Can Loop Quantum Gravity Explain the Pioneer Anomaly?

[marcus]

Pioneer anomaly--LQG style

an effort is being made to see if the Pioneer anomaly can be understood
within the context of Loop gravity

why should acceleration taper off so slowly after a while, or not at all?

we should have the data handy, like in this paper:

http://arxiv.org/abs/gr-qc/104064
Study of the anomalous acceleration of Pioneer 10and 11
JohnD. Anderson, PhilipA. Laing, Eunice L. Lau, AnthonyS. Liu, Michael MartinNieto, andSlavaG. Turyshev


or the "Independent Confirmation" paper of Craig Markwandt
http://arxiv.org/abs/gr-qc/0208046

------
the clue being pursued is this odd coincidence, accelerating expansion space on large scale is observed and the cosmological constant determined to be
Lambda = 1/L²

where L is 9.5 billion lightyears or in metric terms 9E25 meters.
So this length L (which may be a universal fundamental constant)
has something to do with accelerating expansion on large scale

however if one forms the only acceleration quantity possible (dimensionally speaking) with just the speed of light and L, namely the acceleration
c²/L
then one gets the anomalous Pioneer acceleration (pinch me)
I have to recalculate this each time to convince myself.
So what, if anything, is going on?
It probably would be unwise not to check it out and some people at perimeter are checking it out to see if there is any possible theoretical connection (or is it merely a coincidence)

the pioneer space crafts are only some 70 AU out from the sun, so if there is an actual connection it is a correlation between something happening on a scale of 13 billion light years on the one hand
and a few light-hours on the other------an enormous span between small and large scale.

a discussion of this is in Smolin's third lecture at the February
WS-2004 symposium. I'll get the link
http://ws2004.ift.uni.wroc.pl/html.html

 

[marcus]

just to verify the calculation, this first paper
http://arxiv.org/abs/gr-qc/104064
Study of the anomalous acceleration of Pioneer 10 and 11
John D. Anderson, Philip A. Laing, Eunice L. Lau, Anthony S. Liu, Michael Martin Nieto, and Slava G. Turyshev

finds that the residual unexplained acceleration towards the sun is
(8.74±1.33)×10^-8cm/s² which is the same as
(8.74±1.33)×10^-10m/s².


a simple-to-write value within their error bounds is E-9 meters per second per second.

compare this with c²/L, where L is 9E25 meters, the reciprocal square root of the cosmological constant.

c² = 9E16 meter²/second²

c²/L = 9E16/9E25 = E-9 meters per second per second.

so it comes out equal not only within OOM (order of magnitude) but in fact equal to within experimental error


As a double check let's look at the "Independent Confirmation" paper of Craig Markwandt
http://arxiv.org/abs/gr-qc/0208046
he did his own analysis of the data and found
(8.60 +/- 1.34) ×10^-8cm/s²

that is about the same as the other people's, so essentially the same conclusion (remember there is also some uncertainty in measurements of the cosmological constant).

------

 

[arivero]

an effort is being made to see if the Pioneer anomaly can be understood within the context of Loop gravity
where L is 9.5 billion lightyears or in metric terms 9E25 meters.
So this length L (which may be a universal fundamental constant)
has something to do with accelerating expansion on large scale

however if one forms the only acceleration quantity possible (dimensionally speaking) with just the speed of light and L, namely the acceleration
c²/L
then one gets the anomalous Pioneer acceleration (pinch me)

a discussion of this is in Smolin's third lecture at the February
http://ws2004.ift.uni.wroc.pl/html.html

ws2004 website seems to be unstable.

As for the relation with L, also Nottale noticed it, but he suggests an
additional sqrt(3) factor, see gr-qc/0307042

 

[marcus]

ws2004 website seems to be unstable.

As for the relation with L, also Nottale noticed it, but he suggests an
additional sqrt(3) factor, see gr-qc/0307042

first time I have seen WS2004 be down like that,
this morning was OK, hope it is just temporary
in the meantime , as a substitute source for any newcomers
to the topic, here is one of the MOND sources Smolin
uses rotation curves from
see figure 4 on page 42 for example

http://arxiv.org/astro-ph/0204521
Sanders and McGaugh
Modified Newtonian Dynamics as an Alternative to Dark Matter

Smolin slides show some 26 galaxy where the fit is impressively good
Sanders and McGaugh show same and more----about 84 galaxies have
been analyzed and shown excellent fit

Alejandro I will have a look at that Nottale paper you mentioned
(the coefficient, among other things, is still quite a puzzle for me)
http://arxiv.org/gr-qc/0307042

 

[arivero]

OK, the link works now. From the list of speakers, I would say it is Quantum Gravity, yes, but more about DSR than LQG.

By the way, it is Karpatz winter school, isn't it? There I heard Lukierski, ten years ago, explaining its kappa-Poincare thing. Snowy place.

 

[marcus]

By the way, it is Karpatz winter school, isn't it? There I heard Lukierski, ten years ago, explaining its kappa-Poincare thing. Snowy place.

Yes it is the Karpatz winter school. Nice idea to have a winter school of physics where people can ski if they like.

You got in on the ground floor with the kappa-Poincare thing!

From the list of speakers, I would say it is Quantum Gravity, yes, but more about DSR than LQG...

Since Smolin and Jerzy Kowalski-Glikman posted
"Triply Special Relativity"
I am often wondering how exactly to distinguish.
the idea seems to be that one is the flat limit of the other.

If DSR is getting to the point of testing sooner, there could be a big
motivation for LQG to ride the coat-tails

 

[arivero]

Just to give you an idea, this is -or it was, ten years ago- the door of the classroom in Karpatz:
http://dftuz.unizar.es/album/karpatz.8.gif

About TSR, I am not sure of its usefulness. Neither about Nottale; a revolutionary friend told me about him a few moths ago, but I had never heard about his research until then.

 

[sol2]

Is this the same Winter School in 1999?

http://gravity.psu.edu/online/Html/Seminars/Fall1999/Amelino-Camelia/Slides/s01.html

 

[arivero]

Lubos has uploaded a note about MOND
http://motls.blogspot.com/2004/10/mond-and-holography.html

 

[marcus]

Hi Alejandro,
we just were calculating Lambda in Planck terms, so let's see what this length L is (which several people would like to see involved in explaining Pioneer anomaly and galaxy rotation curves---replacing dark matter)

In Planck terms, the cosmological constant Lambda turned out to be
3.4 x 10^-122
L = Lambda^-1/2

= 0.54 x 10⁶¹ = 5.4 x 10⁶⁰

Earlier in this thread the figure I had for it was, in metric terms,
9 x 10²⁵ meters.

I believe that agrees, because Planck length is 1.6E-35 meter
so 5.4E60 Planck lengths, times 1.6E-35 meter per Planck length
equals 8.7E25 meters.
OK, so the length L which the French author you mentioned, and Smolin also, were using actually is this 9E25 meters, or 9.5 billion lightyears,
and is the same as this 5.4E60 Planck----the reciprocal square root of the cosmological constant.

Smolin was suggesting, in effect, that we have a new fundamental physical constant which is a length and which is 5.4 x 10⁶⁰ Planck,

and that the cosmological constant (a curvature) is the inverse square of this length.

and that the acceleration you get from the speed of light and this length
is the acceleration that shows up in galaxy rotation and in the Pioneer trajectory.

a very curious business, if true.

Interesting this should get a nibble from Motl

 

[arivero]

Yep, Motl points out that the holography principle, going from 3dim space to 2dim hologram, is a good trick to get a stronger force law 1/r in some situations. It is very in the spirit of using stringlike math to get first approaches to some result; very much I like to use Newtonlike math.

It should be nice if someone where able to explain here, in two lines, the issue of galaxy dinamics and how it relates to 1/r vs 1/r^2 transitions. Of course all of us learn in the school that a 1/r^2 to constant force happens due to Gauss' theorem when we go inside a spherical matter body, and in the case of elliptical matter bodies, as galaxies, such transition must happen too. The MoND dynamics would be, I expect, more sophisticated, but bet that divulgation magazines will get it all mixed.

 

[marcus]

...
It should be nice if someone where able to explain here, in two lines, the issue of galaxy dinamics and how it relates to 1/r vs 1/r^2 transitions. Of course all of us learn in the school that a 1/r^2 to constant force happens due to Gauss' theorem when we go inside a spherical matter body, and in the case of elliptical matter bodies, as galaxies, such transition must happen too. The MoND dynamics would be, I expect, more sophisticated, but bet that divulgation magazines will get it all mixed.

I may not understand what you want to be explained. You may have to ask the question several times, just so I understand the question.
Don't worry yet about what is the answer!

Smolin described MOND this way when he showed slides of some 2 dozen galaxy rotation curves and how closely MOND fit the curves:

1. there is a tiny constant acceleration a₀

2. in the galaxy, if you go out from the center far enough that the
Newtonian acceleration a_Newt becomes less than a₀

then from that point on out the REAL acceleration a_Real
does not fall off as sharply as a_Newt anymore

3. From then on, the real acceleration, instead of being the Newtonian one, is the GEOMETRIC MEAN of a_Newt
and a₀:
a_Real = sqrt( a_Newt a₀)

4. And Smolin says that the a₀ that works just happens to be, by a strange coincidence, the acceleration you would calculate using the speed of light c and the length constant L you get from the cosmological constant namely
a₀ = c²/L

Since L is the inverse square root of Lamda this is same as saying

a₀ = c² Lambda^1/2


I think that is something like a preliminary to your question, which I don't yet understand.

I have no clue about a mechanism that could result in this kind of effect.

 

[arivero]

Well marcus, the point is that the calculations are obscured because we are speaking of gravity *inside* a body (in this case, a galaxy). So a previous integration is needed, just the kind one uses to get the intensity of gravity force in the interior of Earth, or the intensity of electrostatic force inside a charged ball.

 

[arivero]

Just for the gallery, let me to review how the same holagraphic result of Lubos can be argued from dimensional analysis. We will need only to assume a pair of universal constants of velocity and action, which we will name as c, h.

Consider a two body system under reciprocal force
$$F=K_d {m_1 m_2 \over r^d}$$
Note that the coupling constant can be written in terms of a fundamental length via
$$K_d= {(L_d)^d c^3 \over \hbar}$$

We look for the simplest, circular solution of movement.

Solving the system in center of mass coordinates we get:
$$K_d \mu^2 M = J^2 r^{d-3}$$
where $$\mu$$ is the reduced mass of the system, $$M$$ is the total mass of the system, and $$J=R P = \mu \omega R^2$$ is the torque or the system, P being of course the linear momentum of any of the two particles as seen in the center of mass reference system.

Now let's use h and c to put everything in terms of associated lengths. We have
$$(L_d)^d = L_M L_\mu^2 {J^2\over \hbar} R^{d-3}$$

Our couriosity is to ask in which conditions will the fundamental dimension of the coupling constant disappear from the equation. If neither of the other length-like quantities depend on the fundamental one, then only the constant force d=0 gets rid of it (and in this interesting but degenerate case, we must to use the potential to interoduce some scale of forces).

If the reduced mass of the system (or the mass of the test particle in usual approximated models) is to be depending of the fundamental length, $$L_\mu = p L_d$$, we have
$$(L_d)^d = L_M p^2 L_d^2 {J^2\over \hbar} R^{d-3}$$
and d=2 cancels out the fundamental scale. This is to say, the usual force with inverse square of distance.

If the total mass of the system (or the mass of the central particle in usual approximations) is the one depending of the fundamental, $$L_M = q L_d$$, we have
$$(L_d)^d = q L_d L_\mu^2 {J^2\over \hbar} R^{d-3}$$
and d=1 cancels out the fundamental scale. This is to say, the 1/r force.

So we have obtained the same results that Lubos but in a general way, without asking for holography. In some limit, the holography argument would surely to meet these equations.

Last, the case where both lenghts are depending of the fundamental is interesting to look for. In this case d=3, and the explicit radial dependence falls out from the equation:
$$1 = q p^2 {J^2\over \hbar}$$
Still we have an implicit radial dependence in the equation of J, so one can research if the angular velocity (or the period of the orbit) is more important than the angular momentum. This idea is generally intriguing because the reduced mass appears inside J, so it cancels out, and the equation only depends on the total mass (!?).

Note also that we have not studied the possibility of having a radious quantised in units of the fundamental length $$R=s L_d$$, because in such case the equation for dimensions is always independent of d, say either
$$(L_d)^3 = L_M L_\mu^2 {J^2\over \hbar} s^{d-3}$$ or $$(L_d)^{-1} = L_M \omega^2 { \hbar \over c^2} s^{d+1}$$

 

[marcus]

Well marcus, the point is that the calculations are obscured because we are speaking of gravity *inside* a body (in this case, a galaxy). So a previous integration is needed, just the kind one uses to get the intensity of gravity force in the interior of Earth, or the intensity of electrostatic force inside a charged ball.

I think I understand what you are saying, and it strengthens my impression that the MOND effect is doubtful and mysterious. It seems to deny that the classical gravitational field is additive----the principle of superposition---which is against intuition and deeply-held belief.

Ooops, I was replying to post #13, and here is your #14 with more detail.
Maybe this will change the picture.

 

[arivero]

Well I do not think the MoND people has got any elementary mistake, but I am afraid that the divulgators of the theory to the masses (journalistic etc.) could have missed the detail, then obscuring some expositions of the calculations.

 

[marcus]

...assume a pair of universal constants of velocity and action, which we will name as c, h.

Consider a two body system under reciprocal force
$$F=K_d {m_1 m_2 \over r^d}$$
Note that the coupling constant can be written in terms of a fundamental length via
$$K_d= {(L_d)^d c^3 \over \hbar}$$

We look for the simplest, circular solution of movement.

...

I am having difficulty parsing this because I suppose that in our world d=3 or else d=4
I do not believe that i am a hologram.

does this require "willing suspension of disbelief"

OK, for the sake of discussion I say that for our world d=2. Then
the first two equations give me Newtons constant and Newtons law
(dimensionally speaking). I have sort of checked this. and will repeat that

 

[arivero]

Hi marcus. Here I am using smallcaps d, instead of any other letter such as n, but here it is only the coefficient of the force. Your complication is because you ere reading too much into the equation. Think "n" instead of "d" if you want. Of course if the force comes from a point source under Poisson(?) equation, then n= ( Spatial Dimensions - 1). Or equal to (SpaceTime dimension - 2), if you prefer. I choosed "d" to reminder me of this subyacent detail. But at the moment the post only studies the consequence of postulating a force proportional to the masses and inversely proportional to some power n of distance.

Now, as the units of [F] are fixed ([F]= M L T^-2), and so the ones of [m] and [r], you get the units of the coupling constant straightforwardly.

The only notational difficulty could be the use of subscript "d", which is not a mathematical operation, but just the way to name L_d and K_d. On the other hand, upperscript letters are the usual notation for a power, of course.

And no, I do not require an hologram :-) This is dimensional analysis ("unit analysis if you prefer), a traditional technique to anticipate results from purely the mathematical shape of an equation. Lubos hologram seems forced to pass across this point, but any other theory should be.

 

[marcus]

...( Spatial Dimensions - 1). Or equal to (SpaceTime dimension - 2), if you prefer...

good, it is simply the spatial dimension minus 1, or the exponent in the inverse power law.

I should not have been confused.

I was interested by what you said here:

Well I do not think the MoND people has got any elementary mistake, but I am afraid that the divulgators of the theory to the masses (journalistic etc.) could have missed the detail, then obscuring some expositions of the calculations.

I was interested that you seem to be saying that you don't think MoND is wrong. Or at least that it is not wrong in some elementary or trivial way.

(in American English, divulgators are called popularizers----when they explain the theory to the masses they are "popularizing" it)

My mind is often changing about MoND. Sometimes it seems to me to be a dangerous and radical theory that must be wrong because it does not fit with the usual nice form of physical laws.

At other times i am impressed with the remarkable nice fit with galaxy rotation curves and then I think there must be some nice physical law which incorporates this effect

 

[marcus]

Anyway, I recognize what you are saying here, in the special d = 2 case, as being the defintion of the Planck area.

...$$K_d= {(L_d)^d c^3 \over \hbar}$$

...

Because in that d = 2 case the K_d is the Newtonian constant of gravitation.

I cannot verify every detail of your post, but wherever I look it seems right, and so I think this:
that perhaps you have let a little wind out of Lubos blog message about holography.
As it seems that you have preached the same sermon as he did, but without mentioning the Holy Ghost.

 

[arivero]

Yep, I have substituted gods. Instead of the desire for holograms, I have used the desire for equations free of fundamental lengths.

Anyway, I recognize what you are saying here, in the special d = 2 case, as being the defintion of the Planck area.

Of course! L_2 is Planck Length because K_2 is Newton's constant. So L_2^2 is Planck area.

It is very entertaining to do such elementary calculus, and I think that "popularizers" should try it more frequently.


Now a google trick. Search exactly for:
mass of the Earth / mass of the sun
and you will get a good approximation of the quotient reduced mass/ total mass for the earth-sun system.

 

[Garth]

The Pioneer anomaly can be explained by a clock drift between ephemeris and atomic clock time. See Peter Ostermann, "Relativity Theory and a Real Pioneer Effect. 2002" , here.

Of course this could simply be just a coincidence, however there is a second such coincidence.

There have been two articles in 'Astronomy & Geophysics', which reviewed the study of secular changes to the rate of the Earth’s rotation observed by the analysis of ancient eclipse records. (Morrison L and Stephenson R 1998 A & G Vol 39 October), (Stephenson R 2003 A & G Vol 44 April).

They reported that, having allowed for the tidal contribution, there is another long-term component acting to decrease the length of the day by 0.6 milliseconds per century. This component is generally attributed to the decrease of the Earth’s oblateness following the last ice age.

However, while this explanation certainly merits careful consideration there is a remarkable coincidence here. The value of 0.6 milliseconds per day per century is in fact equal to Hubble’s ‘constant’ H!

The measurement has the dimensionality of (Time)^-1 and its inverse gives a time of 14.4 x 10⁹ years, which is a good approximation of Hubble Time. In the usual units of Hubble’s ‘constant’ this is equivalent to the value 67 km.sec^-1.Mpc^-1, which is remarkably close to the recent value of 72 km.sec^-1.Mpc^-1 derived from the WMAP data (e.g. Ostriker & Souradeep 2004).

The question is why should this spinning up of the Earth’s rotation coincidentally have a natural time scale of the order of the age of the universe rather than the natural relaxation time of the Earth’s crust or the periodicity of the ice ages? Therefore this anomaly might possibly be cosmological rather than geophysical in nature.

If this spin-up is a cosmological effect then it can also be interpreted as a clock drift between ephemeris time (recorded by the Moon’s orbital period) and atomic time (recorded by the Earth’s angular momentum).

Just a thought.

Garth

N.B. Such a clock drift is exactly as predicted by SCC.

 

[Rothiemurchus]

Dark energy is a form of pressure.The solar system is surrounded by the Oort cloud -
perhaps a gap in the Oort cloud is letting dark energy into the solar system.
This would explain why the acceleration (which is a measure of pressure in this instance) of pioneer 10 and of distance galaxies at 9 x 10^25 metres is about the same.

 

[Garth]

And the spinning up of the Earth?

Garth

 

[arivero]

Hmm Garth, yep, it seems a very intrusive constant, Hubble all pervading.

Casually I am looking now, due to other thread, an study of I.J Good, one of the few statisticians worried about how to distinguish coincidences in physics measurements.

 

[ohwilleke]

A simpler explanation

The author of the following paper:
http://www.Newtonphysics.on.ca/Anomalous/Acceleration.html

is not mainstream on a lot of points, but his argument for Pioneer 10 and 11 effects being caused by collisions with very sparse cosmic dust is pretty solid and far less problematic than most of the other theories out there.

The trouble with a MOND effect is that the effect is too constant over a sustained distance. Milgrom's estimate was an effect on the order of a tenth of what was seen made here:http://arxiv.org/PS_cache/astro-ph/pdf/0207/0207231.pdf Equally important, MOND effects would vary by a factor of about 1/3rd over the distances involved (since it is basically a 1/r effect) which doesn't fit the data (a good thing if space dust turns out to be the cause).

 

[ohwilleke]

I think I understand what you are saying, and it strengthens my impression that the MOND effect is doubtful and mysterious. It seems to deny that the classical gravitational field is additive----the principle of superposition---which is against intuition and deeply-held belief.

MOND can be formulated to be very well behaved, e.g. preserving the notion of center of gravity, conserving energy, propogating at light speed thus persreving causality, properly creating lensing effects, etc. In general, it can be formulated in a manner which is entirely consistent with GR and which reduces to the Newtonian laws where GR does not apply. This kind of model is found here: http://arxiv.org/abs/astro-ph/0403694

There is no real doubt in my mind that the MOND effect exists. It explains from first prinicipals the Tully-Fisher relation. The fits to hundreds of galaxies of varying types, using a formula that was designed before galaxies of the type analyzed were found and without modification, leaves little doubt that it works. Where it is wrong, it is wrong by factors of two or five, not factors in the hundreds. The question is why. Cold Dark Matter proponents would argue that it is an emergent theory that describes cold dark matter distributions that emerge from galaxy formation. But a mechanism for why almost all galaxies evolve with such a particular CDM distribution is lacking.

In my mind a quantum gravitational effect is more plausible.

 

[marcus]

MOND can be formulated to be very well behaved, e.g. preserving the notion of center of gravity, conserving energy, propogating at light speed thus persreving causality, properly creating lensing effects, etc. In general, it can be formulated in a manner which is entirely consistent with GR and which reduces to the Newtonian laws where GR does not apply. This kind of model is found here: http://arxiv.org/abs/astro-ph/0403694

There is no real doubt in my mind that the MOND effect exists. It explains from first prinicipals the Tully-Fisher relation. The fits to hundreds of galaxies of varying types, using a formula that was designed before galaxies of the type analyzed were found and without modification, leaves little doubt that it works. Where it is wrong, it is wrong by factors of two or five, not factors in the hundreds. The question is why. Cold Dark Matter proponents would argue that it is an emergent theory that describes cold dark matter distributions that emerge from galaxy formation. But a mechanism for why almost all galaxies evolve with such a particular CDM distribution is lacking.

In my mind a quantum gravitational effect is more plausible.

this is a careful and thoughtful comment.
it makes the viewpoint of Mond (instead of dark matter) credible
by its reasonableness

If you Willeke think that Bekenstein formulation is mathematically OK then
we have to take the idea on advisement or something. here is
that link you gave, spelled out:

Relativistic gravitation theory for the MOND paradigm
Jacob D. Bekenstein
http://arxiv.org/abs/astro-ph/0403694

 

[marcus]

MOND can be formulated to be very well behaved, e.g. preserving the notion of center of gravity, conserving energy, propogating at light speed thus persreving causality, properly creating lensing effects, etc. In general, it can be formulated in a manner which is entirely consistent with GR and which reduces to the Newtonian laws where GR does not apply. This kind of model is found here: http://arxiv.org/abs/astro-ph/0403694

...

Here is Bekenstein's abstract
---quote astro-ph/0403694---
The modified Newtonian dynamics (MOND) paradigm of Milgrom can boast of a number of successful predictions regarding galactic dynamics; these are made without the assumption that dark matter plays a significant role. MOND requires gravitation to depart from Newtonian theory in the extragalactic regime where dynamical accelerations are small. So far relativistic gravitation theories proposed to underpin MOND have either clashed with the post-Newtonian tests of general relativity, or failed to provide significant gravitational lensing, or violated hallowed principles by exhibiting superluminal scalar waves or an \textit{a priori} vector field. We develop a relativistic MOND inspired theory which resolves these problems. In it gravitation is mediated by metric, a scalar field and a 4-vector field, all three dynamical. For a simple choice of its free function, the theory has a Newtonian limit for nonrelativistic dynamics with significant acceleration, but a MOND limit when accelerations are small. We calculate the $\beta$ and $\gamma$ PPN coefficients showing them to agree with solar system measurements. The gravitational light deflection by nonrelativistic systems is governed by the same potential responsible for dynamics of particles. To the extent that MOND successfully describes dynamics of a system, the new theory's predictions for lensing by that system's visible matter will agree as well with observations as general relativity's predictions made with a dynamically successful dark halo model. Cosmological models based on the theory are quite similar to those based on general relativity; they predict slow evolution of the scalar field. For a range of initial conditions, this last result makes it easy to rule out superluminal propagation of metric, scalar and vector waves.
---end quote---

have to look more at this. thanks for flagging it