| 您的位置：站长主页 -> 繁星客栈 -> 网友原创作品集 -> sage 文集 | November 22, 2024 |
MOND
- sage -
|
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. ======================================================== 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. ======================================================================= 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 ¦¸=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. |