Pioneer anomaly not gravitational

[bcrowell]

An analysis of the orbits of Neptune's satellites seems to show that the Pioneer anomaly can't be gravitational.

http://www.technologyreview.com/blog/arxiv/24541/

 

[Old Smuggler]

An analysis of the orbits of Neptune's satellites seems to show that the Pioneer anomaly can't be gravitational.

http://www.technologyreview.com/blog/arxiv/24541/

IMO, there were really never any reason to expect that the PA should involve any
real accelerations. That's just a specific interpretation of the PA, even if it is the popular one.
But the fact that the anomalous acceleration is very close to cH, would suggest that
the PA has something to do with mismodeling of null curves in an expanding Universe.
This does not work in GR, but alternative models exist. See, e.g., gr-qc/9910054.

 

[bcrowell]

But the fact that the anomalous acceleration is very close to cH, would suggest that
the PA has something to do with mismodeling of null curves in an expanding Universe.
This does not work in GR, but alternative models exist. See, e.g., gr-qc/9910054.

Interesting. I took a quick, casual look at that paper, and at gr-qc/0112025, which describes his alternative theory of gravity. I don't claim to have examined it carefully enough to have even absorbed the general ideas of the theory. It is interesting that he claims to have a viable non-metric theory that is compatible with all the classic solar-system tests. However, he doesn't seem to have proposed any specific experimental tests other than the Pioneer Anomaly. It would be a lot more compelling if he could say, "Hey, here's this other empirical test where I predict something different from GR -- go measure this and see what happens."

 

[Garth]

You may be interested in the discussion we have already had in physics forums, such as here: The Anomalous Acceleration of the Pioneer Spacecrafts, especially this analysis.

The unexplained residual is consistent with cH.

What actually was being detected was a residual blue shift in the radio signals, which is interpreted as an extra Sun-wards acceleration.

It could just as well be a time drift between atomic and ephemeris clocks.

Garth

 

[edpell]

what is cH please?

 

[bcrowell]

what is cH please?

The speed of light multiplied by the Hubble constant. IMO it's not very impressive that cH happens to be of the same order of magnitude as the anomalous acceleration observed in the Pioneer anomaly, but that seems to be one of the main empirical facts used to support Østvang's QMR theory.

 

[turbo]

The unexplained residual is consistent with cH.

What actually was being detected was a residual blue shift in the radio signals, which is interpreted as an extra Sun-wards acceleration.

It could just as well be a time drift between atomic and ephemeris clocks.

Garth

The observations might be consistent with a variable speed of propagation of light through space that is polarized by gravitation of embedded masses. Such an interpretation of observations would be a game-changer and thus would be anathema to BB cosmology. If it's true, prepare to wait for a century or so before it can become "accepted".

 

[lalbatros]

"The observations might be consistent with a variable speed of propagation of light through space that is polarized by gravitation of embedded masses. Such an interpretation of observations would be a game-changer and thus would be anathema to BB cosmology. "

The use of the conditional tense is appropriate indeed, as always when pure speculation without enough experimental data is involved.

 

[turbo]

"The observations might be consistent with a variable speed of propagation of light through space that is polarized by gravitation of embedded masses. Such an interpretation of observations would be a game-changer and thus would be anathema to BB cosmology. "

The use of the conditional tense is appropriate indeed, as always when pure speculation without enough experimental data is involved.

We have plenty of experimental data, and not just from the Pioneers, but from other probes that are at least partially spin-stabilized. If the apparent "acceleration" is not real, and is not caused by gravitational forces on the probes themselves, we must be prepared to consider that the radio signals could be propagating at something other than c. Einstein's view of space as a polarizable ether was not well-received by his contemporaries nor by modern-day physicists, but it was a view that he held from 1920 onward.

http://www.bartleby.com/173/22.html

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its result hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).

The ether of the general theory of relativity differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not 'absolute', but is determined in it locally variable properties by ponderable matter.

 

[lalbatros]

turbo-1,

How far have you analyzed your experimental data?
Could you make them available as well as your analysis?

I am very far from being a specialist on this topic and I have never seen the full data. I even don't know how I could process them!
That's why I am so sceptical, considering the many effect and sources of error to be taken into account and listed by Turyshev (see for example: http://arxiv.org/abs/physics/0502123). And this list is maybe far from being complete. For example, what would be the impact of disturbances caused by (very) small charge densities dispersed in space? Has this been studied? I would be interrested to know the impact on the experimental data.

For me, the Pioneer anomaly is a very interresting topic, but I doubt it is a "clean enough" experiment to bring us to big conclusions, specially considering the small value of the anomaly.

 

[turbo]

The Pioneer anomaly is being studied by the Planetary Society. A few years ago, years' worth of magnetic data-tapes were recovered, and it's unclear whether they have completed their analysis, from information on their web site. However, a recent publication by Turyshev says:

Initial efforts to explain the Pioneer anomaly focused on the possibility of on-board systematic forces.While these cannot be conclusively excluded (Anderson et al. 2002; Turyshev et al. 2005), the evidence to date did not support these mechanisms: it was found that the magnitude of the anomaly exceeds the acceleration that these mechanisms would likely produce, and the temporal evolution of the anomaly differs from that which one would expect, for instance, if the anomaly were due to thermal radiation of a decaying nuclear power source.

http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.0399v1.pdf

While analysis to that level is pretty impressive, there is another more compelling reason to discount systematics. The anomaly is not confined to the Pioneer craft. Other probes also show evidence of anomalous Sunward acceleration, and when probes have different masses, cross-sectional areas and thermal signatures (due to the various ways RTGs are mounted) it is difficult to come up with scenarios in which the anomaly can be produced for each of them. As in the quote above, if thermal radiation contributed to the anomaly, one would expect that the effect would diminish as the RTGs decayed.

 

[JesseM]

While analysis to that level is pretty impressive, there is another more compelling reason to discount systematics. The anomaly is not confined to the Pioneer craft. Other probes also show evidence of anomalous Sunward acceleration, and when probes have different masses, cross-sectional areas and thermal signatures (due to the various ways RTGs are mounted) it is difficult to come up with scenarios in which the anomaly can be produced for each of them.

Do all the different probes show the same magnitude of anomalous acceleration as a function of distance from the Sun, or is it different for different probes?

 

[Garth]

The Pioneer Anomaly acceleration is constant from the orbit of Saturn outwards and equal on both the Pioneer probes.

Inside the orbit of Saturn other effects would have masked the effect, as indeed they have on other deep space probes, although signs of the effect have been detected on the Voyager probes as well. The Voyager spacecraft 's three-axis stabilization maskes the effect.

The Flyby anomalies are different, though they may be connected.

 

[JesseM]

The Pioneer Anomaly acceleration is constant from the orbit of Saturn outwards and equal on both the Pioneer probes.

Inside the orbit of Saturn other effects would have masked the effect, as indeed they have on other deep space probes, although signs of the effect have been detected on the Voyager probes as well. The Voyager spacecraft 's three-axis stabilization maskes the effect.

The Flyby anomalies are different, though they may be connected.

If there's no clear evidence that the magnitude of the anomalies for different probes are too similar to be explained by quirks of engineering, would you then disagree with turbo-1's statement that "when probes have different masses, cross-sectional areas and thermal signatures (due to the various ways RTGs are mounted) it is difficult to come up with scenarios in which the anomaly can be produced for each of them"?

 

[turbo]

If there's no clear evidence that the magnitude of the anomalies for different probes are too similar to be explained by quirks of engineering, would you then disagree with turbo-1's statement that "when probes have different masses, cross-sectional areas and thermal signatures (due to the various ways RTGs are mounted) it is difficult to come up with scenarios in which the anomaly can be produced for each of them"?

Part of my skepticism of design-dependent systematics arises from the fact that even though the anomaly can be masked in some probes that are not fully spin-stabilized, the anomaly still results in some blue-shifting. If off-gassing, leaking thruster fuel, or thermal radiative pressures can somehow be responsible for the anomalies, why is the thrust always directed away from the Sun resulting in braking? Why no acceleration out of the system resulting in red-shifting?

We don't have enough probes out there to make the lack of red-shifting a "smoking gun". Dedicated spin-stabilized probes with centrally-located RTGs might help clear this up.

 

[edpell]

Sounds like a worthwhile experiment send out 10 probes in different directions. All the probe needs to do is ping once per ten seconds and point towards Earth (that is point the antenna part towards Earth). Say 20Kg per probe 200Kg total. But at so respectable velocity (we don't have all century). Anyone have a feel for the cost?

 

[edpell]

Will Pluto Express gives us usable data on this question? On their web page it says it is three axis AND spin stabilized. I guess it depends how often they fire the reaction wheel dumping thrusters? Anyone know how they will use the probe?

 

[bcrowell]

Sound like a worthwhile experiment send out 10 probes in different directions. All the probe needs to do is ping once per ten seconds and point towards Earth (that is point the antenna part towards Earth). Say 20Kg per probe 200Kg total. But at so respectable velocity (we don't have all century). Anyone have a feel for the cost?

If you look at http://en.wikipedia.org/wiki/New_horizons#Spacecraft_subsystems you can get a feel for sizes of the different stuff that has to go aboard this type of probe. New Horizons is 465 kg, and a lot of the equipment looks like it would also be needed for a dedicated pioneer-anomaly probe. E.g., it's got a really huge radio dish.

There's some more info here about possible dedicated missions or other ways of exploring the Pioneer anomaly: http://en.wikipedia.org/wiki/Pioneer_anomaly#Further_research_avenues

If I were peer-reviewing a proposal for a new dedicated probe, the question in my mind would be this: if it's not a gravitational effect, then what are the chances that it's even interesting physics at all?

 

[hamster143]

While analysis to that level is pretty impressive, there is another more compelling reason to discount systematics. The anomaly is not confined to the Pioneer craft. Other probes also show evidence of anomalous Sunward acceleration,

We have a total of five spacecraft outside Saturn's orbit, two of them Pioneers, and that's really not enough data to go on.

. If off-gassing, leaking thruster fuel, or thermal radiative pressures can somehow be responsible for the anomalies, why is the thrust always directed away from the Sun resulting in braking?

One common theme is that each one of the five probes (two Pioneers, two Voyagers and New Horizons) necessarily consists of a big-*** parabolic dish facing the Earth (i.e., with good precision, the Sun), and some hardware bolted on the back side of the dish.

 

[Old Smuggler]

If I were peer-reviewing a proposal for a new dedicated probe, the question in my mind would be this: if it's not a gravitational effect, then what are the chances that it's even interesting physics at all?

Well, that would depend on your definition of "interesting physics". Some people apparently
think that new physics that is not "mainstream new physics", i.e., not coming from some simple extension of mainstream theory, is uninteresting. Since most gravitational
explanantions of the PA may be classified as mainstream new physics, evidence that the PA
is not gravitational may diminish the general interest in the PA and thus the chances for
a dedicated mission to test it.

More radical explanations of the PA may still be viable, e.g., based on the notion that the
cosmic expansion has observable consequences in the solar system. This confronts the
"well-known" mainstream position that the cosmic expansion does not apply to
gravitationally bound systems. But it is very difficult to unlearn something that is taken for
granted. Thus some radical explanations may seem even more farfetced than what is
really the case, also reducing the motivation for a dedicated test mission.

 

[Al68]

This confronts the
"well-known" mainstream position that the cosmic expansion does not apply to
gravitationally bound systems.

That's not exactly the mainstream position. The mainstream position is that within star systems and galaxies and clusters, gravity is just strong enough to dominate "dark energy", while the gravitational attraction at larger distances is too weak to counteract dark energy.

 

[JesseM]

That's not exactly the mainstream position. The mainstream position is that within star systems and galaxies and clusters, gravity is just strong enough to dominate "dark energy", while the gravitational attraction at larger distances is too weak to counteract dark energy.

Even with no dark energy the expansion would still happen, just at a different rate, right? But either way I guess GR predicts that the local gravity in a bound system dominates over cosmic expansion (I wonder if any numerical simulations have been done to check exactly how small the effects of expansion should be within the solar system according to GR)

 

[Old Smuggler]

That's not exactly the mainstream position. The mainstream position is that within star systems and galaxies and clusters, gravity is just strong enough to dominate "dark energy", while the gravitational attraction at larger distances is too weak to counteract dark energy.

I know what the mainstream position is. Since I was talking about observable consequences
of the cosmic expansion in the solar system, where the mainstream position is that there
cannot be any, I didn't see any reason to include all the buts and ifs appearing if one is
talking about galaxy clusters etc.

 

[Old Smuggler]

But either way I guess GR predicts that the local gravity in a bound system dominates over cosmic expansion (I wonder if any numerical simulations have been done to check exactly how small the effects of expansion should be within the solar system according to GR)

Several studies have been done on the effects of the cosmic expansion within the solar
system according to GR, and also the effect of a cosmological constant of appropriate
magnitude. They all show that such an effect is incredibly small at best, and certainly
not measurable. I don't have a reference at hand right now, but you may try to search
for author(s) Vollick, Faraoni or Cooperstock at the arXiv.

 

[Al68]

Even with no dark energy the expansion would still happen, just at a different rate, right?

Sure, but without dark energy, the rate of expansion would be dominated even by the weak gravity over large distances, ie the rate would be slowing.

But either way I guess GR predicts that the local gravity in a bound system dominates over cosmic expansion (I wonder if any numerical simulations have been done to check exactly how small the effects of expansion should be within the solar system according to GR)

I wonder about that, too, but I would think that it would be negligible, since compared to intergalactic space, the gravitational forces within the solar system are huge, as well as within galaxies and clusters.

I would think if dark energy was strong enough to have any measurable effect within the solar system, it would have expanded the distance between galaxy clusters to way beyond observable distances long ago. Especially if dark energy's effect increases with distance as is suspected.

 

[Garth]

The PA is not cosmological expansion detected within the solar system, the anomalous acceleration is in the opposite direction!

Garth

 

[Old Smuggler]

The PA is not cosmological expansion detected within the solar system, the anomalous acceleration is in the opposite direction!
Garth

It seems that you have the cosmic redshift in mind. But no sane person would identify
the apparent anomalous blueshift inferred from the PA with the cosmic redshift.

However, the cosmic expansion may have another, more subtle effect, namely an
anomalous delay of radio signals used in the telemetry. Since the PA essentially appears
from the calculation of trajectories of the probes, such an anomalous delay could be
interpreted as if the probe's coordinate velocity were slowing down anomalously, thus
indicating an anomalous acceleration towards the observer.

This explanation does not work in GR, but it has been shown to work in another theory.
The bottom line is thus that the interpretation of the PA is crucially theory-dependent,
and that the PA really might be the cosmological expansion detected within the solar system.

 

[Garth]

It seems that you have the cosmic redshift in mind. But no sane person would identify
the apparent anomalous blueshift inferred from the PA with the cosmic redshift.

However, the cosmic expansion may have another, more subtle effect, namely an
anomalous delay of radio signals used in the telemetry. Since the PA essentially appears
from the calculation of trajectories of the probes, such an anomalous delay could be
interpreted as if the probe's coordinate velocity were slowing down anomalously, thus
indicating an anomalous acceleration towards the observer.

This explanation does not work in GR, but it has been shown to work in another theory.
The bottom line is thus that the interpretation of the PA is crucially theory-dependent,
and that the PA really might be the cosmological expansion detected within the solar system.

You have to be very careful in your language to avoid confusion.

To say "cosmological expansion detected within the solar system" is to say the same thing as "cosmic redshift".

I have already said What actually was being detected was a residual blue shift in the radio signals, which is interpreted as an extra Sun-wards acceleration. It could just as well be a time drift between atomic and ephemeris clocks.

Which, as you have pointed out, does not work in GR.

What I have argued on these Forums for several years now, such as here and here: Does the PA show that DM/DE is dynamically important in the outer solar system? is that because the PA anomalous blue shift of radio signals, once non-gravitational effects have been allowed for, is equal to cH to within observational errors, then the effect may well be cosmological in nature and an indication that GR may have to be modified in some way.

Garth

 

[Ich]

Even with no dark energy the expansion would still happen, just at a different rate, right?

Expansion per se (I mean unaccelerated, a~t) can be removed by a coordinate transformation. Therefore it can't have any physical effect on the solar system.
What is relevant for solar system physics are gravitational sources that are unaccounted for in the standard calculations. There are two such sources of "cosmological origin", Dark Matter and http://arxiv.org/abs/gr-qc/0602002" .
We should expect that Dark Matter dominates around the sun, producing indeed an anomalous blueshift - but several orders of magnitude below the observed effect.
So cosmology is not the solution, at least not in GR or other metric theories consistent with observation.

 

[bcrowell]

Expansion per se (I mean unaccelerated, a~t) can be removed by a coordinate transformation. Therefore it can't have any physical effect on the solar system.

I'm sure you're right, but there are a couple of things I don't understand about this argument.

First, if I take a metric ds^2=dt^2-a^2(dr^2+r^2 d\theta^2+r^2\sin^2\theta d\phi^2 ), with a=ut, and calculate the Einstein tensor, I get G^t_t=3t^{-2}, along with other diagonal elements that are nonzero. Doesn't this mean that the a=ut is observable?

Also, there seems to be something missing from your argument, since it makes it sound as though expansion would be unobservable not just at the scale of the solar system but at the cosmological scale as well.

 

[Ich]

First, if I take a metric <br /> ds^2=dt^2-a^2(dr^2+r^2 d\theta^2+r^2\sin^2\theta d\phi^2 )<br />, with a=ut, and calculate the Einstein tensor, I get <br /> G^t_t=3t^{-2}<br /> , along with other diagonal elements that are nonzero. Doesn't this mean that the a=ut is observable?

(didn't check your math, but it seems wrong at first glance)
It is the minkowski metric if you use https://www.physicsforums.com/showthread.php?p=2283519#post2283519"

Also, there seems to be something missing from your argument, since it makes it sound as though expansion would be unobservable not just at the scale of the solar system but at the cosmological scale as well.

Expansion is not unobservable, but it has no physical effect. If all galaxies are tied to constant FRW coordinates, they are moving away from each other in the standard minkowski coordinates. That is surely observable, but it doesn't mean that physics is different. It just means that matter in the universe is arranged such that it is moving apart. No reason for e.g. a solar system to follow that trend, it's the same as if other galaxies were not moving apart. It simply doesn't matter what other things do.

 

[Old Smuggler]

First, if I take a metric ds^2=dt^2-a^2(dr^2+r^2 d\theta^2+r^2\sin^2\theta d\phi^2 ), with a=ut, and calculate the Einstein tensor, I get G^t_t=3t^{-2}, along with other diagonal elements that are nonzero. Doesn't this mean that the a=ut is observable?

FYI, Ich has a serious misunderstanding of differential geometry; he believes that by
linearizing the scale factor in the FRW models one always gets Minkowski space-time. That
this is wrong may be easily shown by calculating the Riemann tensor; it does not
vanish except for the very special case of an empty FRW model.

Unfortunately, a certain crackpot paper was published in American Journal of Physics
in August 2009, advocating an interpretation of the cosmic redshift based on this misunderstanding.

 

[bcrowell]

if I take a metric ds^2=dt^2-a^2(dr^2+r^2 d\theta^2+r^2\sin^2\theta d\phi^2 ), with a=ut, and calculate the Einstein tensor, I get G^t_t=3t^{-2}, along with other diagonal elements that are nonzero.

(didn't check your math, but it seems wrong at first glance)

I didn't do the math by hand. I used a computer algebra system, called Maxima. Of course that doesn't mean the calculation is right. It's conceivable that I set it up wrong, misunderstood the documentation for the software, etc. But in any case, here is my code and the output of the calculation:

Code:

load(ctensor);
ct_coords:[t,r,theta,phi];
a : u*t;
lg:matrix([1,0,0,0],
          [0,-a^2,0,0],
          [0,0,-a^2*r^2,0],
          [0,0,0,-a^2*r^2*sin(theta)^2]);
cmetric();
einstein(true);

Relevant part of output:

                                           3
(%t7)                            ein     = --
                                    1, 1    2
                                           t

                                           1
(%t8)                            ein     = --
                                    2, 2    2
                                           t

                                           1
(%t9)                            ein     = --
                                    3, 3    2
                                           t

                                           1
(%t10)                           ein     = --
                                    4, 4    2
                                           t

It is the minkowski metric if you use https://www.physicsforums.com/showthread.php?p=2283519#post2283519"

A change of variables can't change a nonzero Einstein tensor into a zero Einstein tensor.

Since your claim seems to be controversial, maybe you could show us a calculation that gives a vanishing curvature for this metric.

 

[Ich]

Hi and a happy new year,

sorry, I've been sloppy: What I've been referring to is the empty universe, with negatively curved space and a~t. Try your calculations (or the transformation) with this metric:
<br /> ds^2=dt^2-u^2t^2(dr^2+r^2 sinh(u r)^2 (d\theta^2+r^2\sin^2\theta d\phi^2) )<br />
(I hope it's correct)

 

[bcrowell]

Hi and a happy new year,

sorry, I've been sloppy: What I've been referring to is the empty universe, with negatively curved space and a~t. Try your calculations (or the transformation) with this metric:
<br /> ds^2=dt^2-u^2t^2(dr^2+r^2 sinh(u r)^2 (d\theta^2+r^2\sin^2\theta d\phi^2) )<br />
(I hope it's correct)

Happy new year to you, too!

The way you've written the metric, there'd be an over-all r^4 coefficient in the d\phi^2 term...?

Anyhow, I'm perfectly willing to believe that expansion can be removed by a coordinate transformation in the case of an *empty* universe. In a universe with zero matter, radiation, or cosmological constant, the Einstein tensor vanishes everywhere, so it's reasonable to imagine that it's really just a Minkowski space expressed in strange coordinates.

But I don't understand how that would be relevant to your original statement:

Expansion per se (I mean unaccelerated, a~t) can be removed by a coordinate transformation. Therefore it can't have any physical effect on the solar system. What is relevant for solar system physics are gravitational sources that are unaccounted for in the standard calculations. There are two such sources of "cosmological origin", Dark Matter and Dark Energy. We should expect that Dark Matter dominates around the sun, producing indeed an anomalous blueshift - but several orders of magnitude below the observed effect. So cosmology is not the solution, at least not in GR or other metric theories consistent with observation.

Expansion of our actual universe (dominated by a mixture of matter and cosmological constant) is not removable by a coordinate transformation. The fact that it has no significant effect on our solar system ( http://arxiv.org/abs/astro-ph/9803097 ) is because cosmological expansion in general has no significant effect on small, gravitationally bound systems. A simple, closed-form example is Schwarzschild-de Sitter space, which describes an isolated black hole in a universe with no other matter, but a nonzero cosmological constant. The part of the metric close to the black hole is very close to a normal Schwarzschild metric, so, e.g., if you have a test particle in a circular orbit, the size of the orbit won't change significantly.

 

[Ich]

The way you've written the metric, there'd be an over-all r^4 coefficient in the d\\phi^2 term...?

Yeah, copy & paste error. Erase the last r², maybe it will work then.

But I don't understand how that would be relevant to your original statement

I made two claims:

Expansion per se (I mean unaccelerated, a~t) can be removed by a coordinate transformation. Therefore it can't have any physical effect on the solar system.

and

What is relevant for solar system physics are gravitational sources that are unaccounted for in the standard calculations.

If you're not happy with the empty universe, let's have al look at the equation of motion of a free particle in a general frw spacetime (if you're interested in toy models, https://www.physicsforums.com/showthread.php?p=2089458#post2089458" a funny derivation). In its low speed limit (enough for local physics), in comoving coordinates, it is:
a\ddot r + 2\dot a \dot r = 0
Pick an arbitrary origin and switch to cosmological proper distance x=a\,ras a space coordinate, with
\ddot x = \ddot a +2\dot a \dot r +a\ddot r
you get
\ddot x = x \ddot a / a
"Expansion per se" (\dot a) has vanished from the equation (claim 1).
Instead there's radial acceleration depending on ä, which looks formally like (Newtonian) gravitation from an uniformly distributed source. Using the second http://en.wikipedia.org/wiki/Friedmann_equations" , you find that it actually represents energy and pressure as the source of gravitation in FRW cosmologies (claim 2). (add: try to calculate orbit perturbations due to "expansion" with this Newtonian background as additional gravity source. It works.)
So, for solar system physics, the whole "expanding universe" influence reduces to a background "matter" distribution that you have to account for, and nothing more.

 

[bcrowell]

Ich, I just don't understand the point of what you're doing. We have a variety of arguments to show that in an FRW solution to standard GR, the solar system doesn't expand. Is the point here that you're describing a particular argument that you think is really sweet?

 

[Ich]

Ich, I just don't understand the point of what you're doing.

Just look at what triggered my first reply in this thread:

Even with no dark energy the expansion would still happen, just at a different rate, right? But either way I guess GR predicts that the local gravity in a bound system dominates over cosmic expansion

It is a widely held belief, even among professionals, that gravitationally bound systems withstand the tendency of "Expansion" to tear them apart.
My point is that there is no such tendency.

You couldn't follow my argument as it wasn't exactly well formulated - a~t is necessary, but not sufficient to remove expansion by a global coordinate transformation.
I tried to show the local argument that I had in mind when I wrote my first reply. But obviously, you already know that local physics is independent of \dot a and are now wondering what I'm arguing about.

I didn't notice Old Smuggler's reply until now:

FYI, Ich has a serious misunderstanding of differential geometry; he believes that by linearizing the scale factor in the FRW models one always gets Minkowski space-time.

I admit that I may have given this impression in this thread, but I certainly feel myself being misrepresented by this account. In the https://www.physicsforums.com/showthread.php?p=2154352" Old Smuggler is referring to, I argued that you can express FRW spacetime locally, to first order, by Minkowski-like coordinates and that you'll find neighbouring galaxies to be moving away from each other in this frame. That's called Riemann normal coordinates, and not my own crackpot idea.
BTW, the alleged crackpot paper Old Smuggler mentions ishttp://arxiv.org/abs/0808.1081" , not exactly crackpot for my understanding.

 

[bcrowell]

It is a widely held belief, even among professionals, that gravitationally bound systems withstand the tendency of "Expansion" to tear them apart.
My point is that there is no such tendency.

Sorry, but I'm still completely lost as to what point of view you're advocating. We observe that the time for a laser beam to travel to the moon and back is essentially constant as judged by our clocks (subtracting out a recession related to ocean tide effects, which is well understood). We also observe data from CMB and supernova surveys that are consistent with a certain FRW model with a certain cosmological constant. Are you saying (1) that the lunar ranging data are wrong, (2) that the cosmological analysis is wrong, (3) that the cosmological models don't have to be interpreted in terms of expanding space, (4) that gravitational binding isn't the reason that the moon doesn't recede from us, ... or ...?

 

[Ich]

Sorry, but I'm still completely lost as to what point of view you're advocating.

Ok, I'll restate.
I say, answering JesseM's question, that the value of the Hubble parameter is completely irrelevant for solar system physics. By "completely irrelevant" I don't mean an effect heavily outweighed by "normal, baryonic," gravitation, I mean no effect at all.
You don't have to know whether the universe is expanding (H>0) or contracting (H<0) to calculate the perturbations for solar system orbits, at least not to leading order. It's enough if you know the local density of DM and DE, and Newtonian gravitation.

If you say "everybody knows that", ok, then I obviously misunderstood the posts in this thread. That's ok and I'll stop explaining. I keep explaining because I thought that you doubt this assertion.

As to your points: I don't challenge standard results. So to 1 and 2: no.

(3) that the cosmological models don't have to be interpreted in terms of expanding space

They may be interpreted in these terms, no problem with that. But I strongly disencourage using this picture when it comes to quasistatic, local physics. It means explaining loads of fictitious effects to get a null result, leaving the listener (and the narrator) in total confusion.

(4) that gravitational binding isn't the reason that the moon doesn't recede from us

Actually, yes, in a way. As long as the local DM density more than doubles the DE density, the additional effect to the knon "baryonic" gravitation tends to bind the system even stronger. This should be the case in the outskirts of a galaxy.
Rephrased: If there were no usual gravitation (Mass of Moon and Earth), and both were at rest wrt each other, the gravitation of Dark Matter around the Earth would pull the Moon towards the earth, winning against Dark Energy.
Ah, to avoid misunderstandings: I interpreted "receding" here as "in a larger orbit than without said effects". Of course, bound systems don't break up just because ther's a minor perturbation, they would simply settle in a new equilibrium. So my claim is that the Moon's orbit is a few microns (or whatever) smaller than without DM and DE.

 

[petm1]

Do you think they were just leaving the effective range of our solar systems' accelerated frame?

 

[lalbatros]

Ich,

This is not totally clear for me:

Expansion per se (I mean unaccelerated, a~t) can be removed by a coordinate transformation. Therefore it can't have any physical effect on the solar system.

Couldn't the Pioneer anomaly be wiped out by the same transformation?
In addition, I am not sure that removing the expansion would "remove physics", just as removing a rotation by going in a rotating frame doesn't remove the effect of rotation.
Could you clarify?

Michel

 

[bcrowell]

I say, answering JesseM's question, that the value of the Hubble parameter is completely irrelevant for solar system physics. By "completely irrelevant" I don't mean an effect heavily outweighed by "normal, baryonic," gravitation, I mean no effect at all.

Do you think the calculations in this paper http://arxiv.org/abs/astro-ph/9803097v1 are incorrect? They get an effect that's nonzero, but much too small to measure in the case of, e.g., the solar system.

By the way, I emailed Dag Oestvang to ask a couple of questions about the current empirical status of his quasi-metric relativity (QMR). He says that it predicts an effect on Neptune's satellites from cosmological expansion that is bigger than the GR prediction, but still too small to measure, and therefore consistent with Iorio's analysis. He also says that there are hidden model-dependent assumptions in the analysis of the solar system data, so although QMR predicts expansion of the solar system, it's not inconsistent with existing radiometric data.

 

[yuiop]

I have a question. At what distance apart are two bodies no longer considered to be gravitationally bound? The gravitational equations suggest the influence of gravity of spatially infinite and if gravity waves travel at the speed of light, then any celestial body we can see is gravitationally interacting with us. Maybe there is a difference between being "gravitationally bound" and "gravitationally interacting". Obviously escape velocity is a factor to be considered. If a body recedes from us at greater than the required escape velocity, is it considered to no longer be gravitationally bound even though it is presumably still gravitationally interacting with us? If DE and DM exist and the evidence suggests they do, then presumably they must have some effect within the Solar system even if that effect is too small to detect. No?

 

[bcrowell]

I have a question. At what distance apart are two bodies no longer considered to be gravitationally bound?

Take a look at this paper http://arxiv.org/abs/astro-ph/9803097v1 . It's only an approximation that bound systems don't expand. The more tightly bound they are, the better the approximation is.

 

[Ich]

Couldn't the Pioneer anomaly be wiped out by the same transformation?

The transformation does nothing except removing coordinate artifacts. Solar system physics, including the pioneer trajectory, isn't done in cosmological coordinates (cc) anyway, so there can't be confusion from a misinterpretation of those.

In addition, I am not sure that removing the expansion would "remove physics"

(the following section deals with the empty universe, as my original statement was intended to)
No, it shows that there is no such physics in the first place, which can't be seen easily in cc.
In cc, you have galaxies "at rest" and "space expanding" between them. It is not clear, neither from the mental picture nor from the equation of motion, how this expansion changes the laws of local physics. It is widely believed that things are totally different from what we know, and that calculations are tedious and subject to interpretation.
In Minkowski coordinates, there is standard spacetime and the galaxies are moving away from each other. It is therefore immediately clear that physics is the same, no matter whether some galaxies are moving outward or not.
That's not different physics, it's just the appropriate description for the purpose of analyzing local dynamics. cc doesn't predict something different, it's just a total mess.

 

[Ich]

Do you think the calculations in this paper http://arxiv.org/abs/astro-ph/9803097v1 are incorrect?

No, why should I? You surely noticed that their eq. 2.8 is exactly what I posted here, and therefore the results should be the same.
In detail:
They do exactly what I'm promoting in this thread (and in the other thread Old Smuggler referred to):
They go to Riemann Normal Coordinates, a LIF, as they call it, and do their calculations there.
They lament the often obscure use and misuse of different coordinate systems that makes results difficult to understand and compare (see e.g. eq. 4.1, a result that's not in line with the other results, except that "r" may mean something completely different here).

However, I'm going a step further, by connecting \ddot a / a with the matter density via the Friedmann equations. That's also not "new physics" or original research, but it it very instructive.
Because, if you do so, you see that you can reproduce their result for two body systems with ordinary Newtonian gravity, if you add the averaged mass density of the universe as a perturbation. Their result of growing orbits immediately explains itself as being due to a constantly decreasing amount of matter within the orbit of the planet in their model universe.
You see further that the assumption of an homogeneous, isotropic universe doesn't make sense in this context. For example, it is reasonable to assume that the dark matter density in the solar system is much higher that the universe average, and that it remains essentially constant, as it is bound to our galaxy cluster. Therefore, in our universe, with WIMP-like CDM, the perturbation of the orbit is negative and constant. In a de Sitter universe, it would be positive and constant.
So

It's only an approximation that bound systems don't expand.

is not correct IMHO. The result that systems expand itself stems from an approximation, namely that the matter density in the region of interest equals the averaged matter density of the universe.

 

[Garth]

It's only an approximation that bound systems don't expand.

is not correct IMHO. The result that systems expand itself stems from an approximation, namely that the matter density in the region of interest equals the averaged matter density of the universe.

Actually Ich there is an issue here.

Orbital dynamics in GR are calculated in the Schwarzschild solution of the one body case.
That solution is embedded in flat non-expanding Minkowskian space, i.e. g_{\mu\nu} \rightarrow \eta_{\mu\nu} as r \rightarrow \infty

There is a question about what the result would be if the Schwarzschild solution was embedded in an expanding cosmological metric.

However, the problem with such an approach is that any consequential motion or acceleration would be expected to be in the opposite sense to the PA, i.e. outwards and not sunwards.

Garth

 

[Ich]

There is a question about what the result would be if the Schwarzschild solution was embedded in an expanding cosmological metric.

As long as you assume spherical symmetry, if you cut out a spherical cavity, you will have flat spacetime inside (see e.g. the paper cited by bcrowell and references therein).
So that means that the reason for any deviations from flatness must lie within that cavity.
If you "refill" it with Dark Matter, it will have negligible pressure and velocity within some fairly big radius, so you won't make much error if you treat it as homogeneous, istropic and non-moving (as measured in the LIF) dust. You can handle that in Newtonian approximation.
It's even easier with Dark Energy, as it is has no rest frame. There is an exact solution for the whole problem, http://arxiv.org/abs/gr-qc/0602002" , which reduces to an effective negative mass density in Newtonian approximation.

Of course, you would not want to embed the Schwarzschild metric in an expanding metric. I don't see how this should be done.
You'd have to embed it in appropriate static or quasistatic coordinates. These deviate only slightly from Minkowski coordinates at galactic scales, and can be managed as a perturbation of the original Schwarzschild metric.

However, the problem with such an approach is that any consequential motion or acceleration would be expected to be in the opposite sense to the PA, i.e. outwards and not sunwards.

As I said earlier, you'd actually expect sunward acceleration if you include dark matter. But it's ~5 OOM too small to explain the anomaly, IIRC.

 

[heldervelez]

https://www.physicsforums.com/showpost.php?p=2522588&postcount=23" (not inertial) can translate in fictious forces not accounted in the analysis.
I think that we don't have the required equations.