Unravelling the Universe one particle at a time

Dark Matter - II 

Hello readers, this article is in continuation with my previous article on dark matter. So, if you have not read it before I’d recommend you to do check it out. Without further ado, let’s begin.

We left the article with a series of unanswered questions. So, let’s pick the first one from the list. What can and cannot be dark matter? What are the possible candidates of dark matter? 

Dark Matter - A scientific bewilderment

What dark matter cannot be?

The abundant amount of light elements created during the big bang nucleosynthesis (production of nuclei other than those of the lightest isotope of hydrogen after the big bang during the earlier phases of the universe) can rule out the possibility that dark matter particles are baryonic (Baryons contain an odd number of quarks, minimum 3. Protons and neutrons are the most common example of baryonic particles). The nucleosynthesis depends strongly on the baryon-photon ratio. This is also supported by the observations of cosmic microwave background radiation.

1. The main baryonic candidates are the massive astrophysical compact halo object (MACHO) class of candidates. These mainly include brown dwarf stars, Jupiter-like planets, and 100 solar mass (1 solar mass = 1.989 * 10³⁰ Kg) black holes. Searches such as MACHO collaboration and EROS-2 have ruled out the possibility that these objects make up a significant fraction of dark matter in our galaxy.

   

   How MACHOS can focus light via gravitational lensing

   
   
2. Next in line with the particles that can be ruled out from the equation is relativistic neutrinos. Neutrinos are expected to have been produced profusely in the very initial stages of the universe. Similar to the microwave background radiation which are the fossil remnants of the hot radiation which characterised the dense phase of the early universe, we also expect fossil remnants of neutrinos which now form a background. With an estimated density of about 150/cm³, per species and this summed up over all the six species, we expect a fossil neutrino background with a number density of 1000/cm³. Even with this density, and mass as low as 0.1eV to 0.01 eV, it would account for less than a per cent of the missing dark matter.

   

   Cosmic neutrino background

   
   
3. There are a few other proposals that can be easily ruled out from basic astrophysical considerations. Highly relativistic protons trapped in halos of galaxies is one of them. Other rejected baryonic candidates are brown dwarfs, old white dwarfs, neutron stars, stellar-mass black holes, solid H₂, dense cold molecular clouds in galaxies, etc.

   

   Brown dwarf

   

   Ancient white Dwarf Star

   

   Neutron star

   

   A black hole weighing 70 solar masses

   
   

   

   Giant interstellar hydrogen iceberg

   
   

   

   Molecular clouds in the neighbouring WLM galaxy

   
   

What are some possible candidates for dark matter?

The range of ideas when it comes to what dark matter can be has no shortage. Serious candidates with masses ranging from 10^-5 eV to 10⁴ solar masses have been proposed. That’s a whooping range of masses of over 75 orders of magnitude!
As we have already discarded the notion of baryonic matter to be the dark matter, we shift our focus to non-baryonic matter. The non-baryonic candidates are basically elementary particles that are either not yet discovered or have non-standard properties. There are many propositions for the possible candidates. Many of them, like axions, neutralinos, gravitinos or composites these have been theorised. So, let’s look into them one by one.

1. A fraction of a second after the Big Bang, the universe was so hot that new particles and anti-particles were created and destroyed all the time. Calculations show that a stable particle of mass near 100 GeV and interacting with weak forces will leave just about the right amount of “leftovers” to account for the observed dark matter density. In particle physics, the Standard Model says that each particle has a heavier partner of different spin but similar interactions. The lightest of these particles is stable in many cases, which is an excellent dark matter candidate. Many theories which talk about higher dimensions, talk of different dimensions altogether in which these particles are curled up. The lightest of these particles, e.g., Kaluza-Klein particle, make for excellent dark matter candidates.

   

   Kaluza-Klein Theory

   
   
2. There are other possible dark matter candidates which do not fit into the above framework. One of these particles is the axions. An explanation for why axion is a good candidate goes beyond the scope of this article. Its explanation requires a pre-requisite knowledge of various types of symmetries which we would talk about in later articles.

   

   Newly found quasiparticles mimic hypothetical dark matter axions

   
   
3. Primordial black holes have also been suggested as a possible candidate for dark matter. Primordial black holes are hypothetical black holes that were formed after the big bang. It is found that black holes in the intermediate-mass range of one solar mass to a thousand solar mass and sub-lunar black holes in the range of 10¹⁷ – 10²¹ Kg can still produce all the dark matter. There are many constraints to that and the mathematics to it is still blurry, but we can be optimistic.

   

   Primordial black holes just after big bang

   
   
4. We have a few exotic candidates that have been suggested – WIMPzillas, gravitinos, gluinos, Q-balls, Q-nuggets, SIMPS, etc. There is a range of possible dark matter models. One other model is that baryons can be ‘packaged’ in non-luminous forms. There is also evidence that much of the dark matter may be made up of as yet undiscovered particles with several experiments all over the world trying to detect these. Many of these particles are in the preferred range of 100 GeV to a TeV. There could be dark matter objects or clumps made up of these particles bound by their mutual self-gravity and limits have already been placed on the abundance of these objects.

   

   Gravitino - Warm dark matter

   
   
5. There are several new classes of dark matter objects. One of the favoured dark matter candidates called the WIMPs (weakly interacting massive particles) has masses from about 10 GeV to 1 TeV. It can gravitate to form a new class of objects in dark matter halos or around the galactic centre. The role of dark matter in planetary formation and evolution has been considered by several authors.

   

   Theories of dark matter

   
   
   
6. Another alternate candidate to standard dark matter is the mirror matter-type dark matter. They have the right properties to be identified with the non-baryonic dark matter in the universe and make for an excellent candidate. I hate to say it but we are not ready for an in-depth discussion on mirror particles just yet.

Keeping in mind that I do not have to make my articles very lengthy, I would finish this topic for today. Needless, to say this will open new horizons to our discussions and give us a lot more fundamental words to use for the future. I hope the article kept you engaged, made you curious and fascinated you. Because these are the seeds for an inquiring mind that is ready for facing the challenges of Physics head-on. And even if today was a boring lecture, well, there would always be parts that you just do not like so much. Don't be disheartened and consider it one necessary evil. With that note, I would take your leave. Hope to see you soon.

 Auf Wiedersehen!

Footnote: I have written mass in terms of energy, more specifically electron volts(eV) in the whole article. This way of representing masses with electron-volts has its roots in the famous mass-energy equivalence equation, E = mc². Dividing 1 eV energy with c² gives the mass in kg.

1eV = 1.6 x 10-19 joules (J)

The various prefixes like K, M, G, and T. stands for kilo, mega, giga, and terra respectively, with the orders of magnitude being 10³, 10⁶, 10⁹, and 10¹², respectively.

It's all dark up there!

Dark Matter

 

Hello readers, it has not been a long time since we last talked about dark matter. However, one blog was not enough to cover what I wanted to convey. So, here is another one. But, before moving ahead, I would strongly recommend reading the articles I had posted on particles and dark matter and dark energy. Many topics are in continuation with the mentioned articles. So, without further ado, let’s dive deeper into the realm of mystery and the intriguing universe we live in.

One of the most intriguing things about the universe is, it is not dominated by ordinary baryonic matter (hadrons with spin number of the form n/2), but by a form of non-luminous matter that is as much as five times the amount of baryonic matter.

The universe is very nearly spatially flat, as is indicated by the measurement of cosmic background radiation, yet 70% of its mass is unaccounted for. Detailed measurements of the universe revealed a value that is 30% that of the critical mass density. The unaccounted matter called the dark matter has eluded us for decades. Several experiments to detect it has been running for several years without yielding a positive result.

What observational evidence do we have of the existence of dark matter?

Zwicky, in 1973 was trying to estimate the masses of large clusters of galaxies. The dynamic mass of the cluster, deduced from the motion of the galaxies, were at least a hundred times their luminous mass. This led Zwicky to conclude that most of the matter in such clusters is not made up of luminous objects like stars, or clusters of stars, but consists of matter that does not radiate.

Dark Matter Halos and Galaxy Mass Distributions

One more phenomenon that we discussed in one of my previous articles was how at a very large scale, the stars or other orbiting bodies, orbiting the galaxy at larger distances from the galactic centre, move around it at more or less the same velocity as objects much closer to the centre, contrary to what is expected. The rotational velocity is supposed to be proportional to r^-2, but here it’s almost constant as if the mass is somewhat related to the distance from the centre. This tells us mass is growing even after light dies out. As much as 90% of the galaxy mass is due to dark matter. Mass increases as we move farther and farther away from the central region. The relation between increasing mass and radius may seem strange to us but it would become clear as we move further. So, let’s mark it as one of our questions.

Difference between measured and calculated rotational velocities

To better emphasise our previous point, we have what we call ultra-diffusive galaxies, these have sizes of giants but the luminosity of dwarf galaxies. They have a large amount of dark matter but very few stars, making them difficult to detect due to their inherent faintness. An example could be the coma cluster.

Coma cluster

Apart from the velocity distribution of galaxies and galaxy clusters, there is other evidence pointing to the existence of dark matter. Extended emission in X-ray observations of clusters of galaxies indicates the presence of hot gas distributed throughout the cluster volume. From the observed emitted rays, luminosity can be measured. It depends on the density, temperature, and volume of the cluster. The mass required to hold hot gas in the cluster estimated requires a vast amount of dark matter.

The gravitational lensing map (blue), overlayed over the optical and X-ray (pink) data of the Bullet cluster. The mismatch of the locations of the X-rays and the inferred mass is undeniable.

The very presence of complex structures is also proof of the existence of dark matter. Cosmic Microwave Background anisotropy measurements indicate a model with predominant dark matter. The gravity from dark matter increases compaction, allowing the formation of structures.

The large scale structure of the Universe

How do we classify dark matter?

An important classification for dark matter particles is the ‘hot’ vs ‘cold’ classification.

Hot vs Cold Dark Matter

Hot dark matter particles are those that are described by a relativistic equation of state at the time when galaxies could just start to form. As far as I think, the immensely hot universe might have led to the creation of particles with low mass and high kinetic energy, making the velocities > 0.1 c (c = speed of light).

Cold dark matter is those that are described by a non-relativistic equation of state at the time when galaxies could just start to form.

Hot matter cannot cluster on galaxy scales until it has cooled to non-relativistic speeds. Warm dark matter is another hypothesised form of dark matter that has properties intermediate between those of hot dark matter and cold dark matter. The most common warm dark matter particles candidates are sterile neutrinos and gravitinos.

From observations from our current favourite model for the universe, the matter is mostly cold dark matter (with a large cosmological constant).

Do dark matter decay? What might be their half-life?

Dark matter has survived until the present day, accounting for almost 26% of the present energy density of the universe. It is still unknown whether they are stable or have a finite but very long lifetime. This could be a possibility because there is no theoretical basis predicting their stability.

Emission line-like spectral features at energy E equivalent to 3.5keV in the long exposure X-ray observations of several dark matter-dominated objects, such as the stack of 73 galaxy clusters and Andromeda and Perseus galaxy cluster has recently been observed. The spectral lines may indicate a decay of some sort. The possibility that this spectral feature may be the signal from decaying dark matter has piqued a lot of interest, and many dark matter models explaining this signal have been proposed.

 

Dark matter (X) annihilates into dark photons (A) which couple to Standard Model particles that eventually decay into photons

What can and can not be dark matter? What might be some of the possible candidates for dark matter? What is this new thing called mirror dark matter? What is our plan to detect dark matter particles? These are few questions that have yet not been answered. To keep this article short and brief, I would talk about these topics in my next article. The topic might be overwhelming at this point. But, I hope you liked the article.

Auf Wiedersehen!

Image Credits: Google Images

The Big Bang

Big Bang Theory

What is cosmology?

I started this blog to study and try to understand the various aspects of the universe. The name of our blog is thecosmonerds - a place designated for brains with similar interests. A question that still baffles many people as soon as they hear the term cosmology is, what does it mean? Cosmology is the study of the origin and formation of the universe. From the big bang (the theory we are going with and the blog’s topic) to its current state, and the future. It is the study of the large scale properties of the universe as a whole.

Big bang theory is the most acceptable theory when it comes to all the theories surrounding how the Universe originated. The two most important observations that led to the conclusion of an ever-expanding universe that originated from a singularity are namely, the Hubble expansion and the Cosmic Microwave Background Radiation.

Hubble noticed an interesting observation while observing galaxies. He found that the galaxies are moving farther away from us. The farther the galaxy was, the greater was its velocity (now called the Hubble Flow.)  He established the linear relationship,

    v = H * r

where,    v = recession speed

               H = Hubble Constant

               r = radial distance

Finding the exact value of H is a difficult task as it involves measuring the distances of distant galaxies. It has been assigned a value of approximately 21.8 mm/s.ly.

It is natural to conclude, and hence, question; if the galaxies are moving farther apart, there must have been a time they were very close. How close were they? And most importantly, what caused them to move away? The energy released must have been enormous if the galaxies are still receding away from each other despite the gravitational attraction. Was there an explosion? If there was, there might be a factor that is constant throughout the universe.

The last inquiry leads us to the phenomenon called, Cosmic Background Radiation. The cosmic microwave background radiation is the leftover radiation from the Big Bang or the time when the universe began. It is known to be the light that has been in flight across the universe shortly after the universe was born. The light is now so red-shifted that it is in the microwave region of the electromagnetic spectrum. These radiations give the average temperature of the universe, i.e., 2.7 K. The universe had a temperature of 10³² K at the time of big-bang!

So, after briefly discussing the phenomenons that led to the conclusion, we are now brought back to our original topic of discussion, The Big Bang!

The universe began as a singularity, and as we have discussed in previous articles, physics breaks at singularities. So, we can’t exactly talk about the exact time at which the universe formed, say at, T = 0 s. What caused the biggest explosion that would ever happen? What was there before it, if there was a before or is the before even a viable possibility? These questions elude us. But, we can certainly talk about what happened a while later.

T ≈ 10^-43 s. The earliest time at which we could even begin to talk about time. This is the smallest duration of time, called the planck second, the time at which no smaller meaningful length can be validly measured. So, this is the time at which we can say anything meaningful about the development of the universe. It is at this moment that space and time had any physical meaning. The universe was so small that its spatial length was much smaller than that of a proton. It was immensely hot at a temperature of about 10³² K. Quantum fluctuations lay seeds for the universe as we know it.

T ≈ 10^-34 s. The universe had gone under a tremendous expansion increasing in size by a factor of about 10³⁰, The fluctuations have led the universe to become a hot soup of photons, quarks, and leptons at a temperature of 10²⁷ K. Still too hot for protons or neutrons to form.

T ≈ 10^-4 s. Quarks now combine to form protons and neutrons and their antiparticles. The photon is not strong enough to break them. The matter and antimatter particles annihilate and produce energy. For reasons yet unknown, there is a slight excess of matter, and this is the matter that would lead to the formation of galaxies, clusters of galaxies, superclusters of galaxies and us.

T ≈ 1 min. The universe has cooled down enough to allow low mass nuclei ²H, ³He, ⁴He, and ⁷Li. The relative primordial abundance of these light elements is a testimony to our theory. The radiation is present but still can’t move far without colliding with a nucleus. The universe is pretty much opaque at this point.

T ≈ 379000 y. The universe has a temperature of about 2970 K, and electrons can stick to bare nuclei to form atoms. The light is now free to move great distances and thus it begins its never-ending journey. This is what we earlier discussed as the Cosmic Background Radiation. Now, red-shifted enough to be in the microwave range of the electromagnetic spectrum.

T ≈ present. The universe is still expanding at speeds higher than even the speed of light. Leave alone expanding at a constant velocity, it is accelerating! :o Physicists attribute the rate of this expansion to the mysterious form of energy, called dark energy. The general outward motion of galaxies resulting from the expansion of energy is called the Hubble Flow. Apart from this velocity, the galaxies also have been found to have a peculiar velocity that is attributed to some localised attractive forces at work, called the Great Attractor. Calling it as some localised mass would be great injustice because whatever that is it is pulling our galaxy at a rate of 7.78 * 10¹² m/s. Impressive, right?

So, I would conclude this article at this point. It would not have been a difficult thing to notice that many interesting topics diverge from today’s discussion. Be it dark matter, dark energy, quantum fluctuations, or, the great attractor. It surely bores seeds for countless discussions. See you next time.

 Auf Wiedersehen!

 

The Dark Arts

Dark Matter and Dark Energy - Basics

In my last article the Building Blocks of Nature, I talked about various fundamental particles of the universe. How they make the four fundamental forces and the particles of matter. But at the last, if you remember, I mentioned that these particles only make for about 4% of our universe. What about the other 96%. We classify the other constituents of the universe as dark matter and dark energy. Dark matter constitutes for about 22% of our universe and dark energy makes 74% of our universe. For how big a part they form of our universe our knowledge of them is very limited. As we talk further about it, it is important to know where the discussion about them originates from.

For long, we have believed in a static (non-expanding) universe. The idea was so deep built into our thoughts that when The General Theory of Relativity proposed of its existence in 1915, Einstein went against his own finding and proposed a cosmological constant, that could be thought of as an antigravity force. He postulated that this was an intrinsic property of the fabric of space-time. He claimed that space-time had an inbuilt tendency to expand, and this could be made to balance exactly by the attraction of all the matter in the universe so that a static universe would result.

The idea was largely accepted, but there was a brave scientist, Alexander Friedmann, who decided to not go against the nature of the universe predicted by the General Theory of Relativity and made two very simple assumptions; the universe looks identical in every direction we look, and this would be true if we were observing the universe from anywhere else. Thus, in 1922 Friedmann had predicted exactly what Hubble found several years later in 1965. Friedmann’s work remained largely unknown in the west until similar models were discovered in 1935 by the American physicist Howard Robertson and the British mathematician Arthur Walker, in response to Hubble’s discovery of the uniform expansion of the universe.

There are three different kinds of models that obey Friedmann’s two fundamental assumptions.

1.   The Universe is expanding sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and eventually to stop. The galaxies start to move towards each other and the universe contracts. The universe would end in a Big Crunch similar to the Big Bang. It suggests an expanding universe that is not infinite in space, but neither does space have any boundary. Space could be thought of as the surface of Earth that closes upon itself but rather than the two-dimensional surface of Earth it is three-dimensional. The fourth dimension, time, is also finite in extent, but it is like a line with two ends or boundaries, a beginning, and an end.
   
2.    The Universe is expanding so rapidly that the gravitational attraction can never stop it, though it does slow it down a bit. The expansion would reach a steady speed. Space in this model is infinite bent like the surface of a saddle.
   
3. The Universe is expanding only just fast enough to avoid collapse. The speed at which the galaxies are moving apart gets smaller and smaller, although it never quite reaches zero. The space in this model is flat and infinite.
   

But which Friedmann model describes our universe? Will the Universe eventually stop expanding and start contracting, or will it expand forever? To answer this question we need to know the present rate of expansion of the universe and its present average density. If the density is less than a certain critical value, determined by the rate of expansion, the gravitational attraction will be too weak to halt the expansion. If the density is greater than the critical value, gravity will stop the expansion at some time in the future and cause the universe to recollapse.

However, the average mass density which comes from adding all the masses of the stars that we can see in our galaxy and other galaxies, the total is less than one-hundredth of the amount required to halt the expansion of the universe, even for the lowest estimate of the rate of expansion! Our galaxy and other galaxies, however, must contain a large amount of “dark matter” that we cannot see directly, but which we know must be there because of the influence of its gravitational attraction on the orbits of stars in the galaxies. Moreover, most galaxies are found in clusters, and we can similarly infer the presence of yet more dark matter in between the galaxies in these clusters by its effect on the motion of the galaxies. When we add up all this dark matter, we still get only about one-tenth of the amount required to halt the expansion. However, we cannot exclude the possibility that there might be some other form of matter, distributed almost uniformly throughout the universe, that we have not yet detected and that might still raise the average density of the universe up to the critical value needed to halt the expansion. The present evidence, therefore, suggests that the universe will probably expand forever.

An interesting term that I mentioned in the paragraph above and also in the first paragraph is the existence of dark matter. We have no clue on how they work and how to study them, but we know they exist. The matter present in our Universe is not sufficient enough to form galaxies and hold stars in clusters. Stars should be scattered and not hold structures, thus, there must be some undetectable mass holding these galaxies. We call this matter – Dark Matter.

They do not interact with light. They do not emit or reflect them. Places with a high concentration of dark matter bend light passing nearby. From this, we know that it interacts with gravity. This is both interesting and overbearing to know that we know more about what dark matter is not, more than what it is. We know that dark matter is not clouds of normal matter without stars, because it would emit detectable particles. We know it is not anti-matter because anti-matter in the presence of matter annihilates it and emits Gamma rays. We know they are not made of black holes as black holes are the vacuums of space and the particles of dark matter do not interact with light and matter in a manner we would expect from black holes.

The mystery intensifies when we talk about Dark Energy. We can’t detect, measure, or taste it. We know that universe is expanding and not at a constant rate, but it is accelerating! Space does not change its property when it expands, there is just more of it. New space is constantly created. Wherever there is empty space in the Universe, more is forming every second. Dark energy is a property intrinsic to empty space. It is energy stronger than anything we know and keeps getting stronger as time passes by. Empty space has more energy than everything in the Universe combined.

There is a popular theory that all particles, whether of matter or anti-matter or even dark matter are made of fundamental strings that vibrate in various dimensions. Different particles are only different harmonics of the vibrating spring. Just compare it to any string instrument you love. This forms the foundation of The String Theory and our next discussion. See you then. I hope you liked the article. Interact and support. Thank you.

Building blocks of Nature

Particles

For long people have gazed upon stars and wondered what makes this universe? How do stars twinkle? What makes things move? Is matter continuous like the water appears to be or is it coarse and divisible like particles of a heap of sand? When do we stop dividing and expect that what we are looking at is the fundamental particle that has made it? Does every matter in this world however different they may seem come from some basic elementary particle? What makes everything? What drives them? How do they combine? What is force or energy? How are these fundamental particles glued together? Are energy and matter the same, even though when one can only be felt and the other perceived? And when would we know that we have ultimately found the building block of everything?

There was a time when these questions were very far-fetched. We did not have the knowledge nor the means to probe into them. All we had were opinions. Opinions from different philosophers and scholars of the time.

Given the decades of pondering, theorising and experimenting, we do have answers to a few of these questions today.

Particles - The building blocks of nature

Particles have different characteristics; mass, spin, charge, decay, etc. But today, while we look upon forces and matter, we talk about the special characteristic which makes this distinction possible – spin. What did I say you ask? Particles of force? Yes, you heard it right. Particles of force! Using the wave/particle duality, everything in the universe, including light and gravity, can be described in terms of particles.

The broad distinction between particles by the Standard Model of Particle Physics

Based on the spin of a particle, they can be divided into two types – Fermions and Bosons.

Fermions are particles with a spin number in the form of n/2 where n ϵ I – {0}. And,

Bosons are particles with a spin number in the form of n, where n ϵ I.

Calling them spin can be misleading because quantum mechanics tells us that the particles do not have any well-defined axis. What it really tells us is how particles look from different directions.

A particle of spin 0 is like a dot. It looks the same from every direction. A particle of spin 1 is like an arrow: it looks different from different directions. A rotation of 360^𝜊 gives the same look. A particle of spin 2 is like a double-headed arrow: it looks the same when turned around half a revolution, i.e., 180^𝜊. Higher spin particles look the same if one turns them through small fractions of a complete revolution.

One really interesting fact is that there are particles that do not look the same if one turns them through just one revolution. You have to turn them through two complete revolutions! Such particles have a spin of ½.

Fermions form the matter in the universe and bosons give rise to the force between the matter particles.

One interesting thing that distinguishes matter particles from force particles is that the matter particles follow Pauli’s Exclusion Principle. It says that two similar particles cannot exist in the same state; that is, they cannot have both the same position and the same velocity, within the limits given by the uncertainty principle. If the matter particles have very nearly the same positions, they must have different velocities, which means that they will not stay in the same position for long. This explains why matter does not collapse over each other under the influence of forces with spin numbers 0, 1 or 2. If it were the case, all particles would collapse into each other and what we will have would be a uniform dense “soup”. Even an atom could not be formed let alone us, or life.

Fermions can be further classified into quarks and leptons.

Quarks come in six “flavours” – up, down, charmed, strange, bottom and top. These “flavours” come in three “colours”. It is important to keep in mind that when I write colour, I don’t actually mean colour as we know it in our worldly sense but these are just for some fun naming purposes.

A proton or neutron is made up of three quarks, one of each colour. A proton contains two up quarks and one down quark; a neutron contains two down and one up. We can create particles made up of the other quarks (strange, charmed, bottom, and top), but these all have a much greater mass and decay very rapidly into protons and neutrons.

Up and down quarks make protons and neutrons

Leptons are further of six types – electron, electron neutrino, muon, muon neutrino, tau and tau neutrino. The most famous one is, obviously, electron.

The six leptons

The particles have a matter-antimatter pair too. Antimatter is the same as matter and differs only in electric charge. When matter and anti-matter come in contact, they annihilate each other and only energy is left. Anti-matters make for an interesting topic for discussion but this would be beyond this article's word limit.

Matter - Anti-matter annihilation

So, some other day.

Coming to bosons, bosons are characterized by Bose-Einstein statistics and all have integer spins. Bosons may be either elementary, like photons and gluons, or composite, like mesons. They make what we call force particles.

A matter particle, such as an electron or a quark, emits a force-carrying particle. The recoil from this emission changes the velocity of the matter particle. The force-carrying particle then collides with another matter particle and then is absorbed. This collision changes the velocity of the second particle, just as if there had been a force between the two matter particles. Force carrying particles do not obey the exclusion principle. This means that there is no limit to the number that can be exchanged, and so they can give rise to stronger forces. If the force-carrying particles have a high mass, it will be difficult to produce and exchange them over a large distance. So, the forces that they carry will have only a short range. On the other hand, if the force-carrying particles have no mass of their own, the forces will be long-ranged. 

The force-carrying particles exchanged between matter particles are said to be virtual particles, because, unlike “real” particles, they cannot be directly detected by a particle detector. We know they exist, however, because they do have a measurable effect. They give rise to forces between matter particles.

We group force-carrying particles into four categories according to the strength of the force that they carry and the particles with which they interact. They are gravitational force, electromagnetic force, weak nuclear force and strong nuclear force.

The force particles

However deeply I wish to discuss these forces in detail, the word limit won’t allow me to do so, so, maybe some other time.

I’ll only name the particles associated with each force. Gravitational forces are carried by gravitons. It is a long-range force with mass 0 and spin 2. Electromagnetic forces are carried by photons. It is a long-range force with mass 0 and spin ±1. Weak nuclear forces are carried by W and Z bosons with mass 80.4 GeV/c² and 91.2 GeV/c² respectively and a spin number 0. It is a short-range force. Lastly, strong nuclear forces are carried by gluons whose mass is zero and the spin number is 1. 

So, this was about the 4.6% constituents of our universe. Say again? Where's the rest 95.4%? Well, for starters it is undetectable and for the second, we would talk about it on my next blog. So, see you again. 

Auf Wiedersehen!

Photographing black holes

Photographing black holes

 Image of Black Hole and its shadow - M87 Galaxy

So, here it is the landmark achievement of the decade and one of the most significant moments in the history of humankind! 

The first-ever photograph of a black hole.

A zoomed image of the black hole at the centre of M87 Galaxy

All the theories built on mathematical models make sense now. Here, it is. Its proof. Its photograph, for seeing is believing!

As we all know, at 06:30 pm (IST), April 10, 2019; the first-ever picture of a black hole was released by the National Science Foundation.

Targeted galaxies for the operation were Sagittarius A*, the black hole at the centre of our galaxy (closer in cosmic terms, 26000 light-years) and Messier87 the largest galaxy that we know of (54 million light-years) away.

And there it was the image of the black hole and its shadow. Both appearing approximately equal in size. Well, M87 is quite far. It's not like we can blame anyone. XD

The event horizon of Sagittarius A* is 20-million-kilometre-wide with a mass of about  4.31± 0.38 million solar masses (1 solar mass = 2*10³⁰ Kg). The event horizon of Messier87 has an angular diameter of 42 micro-arc seconds, implying that it would take 23 quadrillion black holes of equivalent size to fill the entire sky. It has a mass 6.5 billion times as great as our sun.

So, after all the celebrations, we cosmo nerds would be very much interested in knowing how we obtained these images.

Obtaining the image was no easy task. It required a telescope that was as large as our planet itself, which we all know is well not possible for now. So, what did we do?

It was made possible by VLBI (very-long-baseline interferometry) - a technique used in astronomy to obtain high-resolution images of the sky using a network of telescopes across the planet. It can, with the aid of high-tech computing come close to mimicking the sharpness of a hypothetical telescope nearly as large as the planet! It is commonly used to image distant cosmic radio sources, such as quasars, although it is also sometimes used to study stars.

VLBI did a great job, indeed. But do you know an interesting fact about it? It works on a two-decades-old principle. The principle of Young’s double-slit experiment! The light source is replaced by a distant source of radio waves like a black hole and the slits are replaced by radio antennas on the telescope.

Young's Double Slit Experiment

Very-long-baseline interferometry (VLBI)

Since Earth is rotating, the antennae are in motion relative to the black hole and receive the radio waves at different times. When these signals are allowed to interfere with each other, they produce an interference pattern that is processed at a central location to recreate the state of the black hole, whether visually or any other way.

For this purpose, radio telescopes were used.

Radio waves have a greater wavelength than visible light. So, radio telescopes have an inherently poorer angular resolution than optical telescopes. For example, a 50-meter-wide telescope will have an angular resolution of ~41.2 arc second. An optical telescope of the same size will have an angular resolution of 0.004 arc-second (An arc second = 0.000277778 degrees).

Angular diameter

Arc seconds, arc minutes and degrees

Why aren't we using visible light then? Well, we do have good enough reasons.

Astronomical objects that do emit radio waves encode certain information in them which the visible radiation does not carry. The radio waves of wavelength 1.3 mm – that the EHT (Event Horizon Telescope) tracks are not absorbed or scattered by the dust in the Milky Way, or in Earth’s atmosphere, allowing antennas on the surface to capture them. But this, in turn, does require a telescope dish antenna to be wider than Earth. How do we solve that? Here, to our aid comes into picture gravitational lensing. Gravitational lensing can magnify the whole view by five times. This reduces the size of the telescope required to a size of a few thousand kilometres. Trust me, this was much more manageable. 

So, the problem got resolved to some extent. Now what?

Here, enters VLBI aka very-long-baseline interferometry. In VLBI, because multiple telescopes are receiving the radio signals, the angular resolution of a so-called interferometric telescope is defined differently. It is the ratio between the telescopes in the array, called the baseline. If, say, the baseline is 1000 kilometres, the angular resolution of an array of telescopes already becomes 20,000 times better.

With the advent of atomic clocks, telescopes could be placed on different continents because the clock was kept in sync using international protocols.

To sum it up, a telescope receives a radio signal, a computer sticks a timestamp on it and sends it to the receiver. The receiver collates such data from different telescopes and creates the characteristic interference pattern. Using this pattern, a processor recreates the source of all the radio waves at different locations, together with the time at which each signal was received.

There are also many systems in between to stabilize and improve the quality of the signal to coordinate observations between the telescopes, etc. But the basic principle is the same as in Young’s Double-slit experiment two centuries ago.

The EHT has over eight ground-based participating radio telescopes spread over North and South America, Europe, The Pacific Ocean and Antarctica.

The EHT can study the Sagittarius A* - the site only when there are clear skies over all these telescopes at the same time. This is about one week per year – which makes each observation very precious. 

After all this hard work, we obtained a pixelated image of the black hole. And here it is… 

The black hole at the centre of galaxy Messier87

The credit's due where the credit's due. It would not have been possible without the stars and the other bodies that died being torn apart by the black hole. This is the accretion disk and a blurred event horizon that we are seeing in this picture.

Her smile says it all

I hope I could help you in understanding this discovery better.

A homage to Thomas Young, Albert Einstein, Karl Schwarzchild, and Stephen Hawking.

With this article, our series of articles on the black holes come to an end.

It was a delight to write. I hope you understood it better too.

"If I have seen further than others, it is by standing upon the shoulder of giants.”

-        Isaac Newton

Deleting the Universe

The Black Hole Information Paradox

Paradoxes – just thinking about one leaves you scratching your head and sends you into endless spirals of thought. And what if it concerns one of the most mysterious objects of the universe? Well, double the head-scratching! What do you say?

Today, we will discuss one such paradox that has been driving physicists crazy since its introduction – The Black Hole Information Paradox.

Before we look at what the actual paradox is, it is important to wrap your head around a few concepts. 

The first being, the Law of Conservation of Information.

This is a basic law of Quantum Mechanics. It talks about the need for information to be conserved. It says information like energy can never be destroyed or created. It has to be conserved. Information refers to the specific state of every single particle. Its energy, mass, spin, temperature, and more. Atoms may react, be crushed or fuse, their quantum wave function that describes them must always be conserved. The information must live on.

Quantum no-hide theorem confirmed experimentally for the first time

The second concept is that of time dilation.

So, what is it?

In our previous article when we were talking about the consequences of an object that falls in a black hole, I had once mentioned the term time-dilation. It can be defined as the difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from a gravitational mass or masses (Think Interstellar!).

As we know, gravity is so strong near a black hole that even time gets slow near it, and when one falls inside one, the mass is lost forever. But for an observer who is looking at the falling object, the object appears to be slowing down until it reaches the event horizon. It looks frozen in space. As time passes, the object starts looking increasingly reddish until it begins to fade and finally vanish. Its wavelength increases and thus it is red-shifted. The wavelength keeps on increasing and would take an infinite amount of time to completely vanish. Thus, we can be happy that information is safe on the surface of a black hole or is conserved. The surface of the event horizon holds information on all the matter that has fallen in.

Information of object which enters a black hole is preserved by time dilation.

BUT, the real trouble started when Stephen Hawking in 1974 calculated that Black Hole has a temperature. It meant that it is radiating energy. And anything that radiates energy loses mass. This meant the black hole is losing mass and though slowly would evaporate with time. The radiation unsurprisingly was called the Hawking Radiation.

Now, came the real question. What happens to the information which was preserved on the surface? Until now, we were quite happy with the explanation that time dilation is conserving information on the surface, and information is not being lost. But the loss of energy from a black hole predicted otherwise. The black hole will disappear one day and so will the information which was supposed to be conserved.

This started a paradox which we now know as the Black Hole Information Paradox. It puzzled physicists for decades. New possibilities flew in. People began speculating and coming up with creative questions. Was Hawking wrong from the beginning to start with and there was no such thing as Hawking Radiation? Or, does the black hole holds the information in it till the very last and when the last of the two particles evaporate, all is suddenly released in the Universe at once? Or, is the black hole compressing information in a microscopic space that remains even after the black hole itself is evaporated. Who knows?

The black hole information paradox

At first, Hawking was not much concerned with this loss in information. But over time he realized information had to be preserved in some way. Conservation of information was too important a law to be abandoned. So, he put forward some new possibilities. He put forward the idea that the new Hawking Radiation preserves the information of all that is falling in. The radiation can be imprinted by the information of the new matter that fell in, and then releases the information when it escapes into the Universe. The information does not remain of much use after that. Much like a burnt encyclopedia! Information that the encyclopedia holds is in some way conserved in the ashes but does not remain of much use.

But a solid explanation has not been obtained to date. Even the existence of Hawking Radiation has not been confirmed experimentally. This shows how naïve we actually are when it comes to understanding the Universe. Much work has been done but a whole lot needs to be done. We hope of finding an explanation soon...

Now, we have reached the end of the article. I hope you liked it and found it useful and I was able to make you a bit curious at least because in the end that is what drives science. Thank you very much.

Auf Wiedersehen!