Re: SR time dilation on remote objects ?

From: Marcel Luttgens (mluttgens_at_wanadoo.fr)
Date: 08/09/04 

Date: 9 Aug 2004 04:17:10 -0700

Bjoern Feuerbacher <feuerbac@thphys.uni-heidelberg.de> wrote in message news:<ceqahd$f84$1@news.urz.uni-heidelberg.de>...
> Sorry for the late reply - I was on holiday for a week...
>

We are going round in circles. Here is the summary I told you about.

FALSIFYING SR

As no inertial frame can be found in the Universe, no real (physical)
experiment can falsify special relativity.

There are however two other possibilities:
1) To demonstrate that the derivation of SR formulas has a logical
   flaw, see http://perso.wanadoo.fr/mluttgens/LTfalse.htm
2) By way of a thought experiment, proving that mutual time dilation
   is a hoax. Hereafter is such experiment:

Aircrafts thought experiment:
____________________________

A departure (and arrival) airport is situated exactly at
the North Pole.
At take-off, two aircrafts A and B synchronize their clocks
with the airport clock. All three clocks are set to 0.
Immediately after synchronization, they fly in opposite directions,
approximately at ground level, at some ground velocity v, each
following the same meridian.
At landing, after one circumnavigation, the readings of the clocks
A and B are compared, and found to be identical.

Let's notice that, according to the North Pole observer, the
circumnavigation took approximately t(P) = 2*pi*R/v sec,
where R is the Earth's radius.
Hence, at landing, the clock of aircraft A reads
tA = t(P) * sqrt(1-v^2/c^2) sec,
and the clock of aircraft B reads
tB = t(P) * sqrt(1-v^2/c^2) sec.
Thus, tA = tB, i.e. the readings of clocks A and B are identical.

This conclusion is compatible with the results of the Hafele
& Keating experiment, performed during october 1971:
"Four caesium clocks flown around the world on commercial jet flights,
once eastward and once westward, recorded directionnaly dependent
time differences which are in good agreement with predictions of
conventional relativity theory. Relative to the atomic time scale
of the U.S. Naval Observatory, the flying clock lost 59+-10
nanoseconds
during the eastward trip and gained 273+-7 nanoseconds during the
westward trip." (Cf. article in Science, Vol. 17, 14 July 1972,
pp. 166-179).

Readings tA(d) and tB(d) of clocks A and B at a distance d
__________________________________________________________
from the Pole:
_____________

Assuming a homogeneous and spherical Earth, the readings
would be
tA(d) = tA * d/2*pi*R sec, and
tB(d) = tB * d/2*pi*R sec.

Symplifying, one gets
tA(d) = 2*pi*R/v * sqrt(1-v^2/c^2) * d/2*pi*R
      = d/v * sqrt(1-v^2/c^2) sec
Similarly,
tB(d) = d/v * sqrt(1-v^2/c^2) sec, meaning that clocks A and B
tick at the same rate.

Let's notice that tA(d) = tB(d) = d/v * sqrt(1-v^2/c^2) sec is
independent from the Earth's radius R.

Hence, if R is infinitely increased, one is left with a *pure
SR situation*, where two objects A and B leave at a time 0, in
opposite
directions and at some velocity v, a third object P .
 
As shown above, at some distance d from P, both clocks on A and B read
d/v * sqrt(1-v^2/c^2) sec, meaning that they tick at the same rate.
Let's also notice that the velocity v is not necessarily constant.
For instance, it can be a function of the distance d. The clocks
A and B will tick at the same rate at any distance from each other
if, at every instant, A and B have the same opposite velocity.

Aplication to an expanding universe:
___________________________________

In such universe, observers A and B separated by a distance d move
*from each other* at a velocity v, which is a function of d.
It has been shown above that *in such situation*, A and B clocks
tick at the same rate.

Applying SR, observer A situated at a distance d from observer B
will claim that tB = tA * sqrt(1-v^2/c^2), but, in his frame of
reference, observer B is perfectly right (sic) to claim that
tB = tA * sqrt(1-v^2/c^2)!

This can rightly be called a hoax, because both clocks keep ticking
at the same rate, meaning that neither A nor B can observe a
time "dilation" on the other's clock.

Conclusively, this "aircrafts thought experiment" falsifies SR.

As clocks A and B always tick at the same rate, light emitted
for instance by A will be observed by B to be redshifted according
to the *kinematic* Doppler formula.

- According to an article published in 1999 by © CAMBRIDGE UNIVERSITY
PRESS (THE ORIGIN OF THE REDSHIFT, see
http://nedwww.ipac.caltech.edu/level5/Peacock/Peacock3_3.html ):

"For small redshifts, the interpretation of the redshift as
a Doppler shift (z = v / c) is quite clear. What is not so clear
is what to do when the redshift becomes large. A common but
incorrect approach is to use the special-relativistic Doppler
formula and write
 1 + z = sqrt((1+v/c)/(1-v/c))
This would be appropriate in the case of a model with Omega = 0,
but is wrong in general."

In fact, it is *never appropriate* to use the special-relativistic
Doppler formula, because expansion cannot have a decelable SR
effect, as clocks keep ticking at the same rate. Only a kinematic
Doppler redshift can be observed.
The error made by contemporary cosmologists is due to their
blind faith in SR, leading them to believe in the so-called
mutual time dilation. As this is a mere hoax, the special-relativistic
Doppler formula
1 + z = sqrt((1+v/c)/(1-v/c)), or rather
1 + z = sqrt (1-v^2/c^2) / (1-v/c)
reduces to
1 + z = 1 / (1-v/c), or
z = v / (c-v)

Assuming that v = Hd, and R (the radius of the observable universe)
= c/H0, one gets
d = (c/H0) * z/(1+z), whre d is the distance between the observer and
the emitter at the instant when the light was emitted.

One can disagree with those assumed values for v and R, but the
formula d = (c/H0) * z/(1+z) nevertheless leads to realistic results.
For instance, for z = 10 and assuming that
H0 = 71 km sec^-1 Mpc^-1, which corresponds to 13.772 Gly,
d = 13.772 * 10/11 = 12.52 Gly.

Let's compare this value with that obtained by Wright in
his article "Most Distant Object Record Smashed"
( http://www.astro.ucla.edu/~wright/cosmolog.htm ):

"1 Mar 2004 - Pello et al. have found a galaxy much further away
from us than any previously known. The evidence comes from a single
line observed in the infrared which implies a redshift of z = 10.
The source is seen magnified by a cluster of galaxies, Abell 1935,
acting as a gravitational lens, and the source location is where
sources with 9 < z < 11 should be very highly magnified. The colors
of the source are also very consistent with z = 10. The technical
paper and the press release both give pictures and spectra of
this object. My Cosmology Calculator gives for z = 10 and the
WMAP cosmic parameters (Ho=71, OmegaM=0.27 in a flat Universe)
an age of the Universe of 0.48 Gyr at the time the light we see
was emitted, a light travel time of 13.18 Gyr, and a current
distance of 31.5 billion light years. This distance is much
greater than the speed of light times the light travel time
because the Universe has expanded by factors between 1 and
1+z=11 since the light did its traveling.".

In view of the incertitude about which parameters to use
(vacuum-dominated flat model, OmegaM=0.27, etc...), one
cannot be sure that 13.18 Gly is the "true" value. It could as well
be 12.52 Gly.

- The mutual time dilation fantasy is also implicitly admitted
in article
"The same High Redshift Supernovae from the IfA Deep Survey:
Doubling the SN Sample at z > 0 . 7", by Brian J. Barris et al.
(arXiv: astro- ph/ 0310843 v1 29 Oct 2003)

Excerpt (p.12):

"Typically, the discovery epoch of a high-z supernova
is a few days before maximum brightness, and although
the time dilation factor of (1 + z) works to lessen
the delay in the rest frame, etc...".

>From http://www.astro.ucla.edu/~wright/tiredlit.htm

"The tired light model does not predict the observed time dilation of
high redshift
supernova light curves. This time dilation is a consequence of the
standard
interpretation of the redshift: a supernova that takes 20 days to
decay will
appear to take 40 days to decay when observed at redshift z=1."

>From arXiv: astro- ph/ 9707260 v1 23 Jul 1997
Time Dilation from Spectral Feature Age Measurements of Type Ia
Supernovae
A. G. Riess et al.

"A beguiling prediction of an expanding Universe is that distant
objects will appear to
age at a slower rate than nearby ones."

Conclusion:
__________

Einsteinian relativists overlook that, in an expanding
universe, objects are *simultaneously* moving wrt each other
with the same opposite velocity.

They hypothezise that
1) B moves at v wrt A considered at rest, and
2) A moves at v wrt B considered at rest.
Or neither A nor B are at rest relative to each other.
 
Both objects are moving relative to each other, hence clocks on
A and B tick at the same rate (as shown above), and the
special-relativistic Doppler formula, or *any other formulae
directly or indirectly* based on kinematic time dilation, are false.

Stable universe
_______________

The formula d = (c/H0) * z/(1+z) is straightforwardly
obtained when hypothesising a stable (not expanding) universe
with a cosmic negative acceleration cHo:

A light ray of wavelength lambda is sent from a point P.
At a distance d from P, the energy loss of a photon of frequency Nu is

(hNu/c^2) * cH0 * d = hNu * (H0/c) * d,

where h is the Plank constant, and H0 is the Hubble constant.

Hence, the residual energy hNu(o) of the photon at the distance d is

hNu(o) = hNu - hNu * (H0/c) * d = hNu (1 - H0*d/c), hence
Nu(o) = Nu (1 - (H0*d/c), and
lambda(o) = (1 - (H0*d/c) / lambda

(Let's notice that H0*d corresponds to the recession velocity
v = H0*d assumed in an expanding universe.)

Hence,

z = (lambda(o) - lambda) / lambda
  = (H0/c)d * (1+z), and

d = (c/H0) * z/(1+z)

Marcel Luttgens
 
> Bye,
> Bjoern