# Pioneer anomaly-LQG style

1. Aug 26, 2004

### 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 [Broken]
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 [Broken]

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2. Aug 26, 2004

### marcus

just to verify the calculation, this first paper
http://arxiv.org/abs/gr-qc/104064 [Broken]
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).

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Last edited by a moderator: May 1, 2017
3. Aug 26, 2004

### arivero

ws2004 website seems to be unstable.

As for the relation with L, also Nottale noticed it, but he suggests an

Last edited by a moderator: May 1, 2017
4. Aug 26, 2004

### marcus

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 [Broken]
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 [Broken]

Last edited by a moderator: May 1, 2017
5. Aug 27, 2004

### 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.

Last edited: Aug 27, 2004
6. Aug 27, 2004

### marcus

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!

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

7. Aug 30, 2004

### 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.

8. Aug 30, 2004

9. Nov 6, 2004

### arivero

10. Nov 6, 2004

### 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

11. Nov 6, 2004

### 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.

12. Nov 6, 2004

### marcus

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.

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 aNewt becomes less than a0

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

3. From then on, the real acceleration, instead of being the Newtonian one, is the GEOMETRIC MEAN of aNewt
and a0:
aReal = sqrt( aNewt 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 Lambda1/2

I think that is something like a preliminary to your question, which I dont yet understand.

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

13. Nov 7, 2004

### 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.

14. Nov 7, 2004

### 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 writen 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 lets 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 $$(L_d)^{-1} = L_M \omega^2 { \hbar \over c^2} s^{d+1}$$

Last edited: Nov 7, 2004
15. Nov 7, 2004

### marcus

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.

Last edited: Nov 7, 2004
16. Nov 7, 2004

### 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.

17. Nov 7, 2004

### marcus

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

Last edited: Nov 7, 2004
18. Nov 7, 2004

### 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.

Last edited: Nov 7, 2004
19. Nov 7, 2004

### marcus

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:

I was interested that you seem to be saying that you dont 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

20. Nov 7, 2004

### marcus

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

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

I cannot verify every detail of your post, but whereever 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.