Dark Matter Cephalalgia

Every time when some idiot Baba-ji or Guru-ji or a self proclaimed spiritual master talks about Dark Matter its always that mysterious or spooky nonsense which eventually leaves you more confused about the Dark matter rather then understanding what it is so they can sell you something. First they are not the authentic authority to actually understand this advance physics concept and second most of the times its about your money not about increasing your intellect or enrich knowledge. Scientist are mostly at the peak of their ivory tower and and science communication is doomed too in this country. but you do not worry for a layman to actually understand the basic idea and concept of dark matter without dwelling deep into the complex mathematical and technical research papers I wrote this article two year ago. lets GO!!!

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There are six part of this article

Einstein’s General Relativity & Standard Model
Fritz Zwicky & Coma Cluster (1930s)
Vera Rubin & Galaxy Rotation (1970s)
Dark Matter as a Balancing Factor-X
Properties of Dark Matter
Dark matter as an well articulated hypothesis

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Einstein’s General Relativity & Standard Model

In physics, we have two important keys to understand the universe. Einstein's "General Theory of Relativity"[1] for understanding gravity and spacetime, and for studying the universe at the subatomic level, we have the "Standard Model of Particle Physics". The second one is actually a group of 25 fundamental particles. Particles that cannot be divided into smaller particles, such as electrons, photons, bosons, etc. Think of it as the periodic table of particles but dynamic not static.

These two theories are exceptionally great in their relative domain to explain fundamental of universe and so does the Quantum mechanics but we will not talk about it here. General relativity explains how universe and fundamental laws of physics behaves under the pressure of gravity and speed and why newtonian mechanics takes a back seat.

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Fritz Zwicky & Coma Cluster (1930s)

The problem began in the 1930s when Swiss American astronomer Fritz Zwicky was studying the Coma Galaxy Cluster. A galaxy cluster is a group of galaxies that may contain 100-1000 galaxies, all held together by their collective mass (10¹⁴–10¹⁵). The Coma Cluster contains hundreds of galaxies and is approximately ~321 million light-years away. Fritz Zwicky focused on eight galaxies and mathematically studied the masses and velocities of these galaxies using the "Virial theorem".[2]

So what is virial theorem? its simply means that- the greater the total mass of a galaxy cluster, the greater the average velocity of the galaxy.[3] Fritz Zwicky's study made it clear that the luminous matter of galaxies (this is normal matter that interacts with other matter in the form of electromagnetic radiation and gravity, but in the context of galaxies it is called "luminous matter") was not enough to maintain the observed velocity of the galaxy cluster.

This observed velocity is so high that galaxies should break apart from the cluster, yet how is everything perfectly fine and intact?
Despite such an average velocity, the cluster is in a state of equilibrium. Whereas the amount of matter present to maintain this velocity is only ~0.2-0.5% (1/400 to 1/200)! So where is the rest of the 99.95% of matter?
So zwicky thought there must be some Invisible mass responsible for maintaining this equilibrium. When they measured the amount of this invisible matter, it turned out to be 400 times more than the existing luminous matter.
But this data is old. However, according to X-ray gas and other new data, we know that this figure is around ~5-10x of the luminous matter.

This invisible but hypothetical matter responsible for the equilibrium that hold the galaxy together so it won't scatter away was named "Dunkel Materie" aka "Dark Matter" by "Fritz Zwicky" and this was the first observational evidence of dark matter 92 years ago.

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Vera Rubin & Galaxy Rotation (1970s)

The second time the galaxy was studied in the framework of the Doppler effect was by astronomer Vera Rubins[4].

What's Doppler Effect you ask? In the context of light sources, the Doppler effect is that "as a light source moves away from the observer, its wavelength increases and visible light shifts towards red colour or spectrum this is known as Red Shift and as the light source comes closer to the observer, its wavelength decreases and visible light shifts towards blue colour or spectrum aka Blue Shift. As the galaxy rotates, this light source appears half blue and half red.

Vera Rubins' guessed that the same principle should apply to galaxy rotation. The red-blue shift at the centre should be greater than the outer parts of the galaxy because the centre is rotating rapidly. Vera Rubins, along with another astronomer William Kent Ford Jr., measured H-alpha lines in spiral galaxies. The expectation was that the rotation velocity would decrease in proportion to the Kepler distance, but . . . ![5]

They continue studied many nearby galaxies and found the velocity stayed constant but not the colour shift and galaxy rotation was much faster than mathematical predictions.

Along with this, Kepler's 3 laws are used for the motion of planets in classical mechanics, and the third law says that "The time taken by a planet to complete one revolution around the Sun is directly proportional to the distance of the planet from the Sun. That is T² ∝ a³ .
Its direct application is that as the distance of a planet from the Sun increases, the time taken by it to complete one revolution around the Sun will also increase.
The planets near the Sun will revolve around the Sun faster and the planets farther away will revolve slowly.[6]
Now this is a well-known fact and you usually see this like the Earth completes its revolution around the Sun in 365.26 days and Jupiter in 11.86 years. Whereas Neptune takes 164.79 years to complete this task. (If you were born in 1857 then this year is your 1st birthday on Neptune. Congratulations! )

This is called a rotation curve, which shows how the orbital velocity(V) changes with the distance(R) from the centre of the object. Rotation curves are commonly used in astronomy to represent the mass distribution in a solar system. Now the thing is that this mathematics fits the solar system, but when this theory is applied to any galaxy, there is a huge conflict between mathematics and observation. Galaxies are not point masses like planets. The mass of a galaxy is distributed.[7]

The conflict is that the rotation of a star in a galaxy around the centre (usually in a circular path) depends on the gravity exerted by the centre on it. This gravitational pull comes from the mass of the galaxy. The mathematics of the rotation curve is that the rotation velocity of stars near the centre will be constant and then keep increasing as the distance from the centre increases. After a certain level, it will start decreasing relative to the distance and will keep getting less and less. The orbital period of distant stars should be very high.

But our observations do not lead us to these conclusions. Why? The graph is accurate for stars near the galaxy's centre, but as the distance from the centre increases, the period of rotation of stars becomes constant instead of increasing, and even the stars at the edge of the galaxy revolve as fast as the stars located several light years away.

This is rally a mind bending phenomenon. classical physics is done here at this point because this should not happen.

Gif Credit: nasa[8]

Image Credit: EDN[9]

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Dark Matter as a Balancing Factor-X

Since there was no logical solution to the above problems, the only solution available to physicists was to assume that galaxies and galaxy clusters are surrounded by some invisible matter. A matter that is responsible for their equilibrium and the current observations.

This conclusion is not taken in haste, it is simply that this following solution is the simplest way to solve the above problems.

Because, as I have mentioned, Einstein's "General Theory of Relativity" is the key to understanding gravity and spacetime. We use Einstein's field equations and find solutions to our problems.

This is Einstein's field equation in the blue box.

On the left side (L.H.S.) of the equation we have a mathematical function for spacetime curvature and on the right side (R.H.S.) we have a function for mass and energy. This is not a single equation, it is a group of 16 different equations as the μ and 𝜐 indices have different values from 1 to 4.[10]

Now we have transformed these 16 equations into 10 independent equations.

at this point our challenge is that the L.H.S. and R.H.S. functions are not equal to each other, there are about 16 field equations which we have to simplify to 10 to explain the above problems. We are not able to find any way to solve and explain the matter problem of galaxy clusters and problems like rotation curve, gravitational lensing, cosmic radiation background, structure formation etc. Then what we did was to add a new balancing factor 'X' to the equation which we call "Dark Matter Density" and after this we balanced all the equations with the help of this X and solved them.

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Now at this point you can say that this is wrong! This way, you will add any new variable to simplify every problem. Tomorrow if any mathematics doesn't match with your new observation or experiment, then you will bring some new balancing factor. Today its dark matter density or X factor, tomorrow you bring the 'blue ghost' or 'red kettle' theory? This is not good science. this is making styuff out of the box and confusion layman. This is why people do not like scientist and mathematicians they are out of their head and mock us that look you can't do Mathematics.

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Look ! It's just making new maths and justifying hypothesis because this is a very precise science! I told you, you have to simplify 10 equations. Now either we have to find a new balancing factor for each equation and solve the above problem from the point of view of 10 new X factors. Then at least 10 new theories will have to be formulated using this method and good luck studying and understanding 10 new books.

One factor for each equation means a different theory for each problem, i.e. entry of 10 new 'X' in 10 equations or we can do one solution for all the problems.
A universal balancing factor means only one theory on which everything can be blamed!
"Dark Matter" is the only theoretical picture that fits in this framework and our X is this brand new "dark matter density" whose value we can put in the field equation and study the space time curve.
It’s not Hasty; it’s Pragmatic

This does not mean that you think that "Dark Matter" is some extra ordinary substance with undefinable properties. In physics we have given dark matter certain properties. It's a plausible solution only and only if it meets these properties. My personal problem with this theory starts with these very properties we have assigned to this 'Dunkel Materie'.

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Properties of Dark Matter

Now Lets understand the very specific properties of dark matter.

Most important It does not emit, absorb, or interact with electromagnetic radiation. like light and this is why its not visible through telescope.
Since it is not visible through a normal telescope and it is also certain that it exists. Then it must be a cold and collision less matter.
Cold means that it is very slow relative to the speed of light. (sub-relativistic: ~10³-10⁵ m/s)
Collision less means that it does not have any kind of electromagnetic/weak/strong interaction with normal matter too.
It does not even interact with itself.
It is even weaker than the weak nuclear force.
It only interacts with gravity.
It is not a normal matter because almost all particles interact with light, that's why it's not a matter made of normal particles.
It is not Baryonic, meaning it is not made of leptons and quarks.
It is stable, so it is not made of the Higgs particle, because if it were, it would be there today and not there tomorrow (the Higgs decays in ~10⁻²² s). And there are not enough neutrinos in the universe to make up enough dark matter.
Dark matter is all around us and is present in greater quantities than ~5.4 times the amount of matter in the universe that makes up the sun, planets, black holes and all of us and entire universe.
Some theorise Dark matter is made of Weakly Interacting Massive Particles (WIMPs)[11]. Some call them axions, and there are still dark matter particles passing through you but you can’t detect them.
and eventually when scientist tried to detect these WIMPs using the LUX-ZEPLIN (LZ)[12] experiment, still we found nothing year till year 2025.

In fact, we have not been able to detect Dark Matter in any way yet. We do not have any such equipment that can detect it. We do not even know exactly what it is made of, there are only speculations that it could be made of exotic particles like WIMP.[13]

It's colourless and has no spectrum, no fluidity and it is dark only in name. It is not even black. It is completely invisible. Apart from all this, ladies and Gentleman This is what we known as Dark Matter.

And now if you have a headache, then congratulations, now you probably know what "Dark Matter" is and you now possess this ability to justify the articles heading too.

Image Credit: Wikimedia[14]

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Dark matter as an well articulated hypothesis

"Dark Matter Hypothesis" would be more accurate, but instead, popular science has repeatedly spiced up discussions about it, creating the illusion in your mind that dark matter is a substance found in the universe that you can put in a box. That is why I have never written an answer on it till date because it is such a difficult but interesting scientific hypothesis that it is difficult to write on it and then justify its existence in normal language. Dark matter has not been discovered till date, nor do we have any equipment or detector that can find dark matter. Whether it is being created or will be created is a different matter, nothing is there right now. Many physics problems can be solved by its theoretical analysis and it also fits accurately in simulations, but there are many problems which it cannot solve. For example: Galaxy cusps and dwarf galaxy predictions. [15]

But still it is important to study it because the observational evidence of its existence are very solid. For example, when the universe was initially new, all the mass was distributed equally. After that, the dark matter simulations and actual observations of the galaxy and universe as we see it today are exactly the same. For many years we were unable to explain galaxy formation in any other way.

The above simulation tells you why galaxy cluster observations are exactly as we see them. There have been other hypotheses and explanations for cluster formation in the past. But when the simulation was done by factoring in dark matter density, it was perfect and accurately depicted the existing galaxy clusters. This is also a proof that this theory needs to be studied. Apart from this, gravitational lensing, cosmic microwave radiation and structure formation are also observational evidence of the dark matter hypothesis. This is a difficult but evolving science.

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Apart from the dark matter theory, there are some other theories that may have potential to eliminate the need of Dark matter Theory which need to be studied. including:

MOND[16]
Tensor-Vector-Scalar modified gravity[17]
f(R) Gravity[18]

"Which we will discussed some other time, cause the excitement must remain."

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In the end, I would just like to say that most of the things you have heard or read about dark matter till date have nothing to do with physics. A particular section just creates new dimensions of the height of stupidity. For them every advanced physics theory is a copy of the pages of their religious book or an extension of the gibberish of spiritual philosophy. Stay away from such fools and always study theories or get information from "legitimate" scientific sources only. You have learned the "X" factor of the dark matter hypothesis and now no one will be able to sell you the magical dark pea by calling it dark matter.

m. दिनेश

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M.Dinesh

M.दिनेश©

-Dinesh Mandora

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DARK PEN