieve c and never escape the horizon.
|
|
| | For a signal passed from the more distant object, to the intermediate
| | object, to you, the frequency of the light (according to old emission
| | theory) would be freqOriginal×0.5×0.5 ,
|
| It would be (and still is) f'/f = (c-v-u)/c = 0.
|
| I think that if you work it through, you'll find that it's different.

Think again.


|
| The reason why the modern SR logic doesn't work for old emission
| theory (or for old dragged-light theories), is that in these examples
| we don't have a single uniform speed of light applying throughout the
| experiment that can be used as a globally-agreed reference.
| Under emission theory, we actually have two different lightspeeds in
| play, we have the speed of light given off by A, and we have the
| different speed of light emitted at the second stage, by B.
|
| If you only use cA throughout, then of course you can "prove" that the
| signal must arrive with the same frequency regardless of what B does
| ...
| ... but that's not the correct way to describe the problem under
| emission theory, which says that the signal that we see relayed from B
| is moving at a different speed, cB, which puts it out of sync with cA.
|
|
| | so you'd expect to see the
| | furthest object's signals, relayed vie the intermediate object, to
| | have one quarter of their original frequency, as we'd expect under
| | emission theory if we'd observed it directly while it was only
| | receding at 0.75c, rather than c.
|
| No I would not. I'd expect (and get) zero. Nor does the second
| emitter have to be "more distant", it can quite easily be catching up to
| and passing the first emitter. The light it emits is INDEPENDENT of
| the first emitter.
|
| I was trying to use the most simple scenario, in which both relative
| velocities act in the same direction and have the same sign (both
| recession or both approach). Those are the conditions for using the
| version of the SR v.a.f that Einstein quoted in his 1905 paper.
|
|
| | The "effective" recession velocity calcualtion for the
| | indirectly-observed object under emission theory would then be
| | 0.5c+0.5c = 0.75c
|
| Wrong. 0.5c +0.5c = 1.0c.
| You are playing games with Xeno's paradox.
|
| Nope, I'm calculating the frequency-shift, as a ratio, that's induced
| by the first velocity transition, and then I'm multiplying this new
| frequency by the frequency-shift, as a ratio, that's induced by the
| second velocity transition.
| Calculating a model's predicted shift ratios for each stage and then
| multiplying them together is pretty much guaranteed to give the right
| answer for that model.
|
| People well-practised in SR may well find it faster to apply the
| v.a.f. method, but under other theories the correct application of the
| "v.a.f." approach isn't always obvious, and it's usually safer to just
| "chicken out" and do the calculation in individual stages.


Wrong. 0.5c +0.5c = 1.0c.
You are playing games with Xeno's paradox.


|
|
| | Similar "non-Galilean" patterns show up under other models where
| | lightspeed is variable, and can be justified by pointing out that a
| | relative "velocity", defined as a fraction of the speed of light, can
| | end up being assigned a different nominal value when the speed of the
| | light-signal that's being used as a reference changes.
| |
| |
| | Obviously, a lot of the old models were pretty stinky in places, but
| | we have to remember that the main advantage of the Galiean transforms
| | isn't perhaps so much their historical relavance, as their narrative
| | value in explaining the thought-processes that take us from (a)
| | assuming that the speed of light is globally fixed in the laboratory
| | frame (fixed stationary absolute aether), to (b) arriving at a
| | "relativised" version of that global-c description, provided by
| | special relativity.
|
| Einstein said:
| 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.
|
| That's the garbage relativity is built on.
|
| Okay, I'll take the bait !
|
|
| My own //personal// view of modern SR is that it's an
| impeccably-constructed piece of geometry and mathematics that's built
| on some physically-incorrect starting assumptions.

Modern SR? No such animal, SR is Einstein's SR, nobody else's.
I'm not dealing with SR according to Roberts or Kolker or Dork
Van de merde or Eric Baird or "Professor" Baez or anyone else.
There is nothing impeccable about it, it is circular nonsense as clearly
shown he
http://www.androcles01.pwp.blueyonde...mart/Smart.htm



|
| I think it's a beautiful, geometrically-perfect answer to a bad
| question.


Think again, time is not a vector.
http://www.androcles01.pwp.blueyonde...tor/Vector.htm

Einstein's "special" theory is founded on a pure, "flat"
| metric in which the propagation of light passing through a region is
| supposed to be 100% unaffected by the presence and relative motion of
| any objects that it encounters en route, and that description doesn't
| seem (IMO) to correspond to real physics.

It's not a question of your opinions, Eric. Nature doesn't give a hoot
about
your opinions or Einstein's crappy, idiotic, illogical and wrong symbol
shuffling.



| In real life, we know that if we populate a region with a lot of
| particles all moving in the same direction, and we aim a lightbeam
| through that region, the beam moves faster when it's moving in the
| same direction as the particles than it does when it's aimed the other
| way, which is the result that we'd expect if moving bodies dragged
| light along in their immediate vicinity.
|
| Since the output of a mathematical theorem is supposed to be wholly
| defined by its starting assumptions and definitions, and since SR
| (like most theories) starts out by making some unrealistically
| idealised initial assumptions, the next question would seem to be
| whether the //form// of those idealisations has significantly affected
| the way that SR works, or whether SR manages to get away with it.
|
| Is SR "robust" wrt small perturbations of its initial idealisations?

No.

Catch 22:

A) If you use c+v you can write:
http://www.fourmilab.ch/etexts/einst...ures/img22.gif
(which is nonsense anyway.)

B) From that you can derive the cuckoo malformations:

http://www.fourmilab.ch/etexts/einst...ures/img53.gif

C) From that you arrive at:
http://www.fourmilab.ch/etexts/einst...ures/img76.gif

which says you cannot use c+v.

D) Goto A).

Heller wrote: "There was only one catch and that was Catch 22, which
specified that a concern for one's safety in the face of dangers that were
real and immediate was the process of a rational mind.
"Orr (a character in the novel) was crazy and could be grounded. All he had
to do was ask, and as soon as he did, he would no longer be crazy and would
have to fly more missions.

"Orr would be crazy to fly more missions and sane if he didn't, but if he
was sane he had to fly them. If he flew them he was crazy and didn't have
to; but if he didn't want to he was sane and had to."

In Einstein's case if you use c+v you can derive c = (c+v)/(1+v/c) from
the cuckoo malformations he blamed on Lorentz. That says you can't
use c+v.

Troll kooks such as

Uncle Schwartzschit,
Blind Poe,
Moron McCullough,
Humpty Roberts,
Phuckwit Duck Draper,
Sad and Lonely sal Lawrence,
Tusseladd ASSistant professor Andersen,
Shrine to Spirits Nieminen,
Ghost ewill,
Goosey Gisse,
****** Olson,
Minor Crank Tom & Jeery,
Fecal Jekyll,
Bilewacky,
Dork Van de merde et. al.
fail to realise is the existence of isomorphism

http://en.wikipedia.org/wiki/Isomorphism

between Sagnac's real experiment and Einstein's hallucination experiment,
shown he
http://www.androcles01.pwp.blueyonde...oSpeedRack.gif

Einstein sends light along the rack and back again, the rack
moving at velocity v in his pipe dream.

Sagnac sends the light around the gear wheel for real.
If you analyse one you should get the same result as the other, but
you cannot use SR to derive SR, that is petitio principii, circularity.
http://en.wikipedia.org/wiki/Begging_the_question

c+v is essential to the derivation of the cuckoo malformations, the
part where Einstein screws up is:
'we establish by definition that the "time" required by
light to travel from A to B equals the "time" it requires
to travel from B to A' because I SAY SO. -- Rabbi Albert Einstein

What he is claiming is that his "definition" is true for all frames of
reference. The absurdity that the velocity of light is the same
in all frames of reference is a consequence of that claim.


http://www.androcles01.pwp.blueyonde...rt/tAB=tBA.gif

Here are some mathematical proofs:
http://en.wikipedia.org/wiki/Mathematical_proof

Not included are
Proof by "because I say so",
Proof by "everybody knows",
Proof by "it is written",
the three most popular forms used in sci.physics.relativity.

You'll often see this pathetic mob muttering "Lorentz Transformations"
but they haven't a clue how they are derived and faithfully follow their
indoctrination like lemmings.

Catch 22:
http://www.fourmilab.ch/etexts/einst...ures/img22.gif
http://www.fourmilab.ch/etexts/einst...ures/img76.gif

Prediction:
The troll kooks will ignore it, they are too stooopid to understand a
proof.

RULES OF REASONING IN PHILOSOPHY.

RULE I.
We are to admit no more causes of natural things than such as are both true
and sufficient to explain their appearances.

To this purpose the philosophers say that Nature does nothing in vain,
and more is in vain when less will serve; for Nature is pleased with
simplicity,
and affects not the pomp of superfluous causes.

-- Sir Isaac Newton


["tj Frazir"]
If you pushed a rod 1 light year long the other end wont move for 1 year.

["CWatters"]
Suppose you apply a small displacement by compressing one end with a
hammer.
Does the shock wave still travel at the speed of light?

[Androcles]
Clearly the extrapolation (increasing rigidity yields increasing speed
of sound) indicates either there is limit to rigidity or there is a limit to
the speed of sound in a material body.
Given that a material body is made of atoms then atoms are
not rigid... but we do not expect them to be anyway, the model of
an atom is that of a nucleus surrounded by a mantle of empty
space and a shell (or shells) of electrons. By compressing the
atom we force the electrons into the nucleus, the charges cancel
and we are left with a nucleus of incompressible neutrons where
the limit to rigidity has been reached; for either the neutron is totally
rigid or the speed of sound in neutrons exceeds the speed of light.

"Thus with the help of certain imaginary physical experiments we
have settled what is to be understood by"[1] neutron stars and proven
black holes do not exist, the extrapolation has gone too far.

[1] Einstein's verbal diaorreah to impress neanderthals and gorillas.


|
| The trouble with SR as foundation theory (IMO) is that parts of the
| theory seem to be very sensitive to //any// deviations from its
| perfect propagation model. Minkowski spacetime requires
| //perfection//, it doesn't tolerate even small local
| velocity-dependent variations in lightspeed. If you allow the motion
| of a body to physically alter the propagation of light in its immedate
| vicinity, you no longer have the Minkowski metric, and since SR can be
| presented as "how physics operates within Minkowski spacetime", if you
| change that lightbeam geometry, you also change some of the key
| relationships.
|
| In computing, this sort of thing is referred to as "GIGO".

You cannot use a computer to derive the cuckoo malformations,
computers are logical machines.
In computing, this sort of thing is referred to as a "BUG".
The commonest bug is division-by-zero, and that's just what Einstein
does.

|
|
|
| //Some// results of the special theory seem to be pretty robust (e.g.
| E=mc^2, which is also a result of Newtonian emission theory), but
| others aren't ... and if you change //those//, you arguably aren't
| doing special relativity any more.

Nobody can "do" SR, it's been around for over 100 years and no
use to anyone, all that happens is they talk about it.


|
| Where the mainstream SR guys haven't done a good job (IMO) is that
| they don't seem to have made a proper study of these dependencies.




|
| | If we're going to try to make a fair comparison,
|
| Fair comparison?
| There is NO comparison between sense and nonsense, Eric.
|
| grin
|
| I usually try to go out of my way to give SR the benefit of the doubt,
| partly as an exercise for my own benefit, and partly because I figure
| that that way, people are more likely to take my objections seriously.

In agreement with experience we further assume your objections do not
merit the praise you give to the incomprehensible garbage that was the
product of a charlatan.



|
| It also pre-empts a few pointless discussions that'd otherwise almost
| certainly happen, where someone explains to me that the reason for my
| "mistake" is that I supposedly don't understand "X".
| If I'm going to have to explain that I //do// understand "X", I find
| that it's usually easier to get in first and say so, up-front.
|
| I reckon that if I'm demonstrating that I appreciate the arguments in
| SR's favour, but I //still// think that the theory's relationships
| might be wrong, then people are slightly less likely to think that my
| attitude is based on ignorance.
| If I can show that I can make the case for SR better than most of the
| theory's proponents can, that I understand their reasoning and why
| their conclusions appear inescapable to them, and that I can "prove"
| that the theory must be right, if I start with the same initial
| assumptions that they start with ... but I then point out that by
| changing those initial assumptions in a reasonable way, a different
| sort of theory emerges ... then perhaps a few people might perk up and
| start to realise that other systems are possible once we step outside
| the rigid confines of SR-based definitions.
|
|
|
| I also quite like to demonstrate that it's perfectly possible to
| "operate" SR, and derive and explain it, without actually believing
| that the thing is necessarily correct.


Only if you say such stupid mysticism as:
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.






| I think that that demonstrates that being an "SR believer" doesn't
| necessarily confer any advantages. It's quite possible for a scientist
| to use whatever models or math they find convenient at the time
| without having to sign an oath of allegiance to a particular theory.

You haven't shown me any evidence of thinking. You are clearly
in need of some rigorous mathematical training.



| And for some problems, not being too committed to SR can give a
| functional advantage. There are certain problems in advanced
| theoretical physics where the community tends to struggle a bit, but
| where one can gain an unfair advantage, and explain why certain models
| //have// to interact in particular "odd" ways, by saying, "Well,
| they'd have to behave like this, if special relativity was wrong, but
| we were assuming that it had to be right".
|
| "Special relativity is wrong" seems to be the most efficient
| explanation that we have so far for, say, the disagreement between
| GR1915 and quantum mechanics regarding black hole emissions. It
| //explains// why GR1915 has to predict the complete absence of
| emissions even though this seems to run counter to general
| thermodynamic rules and to QM.

Find me a black hole, I'll see what it emits.

--
This message is brought to you by Androcles
http://www.androcles01.pwp.blueyonder.co.uk/



|
| The idea that SR might not be right is a useful tool, and I think that
| some relativity guys are missing out by not being able to use it.
|
| =Erk= (Eric Baird)
| www.relativitybook.com
|