Luminosity Distance & Redshift in SR & GR

[Chalky]

[[ Note to moderator - this is now the preferred wording afaict. The
provisional draft of earlier today has already been published, warts
and all, at spf. Consequently, I would recommend that this version is
given preference here, and the prior version discarded/rejected.
Statement 2{g} may still be potentially problematic. However, it is
true for the pregeometric solution and may well also be true for the
concordance model of the geometrodynamic solution (please advise) ]]

[Moderator's note: If someone has already approved it, it is too late.
-P.H.]

In the light of constructive criticism of my original postings on this
subject, both at spr and spf, I would like to now redraft those
postings in a way that is, hopefully, more accurate and more
unambiguous, as well as rendering the associated question, itself more
clear.

Hence:

Relative to an inertial observer, and within the context of SR:

1{s} The redshift of an emission event depends on the recession
velocity of the emitter at the time of emission, and relative to that
inertial detector.
2{s} This is observed after a time delay of del t where del t = d/
c , and d is the spatial proper distance between the emission event
and the observer at the time of observation. ( This distance is also
equal to and equivalent to the distance of the emission event that
the observer actually sees, at the time of detection.)
3{s} The luminosity distance of the emission event is thus observed,
at the time of detection, to be a function of both the Doppler shift
at the time of emission, and a distance of d = c (del t).
4{s} Thus the luminosity distance of the emission event is
proportional to the light travel delay between emission and detection.

However, relative to an inertial observer in a general relativistic
universe, then provided there is negligible peculiar velocity
difference between the emission event and the detection event:

1{g} The cosmological redshift of that emission event depends on the
cosmological time difference (del t) between the emission event and
the detection event .
2{g} This time difference is associated with a spatial separation
between emission event and detection event, of d = c(del t)
3{g} The luminosity distance of the emission event is now observed,
at the time of detection, to be a function of both the cosmological
redshift and the spatial proper distance (d2) of the emission event,
at the time of detection.
4{g} Thus the luminosity distance of the emission event is
proportional to distance d2 (which is always greater than d, unless
emission event and detection event are coincident and simultaneous).

The following fundamental differences thus obtain between the SR and
GR situations.

1) SR Redshift depends on peculiar velocity difference.
Cosmological redshift does not. Instead it depends on cosmological
time difference between emission and detection events.

2) SR luminosity distance is proportional to the distance d = c (del
t).
Cosmological luminosity distance is not. Instead it is proportional
to the spatial proper distance of the emission event , at the time of
detection.

====================================================================
That's about it, thus far, afaict.

.Consequently, does anyone have any constructive criticism to make
about

a) The veracity of the above statements
b) The clarity of the above statements
c) The disambiguation within final statements 1 and 2

[ {Please} speak now, or forever hold your peace. {:-) ]

Thanks also to all, for your patience and comments thus far, and
particularly warm thanks to Jonathan Thornburg, for his.

N.B. The spatial proper distance (d2) of the emission event, at the
time of detection, is dependent on the general relativistic solution
chosen, and, in the case of geometrodynamic field theory and Friedmann
cosmologies, also dependent on retrofit adjustment of their various
free parameters for optimal fit to observational evidence.

Consequently, for maximum generality, it is preferable to leave the
calculation of d2 unspecified, until after the preferred solution is
selected.

[Chalky]

There is just one final correction I would like to include here:

On Mar 20, 1:50 pm, Chalky <chalkys...@bleachboys.co.uk> wrote:

> 1{g} The cosmological redshift of that emission event depends on the
> cosmological time difference (del t) between the emission event and
> the detection event .

The second instance of "cosmological", only recently inserted into
this sentence,should now be deleted again for accuracy, so that
sentence reads:

1{g} The cosmological redshift of that emission event depends on the

time difference (del t) between the emission event and
the detection event .

Given the prior qualification

"relative to an inertial observer in a general relativistic universe",

the second instance of "cosmological" is not only linguistically
superfluous and inelegant, it is also scientifically inaccurate.

(I could elaborate on this further if anyone wants)

[Thomas Smid]

On Mar 20, 1:50=A0pm, Chalky <chalkys...@bleachboys.co.uk> wrote:
> SR Redshift =A0depends on peculiar =A0velocity difference.
> Cosmological redshift =A0does not. =A0Instead it depends on cosmological

> time difference between emission and detection events.

There is factually no difference between these two viewpoints. In
mathematical models of space-time they correspond merely to different
coordinate systems being used here (see
http://math.ucr.edu/home/baez/physics/Relativity/GR/hubble.html ).

The more important question would be whether the redshift is
associated with an expansion of the universe at all, or whether there
are mechanisms that could produce it in a static universe.

Thomas

[Chalky]

On Mar 27, 7:01pm, Thomas Smid <thomas.s...@gmail.com> wrote:

> There is factually no difference between these two viewpoints. In
> mathematical models of space-time they correspond merely to different
> coordinate systems being used here
> (see http://math.ucr.edu/home/baez/physics/Relativity/GR/hubble.html).

Yes, I recall this stretched light interpretation from way back when.

Your reference, however, does not explain why the spaces between the
speckles stretch with increasing cosmological time, whereas the spaces
between the stars within the speckles do not.

Equivalently, why are the comoving coordinates of the stars within the
speckles decreasing with increasing cosmological time, whereas the
comoving coordinates of the speckles are not?

Yes, I am also familiar, from way back when, with the old chestnut
about our solar system, our galaxy, and the local galactic cluster
being different because they are gravitationally bound whereas the
"speckles" are not gravitationally bound to each other. However, this
merely raises more questions in my mind.

1) Why should that make any difference?

2) Why were MTW already trotting out this old chestnut in 1972, (long
before the cosmological constant was resurrected), given that they
then believed the main cosmological question at the time was whether
the universe would end in a big crunch, or not?

A big crunch would indicate the "speckles" were gravitationally bound,
after all, afaict.

[Thomas Smid]

On Mar 31, 3:30 pm, Chalky <chalkys...@bleachboys.co.uk> wrote:
> On Mar 27, 7:01pm, Thomas Smid <thomas.s...@gmail.com> wrote:
>
> > There is factually no difference between these two viewpoints. In
> > mathematical models of space-time they correspond merely to different
> > coordinate systems being used here

> > (seehttp://math.ucr.edu/home/baez/physics/Relativity/GR/hubble.html).

>
> Yes, I recall this stretched light interpretation from way back when.
>
> Your reference, however, does not explain why the spaces between the
> speckles stretch with increasing cosmological time, whereas the spaces
> between the stars within the speckles do not.
>
> Equivalently, why are the comoving coordinates of the stars within the
> speckles decreasing with increasing cosmological time, whereas the
> comoving coordinates of the speckles are not?
>
> Yes, I am also familiar, from way back when, with the old chestnut
> about our solar system, our galaxy, and the local galactic cluster
> being different because they are gravitationally bound whereas the
> "speckles" are not gravitationally bound to each other. However, this
> merely raises more questions in my mind.
>
> 1) Why should that make any difference?
>
> 2) Why were MTW already trotting out this old chestnut in 1972, (long
> before the cosmological constant was resurrected), given that they
> then believed the main cosmological question at the time was whether
> the universe would end in a big crunch, or not?
>
> A big crunch would indicate the "speckles" were gravitationally bound,
> after all, afaict.

I think it is fair to say that cosmology has no real answers to these
questions, only hand-waving arguments that can easily be shown to hold
no water (I have addressed this issue recently in the spf newsgroup;
see the post

http://groups.google.com/group/sci.physics.foundations/tree/browse_frm/
thread/78e3f4907033b532/bb42aa3e89829ca7?rnum=11&_done=%2Fgroup%2F
sci.physics.foundations%2Fbrowse_frm%2Fthread%2F78e3f4907033b532%3F
scoring%3Dd%26&scoring=d#doc_ef65363343be42b9)

Thomas

[Tom Roberts]

On 3/31/12 3/31/12 - 10:30 AM, Chalky wrote:
> Yes, I am also familiar, from way back when, with the old chestnut
> about our solar system, our galaxy, and the local galactic cluster
> being different because they are gravitationally bound whereas the
> "speckles" are not gravitationally bound to each other.

> 1) Why should that make any difference?

Think of what it means for a set of objects to be "bound" -- it means that their
motions and spatial relationships are well modeled by a local Lagrangian that
describes the binding. For a ruler, the Lagrangian describing the motions and
positions of its atoms will have an equilibrium solution with the atoms evenly
spaced at their usual inter-atomic distance. For the solar system, it means the
planets remain in their Keplerian orbits.

Note in particular that these are LOCAL Lgrangians, and that "distance" in them
always means proper distance measured locally. The proper distance is obtained
by integrating the metric over a simultaneous spacelike path in the appropriate
local coordinates. This directly implies that the existence of a Lagrangian
describing a bound system implies it retains its overall size, independent of
the variation in the metric components that characterize the expansion of space
(and contraction to a big crunch).

> 2) Why were MTW already trotting out this old chestnut in 1972, (long
> before the cosmological constant was resurrected), given that they
> then believed the main cosmological question at the time was whether
> the universe would end in a big crunch, or not?

Because even without a cosmological constant, one must discuss why rulers and
the solar system do not expand along with space.

> A big crunch would indicate the "speckles" were gravitationally bound,
> after all, afaict.

No. There's no local Lagrangian that applies. Indeed, in the FRW manifolds the
dust particles are not gravitationally bound to each other, and they all spread
out with the expansion of space. Speaking loosely, the gravitational attraction
of this dust particle to that dust particle is always cancelled by the
attraction of a different dust particle in the opposite direction, so they
aren't bound to each other.


Tom Roberts

[Chalky]

AFAICT you have done nothing more than re-assert the same "old
chestnut" using different words, whilst doing nothing to resolve the
implied contradiction. Where, for example, do you draw the line
between systems in which a local Lagrangian applies, and one where it
does not?

Chalky

[Chalky]

On Apr 3, 5:58 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

> Speaking loosely, the gravitational attraction
> of this dust particle to that dust particle is always cancelled by the
> attraction of a different dust particle in the opposite direction, so they
> aren't bound to each other.

If so, why does a Friedmann universe still decelerate without a
cosmological constant?

[Phillip Helbig---undress to reply]

In article
<fa5533d3-a760-4252...@s7g2000yqm.googlegroups.com>,

Chalky <chalk...@bleachboys.co.uk> writes:

> AFAICT you have done nothing more than re-assert the same "old
> chestnut" using different words, whilst doing nothing to resolve the
> implied contradiction. Where, for example, do you draw the line
> between systems in which a local Lagrangian applies, and one where it
> does not?

A good antidote for the chestnut anecdote is
arxiv.org/abs/astro-ph/0310808 where Davis and Lineweaver, in a paper
called "Expanding Confusion", discuss this topic in detail with many
references.

[Tom Roberts]

Because that's how the dynamics work out. This is a global aspect of the entire
manifold, not any local binding.

Of course it appears that the dynamics of the universe we inhabit is making its
expansion accelerate. In GR this is modeled via a non-zero cosmological constant.


Tom Roberts

[Tom Roberts]

On 4/8/12 4/8/12 2:52 AM, Chalky wrote:
> On Apr 3, 5:58=A0pm, Tom Roberts<tjroberts...@sbcglobal.net> wrote:

>> [... local binding and how that explains rulers not expanding]

>
> AFAICT you have done nothing more than re-assert the same "old
> chestnut" using different words,

"Old chestnuts" and cliches are called that because they are so frequently
appropriate. This is no argument.

> whilst doing nothing to resolve the
> implied contradiction.

I see no contradiction, implied or otherwise. Apparently you have managed to
make up one yourself:

> Where, for example, do you draw the line
> between systems in which a local Lagrangian applies, and one where it
> does not?

There is no such "line". Either such a local Lagrangian provides a good
description of a system of objects, or no such Lagrangian does so. This, of
course, depends on one's meaning of "good", one's measurement accuracy, one's
time scale for observation, etc. But it is clear that for a ruler's atoms, and
for the orbits of planets in our solar system, there are such a local
Lagrangians (because they are well known, independent of GR and modern
cosmology). And it is clear that on the largest cosmological scales there is not.


Tom Roberts

[Chalky]

On Apr 11, 5:53=A0pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

> But it is clear that for a ruler's atoms, and
> for the orbits of planets in our solar system, there are such a local
> Lagrangians (because they are well known, independent of GR and modern
> cosmology).

Agreed. One could say that that this argument is based on pragmatic
considerations. There is no evidence of an expansion of space on the
local scale of the solar system, therefore you conclude there is no
local expansion of space. However, this line of reasoning is weak,
because there would be no local evidence of an expansion of space, if
local measuring rods also expand at the corresponding rate.

[Tom Roberts]

Think about it! If our local rulers expanded at the same rate as the universe as
a whole, we could not observe the latter -- we would observe no expansion
anywhere, local or global. Because our standards of length would also expand.


Tom Roberts

[Chalky]

On Apr 11, 5:53 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:
> On 4/8/12 4/8/12 2:52 AM, Chalky wrote:

[[Mod. note -- 16 excessively-quoted lines snipped here. -- jt]]

> > Where, for example, do you draw the line
> > between systems in which a local Lagrangian applies, and one where it
> > does not?
>
> There is no such "line". Either such a local Lagrangian provides a good
> description of a system of objects, or no such Lagrangian does so. This, of
> course, depends on one's meaning of "good", one's measurement accuracy, one's
> time scale for observation, etc. But it is clear that for a ruler's atoms, and
> for the orbits of planets in our solar system, there are such a local
> Lagrangians (because they are well known, independent of GR and modern
> cosmology). And it is clear that on the largest cosmological scales there is not.
>
> Tom Roberts

Are you actually claiming that the general relativistic deviations
from local Lagrangian physics are so small that they are imperceptible
on the scales of the solar system, the local galaxy, and the local
cluster of galaxies, but not on the scale of the separations between
these (arbitrarily defined) local clusters?

[Tom Roberts]

On 4/13/12 4/13/12 11:44 AM, Chalky wrote:
> On Apr 11, 5:53 pm, Tom Roberts<tjroberts...@sbcglobal.net> wrote:
>> On 4/8/12 4/8/12 2:52 AM, Chalky wrote:
>>> Where, for example, do you draw the line
>>> between systems in which a local Lagrangian applies, and one where it
>>> does not?
>>
>> There is no such "line". Either such a local Lagrangian provides a good
>> description of a system of objects, or no such Lagrangian does so. This, of
>> course, depends on one's meaning of "good", one's measurement accuracy, one's
>> time scale for observation, etc. But it is clear that for a ruler's atoms, and
>> for the orbits of planets in our solar system, there are such a local
>> Lagrangians (because they are well known, independent of GR and modern
>> cosmology). And it is clear that on the largest cosmological scales there is not.
>

> Are you actually claiming that the general relativistic deviations
> from local Lagrangian physics are so small that they are imperceptible
> on the scales of the solar system, the local galaxy, and the local
> cluster of galaxies, but not on the scale of the separations between
> these (arbitrarily defined) local clusters?

No. I am claiming what I said. I.e. what is OBSERVED -- a local
Lagrangian models a ruler to the accuracy with which we can measure it
[#]. And a local theory describes the solar system to the accuracy we
can measure it [@]. At larger scales the situation is not so clear, and
at the largest observable scales it's clear that a global cosmological
model is required.

[#] This is quantum mechanical.

[@] The post-Netwonian approximation to GR.


There is no "line", and attempts to "dichotomize" this are doomed to
failure. There are regions where a local Lagrangian is known, and there
are reasonable cosmological models at the largest scales; in between
there is a smooth gradation about which the details are fuzzy.

Like so many aspects of life and the world we inhabit,
excessively naive people attempt to force a continuous
gradation into categories of black and white. Don't do that.

Tom Roberts

[Chalky]

On Apr 12, 11:30 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:
> On 4/12/12 4/12/12 6:01 AM, Chalky wrote:

> > Agreed. One could say that that this argument is based on pragmatic
> > considerations. There is no evidence of an expansion of space on the
> > local scale of the solar system, therefore you conclude there is no
> > local expansion of space. However, this line of reasoning is weak,
> > because there would be no local evidence of an expansion of space, if
> > local measuring rods also expand at the corresponding rate.
>
> Think about it!

I have thought about it, for rather a long time.

> If our local rulers expanded at the same rate as the universe as
> a whole, we could not observe the latter -- we would observe no expansion
> anywhere, local or global. Because our standards of length would also expand.

I, for one, have not observed the universe actually expanding. Have you?
The total area of _observed_ sky is always larger at higher redshifts.

[Phillip Helbig---undress to reply]

In article
<7b404c1e-f2c4-4a80...@w7g2000vbg.googlegroups.com>,

Chalky <chalk...@bleachboys.co.uk> writes:

> I, for one, have not observed the universe actually expanding.

It is a matter of definition what it means to observe something
"directly".

> The total area of _observed_ sky is always larger at higher redshifts.

It is not clear what this means and what, if anything, it has to do with
the expansion of the universe. It might mean the area of a circle
corresponding to objects at the redshift in question. Even if one takes
the current area, rather than that at which the light we receive now was
emitted, then whether or not such an area is larger at higher redshift
depends on the cosmological parameters. In principle, this is something
which can be observed. In practice, it is difficult. Currently
accepted values of the cosmological parameters do indicate that the area
(at the present instant of cosmic time) should increase with redshift,
at least for the redshifts we can observe, but this is only marginally
related to the question of expansion.

[Chalky]

On Apr 16, 4:35 pm, hel...@astro.multiCLOTHESvax.de (Phillip Helbig---
undress to reply) wrote:
> In article
> <7b404c1e-f2c4-4a80-84f4-d70fe004c...@w7g2000vbg.googlegroups.com>,

I don't see that cosmological parameters have anything to do with it.
>From our perspective, the observed surface area of the night sky
(hemisphere) at a distance R is 2piR^2. This remains the case
observationally, no matter how far out we look, and how powerful our
telescopes are.

[[Mod. note -- I don't think the above statement is true in general.
The problem is, what do you mean by "at a distance R"? In a curved
spacetime (such as "the universe") there's more than one way to define
this, and they give somewhat different answers.
-- jt]]

How we choose to interpret that basic observational fact, however, is
another matter.

[Phillip Helbig---undress to reply]

In article
<d9bb8a85-f214-4a30...@f5g2000vby.googlegroups.com>,

Chalky <chalk...@bleachboys.co.uk> writes:

> I don't see that cosmological parameters have anything to do with it.
> From our perspective, the observed surface area of the night sky
> (hemisphere) at a distance R is 2piR^2. This remains the case
> observationally, no matter how far out we look, and how powerful our
> telescopes are.
>
> [[Mod. note -- I don't think the above statement is true in general.
> The problem is, what do you mean by "at a distance R"? In a curved
> spacetime (such as "the universe") there's more than one way to define
> this, and they give somewhat different answers.
> -- jt]]

Right; that's what I meant. Yes, the area is 2piR^2 but if Omega +
lambda > 1 then R as a function of redshift z has a maximum at some
redshift then starts getting smaller, even reaching zero at the
antipode. And this R is not the proper distance (what one would measure
with a rigid ruler) either.

[Anon E. Mouse]

I have thought about it, for rather a long time.

> If our local rulers expanded at the same rate as the universe as
> a whole, we could not observe the latter -- we would observe no expansion
> anywhere, local or global. Because our standards of length would also expand.

Like Chalky I have thought about this question for a long time.
Recently, as a result of this discussion I had some fresh thoughts.

The first was, Einstein *(1905) determined that his equations were
correct to first and second order if and only if Lorentz time dilation
was correct. I consider that question asked and answered. Lorentz and
Einstein were and are correct, but only to first and second order,
according to Einstein.

So, if models based on these equations predict a certain red-shift for
a given expansion and we observe more red-shift it is possible that
the difference is a 3rd or 4th order effect not included in the basic
equations of the model.

The second thought was, If our rulers are all getting longer, where
would the difference in space - time show up? The obvious answer was
and is, in time.

Given this basis I considered, is there a temporal relation on the
local scale that would confirm, or tend to confirm the effect of a
local increase in the amount of global space.

Well, an increase in the global spatial parameter value would over
time result in a reduction in the local space - time density. All
other things being equal, orbital objects would speed up.

Well, an object in orbit that has an increase in speed will adopt a
higher orbit. Higher orbits = longer orbital periods. So, I asked
myself, is there evidence of increasing orbital periods within the
time period we have been keeping such records.

The moon's orbital period is increasing, and at a rate that is non-
conservative, meaning something must have happened in the moon's past
or is happening at present to cause this.

I believe both possible causes are in part responsible for the
observed increase in periods. Gordon Darwin, Charles Darwin's son
extracted long term tidal data from tidal basin sediments that
indicate this increase has been going on a long time and was greater
in the past than it is at present.

I am also aware that the Earth's orbital period has been increasing
slightly but I no longer recall the details. Something like an 1/8th
of a day per century.

Of course over very long periods the length of days also varies due to
tidal effect, also increasing the daily period, I believe. So, this
effect could make any historical data difficult to interpret.

So, I will simply put forward an untested hypothesis that says, "The
apparent expansion of the astronomically observable universe is
reflected in a similar expansion of the Solar system, as evidenced by
a measurable increase in the orbital periods of the planets over
time."

I am sure that the astronomers in the group will be familiar with, and
know where to find the historical data on many of the other planets in
our system and I look forward to hearing from them.

AAG

[Phillip Helbig---undress to reply]

In article
<fdfa951c-ba15-4669...@p6g2000yqi.googlegroups.com>,

"Anon E. Mouse" <agal...@gmail.com> writes:

> The first was, Einstein *(1905) determined that his equations were
> correct to first and second order if and only if Lorentz time dilation
> was correct.

Let's call this statement A.

> I consider that question asked and answered.

> Lorentz and
> Einstein were and are correct, but only to first and second order,
> according to Einstein.

Let's call this statement B. Note that: (1) A and B are different, (2)
B does not follow from A and (3) A does not follow from B.

Does anyone claim statement B except you?

> So, if models based on these equations predict a certain red-shift for
> a given expansion and we observe more red-shift it is possible that
> the difference is a 3rd or 4th order effect not included in the basic
> equations of the model.

First, this is pure speculation. Second, note that we observe
redshifts, angles and flux. We don't observe expansion "directly".
What happens is that one calculates the dependence of some quantity
(usually related to an angle, which flux is as well since it depends on
solid angle) as a function of redshift for various values of the
cosmological parameters, based on some theory, then determines these
cosmological parameters from the best fit. The theory then gives the
expansion history.

> The second thought was, If our rulers are all getting longer, where
> would the difference in space - time show up? The obvious answer was
> and is, in time.

This is far from obvious. However, the whole discussion is rather
pointless. We have "observed" the expansion of the universe. Even if
one thinks there is some other explanation for this observation, the
fact is that the observation still exists. Any sort of universe where
expansion were hidden because of the expansion of local standards is
obviously not our universe, since in that case there would be no
observations which could be interpreted as evidence for expansion.

> The moon's orbital period is increasing, and at a rate that is non-
> conservative, meaning something must have happened in the moon's past
> or is happening at present to cause this.

This is well known and is explained through conservation of angular
momentum to compensate the slowing of rotation caused by tidal friction.

> So, I will simply put forward an untested hypothesis that says, "The
> apparent expansion of the astronomically observable universe is
> reflected in a similar expansion of the Solar system, as evidenced by
> a measurable increase in the orbital periods of the planets over
> time."

This is wrong. Even if some such effect existed, it would be far
smaller than any observed effects on the scale of the solar system.

[Anon E. Mouse]

> Does anyone claim statement B except you?
>

>From Part 1 section 4 of On the Electrodynamics of Moving Bodies,

"Thus the law of the parallelogram of velocities is valid according to
our theory only to a first approximation."

>From section 8,

"In agreement with experiment and with other theories, we obtain to a
first approximation

>From the introduction,

"They suggest rather that, as has already been shown to the first
order of small quantities, the same laws of electrodynamics and optics
will be valid for all frames of reference for which the equations of
mechanics hold"

The exact section I was originally referring to is from section 4.
Physical Meaning of the Equations Obtained in Respect to Moving Rigid
Bodies and Moving Clocks,

"From this there ensues the following peculiar consequence. If at the
points A and B of K there are stationary clocks which, viewed in the
stationary system, are synchronous; and if the clock at A is moved
with the velocity v along the line AB to B, then on its arrival at B
the two clocks no longer synchronize, but the clock moved from A to B
lags behind the other which has remained at B by $\frac{1}{2}tv^2/c^2$
(up to magnitudes of fourth and higher order), t being the time
occupied in the journey from A to B."

as this seems to me to apply exactly to the point being discussed.

> First, this is pure speculation.

Yes, I clearly labeled it as a "thought", an idea, someone deeply
interested in the topic could examine the possibility in more detail
if they wish.

> > The moon's orbital period is increasing, and at a rate that is non-
> > conservative, meaning something must have happened in the moon's past
> > or is happening at present to cause this.
>
> This is well known and is explained through conservation of angular
> momentum to compensate the slowing of rotation caused by tidal friction.
>

Tidal friction causes loss of delta v and lower orbits would result.
This "explanation" is inconsistent with known orbital mechanics.
[[Mod. note --
The author is mistaken: tidal friction removes angular momentum from
the Earth (slowing the Earth's spin), so by conservation of angular
momentum it must add angular momentum to the Earth-Moon orbit, i.e.,
it makes the Earth-Moon orbit *expand*. Quoting from A. E. Roy,
"Orbital Motion" (2nd Edition, Adam Hilger, 1982), section 9.12
"Secular Acceleration of the Moon",
The Earth, rotating once every siderial day, tries to carry the
tidal bulges produced by the Moon's gravitational pull around
with it; the Moon holds them back since it revolves about the
Earth in the much longer period of the siderial month (27.22 days).
The consequence is that angular momentum is lost by the Earth by
tidal friction, principally in the shallower seas, so that the
Earth's period of rotation increases. The transfer of angular
momentum to the Moon causes it to recede from the Earth, increasing
the length of the month.
For a detailed analysis, see Murray and Dermott, "Solar System Dynamics"
(Cambridge U.P., 1999), sections 4.9 "Tidal Torques" and section 4.13
"Tidal Evolution". The explicit statement that the Moon is slowly
*receding* from the Earth can be found in section 4.9, just after
equation (4.152).
-- jt]]
However, the point I wished to make was, the Moon's data likely does
not apply to the question of increasing planetary orbital periods and
that this is well known.

> > So, I will simply put forward an untested hypothesis that says, "The
> > apparent expansion of the astronomically observable universe is
> > reflected in a similar expansion of the Solar system, as evidenced by
> > a measurable increase in the orbital periods of the planets over
> > time."
>
> This is wrong. Even if some such effect existed, it would be far
> smaller than any observed effects on the scale of the solar system.

The tiny amount of data that I know that I know seems to confirm my
hypothesis. Old galaxies are small and dense modern ones are large and
expansive. This, in contravention of kinematic models that seem to say
it should be the other way round. The only long term trend in
planetary orbital period I believe I once read said Earth's orbit
period has and is increasing at a tiny amount per century.

If it helps, I can state my hypothesis in terms more compatible with
relativity as it is commonly applied to cosmology. It would sound
something like, "If the action of a negative cosmological constant
were applied to the orbital period of the planets of the Solar system,
I propose that the effect would be comparable to a "red-shifted"
apparent mass reduction in the planets causing them to adopt higher
orbits with longer periods.

I dislike this format for several reasons, first, I am more familiar
with my own manner of understanding relativity. Second, the actual
hypothesis is that the expansion of the universe is causing local
space and time to thin. I have not conceived any direct method of
testing the lengthening of our rulers, but this test of the local
thinning of space-time in response to universal expansion seems
plausible in that the general form of the math "works". Finally, I
have always been disquieted by the concept of relativistic alterations
of a moving bodies apparent mass, even if the effect is apparently
confirmed by particle physics experiments.

Since through this post I am seeking data which I may use as a check
upon any computed result, clearly I have not done the calculations
themselves, but equally clearly neither have you.

I know I may be mistaken. Even though I can tell that the premiss
seems correct and the general form of the predicted result is, I
believe correct I am far, far, far, from certain this hypothesis I put
forth is capable of confirmation.

> This is wrong. Even if some such effect existed, it would be far
> smaller than any observed effects on the scale of the solar system.

I would very much appreciate it if any reader knows where planetary
orbital period trend data might be found and will contribute a
reference or citation.

respectfully,

AAG

[Tom Roberts]

On 4/17/12 4/17/12 - 1:37 AM, Anon E. Mouse wrote:
> The first was, Einstein *(1905) determined that his equations were
> correct to first and second order if and only if Lorentz time dilation
> was correct. I consider that question asked and answered. Lorentz and
> Einstein were and are correct, but only to first and second order,
> according to Einstein.

It is rather silly to consider century-old statements to be completely
correct in all details, without checking them. ESPECIALLY when the
theory being discussed had not yet been adequately explored or tested.

Your claim here is downright wrong, and we now KNOW that the equations
of SR are valid to much better than second order:

Consider the factor called gamma. To second order in v/c,
gamma = 1 + (v/c)^2/2 + O((v/c)^4)
At LEP, electrons were routinely accelerated to 100 GeV,
corresponding to gamma ~ 200,000, while their speed was
indistinguishable from c. So "second order" is wrong
by a factor of ~100,000.

> The second thought was, If our rulers are all getting longer, where
> would the difference in space - time show up? The obvious answer was
> and is, in time.

While that sounds cute, there is no basis in GR for this.

GR itself is scale independent. The only way to establish either a
length or a time scale is to use a ruler or clock which are based on
quantum phenomena [#]. For instance, attempting to use earth's orbit as
a "length scale" fails because you cannot determine the mass of the sun
independent of the "length scale". Fortunately, the world we inhabit is
a quantum world, and quantum theory is not scale independent.

[#] Of course we routinely do this. This is now so ingrained in
our minds that many people do not even realize the need.

> The moon's orbital period is increasing, and at a rate that is non-
> conservative, meaning something must have happened in the moon's past
> or is happening at present to cause this.

The earth's oceans have lunar tides, which account for the increase in
the moon's orbit, via conservation of angular momentum.

The cosmological expansion, applied to the size of the moon's orbital
radius, is VASTLY smaller than the observed increase.

In summary, physics is a QUANTITATIVE science. Your cute but untested
qualitative notions are easily disproved by a simple quantitative
analysis.

Tom Roberts

[Anon E. Mouse]

>
> The cosmological expansion, applied to the size of the moon's orbital
> radius, is VASTLY smaller than the observed increase.
>

This is EXACTLY why I originally stated that the expansion of the
Moon's orbit should not be considered evidence for Hubble flow type
expansion.

The planetary orbital data I seek may be of a different character,
although now that I correctly understand the tidal friction theory I
see that it could similarly apply to planetary orbits and that could
explain why the tiny amount of actual data I think I actually recall
seemed so out of scale for the small effect I would expect from
cosmological expansion.

In considering the matter further as I have been defending my
"thoughts" I find that the crux of the matter lies in manner in which
relativity theory treats moving masses. These either gain or lose
according to their changing or relative velocity.

For particle physics this works well, although some including myself
find it awkward, for the consideration of cosmological expansion
considering relative mass change over epochs of time is problematic.

A basic assumption of cosmological expansion is that space is
increasing over long periods of time and thus the space-time density
is decreasing. The LONG PERIODS OF TIME is what makes this a higher
order effect, that standard relativity theory as given is not
necessarily capable of modelling.

My dispute is NOT with SR or GR first, or second order accuracy. So
proofs of SR or GR based on particle physics are not needed, wanted,
or on topic. This discussion is more appropriately focused on the
problematic role of the cosmological constant.

The cosmological observation that the expansion of the universe is
presently increasing its pace contradicts the idea of a cosmological
constant.

This data says that constant is a variable. That is exactly the sort
of fourth and higher order effect Einstein was stating might not be
encompassed by his theory.

All other things being equal, if space and time are indeed thinning
one would expect that velocity would be effected and mass would not,
and I believe that this empirical expectation matches the available
data fairly well, but the dominant effect of tidal transfer of
momentum effect, plus other possible causes should make this possibly
small effect difficult, or more likely impossible, to observe.

I simply want to see some data before I try and decide! If solar tidal
transfer is causing the increase in planetary periods I believe is
happening then this should follow a inverse square relation which
would be apparent in the planetary period data. If Hubble flow is the
cause then the increase in period should follow a nearly linear
relation. If it were simply a matter pf googling it, I would do this
myself, but I know from experience to referencing data this specific
is hard work, on the other hand if someone knows an appropriate data
source, they simply share this knowledge and all is simple and
beautiful...

I believe that this is not the first time that I have misunderstood
the comments of moderators and others with regard to tidal transfer of
momentum and I promise I will, before making any further comments that
may be either incorrect, or misunderstood I will read McDermot and
Murray. That the spinning tidal bulges would do work upon the Moon
increasing its orbital speed, period, and radius makes sense, however,
i have never seen an example of a fully integrated mass body
computation of this type. I will be interested to explore this topic
more.

My thanks also to the other commentators. I am especially appreciative
of the reader who sent me a most interesting previously published
paper of his own authorship giving a very detailed expansion of GRT
that encompasses Hubble flow. I was and am most impressed with the
quality of this work, but - I still want to see the data!

Best regards to all and sundry,

AAG

[Phillip Helbig---undress to reply]

In article
<1d890842-3067-4131...@35g2000yqq.googlegroups.com>,

"Anon E. Mouse" <agal...@gmail.com> writes:

> The cosmological observation that the expansion of the universe is
> presently increasing its pace contradicts the idea of a cosmological
> constant.

Why?

> This data says that constant is a variable. That is exactly the sort
> of fourth and higher order effect Einstein was stating might not be
> encompassed by his theory.

No.

First, some linguistic matters. The Hubble constant is called
"constant" since is a constant like m in the y=mx+b equation for a
straight line. It is constant in all directions and at all places at a
given time but in general varies with time. The cosmological constant,
Lambda (capital) is constant in time, i.e. a given amount of space
contains a certain amount of this. It has negative pressure which
causes repulsion. Since it is constant per volume, a pure positive
cosmological constant leads to exponential expansion. Usually, one
defines lambda=Lambda/3H^2 as an "observable" quantity, also called the
cosmological constant, which varies if and only if H varies in time.

The data do not say that it is variable. A constant cosmological
constant does not imply constant expansion. This stuff was worked out
by Lema?tre back in the 1920s.

[Tom Roberts]

On 4/20/12 4/20/12 9:33 AM, Anon E. Mouse wrote:
> In considering the matter further as I have been defending my
> "thoughts" I find that the crux of the matter lies in manner in which
> relativity theory treats moving masses. These either gain or lose
> according to their changing or relative velocity.

This depends on what you mean. The current accepted usage of the word "mass" is
that it is invariant, and therefore a given object's mass is independent of its
velocity relative to any observer. Mass is an inherently INTRINSIC property of
an object, and thus cannot possibly be observer dependent.

Historically, SR has been described with a velocity-dependent "relativistic
mass", but this has become an anachronism. Moreover, that's essentially hopeless
in GR.

Note that "relativistic mass" isn't mass in any traditional
sense, and is identical to what we call "energy" in SR.

> For particle physics this works well, although some including myself
> find it awkward, for the consideration of cosmological expansion
> considering relative mass change over epochs of time is problematic.

Particle physicists also find "relativistic mass" to be problematic, and were
among the instigators of removing "relativistic mass" from modern discussions.
In GR it is unsupportable and essentially useless.

This goes much deeper. In general, describing things in
terms of invariants is MUCH easier and almost always better
than using non-invariants. Compare Lagrangian mechanics to
Newtonian mechanics.... That is almost trivial compared to
the advantage of using invariants in GR.

> A basic assumption of cosmological expansion is that space is
> increasing over long periods of time and thus the space-time density
> is decreasing. The LONG PERIODS OF TIME is what makes this a higher
> order effect, that standard relativity theory as given is not
> necessarily capable of modelling.

Hmmm. Are you harking back to your error in thinking that the equations of
relativity are valid only to second order?

> My dispute is NOT with SR or GR first, or second order accuracy.

Ah yes, you are harking back. You were and are wrong about that -- SR is valid
to MUCH higher than second order in v/c. See my previous post about this.

> The cosmological observation that the expansion of the universe is
> presently increasing its pace contradicts the idea of a cosmological
> constant.

Not true. The cosmological constant is indeed constant, but it can generate an
accelerating expansion. Perhaps you should learn what GR is and says before
attempting to criticize it.

> This data says that constant is a variable.

Apparently you have fooled yourself into think that since "constant" is part of
its name, the cosmological constant must imply a "constant universe" (or
somesuch). That is simply not true. Nor does it imply "constant expansion", or
even "a time-independent value of Hubble's constant" (which we know to vary over
large time scales).

Beware of PUNS -- for instance, "Hubble's constant" uses the word
"constant" to mean the same for many different galaxies observed
NOW, not for a quantity that does not vary over time. You used the
word "constant" in at least three different ways, without carefully
distinguishing among them.

Yes, the cosmological constant is a constant. THE ONLY THING that implies is
that the cosmological constant ITSELF does not vary over space or time.

> That is exactly the sort
> of fourth and higher order effect Einstein was stating might not be
> encompassed by his theory.

You are still wrong about this. Back in 1905, Einstein did not know how valid SR
would turn out to be, but today _WE_ know that the equations of SR are valid to
much higher order than second. Indeed, nobody has ever observed a significant
difference between measured values and the predictions of SR, within its domain
of applicability.

Truncating the Taylor's expansion of gamma to 1,000-th order (!)
in v/c, the value of gamma for v/c->1 is 25.25, still a factor of
almost 10,000 smaller than the value achieved in LEP. The series
converges slowly, and Mathematica cannot handle enough terms to
come anywhere close to the correct value of 200,000.


Tom Roberts