sage
发表文章数: 1125
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Modification of Gravity II: MOND
this is not the usual modification on people's mind. Nevertheless, it is interesting and easy to motivate. therefore, I do it first. Caution, I am not an expert on this subject. thereofore, there might be mistakes on various levels.
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Dark Matter and MOND
One of the most celebrated evidence for the existence of Dark Matter
is the rotational curve of the stars in our galaxy. To keep the
discussion simple, I will have to idealize it a little bit. We know that
the velocity of some star circlig around the center of the galaxy at a
distance r is G M(r)=v^2 r, where M(r) is the mass within the circle. Now,
let's suppose that stars and visible gases and so on is all the masses we
know in the galaxy. then, suppose we look at some stars far far away from
the bulk of the matter of the galaxy (those objects are rare and hard to
see, but astronomers are incredibly patient and capable). for them, the
mass inside their orbit is almost a constant. therefore, we expect to see
their velocity v^2 proportional to 1/r. On the other hand, it is not
observed to be that way. the velovity as a function of r, the so called
rotational curves, does not fall off like 1/r. On the other hand, it goes
out like a constant. Therefore, the matter in the space in and around our
galaxy cannot just be those stars and things that we see. There must be
something else! One obvious candidate for that something else is a halo of
dark matter which extends beyond the boundary of visible galaxy. It would
have a mass distribution in such a way so as to make the M(r) proportional
to r when r is bigger than the radius of our visible galaxy in order to
understand the flatting behaviour of the rotational curve.
this is all very good and claimed to be the most prominent evidence
for a cold (so that they cluster more) dark matter.
On the other hand, notice that this whole argument is based on the
fact that gravitational force F=m*a. A natural thing to do is than
to ask what if it is not. Now notice that F=m*a for gravitational force is
already very well tested in the solar system. Therefore, we better not to
mess up with it. On the other hand, one of the greatest lessons that 20th
century physics taught us is that physics laws could be very different
on different scales (classical mechanics on large scales vs quantum
mechanics on very small scales, for example). Therefore, one could imagine
that for gravity, F=ma does not hold for larger distances. Or, more
specific to the problem of rotational curve, it might be different for
smaller accelerations. More specifically, one version of it has that when
the accelleration is smaller than some critical value a_0, the force law
is F=m*a^2. Then, we have G M = v^4, i.e., v is a constant! this is called
MOND, Modification Of Newtonian Dynamics. It says somehow Newtonian
dynamics is modified for some very small accelerations.
One would think that such a modification would be immediately ruled out.
However, amazing, it is not since the threshold acceleration is very
small. It can also perfectly fit the data of rotational curves and pass
various test at the scale of galaxies.
On the other hand, such a modification totally does not make sense. for
one thing, it is not even Lorentz invariant, never mention GR or
equivalence principle. It also remains to be seen that if such an
modification would change the early universe cosmology a lot so that it is
disfavored.
Recently, a paper by Bekenstein made a first apparently successful stp
towards writing down a sensible, Lorentz invariant, theory which give rise
to MOND at some limit. It is a peculiar theory. at the same time, it is
important to have an example which could be consistent and in principle
could be embedded into a general covarient theory at all.
| 发表时间：2004-07-01, 00:04:11 |
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可见光
发表文章数: 421
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Re: Modification of Gravity II: MOND
Recently, a paper by Bekenstein made a first apparently successful stp
towards writing down a sensible, Lorentz invariant, theory which give rise
to MOND at some limit. It is a peculiar theory. at the same time, it is
important to have an example which could be consistent and in principle
could be embedded into a general covarient theory at all.
实验观测的确是科学发展的真正源泉，往往是我们意想不到的。说不定下次物理学的革命，就是来自于宇宙学。以往每次突破，总是往微观里进行中出现的。
宇宙中不发光的暗物质理应存在，只是想不到会占那么大的比例啊。要是真的需要修改现有一些理论公式，那太妙了！要是自然界不止存在四种力，那么现在的统一场理论的努力，大概跟爱因斯坦不知道强和弱相互作用时的努力，是五十步跟百步的关系吧！
你看不到我的眼泪，因为我在水里
| 发表时间：2004-07-01, 06:42:30 |
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卢昌海
发表文章数: 1617
武功等级: 北冥神功
(第一重)
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Re: Modification of Gravity II: MOND
Very interesting point!
The only thing I'm wondering about is that currently, the ingredient of the universe seems to be (roughly):
5% visible matter
25% dark matter
70% dark energy
If MOND eliminates the need of dark matter in the galactic halo. It basically iliminates that 25% of the dark matter (maybe not completely, but at least a significant part of it). Unless it also alters the measurement/calculation of the total amount of visible matter and dark energy in a way that compensates the 'loss' of the dark matter, it will challenge the Ω=1 prediction of inflation (which has recieved observational support - but I need to check reference to make sure that such support does not rely on the regular galactic rotational curve argument MOND tries to rule out), and the calculation of the age of the universe based on energy compositions (this is not conclusive, can be made larger, but can hardly be made smaller).
Modern cosmology and current observation have setup a series of cross-references among various parts of the cosmological ingredients, by eliminating one of them, there will be lots of consistency checks to do.
宠辱不惊，看庭前花开花落
去留无意，望天空云卷云舒
| 发表时间：2004-07-01, 08:17:51 |
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星空浩淼
发表文章数: 1743
武功等级: 九阳神功
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Re: Modification of Gravity II: MOND
天问：
1）现有的天文观测手段，以及它所依据的原理是不是100%正确？
不知道会不会有意想不到的物理因素没有考虑进去？比如所有导致红移的因素里，会不会还有一些未知因素也在里面，有时甚至会起主导作用？
2）不知道在宇宙的遥远深去，那里会不会有着跟我们不一样的物理真空背景？（例如我们的粒子质量，在他们看来只是等效质量？）
3）不知道我点燃一个鞭炮，在爆炸的那一瞬间，这个里面的绕某一个原子旋转的某一个电子上面的某一个国度里，是不是有一群科学家经过50年的观察和研究之后，发现他们所谓的“宇宙”正在膨胀？
4）我们所谓的“整个宇宙”，不知道会不会是真正的一个很大的空间里面的一粒灰尘？
呵呵，问题越来越儿科了，恐怕早就被人想过无数回。只是不知道这些幼稚的问题，将来会不会回头来，经过严格的物理包装之后，被重新认真考虑一回？
持之以恒就是胜利
| 发表时间：2004-07-01, 09:24:09 |
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sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Re: Modification of Gravity II: MOND
ery interesting point!
The only thing I'm wondering about is that currently, the ingredient of the universe seems to be (roughly):
5% visible matter
25% dark matter
70% dark energy
If MOND eliminates the need of dark matter in the galactic halo. It basically iliminates that 25% of the dark matter (maybe not completely, but at least a significant part of it). Unless it also alters the measurement/calculation of the total amount of visible matter and dark energy in a way that compensates the 'loss' of the dark matter, it will challenge the Ω=1 prediction of inflation (which has recieved observational support - but I need to check reference to make sure that such support does not rely on the regular galactic rotational curve argument MOND tries to rule out), and the calculation of the age of the universe based on energy compositions (this is not conclusive, can be made larger, but can hardly be made smaller).
Modern cosmology and current observation have setup a series of cross-references among various parts of the cosmological ingredients, by eliminating one of them, there will be lots of consistency checks to do.
================================================
very interesting point. let's review a little bit why we think the matter/energy budget of universe is the way you mentioned.
first, cosmic microwave background measurement from KOBE and WMAP exoeriments show that our universe is flat, i.e., Omega=1 (hmm, how did you do the Greek letter Omega? ) It does not say precisely what is the proportion. then there is the supernovae redshift experiment measuring the equation of state of the universe. it says that it is probably less then zero. however, it does not say precisely how much dark matter it will be. only overlaying this two experiments you see they intersect roughly at the point you mentioned. on the other hand, the redshift experiments are not precise enough yet. The CMB fitting will depends on the assumption that we have standard cosmology (which MOND will change. ) and cold dark matter and dark enegry dominates. Therefore, i think there are still room for a rather small dark matter content. There are other constraints such as 1) structure formation, but there you suffer from the limitation of n-body simulation. 2) gravitational lensing seems to favor the dark matter scenario, but it is certainly not conclusive yet. The bottom line is that we did not know very precisely yet. the rotational curve so far remains the most compelling evidence for dark matter.
of course, MOND would have to be checked against the early universe obseravbles. on the other hand, passing all the galaxy scale tests is already highly non-trivial for such a crazy idea.
| 发表时间：2004-07-01, 10:41:40 |
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卢昌海
发表文章数: 1617
武功等级: 北冥神功
(第一重)
内力值: 602/602
Re: Modification of Gravity II: MOND
:: hmm, how did you do the Greek letter Omega?
You can copy it (and many more) from the character map that comes with the operating system. :-) The input window allows all these characters, it is the keyboard that lacks the capability of entering them (unless certain language utilities are installed).
宠辱不惊，看庭前花开花落
去留无意，望天空云卷云舒
| 发表时间：2004-07-01, 11:29:22 |
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