Planetary drift
Dirk Bruere at NeoPax
It concerns the effect of quantum randomness (or at least, non
deterministic randomness) on planetary positions given that the solar
system exhibits chaotic phenomena in a multibody gravitational interaction.
If we take the position of (say) Earth at t=0 and later at t=n seconds
how well can we predict the precision of its location at t=n? For
example, one might suppose that some random event might lead to a solar
flare whose mass ejection might vary by several seconds depending on
initial quantum uncertainties being amplified in a chaotic system to
macroscopic levels. This in turn would cause an impact on Earth's
magnetosphere, shifting its position slightly. Is there any way of
estimating (even ballpark) the kind of effects the sum of such
uncertainties might have over a long period of time?
To put it yet another way, suppose we have N identical solar systems at
t=0. Do they all evolve identically over a long period, and if not what
sort of spread in the position of Earth could we expect over various
timescales?
--
Dirk
http://www.transcendence.me.uk/ - Transcendence UK
http://www.theconsensus.org/ - A UK political party
http://www.blogtalkradio.com/onetribe - Occult Talk Show
[[Mod. note --
In general, solar system dynamics are chaotic even in purely classical
Newtonian mechanics, and adding general relativity effects into the
dynamics doesn't change that. Thus if we start a pair of model solar
systems a distance epsilon apart in phase space, in some cases the
trajectories will diverge exponentially in time. My vague recollection
is that in some cases the e-folding time of this divergence (a.k.a.
the inverse of the largest Lyapanov exponent) is quite short, only a
few 10s of millions of years.
Here's a recent paper on numerical simulations of this sort:
J. Laskar & M. Gastineau
"Esistence of collisional trajectories of Mercury, Mars, and Venus
with the Earth"
Nature volume 459, 11 June 2009, pages 817--819
http://dx.doi.org/10.1038/nature08096
The authors made repeated integrations of a dynamical model of the
solar system (including Sun + 8 planets + Pluto + time-averaged Moon
+ approximate general relativistic effects) using slightly different
initial conditions (varying within the current observational
uncertainties).
For example, in one set of integrations they altered Mercury's
semi-major axis in the initial conditions by 3.8*k cm for each integer
k in the interval [-100, +100]; they report the current observational
uncertainty on this parameter as a few meters. They find that over
billion-year time scales the different initial conditions produced
*very* different outcomes. Interestingly, they also found that adding
general-relativistic and time-averaged Lunar contributions to their
model greatly *reduced* the frequency of violent instabilities.
The paper itself requires a subscription (although the online
supplementary material is free), but I think "fair use" allows me
to quote the abstract:
It has been established that, owing to the proximity of a resonance
with Jupiter, Mercury's eccentricity can be pumped to values large
enough to allow collision with Venus within 5 Gyr (refs 1-3). This
conclusion, however, was established either with averaged equations^1,
^2 that are not appropriate near the collisions or with
non-relativistic models in which the resonance effect is greatly
enhanced by a decrease of the perihelion velocity of Mercury^2, ^3. In
these previous studies, the Earth's orbit was essentially unaffected.
Here we report numerical simulations of the evolution of the Solar
System over 5 Gyr, including contributions from the Moon and general
relativity. In a set of 2,501 orbits with initial conditions that are
in agreement with our present knowledge of the parameters of the Solar
System, we found, as in previous studies^2, that one per cent of the
solutions lead to a large increase in Mercury's eccentricity--an
increase large enough to allow collisions with Venus or the Sun. More
surprisingly, in one of these high-eccentricity solutions, a
subsequent decrease in Mercury's eccentricity induces a transfer of
angular momentum from the giant planets that destabilizes all the
terrestrial planets approx 3.34 Gyr from now, with possible collisions
of Mercury, Mars or Venus with the Earth.
-- jt]]
Phillip Helbig---undress to reply
<dirk....@gmail.com> writes:
> I have a question that I have no seen asked before, let alone answered.
> It concerns the effect of quantum randomness (or at least, non
> deterministic randomness) on planetary positions given that the solar
> system exhibits chaotic phenomena in a multibody gravitational interaction.
>
> If we take the position of (say) Earth at t=0 and later at t=n seconds
> how well can we predict the precision of its location at t=n?
Not a direct answer, but I heard the following in a talk by John Barrow:
Assume you can aim your billiard ball with the maximum precision allowed
by the uncertainty principle. Question: How many collisions are necessary such
that the average uncertainty in the position of the billiard balls is
larger than the billiard table? Answer: Only 12.
On the other hand, we have good evidence that the Earth's orbit has been
more or less stable during the lifetime of the Earth, so chaotic
behaviour in the sense of, say, the weather is not something I would
expect, but if you are talking about details then of course quantum
randomness would do away with complete determinism in the sense of
Laplace's demon.
eric gisse
[...]
> To put it yet another way, suppose we have N identical solar systems at
> t=0. Do they all evolve identically over a long period, and if not what
> sort of spread in the position of Earth could we expect over various
> timescales?
>
Yes. Both general relativity and classical mechanics are deterministic
theories.
However, you have to know the initial conditions with arbitrary
precision with arbitrary accuracy in order to know the positions of the
planets and other bodies at some arbitrary point in the future.
Any imperfection in the initial data will propagate out and ruin your
prediction.
Dirk Bruere at NeoPax
Then let's assume it's a MWI question.
The initial state of N worlds all stem from the same event, and so all
have the same initial conditions.
So if we have a look (somehow...) across those N worlds after t seconds,
how far out of alignment with each other would they be? I assume some
kind of bell shaped curve.
Robert L. Oldershaw
wrote:
>
> To put it yet another way, suppose we have N identical solar systems at
> t=0. Do they all evolve identically over a long period, and if not what
> sort of spread in the position of Earth could we expect over various
> timescales?
>
A minor note: If you mean literally "identical", good luck!!!!
You can find solar systems whose masses, planet distributions,
stellar temperatures, etc. are quite similar, and could be said
to be aproximately the "same". However, if you are looking for
"identical" systems composed of more than 10^56 subsystems,
each of which can be in a huge number of energy states, how can
this be possible!?
I think it might be a good idea for theoretical physicists to at
last discard these irrational idealizations and begin to deal
with reality in a more enlightened manner. Basically this means
giving up absolutes, which is what idealizations really are.
In the present case, that would mean considering solar systems
that are approximately in the same mass/energy state and how
closely their evolutions, or the evolutions of their subsystems,
follow one another.
Observational uncertainties present a separate Pandora's Box.
The problem with idealizations is that they start as rough
working assumptions, and then gradually become "facts".
Like cosmological "homogeneity".
Why not deal with the real world right from the start, even
if it makes the math somewhat more complicated?
Tom Roberts
> Then let's assume it's a MWI question.
> The initial state of N worlds all stem from the same event, and so all
> have the same initial conditions.
> So if we have a look (somehow...) across those N worlds after t seconds,
> how far out of alignment with each other would they be? I assume some
> kind of bell shaped curve.
This is amenable to analysis classically, without any quantum
assumptions: Consider an ensemble of N identical solar systems that
evolve via GR (or Newton, your choice) from initial conditions that are
normally distributed within the experimental resolutions of the observed
configuration at some selected time. Then over short time periods their
alignments will have normal distributions close to each other, but over
large time periods will not. In particular, at large times the
divergence of the ensemble members can be arbitrarily large -- a
hallmark of such chaotic systems. The distribution of "alignments" is
not normal at all. (Normal distribution ~ bell shaped curve.)
[I believe that "large time periods" are at most a few million years
for current resolutions.]
We recently saw an example of this: a comet crashed into Jupiter, the
sort of thing which usually cannot be included in "normal distributions
of alignments".
There now are methods to quantify various aspects of such
distributions....
Tom Roberts
Nicolaas Vroom
"Dirk Bruere at NeoPax" <dirk....@gmail.com> schreef in
bericht news:7mesjsF...@mid.individual.net...
>I have a question that I have no seen asked before, let alone answered.
> It concerns the effect of quantum randomness (or at least, non
> deterministic randomness) on planetary positions given that the solar
> system exhibits chaotic phenomena in a multibody gravitational
> interaction.
>
I have a problem with your question in general:
How can you answer a question when the words used are not clear ?
What means: "quantum randomness ""
What means: "non deterministic randomness"
What means: "exhibits chaotic phenomena"
I expect what you question is (sort of):
Can we predict the positions of the planets with 100 % accury 100 years
from now ?
My answer is first a different question:
Do we know the positions of the planets with 100 % accuracy now ?
IMO the answer is No.
If that is true how can we than claim that we can predict the positions
of the planets 100 years from now which prediction can not be verified
100 years from now ?
>
> [[Mod. note --
>
> In general, solar system dynamics are chaotic even in purely classical
> Newtonian mechanics, and adding general relativity effects into the
> dynamics doesn't change that.
I do not understand this sentence (The sentence is not clear).
What does it mean that the "solar system dynamics are chaotic" ?
Does it mean that solar system is chaotic or that the dynamics
(ie laws, mathematics) that describe the solar system are chaotic ?
I expect the last.
That being the case does that preclude the effort to find laws
(equations) which better describe the solar system and which are
not chaotic ?
Nicolaas Vroom
http://users.telenet.be/nicvroom/nature%2011%20June%202009.htm
Dirk Bruere at NeoPax
Well, let's take a science fiction illustration whereby we can step from
one world of the MWI to another. Opening my slider portal in my basement
on a world that spun off from a common ancestor of this one an hour ago
probably won't cause any problems. I just step through into basement-N.
However, suppose I open a portal onto a world that spun off 100 years
ago (assume an old house). Do I step through into basement-Y or vacuum
as statistical drift misaligned the worlds? Is there any way to estimate
the magnitude of drift? Any ballpark figures?