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Author Topic: Would Dark Matter be needed if everything was bigger and closer than it is?  (Read 2379 times)

Offline timey

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If all bodies of mass in the universe, outside of our solar system that is, were 23% bigger than we estimate, and also 23% closer in distance, what percentage of dark matter would then be necessary?
« Last Edit: 18/11/2015 07:36:14 by chris »


 

Offline evan_au

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Quote from: timey
23% closer in distance
The distance to the nearer stars can be measured from the ground, by using parallax. Some recent space probes have measured the distance to many stars using this method.

So I think a 23% error is unlikely, at least for our neighbourhood in the galaxy.

Greater astronomical distances are measured by a variety of methods, including Cepheid variable stars and supernova explosions.
Quote
all bodies of mass in the universe..were 23% bigger than we estimate?
By "23% bigger", I assume that you mean "23% more massive"?

It is hard to measure the mass of a star directly, unless you can measure the period & radius of a planet's orbit. The Kepler space telescope has given us the period of many planets, but I am not sure if the radius of the orbit can be estimated from this. Some proposed future space probes should be able to image planets directly.

Mathematical models of stars show that the light output is strongly dependent on mass. So by knowing the distance and brightness, it is possible to constrain the mass of visible stars fairly closely. I expect an error of 23% is unlikely.

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what percentage of dark matter would then be necessary?
The anomalies we attribute to Dark Matter were first detected in the rotation curves of other galaxies.

Because the stars in another galaxy are all at roughly the same distance from us, the "23% closer" does not make a difference.

Even if the mass of the galaxy were "23% greater", that would not account for the velocity of rotation of the galaxy remaining fairly constant at different radii. Based on the distribution of visible matter (stars), the more remote portions of the galaxy should rotate more slowly than what is observed.

So these two "23%" assumptions do not eliminate the need for some mass that we just don't see, ie "Dark Matter". We just need to find out what the Dark Matter is; there are a number of theories, and the answer is probably some mixture (and probably some surprises too).

There are even more theories that have been disproved; unfortunately, I think the 23% hypothesis must go into this category.

 
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Offline timey

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Hi Evan

Thank you very much for your informative reply.  I appreciate the effort...  I am of course aware of how parallax works, and how mass is then attributed.  I am also aware of the rotational aspect of the galaxy conundrum that has led to the concept of dark matter.

To be fair to your answer, it is true that I have not presented a 'reason' as to why I am seeking the mathematical equation requested.  I do have a reason, but at this present time am only seeking to understand a mathematical relationship within the parameters of my question.

I do know enough about forum rules 'not' to be presenting a 'new theory' hypothesis on the 'proper' physics board (although to say so I have slipped a bit on other peoples threads here despite myself at times ;) )

It's just that I can't figure out how to calculate what percentage of dark matter would be then be necessary under the remit of my question.

Can you help?

(Edit: perhaps the thread title is a little miss leading Evan, Chris edited it to read as it does.  Originally it stated: "Can anyone help with a hypothetical question regarding Dark Matter?"  Chris's edit is intuitive though, as the notion of Dark Matter being unnecessary is indeed my end purpose, although please appreciate that this question posed is but a small consideration within a bigger picture)
« Last Edit: 18/11/2015 12:41:35 by timey »
 

Offline puppypower

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I have a theory that could eliminate the need for dark matter. The primordial singularity from which our universe expanded, did so via quantum division similar to biological cell division, instead of an atomization expansion into sub particles; big bang. I like this because we live in a quantum universe, while the big bang implies an early continuum universe with some minor discontinuities, that aren't even quantum.



Another difference between the two is the first cell division defines less entropy than does a sub particle atomization into a continuum. An entropy increase needs energy, therefore the cell division method requires much less energy to overcome the initial mother of all black hole starting conditions; all the mass/energy of the universe at one point.

The cell division will form two singularities, separated by space-time, then four, etc., with very little energy needed for each step compared to one big bang expansion which needs all the energy of expansion at once.

This model intuitively accounts for how galaxies, stars and even super structures were able to form so early in the universe. The galaxies puff up from late stage daughter cell singularities, many of which leave behind a black hole. I call this the mini big bang phase.

When the mini big bang phase happens; galaxies puff up, all the galaxies give off energy waves causing expansion relative to the galaxies. These high energy pressure waves also add turbulence and shear. A rotating galaxy did not form from matter attracting, but rather represents remnant of galaxy cell expansion.
« Last Edit: 18/11/2015 13:00:26 by puppypower »
 

Offline timey

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Thanks for that Puppy power.  Digesting!
 

Offline timey

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Ok, well logically speaking - the 4.9% ordinary matter would be 23% bigger, making it 6.027% This being 1.127% bigger, therefore I must minus 0.5635 from both the 26.8% dark matter, and the 68.3% dark energy...making them 26.2365% and 67.7365%.
But everything is also 23% closer, so I think (?) I need to minus 23% from both dark matter and dark energy and add these figures to the ordinary mass percentage:
Dark matter 26.2365 minus 23% (= 6.034395%) = 20.202105%
Dark energy 67.7365 minus 23% (= 15.579395%) = 52.157105%
Now I think (?) I must add the revised 6.027% normal matter to the 6.034395 that I subtracted from the dark matter percentage and the 15.157105% that I subtracted from the dark energy percentage to rebalance the percentage ratio, I think (? scratches head, rubs chin, hmmmm)

6.027 plus 6.034395 plus 15.157105 = 27.64079%

27.64079% normal matter plus 20.2021105% dark matter plus 52.157105% dark energy = 100%

Have I got this right?  Is that the way to calculate this question?
 

Offline alancalverd

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Why "outside the solar system"? What is so special about our nearest star?
 

Offline timey

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Our planet Earth doesn't orbit any other star...

Alan, did I calculate the remit of the question correctly please?
 

Offline timey

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It's just that it did occur to me that in reducing the universe's size by 23%, it might be that I should have instead subtracted the 23% from both dark matter and dark energy combined, by splitting the 23% into 11.5% and subtracting this amount from each...???

I also need to understand the means, ie: maths, by which these given percentages of dark matter and dark energy have been derived as necessary.

Any help appreciated!
 

Offline evan_au

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Quote from: timey
If all bodies of mass in the universe, outside of our solar system that is, were 23% bigger than we estimate, and also 23% closer in distance, what percentage of dark matter would then be necessary?
Quote
27.64079% normal matter plus 20.2021105% dark matter plus 52.157105% dark energy = 100%
Have I got this right?  Is that the way to calculate this question?

Showing that A+B+C=100% does not prove that this is a valid hypothesis.

Dark Energy (C) only shows itself on very large scales, > 5 billion light-years. So it can be ignored on the scale of a single galaxy.

Dark Matter (B) is necessary to explain the rotation curve of a single galaxy. Making the mass of visible matter (stars) much larger and the mass of dark matter smaller does not explain the rotation curve of a galaxy.

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everything is also 23% closer, so I think (?) I need to minus 23% from both dark matter and dark energy and add these figures to the ordinary mass percentage
Gravity works as an inverse square law, so if everything were 23% closer, its gravitational attraction would be around 46% higher. With nonlinear equations, just subtracting 23% from two measures does not balance an equation.

Quoting percentages to 9 significant figures when even the second digit is a bit rubbery shows an excessive obsession with precision, but no concern for accuracy and relevance.

Distance, mass, time, force, velocity and energy are all interlinked in the universe, but you can't just arbitrarily represent them as percentages, and then add and subtract them.

So I suggest that this is not the way to calculate this question (or even a meaningful way to pose the question).
 

Offline timey

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Evan, 'again', please!  I am not proposing a hypothesis here, merely trying to work out a mathematical equation.

I do not have an obsession with precision, just an education cut short age 11 and a maths training cut short at the stage of long division.  I am now in the process of self teaching myself, percentages and ratios are easy, and wiki presented the content of the universe to me in that format.

Yes, I did suspect that A, plus B, plus C would 'not' be sufficient to express this equation, and that I needed help, so thank you.  Gravity would be 46% stronger and this again would reduce the percentage of dark matter needed.  Can you please tell me how to work out how much dark matter would be necessary if gravity were 46% stronger due to reduced distance, and gravity were also, would it be 23% stronger (?), due to a 23% increase in normal mass?

I am aware that dark matter is considered responsible for the rotational curve of a galaxy.  If masses are bigger and distances are closer, the amount needed will be reduced.

This is the basis of my question, I'm not quite sure how else one might pose a maths question as such... If it's the thread title you are complaining about, talk to Chris...
 

Offline evan_au

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Would Dark Matter be needed if everything was bigger and closer than it is?

Yes.

The hypothesis we are considering is that if masses are bigger and distances are closer, the amount of Dark Matter needed in the galaxy (or universe) will be reduced. We are asked to calculate the amount of reduction.

Starting with galaxies: If the masses of stars in the galaxy are greater, and the distances between stars are closer, and there is no Dark Matter (or less Dark Matter), then the outermost parts of the galaxy will have a slower orbital velocity than the more central part of the galaxy.

However, if the mass is greater and the distances are closer, then you actually need more Dark Matter to produce the observed velocity distribution within a galaxy. Not less Dark Matter.

How much more? Perhaps 4 times the density of Dark matter, with a back-of-the envelope calculation as follows:

The attraction of gravity was deduced by Newton as: 
F=GM1M2/r2
where:
G is the gravitational constant
M1 and M2 are the masses of two stars in the galaxy (or a star and all stars within the same galactic radius as the star).
r is the distance between the two stars (or a star's galactic radius)

Now if the mass of every star has increased by (hypothetically) 23%.
And the distance between stars has reduced by 23%
Then the attractive force has increased by (1+23%)*(1+23%)/(1-23%)2 = 2.55

To prevent the galaxy from flying apart, we need to increase the attractive force of Dark Matter by a factor of 2.55. This can be achieve by increasing the density of Dark matter in the galactic halo by about a factor of ((1+23%)/(1-23%))3 ≈ 4.1.

PS: Sorry if my response came across harshly.
I was not criticising the title. It is a nice question.
      But I was (and still am) at a loss about how to describe the history and structure of the entire universe using just addition & subtraction of percentages.
 

Offline timey

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Ok cool, I am digesting that info, and following through with a bit of wiki research.

So... under the remit of the question, a galaxy would need 2.55 times (or is that percent?) more dark matter in order not to fly apart, and to match rotational observations...
3 things:
Would the (hypothetical) physics of all the galaxies being 23% closer and 23% bigger have any bearing on  individual galaxy rotational curve and velocity?
Would the (hypothetical) physics of all the galaxies being 23% closer and 23% bigger have any bearing on individual galaxy rotation, etc, if we (ignoring the redshift phenomenon) dispense with the idea of dark energy and consider a non-expanding universe based purely on inter galactic gravitational and centrifugal forces?
Would the (hypothetical) physics of all the galaxies being 23% closer and 23% bigger have any bearing on individual galaxy rotation, etc, if we (ignoring the redshift phenomenon) dispense with the idea of dark energy and consider a non-expanding universe based purely on inter galactic gravitational and centrifugal forces, whereas the universe's spacial dimensions (ie: space), slowly reduce as matter further clumps?

...and hey, not to worry!  I was probably being a little over sensitive myself :).  I know I have a bit of an upside down, inside out approach to learning, but if you can suffer me, (and I do hope you can), learn I will!   

Hmmmm... I'm not at-all trained in maths, but my analysis is that all formulas and geometry are actually but an expression of percentages in relation to each other... ?
 

Offline evan_au

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Quote from: timey
a galaxy would need 2.55 times (or is that percent?) more dark matter
That is a factor of 2.55, ie an increase of 155%.

Quote
Would the (hypothetical) physics of all the galaxies being 23% closer and 23% bigger have any bearing on  individual galaxy rotational curve and velocity?
You could hypothetically imagine a galaxy from which all the dark matter is suddenly removed. The outer parts of this galaxy, deprived of the attraction of Dark Matter, would fly away into intergalactic space, never to return. The inner parts of the galaxy would fly out further, only to return, in highly elliptical orbits.

You could (hypothetically speaking) imagine that when you removed all the dark matter, you simultaneously increased the mass of all the visible matter by 23%, and shrunk the size of the galaxy by 23%, without changing the angular velocity of the stars. This would boost the gravitational attraction of the galaxy, enabling it to hold onto the outer stars. However, the galaxy would look quite different than it does now, with stars that are much brighter. The rotation curve of this new galaxy would be quite unlike what we see now, with the outer stars moving more slowly than the inner stars (after it settled down from this major disruption).

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dispense with the idea of dark energy

I have ignored dark energy here. When you are talking about the scale of individual galaxies (or even clusters of galaxies), you can ignore dark energy in the current universe.

Some physicists have suggested that if Dark Energy is growing stronger over time, that clusters of galaxies could be torn apart, as could our galaxy, our solar system, the Earth, and even our atoms, in an event nicknamed the "Big Rip".

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consider a non-expanding universe based purely on inter galactic gravitational and centrifugal forces?
Einstein did initially consider the universe to be non-expanding.
However, it was discovered that this is an unlikely scenario, requiring a big coincidence in certain values in the universe.
More likely is to find a universe that is expanding or contracting; a non-expanding universe is unstable, and will collapse.

As you suggest, a rotating universe may well be able to sustain itself against gravitational collapse into a "big crunch".

Quote
I'm not at-all trained in maths, but my analysis is that all formulas and geometry are actually but an expression of percentages in relation to each other... ?
Scientists, mathematicians and Engineers do like "invariants" - things that are true, regardless of the size. That way you only need to remember one fact, instead of different facts for different sizes.

So the angles of an equilateral triangle are all 60.
If you increase the length by 23%, the angles are still all 60. This is an invariant*.

However, there are some things that change with scale in a defined way:
  • So if you increase the radius of a sphere by 23%,
  • the surface area of the sphere will increase by 51% = a factor of 1.51 = (1+23%)2
  • and the volume will increase by 86% = a factor of 1.86 = (1+23%)3
  • In this case, the "unchanged facts" are that the area increases as the square of the radius,
  • and the volume increases as the cube of the radius;
  • these invariants are expressed as a formula. 

Note that just adding 23%+23% does not produce 51%, and adding 23%+23% +23% does not produce 86%. You can't just add and subtract, but for cosmology you must also multiply, take exponentials - and that is not even taking into account Einsteins relativity!

*I know I am ignoring non-Euclidean spacetime, but let's get beyond addition & subtraction of percentages, first...
« Last Edit: 21/11/2015 17:18:29 by evan_au »
 

Offline evan_au

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By the way, the James Webb Space Telescope is due to launch in a few years.

Because it operates at infra-red wavelengths, it is better able to peer through the galactic dust clouds which obscure the vision of Hubble and ground-based telescopes. This should allow a better census of stars, including rather dim stars.

This should allow astronomers to refine their models of the rotation curves of galaxies, and the concentration of dark matter.
 

Offline timey

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Ok, lol... I can see that I am going to have to get my notebook out and mentally juggle this factor of 2.55 being an increase of 155% until I fully understand how...

(Well... To say so Evan, the means by which I came up with this 23% idea is far more complex than merely subtraction and addition of percentages.  In fact I haven't got a clue what it is that I have done mathematically, but I have made a diagram on graph paper, to scale, and applied an idea that I am working on.  This diagram, I think (scratches head), uses Pythagoras, square root, square to diagonal relationship and 2 kinds of squaring and the inverse square law, and constitutes a formula, (perhaps, chuckle) and from this diagram I have derived a mathematical expression of a formula (not expressed in percentages) describing my idea.  I don't feel particularly interested in publishing either to the net at present, (I am not adverse to sending myself up a little, but there is a limit ;). )  If however you are curious enough, I am tech proficient to send you this diagram by email, if you provide me an email address via private message.  I'd be really interested to know what the mathematical expression of this diagram would be!  Warning, my idea is way out there, but on the other hand, it's not run of the mill boring either.)

Back to the parameters of this thread, yes, agreed, of course the universe must be either expanding or contracting.  Looking at the contracting scenario, what interests me is exploring this hypothetical question of the distance between galaxies being 23% lesser, and the galaxies themselves being 23% greater in mass size as well as also being 23% closer together within the galaxy . (my idea and diagram takes care of light source brightness)
Would it be possible to derive the rotational curve and velocities that we observe of galaxies under the remit of this 23% bigger, and 23% closer consideration, without the necessity for dark matter or dark energy, if we also apply a contraction of the universes spacial dimensions that is proportional to distribution of mass?
« Last Edit: 21/11/2015 12:30:37 by timey »
 

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