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  #81  
Old 16-11-2016, 11:14 AM
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My two cents' worth.

If the only reason we had to suspect dark matter was galaxy rotation curves, then a fair amount of scepticism would be warranted, in my view, and tweaking gravity would be a very good candidate explanation.

The problem is that there is a whole pile of other independent evidence that there's a whole lot of mass out there that we just can't see. Unfortunately it doesn't get a lot of public airplay, because it's a bit more abstract and I suspect most science journalists simply zone out.

The wikipedia article is a pretty good high-level overview.

https://en.wikipedia.org/wiki/Dark_matter
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  #82  
Old 16-11-2016, 11:28 AM
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Hi crew, Are the galaxies surrounded by dark matter or actually in clouds of dark matter? Would gravity waves be emitted? Thanks Richard
Richard in answer to the second part of your question any asymmetrical rotating object or objects rotating around a centre of mass can in theory generate gravitational waves.
It depends on whether dark matter in the halo can form clumps which are dense enough to generate waves.

Even if this was possible there is the caveat that such waves could be beyond the range of detection of any current or planned wave detector.
The LIGO detector for example can only detect gravitational waves in the range of 10 Hz - 10 kHz, which corresponds to the orbital decay of dense objects such as Black Hole pairs around a centre of mass.
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  #83  
Old 16-11-2016, 11:51 AM
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Thanks for taking the time to explain. Obviously a lot of very smart people are looking at this and drawing the same conclusions. Can I please trouble you to help me understand the distinction here?

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Originally Posted by madbadgalaxyman View Post
Alex, the sums are not wrong, if we assume conventional gravitational theory, and while it seems far-fetched to believe that 299/300 of the mass of a dwarf galaxy is in some unknown form, very simple algebraic calculations of the sort that some of us learn to do in Year 12 Physics Class show that the gravitational effect of this additional matter is there and likely to be real.
Isn't that just saying gravity theory is correct, but only if you assume it to be correct in the first place? Why assume it to be correct at all when the data suggests otherwise? That's what I don't get!

On the one hand you have the proposition that the physics is somehow wrong at large scales.

On the other you have the idea that most of the universe is made up of matter that doesn't absorb or emit any form of energy, interacts only through gravity and can't be found despite many years of searching.

Surely at some point occams razor cuts the other way where the simplest explanation is simply that conventional gravity is *not correct. Alex nailed it on the head before. Surely the response to data that doesn't line up with your predictions is to change the model and test that? Sure, Dark matter does represent a revision to the model, but why does it represent our best hope over and above any revision to gravity?

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Originally Posted by madbadgalaxyman View Post
The case of dark matter may be compared to the case of the theory of evolution........
the story revealed by science seems extraordinary, and perhaps counter-intuitive, but "these are the truths that we must cling to, in the absence of further observations disproving them or modifying them".
What if the story of dark matter is the same as the story of the Ether? Something made up to make the math work out?
I'm willing to accept things that are not intuitive, with evidence. Quantum field theory in bonkers, but I accept that is how the world is. The evidence in this case may have more than one explanation. Why do we exclude the other one?

Obviously I must be wrong in this because professionals who spend every waking moment of their lives thinking about this stuff all like the dark matter explanation, but I wish I knew why it's more likely than gravity theory needing a tweak. Theories come and go all the time why are we stuck on this one?

To put my devil's advocate hat on for a moment and argue against myself for a moment, I assume that an explanation that tweaked gravity theory would expect the effect to be uniform. You wouldn't have a dwarf galaxy with 300 times the effect, and a normal galaxy with, say 5 times. It would (presumably) consistently be proportional to the amount of observed matter.

*sigh. Now I need a pan-galactic gargle-blaster. :-)

-Markus
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  #84  
Old 16-11-2016, 12:07 PM
croweater (Richard)
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Thanks for your replies SJ and Robert. I guess we have no idea whether the DM is rotating? I assume it would have to be? Thanks Richard
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  #85  
Old 16-11-2016, 12:52 PM
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Sorry another Question. Are there physical or theoretical limits to the frequency of gravitational waves? Cheers Richard
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  #86  
Old 16-11-2016, 01:23 PM
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Hi Julian thank you for all your book recommendations.

This is off topic but I must share.
Some may have guessed I am an athiest who follows the teachings of Jesus but does not believe he is/was God nor do I believe in the resurection.
I often chalenge theists. "have you read the bible cover to cover?"
Once I owned a magnificent library however it was taken along with all my possessions by the bush fires in 2002?

I now have only one book to my name is a copy of the king Georges version of the bible.
How I got it I have no idea maybe I found it in the house in the city...

I just think that is so funny particularly because on another forum I often say to cranks (intelligent design folk, no evolution etc anti science religious folk) .....
"You need to read more than one book to understand cosmology" or similar.

You really have to laugh... and I hope you all have a laugh... its free its on me.
Alex
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  #87  
Old 16-11-2016, 01:41 PM
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Quote:
Originally Posted by Stonius View Post
....
To put my devil's advocate hat on for a moment and argue against myself for a moment, I assume that an explanation that tweaked gravity theory would expect the effect to be uniform. You wouldn't have a dwarf galaxy with 300 times the effect, and a normal galaxy with, say 5 times. It would (presumably) consistently be proportional to the amount of observed matter.

*sigh. Now I need a pan-galactic gargle-blaster. :-)

-Markus
This would be my argumentation in favour of current gravitation theory as well.
Exactly this kind of reasoning suggests that current theories of gravity is correct.
Only we have some excessive but invisible mass which manifests itself by its gravitational attraction.
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  #88  
Old 16-11-2016, 02:23 PM
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I am convinced there may be something wrong with our understanding of gravity.

Unfortunately with no education it is unreasonable to think I have the answer when so many professionals over centuries have built up the current model.

Some older members will remember when I was obsessed with understanding how gravity works seeking a mechanical explanation.
I spent years thinking about it and came up with the notion that therecould be no force we call attraction. To me I could not entertain a mechanism that seemed to require a two way message system. The result of all my thinking lead me to form an idea (please not I do not use the word theory because I understand a d respect science and scientific method) that gravity could be explained by the flow of particles and or energy acting as a pushing force.

I really thought I was going to help humanity with my "unique" idea.
Well the funny thing was a chap named Le Sage came up with the idea in 1745 and it was around in Newtons time and he seemed to have been aquainted with the notion.
I have tried to follow the history and it seems the push gravity idea was certainly around upto the time of GR.

It is said the idea was not taken seriously back in time but frankly I think that has a little to do with installing the new science of GR.

Well at this point most folk who have an idea like mine go crank and anti mainstream but fortunately folk here were kind and helped me, particulary Steven, and extended tolerance I have not noticed such tolerance anywhere else. Steven was very patient and I can never thank him enough for his kind effort as he enabled me to start to understand science how it works what it does and what it does not do.
Thank you again Steven and all the other wonderful members from that time.

I try and work with what I have and I was able to rationalise in my mind that GR did not exclude my idea as to the mechanism.

GR advocates however do not like push gravity and wont have it and you can find folk and lists on the net showing why push gravity is wrong.

Yet GR does not need a force it is a co ordinate system.
I was told I need math and of course that is true but I have little math so given all were happy with GR and it could deliver on predictions I was happy humanity did not need my help. I did predict the pioneer would slow but they have found reasons other than mine but I did think space would slow them and in time stop them. And of course with no math I could not say what time frame..

Nevertheless I did try to do some math.
I first tried to imagine what would pass through a single point in remote space and to make this managable I thought of a sphere ten billion light yeras in diameter with no matter. Thru this point I tried to work out how many trajectories would/could fit.
Sortta like Hershel working out energy from the Sun.. How many points could I fit on the surface of my hypothetical sphere.. Well I did get numbers working on one for each square millimeter but it became apparent that the number of tradjectories were at least geometrically infinite.

So thru our point the tradjectories were vast.

Now what could travel along just one trajectory... particles energy? Well a dam lot what ever it be.. Say just neutrinos to get a mind picture...
Can you see where this is going. It was not an unreasonable conclusion in my view to think simply at one single point there was the potential for a range from nothing to near infinite (I know there is no such number but in this case so large a human could say such a nonsence)
And on this hypothetical sphere we have nothing to contribute to this flow of something other than what galaxies remain on the outside of our sphere .

What percentage of the trajectories carry something I dont know but think of where each tradjectory comes from... Back to cosmic background radiation at least, our sphere really would be our observable universe and that is roughly 90 billion light years dia.

So our one point would have so much passing by I think it offers some hope that space could be looked at as a presure system.

So what difference would a pressure system have from a attraction system.
Well here is my problem I can only suggest that holding things together via attraction which will have a finite power as to a system that has behind it an almost infinite power source to me offers a way of avoiding the need for dark matter.

Also if things work this way one could imagine this way would offer a reason why the universe seems to be expanding as if something was pushing it apart. So we have our dark energy.


Now my belief in GR is such that I believe GR should be able to offer math in support because although I do not understand GR as a professional would I understand it is an attempt to map the flow of space and I believe that GR can only conclude there is no dark matter if it simply maps the flow of space.

Alex

Last edited by xelasnave; 16-11-2016 at 02:34 PM.
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  #89  
Old 16-11-2016, 03:04 PM
julianh72 (Julian)
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Originally Posted by Stonius View Post

Isn't that just saying gravity theory is correct, but only if you assume it to be correct in the first place? Why assume it to be correct at all when the data suggests otherwise? That's what I don't get!

On the one hand you have the proposition that the physics is somehow wrong at large scales.

On the other you have the idea that most of the universe is made up of matter that doesn't absorb or emit any form of energy, interacts only through gravity and can't be found despite many years of searching.

Surely at some point occams razor cuts the other way where the simplest explanation is simply that conventional gravity is *not correct. Alex nailed it on the head before. Surely the response to data that doesn't line up with your predictions is to change the model and test that? Sure, Dark matter does represent a revision to the model, but why does it represent our best hope over and above any revision to gravity?
The simplest way to think of it is to take a look at the observed rotational speeds of stars around galaxies as a function of their orbital radius - which have been measured in the Milky Way, and numerous other galaxies:
https://en.wikipedia.org/wiki/Dark_m...rk_matter_halo

If the distribution of total matter was proportional to the observable (luminous) matter, the overall density would decline with radius, and we would see the orbital speed fall off as the radius increases - just as we see for planets around the Sun, for example. However, what we actually see is that the orbital velocity is relativity uniform over very large scales.

The simplest explanation is that there is substantial distribution of otherwise unobserved matter throughout the galaxy, not just clumped together with the observable matter. The same argument is logically supported when looking at orbital velocities of stars within numerous galaxies, and the interaction of numerous galaxy clusters etc - but the relative abundance of dark matter varies in different galaxies and galaxy clusters.

The alternative explanation (i.e. that we can see all of the matter that is out there, and it is our theory of gravity that requires correction) would require some very strange re-formulation of gravity.

For example - consider two galaxies with different rotational velocity distributions. Postulating a different distribution of dark matter in the two galaxies would account for these variations, but assuming that the observable matter is all of the matter would require a different Law of Gravity in the two galaxies. Occam's Razor suggests that Dark Matter is the simplest solution - now we just need to work out what it is.
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  #90  
Old 16-11-2016, 03:55 PM
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Sorry another Question. Are there physical or theoretical limits to the frequency of gravitational waves? Cheers Richard
The attachment answers your question.
Each phenomena produces gravitational waves of a particular frequency range.
The h axis is roughly a strain measurement for how a interferometer type gravitational wave detector should respond to the incident gravitational wave.

Apart from the direct detection by LIGO, an indirect detection of gravitational waves in the extreme low frequency (ELF) range is theoretically possible by a signature polarization pattern of cosmic background radiation photons produced during the inflation stage of the early Universe.
A discovery was announced by the BICEPS project a few years ago but was withdrawn as scientists underestimated the polarization effect from local sources such as magnetized dust in our galaxy.

A major embarrassment for mainstream science but an example of the relentless analysis and verification procedures when "discoveries" are announced.
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  #91  
Old 16-11-2016, 10:54 PM
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Originally Posted by xelasnave View Post
Hi Julian thank you for all your book recommendations.

This is off topic but I must share.
Some may have guessed I am an athiest who follows the teachings of Jesus but does not believe he is/was God nor do I believe in the resurection.
I often chalenge theists. "have you read the bible cover to cover?"
Once I owned a magnificent library however it was taken along with all my possessions by the bush fires in 2002?

I now have only one book to my name is a copy of the king Georges version of the bible.
How I got it I have no idea maybe I found it in the house in the city...

I just think that is so funny particularly because on another forum I often say to cranks (intelligent design folk, no evolution etc anti science religious folk) .....
"You need to read more than one book to understand cosmology" or similar.

You really have to laugh... and I hope you all have a laugh... its free its on me.
Alex
If we could elect our gods you'd get my vote Alex. I love reading your posts. And I think you'd do a great job.
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  #92  
Old 16-11-2016, 11:02 PM
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Originally Posted by xelasnave View Post
I am convinced there may be something wrong with our understanding of gravity.

Unfortunately with no education it is unreasonable to think I have the answer when so many professionals over centuries have built up the current model.

xelA....this may be an advantage - your mind hasn't been fully contaminated with the Religious Scientific doctrine and fundamentalist scriptural dogma parroted by these laboratory and theoretical Priests carrying these so called "text books" which are commissioned and distributed by the Scientific Jehovahic Churches...

Take String Theory for example - a complete and farcical circus run by deranged ring masters and clown acts

I want to hear more from you xelA about this thing called "gravity"




(Self-education is, I firmly believe, the only kind of education there is. -Isaac Asimov)

Last edited by Eratosthenes; 16-11-2016 at 11:35 PM.
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  #93  
Old 16-11-2016, 11:46 PM
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Originally Posted by Eratosthenes View Post
xelA....this may be an advantage - your mind hasn't been fully contaminated with the Religious Scientific doctrine and fundamentalist scriptural dogma parroted by these laboratory and theoretical Priests carrying these so called "text books" which are commissioned and distributed by the Scientific Jehovahic Churches...

Take String Theory for example - a complete and farcical circus run by deranged ring masters and clown acts

I want to hear more from you xelA about this thing called "gravity"
Hi Peter
I think you are being un necessarily unkind in your generalised criticism but I dont know enough to try and defend those you attack and can only say you are entitled to your opinions.
It is a little unfair to take a swipe at all these folk given as with most human groupings we can find both good and bad humans.
Often the bad ones give the good ones a bad name and that is why it probably is best if you see something deserving critism you be specific.
I do think as a great deal of what we learn about science comes from journalists and writers of popular books which probably does not present the real picture.
I dont know what the real picture is however I look at things this way.
Science occupies many great minds and even if they produce nothing you feel is worthwhile at least we have manyhumans occupied in work they believe in and as such gives them high self esteem.
Now I would not take high self esteem away from any human for it is a most difficult thing to have a human to accept.

I can tell you much about gravity other than as I said I believe it is a flow of space which could be best described as acting as a pressure system.
I believe there is no force whatsoever we describe as attraction and I think it was something we took for granted and never really thought thru.
And so as simple as it sounds GR probably could do away with dark matter and dark energy. I simply think the irony maybe the maths that give us these hidden features in the universe may well be able to remove the very problem they create.

Alex
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  #94  
Old 16-11-2016, 11:50 PM
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If we could elect our gods you'd get my vote Alex. I love reading your posts. And I think you'd do a great job.
Les you could make me blush if my feet were not firmly "pushed" to the ground.
Thank you for your kind words of support.
Keep up the good work.
Alex
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  #95  
Old 17-11-2016, 12:31 AM
croweater (Richard)
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Originally Posted by sjastro View Post
The attachment answers your question.
Each phenomena produces gravitational waves of a particular frequency range.
The h axis is roughly a strain measurement for how a interferometer type gravitational wave detector should respond to the incident gravitational wave.

Apart from the direct detection by LIGO, an indirect detection of gravitational waves in the extreme low frequency (ELF) range is theoretically possible by a signature polarization pattern of cosmic background radiation photons produced during the inflation stage of the early Universe.
A discovery was announced by the BICEPS project a few years ago but was withdrawn as scientists underestimated the polarization effect from local sources such as magnetized dust in our galaxy.

A major embarrassment for mainstream science but an example of the relentless analysis and verification procedures when "discoveries" are announced.
Thanks Steven , your response much appreciated. Very good of you. Cheers,Richard
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  #96  
Old 19-11-2016, 01:09 PM
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Hello Markus,

Since Robert hasn't responded to this post (yet) let me make some comments.

Quote:
Isn't that just saying gravity theory is correct, but only if you assume it to be correct in the first place? Why assume it to be correct at all when the data suggests otherwise? That's what I don't get!
Scientists are adverse to using terms such as "correct theory", as theory is only as good as the accuracy of the prediction being made when compared to the experiment and/or observation.
The other variable is the sensitivity of experiments.
As technology improves the sensitivity of experiments increases which may show up deficiencies in the theory.
For example for 250 years the moon's orbit was modelled as an object in gravitational free fall as described by Newton.
This model agreed with observations of the time until Apollo astronauts put mirrors on the Moon allowing the Earth Moon distance to be measured with greater accuracy and precision.
It is found the Moon Earth distance is increasing in contradiction to Newton's model and is due to the effect of tidal forces that needed to be factored in with the free fall model.

The data does strongly suggest that dark matter exists as explained below.

Quote:
On the one hand you have the proposition that the physics is somehow wrong at large scales.

On the other you have the idea that most of the universe is made up of matter that doesn't absorb or emit any form of energy, interacts only through gravity and can't be found despite many years of searching.

Surely at some point occams razor cuts the other way where the simplest explanation is simply that conventional gravity is *not correct. Alex nailed it on the head before. Surely the response to data that doesn't line up with your predictions is to change the model and test that? Sure, Dark matter does represent a revision to the model, but why does it represent our best hope over and above any revision to gravity?
The alternatives lead to far greater difficulties than the dark matter model.
The entropic model for gravity has been shown to have serious theoretical problems.
Any model that dispenses with dark matter which also includes gravity modified models cannot satisfactorily explain the presence of gravitational lensing beyond the visible boundaries of colliding galaxy clusters such as the Bullet Cluster.


Quote:
What if the story of dark matter is the same as the story of the Ether? Something made up to make the math work out?
I'm willing to accept things that are not intuitive, with evidence. Quantum field theory in bonkers, but I accept that is how the world is. The evidence in this case may have more than one explanation. Why do we exclude the other one?
Ether wasn't made up to make the maths work out.
There is nothing explicit in Maxwell's equations that requires an Ether.
Ether was ruled out by the Michelson-Morley experiment and there was no need to tinker the equations as a result.

The idea that dark matter is made up to make the maths work out is a common misconception.
In a simple solar system involving a star and a single orbiting planet, Kepler's third law is valid. Add another planet to the mix which gravitationally interacts with the existing planet and there is a deviation from Kepler's law.
Newton's theory of gravity being a linear and a perturbative theory allows the mass of this planet to be calculated irrespective of whether it is observable or not.
The same principles apply to much more complicated systems such as galaxies in which dark matter is calculated based on deviations from Kepler's third law.

Deviation from Kepler's third law is the observation of the effects of dark matter.
Another misconception is the complete lack of evidence of dark matter itself. While dark matter hasn't been directly observed, we know of the existence of a dark matter "particle"- the neutrino.
While neutrinos alone cannot be the constituent of dark matter, it possesses a very important property which separates it from ordinary matter, a zero charge instead of a neutral charge associated with normal baryonic matter such as neutrons. A zero charge is a fundametal property for the practically non existant interaction with electromagnetic radiation.

Quote:
To put my devil's advocate hat on for a moment and argue against myself for a moment, I assume that an explanation that tweaked gravity theory would expect the effect to be uniform. You wouldn't have a dwarf galaxy with 300 times the effect, and a normal galaxy with, say 5 times. It would (presumably) consistently be proportional to the amount of observed matter.
If you mean observation to include the deviation from a Keplerian orbit, that's a good reason as well.

Regards

Steven

Last edited by sjastro; 20-11-2016 at 05:08 AM.
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  #97  
Old 20-11-2016, 10:41 PM
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Sorry Steven, took me a while to get to this post. Thanks for replying in such detail.

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Originally Posted by sjastro View Post
Scientists are adverse to using terms such as "correct theory", as theory is only as good as the accuracy of the prediction being made when compared to the experiment and/or observation.
Fair enough :-)

Quote:
Originally Posted by sjastro View Post
The alternatives lead to far greater difficulties than the dark matter model.
The entropic model for gravity has been shown to have serious theoretical problems.
Any model that dispenses with dark matter which also includes gravity modified models cannot satisfactorily explain the presence of gravitational lensing beyond the visible boundaries of colliding galaxy clusters such as the Bullet Cluster.
Fascinating read. Is this the case with most gravitational lensing interaction galaxies? That the baryonic (gas) matter interacts in a different way to dark matter? I mean is this galaxy an anomaly, or increasingly seen as typical?


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Originally Posted by sjastro View Post
Ether wasn't made up to make the maths work out.
There is nothing explicit in Maxwell's equations that requires an Ether.
Ether was ruled out by the Michelson-Morley experiment and there was no need to tinker the equations as a result.
If was a done deal, why did Einstein tinker with Aether 33 years later?

Quote:
Originally Posted by sjastro View Post
Another misconception is the complete lack of evidence of dark matter itself. While dark matter hasn't been directly observed, we know of the existence of a dark matter "particle"- the neutrino.
While neutrinos alone cannot be the constituent of dark matter, it possesses a very important property which separates it from ordinary matter, a zero charge instead of a neutral charge associated with normal baryonic matter such as neutrons. A zero charge is a fundametal property for the practically non existant interaction with electromagnetic radiation.
Okay, that would make a lot more sense to me - that Neutrinos are responsible for dark matter. The particle has very little mass, interacts only very weakly, is predicted by the theory, has been detected. Makes sense. Maybe there are just more of them out there than we thought.

Looking at the rotation curves of the galaxies the thing that strikes me is not that the galaxies are rotating faster than they ought to, but that the galactic rotation curves are linear - the outer parts of galaxies seem to orbit the centre of the galaxies at the same rate as the inner parts. Wouldn't this require an inverse distribution of dark matter to make the outer parts speed up in relation to the inner bits? If it was just more matter, the velocities would be high, but not flat, right? Even with dark matter we still have to explain why the outer parts orbit at similar velocities to the central parts, don't we?

Cheers

Markus
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Old 21-11-2016, 08:47 AM
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Hello Markus,

Quote:
Fascinating read. Is this the case with most gravitational lensing interaction galaxies? That the baryonic (gas) matter interacts in a different way to dark matter? I mean is this galaxy an anomaly, or increasingly seen as typical?
I don’t know whether this is an anomaly or even if colliding galaxy numbers are numerous enough to form a decent sized data set for analysis.

One thing that is known however is that the orbital velocity of individual galaxies in clusters exceeds their escape velocity which formed the original postulate for dark matter in the 1930s.
The total mass of galaxy clusters must exceed the mass calculated from visible matter otherwise the clusters would fly apart.

Quote:
If was a done deal, why did Einstein tinker with Aether 33 years later?
Einstein’s view of aether was very different to the conventional view in the 19th century.
In the 19th century aether was considered to be a medium that allowed electromagnetic waves to propagate through, much like air being a medium for sound waves.
Einstein used the term aether to describe the “physical” properties of space-time in the presence of matter

Quote:
Okay, that would make a lot more sense to me - that Neutrinos are responsible for dark matter. The particle has very little mass, interacts only very weakly, is predicted by the theory, has been detected. Makes sense. Maybe there are just more of them out there than we thought
A problem with claiming that dark matter is composed of neutrinos is the very low neutrino rest mass.
In the early Universe which was much hotter, the neutrino thermal energies would have resulted in a much more even distribution of dark matter.
Instead today dark matter like ordinary matter is concentrated in regions such as galaxies.
One would require a heavier particle in order for gravity to counter the thermal effects in the early Universe.

Quote:
Looking at the rotation curves of the galaxies the thing that strikes me is not that the galaxies are rotating faster than they ought to, but that the galactic rotation curves are linear - the outer parts of galaxies seem to orbit the centre of the galaxies at the same rate as the inner parts. Wouldn't this require an inverse distribution of dark matter to make the outer parts speed up in relation to the inner bits? If it was just more matter, the velocities would be high, but not flat, right? Even with dark matter we still have to explain why the outer parts orbit at similar velocities to the central parts, don't we?
From your attachment you will notice the orbital velocities increase sharply at low radii. This is due to the high density of visible matter at and near the core.
This region rotates as a “solid” object like a wheel, and the tangential velocity is simply the product of the radius and the angular velocity of the individual stars.

As you increase the radius you are adding more outlying mass to the central region that will affect the tangential velocities of the outer stars.
A flat rotation curve is due to the linear increase in central mass with distance.
This can be shown by using high school physics which also serves to illustrate that dark matter was NOT introduced to get the maths right.

An object of say unit mass rotating about a centre experiences a centripetal force equalling v^2/r where v is the tangential velocity and r the radius.
The corresponding centrifugal force has the same magnitude but acts in the opposite direction and equals –v^2/r.
If there is a mass M at the centre the gravitational force of attraction with the unit mass is GM/r^2.
For the orbit to exist to force of attraction must be counterbalanced by the centrifugal force hence.

GM/r^2 -v^2/r=0
M = rv^2/G

Hence the central mass M increases linearly with distance.

Since part of the rotation curve for our own galaxy falls within the visible region where ordinary matter appears to dominate, the linear dependence of central mass on radius can be confirmed.
Since the curve remains reasonably flat where there is less and less visible matter, there must be unseen matter present for the linear dependence on radius to be preserved.

The obvious question that arises here is why dark matter is not simply dark baryonic mass or in other words unseen ordinary matter.
We see the effects of dark baryonic matter when astronomers observe the centre of galaxy which is obscured by gas and dust.
The centre of the galaxy is opaque to observation in the visible spectrum but more transparent in the IR and longer wavelengths.

Given that no difficulties occur when observing through the dark matter halo, it cannot be unseen ordinary matter but matter with very little or no interaction with light.


Regards

Steven

Last edited by sjastro; 21-11-2016 at 10:20 AM.
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