A Pixelated Reality- Emergence Theorem

We all know that the speed of light is somewhere around 299,792,458 m/s, but the general mass is widely unaware of the fact that no one actually knows what its exact value is. Remember, we have a close approximation but not the exact value. The exactness depends upon the precision of the instruments measuring it. But no matter how precise our instruments get we can never perceive the actual value without a theory that tells us what it is and why it is it. All the existing physics theories fail to do so. Einstein’s theory of relativity as well as quantum mechanics both use the speed of light as the starting point. In other words, they use an inexact speed of light without explaining why it is, what it is or why the universe even has a speed limit?

For decades scientists have been working on one comprehensive theory that combines , encapsulates and accounts for everything that occurs in nature from the micro to the macro scale. A Theory of Everything is what Einstein worked on in the last few years of his life. Scientists like Stephen Hawking had devoted almost their entire life behind developing such a theory.

I want to talk to you about Reality and the existence of us as a conscious being in it. Have you ever wondered how are past, present and future is correlated and doesn’t it sometimes feel that we are nothing but one big simulation on a galactic scale? You may be wondering that how does all of these even connect? Well, you are in for a ride!!

But first, let us talk about crystals. Hold on to your thoughts before you imagine a crystal to be a shiny object that makes up your jewellery or a fancy glass that you drink from. The word “Crystal” simply means a pattern that is periodic.

Imagine a chessboard. It is nothing but a periodic pattern of squares. This forms a crystal, i.e. a periodic pattern in 2D. Now the same can be imagined in 3D, for example a Rubik’s Cube. As soon as we project a 3D object onto a 2D plane, the periodicity of the crystal is lost. The projected image on the lower dimensional plane can still be considered a pattern that is aperiodic in nature. This aperiodic pattern is due to the angle of projection of the 3D object. Hence, whenever we project a higher dimensional periodic pattern onto lower dimensions, we get an aperiodic structure known as a Quasi-crystal.

You must be wondering by now that what has crystals got to do with the fundamentals of reality? Well, a group of researchers from Los Angeles is working on a particular theory which takes into consideration the above nature and thus has been able to come up with a theory known as Quantum Gravity or The Emergence Theory.

They have taken an 8D crystal known as E8 lattice which they have then projected onto a 4D plane and furthermore onto a 3D plane thus giving us a fundamental 3D Quasi crystal.

What is the E8 lattice?

Imagine the densest packing possible for circles of the same size.

Image: Hexagonal Packing for 2D circles.

This type of packing is known as hexagonal packing. Similarly, the densest packing possible for a 3D object like spheres is most efficient in the way we generally see oranges stacked at supermarkets. If we simply consider their centres, omitting the body in this densest packing, then we arrive at something know as a point space structure. Thus, to put it simply, E8 is the point space that we get by the densest packing of 8D spheres.

The researchers believe that the final quasi crystal in the 3rd Dimension, obtained by consecutive projections onto lower dimensions mathematically, is the fundamental substructure for all reality. Now this 3D quasi crystal has a fundamental building block, a Tetrahedron, which is an equilateral triangle in 3D, the size of each side being of the planck’s length(the smallest possible unit of length that can exist)~10^-35 m.

The above statements were super confusing right??? Hold on, Let me elaborate!

So, you know how your TV or computer screens can be broken down into building blocks known as pixels. These are the most fundamental indivisible blocks that make up your 2D screens. Now imagine reality as your TV screen but in 3D and think of the “Tetrahedron” as a 3D pixel, the smallest possible indivisible unit of reality in this case. The tetrahedron in the quasi crystals combine with other tetrahedras(plural) using complex mathematical rules to fill up all of the space in the universe. All tetrahedras have only few given states in which it can exist at any given moment. And because of the rules of how these pixels connect to each other, if one tetrahedron is in a certain state, this dictates the state of many other tetrahedras all through out space.

But, if a tetrahedron can be in one state at any particular given moment then who or what chooses the state it should be in at that given moment?

Well for such a choice to be made we need to scientifically, logically and mathematically bring a new element into physics, and that element is “CONSCIOUSNESS.”

Individually theories like String theory, relativity and quantum mechanics are all participants for the Theory of everything but it presumes the speed of light and other constants (Planck constants) without explaining the reason for the exactness of the value. Hence this new theory takes clues from nature to formulate a theory encapsulating Quantum mechanics as well as gravity thus known as “Emergence theory.”

To develop this scientist took ideas from nature. They segregated seven clues that helped them build this theory. They are as follows:

INFORMATON

Scientists believe that reality is made up of Information. But what does that even mean? Well, information is meaning in form of symbolism. A language or a code provides this kind of information conveying symbolism. A very different type of symbol is the one that can represent itself and Geometric symbols can do that. For example, we can give meaning to a cube by symbolizing it for conveying love or it could represent, really, with minimal subjectivity, itself. Quantum as well as Classical physics indicate that reality is made up of information, in this case Energy (which is nothing but information).

Thus, reality is geometric. A geometric language in the form of symbolism might explain how a geometric reality is made up of pure information. Information implies meaning, but what is meaning? Meaning is a comparison, that’s what we do, but we do it so fast that we do not even realize that we are doing it. We look at something and immediately match it with something in our database. So, meaning is a perception of something relative to something else, therefore meaning is subjective and requires choice. Because meaning is subjective, for it to even exist it needs to be perceived or measured by some form of CONSCIOUSNESS.

CAUSALITY LOOP

Einstein showed how the past and the future can simultaneously exist within one geometric object. So, all time exists all the time. How weird is that? Let’s suspend common sense for a while and accept that mathematically and according to the best physics formula that we have, this is true. According to Einstein, this geometry was a block. Now imagine for a while the entire reality that we exist in to be frozen in one particular moment of time just like the frames that makes up cinemas. The tetrahedra’s or the 3D pixels makes up this one frame, frozen in time. Reality is similar to a sequence of frozen frames played forward in time. Hence, all the frames that make up this reality that you and I exist always existed. Each frame is different from the previous one just like in a movie. Your birth influences your death in the same way your death does to your birth. All time is affecting all time, all the time.

So, is reality this deterministic program that is playing itself out? Wouldn’t that imply, in a way, that we are our own creators?

NON-DETERMINISM

The famous Young’s Double slit experiment (read here: https://plus.maths.org/content/physics-minute-double-slit-experiment-0 ) ruled out the possibility of determinism and hence proved that reality is perhaps non-deterministic or basically, free will.

CONSCIOUSNESS

So, it is now safe to say that reality is made of information (also proved by John Wheeler), which is created by observation. The observation should thus be made by something that is conscious.

Hence, we can define an observer as a modern entity whose states correspond to a recognizable caricature of conscious awareness. Now if reality is made of information then it will automatically imply that consciousness is what generates the observation and data from information. Reality deeply ties with consciousness in some fundamental way. As if the fundamental stuff of reality is consciousness.

PIXELATION

Heisenberg discovered the fundamentals of quantum mechanics by using something called Matrix theory. He deduced that space and time was indeed pixelated into indivisible three-dimensional Planck-length units. Simultaneously, there is no evidence for a smooth reality i.e. a non-pixelated space time. Scientist widely accept that there is no length shorter than the Planck’s length which implies reality is pixelated.

Now the question arises that if reality is pixelated then what kind of geometric code would describe such a pixelated reality?

E8 Lattice.

After years of colliding particles at the LHC, scientists have discovered that all the fundamental particles and forces convert from one to the other according to a process known as Gauge symmetry transformation. And all these transformations correspond to a single shape. As discussed, a periodic shape forms a crystal and in this case the crystal formed is of Eight dimensions and astonishingly it turns out to be the E8 lattice.

The crystal is now projected to 4D and then we convert that to a 3D quasi crystal (shown below).

Image: Projection transformation of the 8D lattice onto 3D.

The cell shape of the 8D crystal is a 240 vertices structure known as the Gosset Polytope. Now when this cell shape is further projected to 4D it becomes two identical shape of different sizes. The ratio of their sizes is a unique number, 0.618, also known as the Golden ratio.

GOLDEN RATIO

It is one of the most fundamental constants in mathematics as well as nature (read here: https://www.canva.com/learn/what-is-the-golden-ratio/ )

Image: 4D projections of the Gosset polytope.

Also, this ratio corresponds to:

It is the precise point where a Black hole modified specific heat changes from positive to negative.
It is part of the equation for the lower bound on Black hole entropy.
It also relates to loop quantum gravity parameter to black hole entropy.

Thus, it is clear that the golden ratio is the most fundamental constant in nature because it appears on the equations for black holes which is in turn is the boundary limit where quantum mechanics and general relativity converges.

To sum it up...

So, reality is a mosaic like code or language at the smallest scale possible, i.e., the Planck scale. According particle physics all particles and forces are related to each other by a higher dimensional lattice which is the E8 lattice. But reality is three dimensions and projection of the lattice onto a 3D plane, produces a quasi-crystal code or language that allows these geometric symbols to build up to the ordinary world of particles and forces that we see around us. This geometric language has rules but it also has syntactical freedom like any language and that requires some notion of a chooser to choose the free steps in the language. This eventually pushes the idea of a universal collective consciousness. Physics allows the possibility of all the energy in the universe to eventually convert into a single conscious system that is itself a network of other conscious systems, a massive technologically-based collective consciousness.

Given enough time, anything that can happen will eventually happen. By this axiom, this system of consciousness has already emerged somewhere in the frames of space-time ahead of us. Because it is possible, it is inevitable. In fact according to retro-causality time loops, that inevitable future is co-creating us right now, just as we are co-creating it.

Time: Ticking away the moments that make up a dull day

“So you run and you run to catch up with the sun but it’s sinking
Racing around to come up behind you again.
The sun is the same in a relative way but you’re older,
Shorter of breath and one day closer to death.”

Beautiful Lyrics by Gilmour right? It’s pretty intriguing at the same time though. The clock ticks, minutes become hours and days turn into years. Have you ever thought that the very concept of time and its flow is what defines you, me and every object in space around us? But we perhaps never had the time to sit back and think how this flow and a universal tick of nature defines our life? Doesn’t it feel like time is the only fundamental to nature?

Okay, so what is time in its essence? Physicist recently reviewed Time to be non-fundamental. Duh! How is that even possible right? How is it possible for something completely temporal to emerge from what is atemporal?

The ideas discussed here may challenge your intuition at face value but bear with me and suspend your disbelief for the duration of the article to experience full immersion.

As we dive into the quantum realm, one of the most compelling things we learn is called Einstein, Space and Time. It is perhaps the most counter-intuitive concept of modern physics. The idea that challenged our understanding the most was this notion that the flow of time may be an illusion. I almost cringed when I saw a quote by Einstein endorsing, what seemed to me at the time, the most bizarre implication from the block-universe.

When you hear of time, you often think of this intangible concept advancing single-fold into the future. The idea that time keeps passing outside of our control is almost self-evident with the circular motion of the moon around the earth, and the earth around the sun.

The tools with which we measure time has become so sophisticated and duration is now recorded with such precision that one can hardly doubt the reality that time is constantly advancing. Yet beyond our universe, the concept of time doesn’t exist since time is inextricably linked to space and none can exist without the other.

All time exists all the time.

That was a weird thing to say right? You must be thinking What does the above statement even mean or how is it even possible? Well, as already mentioned time is not fundamental. But is time really this arrow we have come to associate causation with or is it all a subjective process in the mind? The arguments in support of a non-fundamental concept of time also maintains the position that causation itself is a subjective perspective inherent in our temporal agency.

What if I told you that the differentiation between past, present, and future is simply our minds playing tricks on us or perhaps our mind trying to impose its limitations on time. The concept of time flowing from past to future simply doesn’t exist according to the block-universe model given by Einstein.

For the currently accepted concept of time flow to exist, space and time would have to be independent fundamental structures. In this case, events can be pinpointed in various locations in space and we could say that those things happened over time. But according to the special theory of relativity, this idea of independent space and time is abandoned for a much more cohesive interdependent space-time.

Image: Tesseract: Dimension of time, as represented in the movie Intestellar.

Remember that scene from Intestellar, the Tesseract or the 4th dimension? Across different time periods, Cooper could see through the bookcases of Murphy’s old room on Earth and weakly interact with its gravity. So you see, all the different moments from Murphy’s life was already existing in this special dimension and that is why he was able to surf through them to the right moment in time and send a Morse code to Murphy across dimensions.

One of the major consequences from this seemingly counter-intuitive 4-dimensional structure is that nothing changes over time since the past, present, and future are already accounted for in the block-universe. This four-dimensional conception of reality highlights all events across spacetime with the same import. In this system, the past is no more important than the present is from the future.

This insight renders time effectively as one of the required coordinates to specify an object’s location in spacetime. From this new framework, an event in spacetime is already comprised of both time and place — and the whole fabric of spacetime can be understood as a collection of infinite number of events.

Imagine, it’s the 80’s, and you are in a theater watching Scarface. It was originally shot on a 35 mm film.When you pause the movie in any one particular frame (like the one shown below), all of reality everywhere seems to be frozen in this one position. 35 mm movies have 24 frames per second which means there is no actual movement, rather it is a collection of such frozen frames played forward in time.

Simply put, both the past and the future are all coexisting within spacetime. Another alternative idea that has often been entertained is that, perhaps, spacetime is not fundamental and thus emerges from some lower structure. Of course, such an idea would have to overlook the implications of the block-universe.

Time does not flow — just as space does not flow— time simply is. Imagine traveling from Kolkata to Delhi, you do not say that Delhi doesn’t exist because you are not there yet. You know that Delhi is a location in spacetime whether you are there or not. The same idea can be applied to time where the past and future are also there whether you have access to them or not. So the future is not going to happen, it is already there.

Scientific Representation

In physics, this concept can be understood using the Minkowski spacetime diagram. Physicists employ worldlines to represent a point in space using a line in spacetime. This idea takes advantage of cones to simplify the visualization. A present event on this spacetime is shown as the base of a cone which resulted from the contraction (at the speed of light) of the radius of a circle (or sphere in a 3-D space). The entire history of this particular worldline in spacetime can be translated into an expanding and contracting cross-sectional 3-D spheres in space resulting in a 4-D light cone. These events are viewed as the intersection of light with spatial planes. The figure below shows light cones in 2-D space coupled with time.

Einstein, himself, in a letter to the family of his longtime friend Michelle Besso, expressed his doubt about the distinction between past, present, and future:

Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.

Mind you, time itself, is not what is in question here but rather the passage or flow of time. Einstein’s curiosity about simultaneity and his quest to resolve inconsistencies between Maxwell’s constancy of the speed of light and Newton’s absolute space and time, to a great extent, compelled the theory of relativity.

Einstein’s conception of the universe, however, is somewhat lacking a clear definition of duration as Julian Barbour brings up in his ‘What is Time’ interview with the prolific writer and producer Robert Lawrence Kuhn on Youtube. Einstein, however, was able to make the distinction between time used to record historical data and time used in keeping track of duration.

He even exploited and figured out exactly how the two are related to each other as Prof. Sean Carroll of Caltech alludes to in an interview with Robert Lawrence entitled, Is Time Real? The takeaway here is that, the block-universe representation, which Herman Minkowski so masterfully constructed using the framework of Relativity, renders the distinction superfluous. Namely, we do not need the flow of time to make sense of reality.

Misconceptions

One of the current subtle misconceptions is that change is a manifestation of time but if you really think about it, is it not just as logical to infer that time may be our conception of change? If this is the case, then change is a tangible occurrence of reality rather than time. But how could there be change without the passage of time, you may ask? This would be a relevant concern. We are able to recognize changes because of the information recorded in our memory about the past which give rise to the idea that time passes.

Everything we have considered up to this point has been at a Relativistic scale. What do you suppose is the nature of time when we shrink to the sub-atomic scale?

Quantum Mechanical View of Time

One can make the case that the quantization of certain aspects of the universe would imply discrete time at the quantum level. Yet not every facet of the universe is quantized as various experimental undertakings, using pulsating laser beams, have shown. Consequently, any hope of a continuous time lies either at the scale of Planck time (10^-43 seconds) or in the convergence of quantum mechanics and general relativity in a theory entitled quantum gravity.

For all we know, there could also be parallel multiverse with deterministic wave functions that can be evolved backwards and forward giving way to an arrow of time. Nonetheless, since there is no convincing way to obtain definitive proof about the existence of these multiverse, this explanation remains in the foreground.

Here is a little takeaway

Prof. Carroll makes some interesting conclusions at the end of his interview with Robert — that our most accurate model of reality namely quantum mechanics includes a notion of time so therefore it is not an illusion or a figment of our imagination. It becomes abundantly clear though that our conception of the past and future is incomplete — that is to say we do not yet have a complete understanding of time.

One of the main reasons for this incongruence between the arrow of time resulting from quantum mechanics and the lack thereof in the block-universe of relativity could very well be due to the second law of thermodynamics. The total entropy of the universe tends to increase and this disorder may be responsible for the apparent puzzling nature of time.

The laws of physics, as Prof. Carroll emphasizes, do not see the differences between the past and future. At the moment, we can embrace the fine-tuning assurance that, the configuration of this particular universe makes way for an arrow of time. It is highly probable that when we finally resolve current problems within our understanding of the universe, it is likely that time will be one of the remaining components required to understand reality.

If in any case time is done away with, we can still rejoice in knowing that our collective understanding of physics and the universe as a whole will be more refined — so in either case, humanity wins

Darker than Black

Search for the unknown

There are times when it feels like we have seen it all but then with every passing day we keep on striving to explore the infinite more and more. Starting from terraforming Mars to envisioning a Dyson Sphere for harvesting maximum energy from the sun, we humans have tried to push our boundaries to maximize our imaginations and engineering feats with every passing generation. Perhaps maybe this is what the interpretation of Darwin’s theory of Evolution has today summarized to, we as a civilization- the human kind, and its desperate endeavours to be the fittest to survive in this vastness of the cosmic ocean. Today, we have perhaps finally taken a step forward by revolutionizing the way of capturing astronomical magnificence’s on our pixelated screens. The Hubble was one of the first generation of advanced telescopes that gave us few of the most stunning images of our cosmic existence. For the first time ever, humanity had photographed these elusive cosmic beasts, shining light on an exotic space-time realm that had long been beyond our ken.

Picture by Hubble; Scientists estimate that Abell 1689 contains thousands of galaxies and holds up to 500 trillion times the Sun’s mass. All that matter warps surrounding space, distorting and magnifying light from more distant galaxies.

Among such beauties in the night sky there are several ‘dark shadows’ whose existence have baffled scientists for decades. The search for the unknown is what has driven us humans to this point of exploring an ocean of mysteries.

Image: Black holes at the center of M87 and Milkyway galaxy respectively.

It has been almost a month now since we have found answers and explanations to numerous debates and controversies, finally. A black hole at the center of a galaxy known as Messier-87(M87) was observed by a team of 200 scientists from round the globe under the collaboration known as the Event Horizon Telescope. The black hole itself is unseeable, as it’s impossible for light to escape from it; what we can see is its event horizon. The EHT was also observing a black hole located at the center of the Milky Way, Sagittarius A*, but was unable to produce an image. While Messier 87 is further away, it was easier to observe, due to its larger size.

How did we do it?

Image source: Dr. Jean Pierre Luminet’s first rendition of a black hole some 40 years ago.

Black holes and its elusive concept of existence was always very astounding for me to imagine and comprehend. Myths were justified by theories which were further characterized by experiments, but never could anyone have imagined putting forward a comprehensive image of what our mindfulness believed to be a Black Hole.

The very first indication of its existence were confirmed when stars were observed to be dancing and swirling around ‘dark shadows’ in the night sky. Astronomers have also noticed massive jets of matter emanating from the centers of galaxies like that of M82- Cigar Galaxy, sometimes larger than the galaxy itself. What caused them was the primary question that bothered them.

Image source: Picture by Hubble; Fiery plumes of glowing hydrogen erupt from the central regions of this starburst galaxy, also known as M82.

Gravitational waves detected by Lyell in 2015 were the most direct and compelling evidences of black holes today. Detecting gravitational waves is like hearing a black hole. But scientist still wanted to see it. The question now raised was how are we supposed to capture a black object against a black background?

After years of novel research, it was found that this could be only carried out by Back lighting. Now what is that you ask?

Well, matter should emit radiation in the form of heat and light energy as it heats up while circling the edge of the black hole and into the event horizon. If so, then a solution was immediately raised stating that with a big enough telescope scientists should be able to use the radiation as a backdrop to see the silhouette of the black hole itself. This was the very fist idea that gave way to later works that generated the first ever image. But we still had a problem and this time it was an engineering hurdle. Black holes are gigantic and has galactic scale impact, being millions of times larger than our own host star, and due to its distance from us, getting a clear picture would be next to impossible and in order to do so we would have needed a telescope as big as the earth. Now that is craazzyy right?

Enter the Event Horizon Telescope(EHT).

Image source: Nature; Location of the 8 observatories.

The concept was still the same but now instead of one giant telescope we decide to build 8 smaller ones and place them all around the world. The idea was to capture multiple images from different angles as the earth rotated about its axis and then construct one comprehensive picture out of them. This would nearly provide us data from all angles. The process was called Interferometry.

The amount of data collected was more than any other science experiment in history. To construct the final image datas were collected over few nights in 2017. Each night the observatories collected the same amount of data that the Large Hadron Collider does in a year. It then took almost 2 years to piece it all together

Image source: Released by EHT collaboration; Final Image of the black hole produced by the Event Horizon Telescope collaboration.

What is actually going on?

Now let’s shed some light on the image itself. Let me clear this out at first that this what we are going to to talk about is an image and not a photograph, as the image was constructed from multiple sources unlike a photograph. Wondering why is the image so fuzzy and what is that black shadow in the center after all?

Baffling as it seems but sorry to disappoint, the shadow that you see is not the complete or the entire black hole after all, and you will understand this in a short while. Why don’t you let your ship of imagination sail and visualize a non-spinning black hole to be a perfect sphere in a 3-dimensional space time fabric, we can consider the event horizon to be the perimeter with a radius known as the Schwarzschild radius, it is the absolute limit beyond which there is point of no return.

Image: A simple illustration of a non-spinning black hole

The Accretion disc, or the glowing halo in the image is nothing but swirling masses of matter, particularly gasses, circling around the hole at a distance of 3 R_a form its center. Matter orbit nearly at the speed of light thus converting it into a pool of plasma swirling around due to the strong gravitational field. While orbiting, these layers of plasma radiate heat and light energy due to the enormous amount of viscosity in between the layers. If matter crosses the 3 R_a limit, then it will directly go straight into the black hole and it is thus known as the innermost stable orbit. This limit is the minimum point of stability beyond which the gasses will no more orbit the black hole, instead it will spin right into it. Now as photon do not have any mass thus, they can take an orbit much closer to the black hole i.e. at a distance of around 1.5 R_a. This creates a sphere of photons known as the photon sphere. Theoretically, if we stand somewhere in this region, we would be able to see the back of our own head, how cool is that?

So, in reality what is that “shadow” that we see in the image? Is it the event horizon or the photon sphere or the inner most stable orbit? Answering this will be a bit complicated. You see, a black hole warps space-time, hence light rays traveling in a straight path will be curved when space-time is largely curved. Now the best way to imagine this is if we consider light rays to be travelling from the observer be parallel with the geometry of the black hole. Definitely, the rays that fall deeper or on the event horizon are lost forever but now if we keep moving away for the horizon then there will be a point nearly 2.6 R_a distance away from the center beyond which light would no longer be pulled in and will be curved enough by gravity that it will travel parallelly away from it. Now if a ray comes at a distance 2.6 R_aaway then it will just graze the photon sphere at its closest approach and then it will go off to infinity and so the resulting shadow makes it look like it is 2.6 times bigger than the actual event horizon. The shadow thus has the event horizon mapped exactly at its center and the light rays going above or below it ends up crossing the event horizon just on the backside.

Image source: Veritasium; Infinite images of the 3D Event horizon one top of another on a 2D plane.

So, in fact what we get is the entire backside of the 3D event horizon mapped onto a ring in the two dimensional plane i.e the shadow. Looking from our one point perspective we actually see the entirety of the 3D event horizon on our 2D pixelated screens which would have otherwise not have been possible. You must be thinking that there must also be a case when the light that grazes of goes around the back of the horizon and then gets absorbed in the front. Well congratulations because you are right. This maps another image of the entire horizon on top of the previous one just like an annular ring. This phenomenon repeats until we reach the edge of our shadow thus what we actually see is an infinite set of images of the black hole superimposed on the dark shadowed region in the center of our image. The first rays of light captured by our telescopes is actually light grazing of the photon sphere thus creating an underlying circular shadow of radius 2.6R_a.

Image source: Picture by Hubble; Jets of plasma shooting out from M87.

Remember that as of now we had considered a particular case of observing the black hole i.e. parallelly. In reality images can be taken from any angle and if so then we can also observe light from the accretion disc getting bent which thus creates the beautiful halo round the hole. Another major question arises is that why do we see the halo being brighter on the lower half rather than the upper one? This is simply due to a concept know as Relativistic beaming or Doppler beaming. This occurs because matter in the accretion disc is going very fast nearly to the speed of light hence if the rays are coming towards us then it is going to appear much brighter like it does in the lower half while the upper half is much dimmer as light rays move away due to the angle of view of the observer.

Image source:
*International Journal of Modern Physics D*, 28, 1950042 (2019) ;A simulated view of a black hole in front of the Large Magellanic Cloud. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud.

Why is it so important?

It primarily proved the Theory of Relativity that was laid down by Einstein almost a 100 years ago in 1915. We have already got numerous accounts that proves the theory, but we still were unsure about what actually happens under extremities. Gravity as a force is very weak and thus testing the theory under extremities anywhere in space was almost impossible. This is not the case around a Black hole though, as it holds up an extremely strong gravity regime. The relativistic bending of light known as gravitational lensing has hence proved that gravity is actually nothing but a curvature in the space-time fabric created by objects with enormous mass. Around a black hole, due to its extremely high mass to volume ratio, causes the space-time fabric to tear apart and thus arises the concept of Singularity. There are still a lot of mysteries yet to be unraveled from the image. This maybe the first ever picture taken but coded in its pixel could be the answers to questions of the whole universe. High resolution images of black holes are still a long way down the road and here are few simulations, one from Interstellar and another a simulation by Bronzwaer, Davelaar, Moscibrodzka and Falcke / Radboud University which seem to be the most accurate depictions far.

Image: Most accurate simulations of a spinning back hole.

Schrödinger and all that Jazz

Schrödinger was born in Vienna in 1887. He was an exemplary schoolboy, displaying a startling ability in all his classes. He taught himself English and French in his spare time, and nurtured a love of classical literature. By the time he enrolled at the University of Vienna in 1906 he was focused on physics, but still took the time to learn a great deal of biology, which informed his later work – contributions that were cited as inspirational by the discoverers of DNA.

The work for which he is remembered requires some context. As with all science, an individual’s contributions to physics rarely occur in a vacuum. A host of other figures had set the stage for Schrödinger’s entrance. His seminal work began with his attempts to resolve a central mystery of the nascent quantum theory and to understand it let me take you back down the lane when Physics got a new interpretation.

After the startling discovery of the electron in 1897 by J.J.Thompson a new era of thoughts behind the modeling of the atom began. A comprehensive model where the electron revolves around the nucleus seemed to have satisfied the puritanical notion at that point of time, but it was still unclear among physicists, the reason for the electrons not spiraling into the nucleus. If the electron did revolve around the nucleus in fixed paths known as orbits, then by orbiting, electron should lose energy, go lower in its orbit around the nucleus where it should revolve faster and thus emit more energy. Eventually, the electron will collapse into the nucleus. But if such phenomena happened then there would be a complete annihilation and immense amount of energy would have been emitted thus prompting in the end that no living being and so far as that is concerned, nothing would have ever appeared.

In 1900, Max Planck had discovered that the precise nature of the radiation emitted by hot objects could only be explained if the energy of the radiation came in discrete lumps that came to be known as ‘quanta’. He suggested that electromagnetic energy could only be emitted in quantized form, i.e. the energy could only be a multiple of an elementary unit i.e., E = hf, where h is Planck’s constant and f is the frequency of the radiation. The idea soon paved way for Bohr to hypothesize that negatively charged electrons revolve around a positively charged nucleus at certain fixed “quantum” distances and that each of these “spherical orbits” has a specific energy associated with it such that electron movements between orbits requires “quantum” emissions or absorption of energy. By this time, Einstein had also suggested that light can behave as a wave as well as like a particle i.e, it has dual character. Finally, enter the scene- Loius de Broglie. In 1921, he simply rearranged the already know equation between momentum and wavelength(p=h/ λ) thus giving rise to:

λ = h/mv

This raised a motion arguing that just as light which was always thought to be a wave now showed particle like behaviour then can all microscopic particles such as electrons, protons, atoms, molecules etc. also have a dual character? According to de Broglie the answer was “Yes.” He stated that any material body in motion can have wavelength but it is measurable or significant only for microscopic bodies such as electron, proton, atom or molecule.

In 1926, it was this framework that Schrödinger used to develop the ideas in his paper “Quantisation as an Eigenvalue Problem” , which contains the wave equation that bears his name. He said that if electrons really were waves then there motions should be described by wave formulae rather than Newtonian mechanics. Thus, he described a wave equation which was nothing but a mathematical distribution of a charge of an electron distributed through space, being spherically symmetric or prominent in certain directions, i.e. directed valence bonds, which give the correct values for spectral lines of the hydrogen atom. And it is to be noted that electrons won’t orbit the nucleus in the sense planet orbits around the sun, but instead exist as STANDING WAVES.

Now to understand the depth of this beautiful equation we start our journey from the fundamentals of classical mechanics where,

Total energy (E)= Kinetic Energy + Potential energy

E = ½ mv² + V(x) (i)

As p=mv therefore, E = p²/2m + V(x) (ii)

Considering a standing wave given by the function:

Ψ(x,t) = A e ^ikx= A[cos(kx) + isin (kx)]

Hence the function for a travelling wave can be written as:

Ψ(x,t) = A e ^i(kx−ωt)

Here the term ωt gives us the velocity of the travelling wave. We can also say that the wave number(k) is a function of the wavelength as well as momentum, k=2π/λ= p/ ħ. Now differentiating the wavefunction with respect to time we get,

∂Ψ /∂t =−i ω Ψ (keeping x constant)

And, double differentiating the wavefunction with respect to x we get,

∂²Ψ /∂x²= −k²Ψ (keeping time constant)

As already described earlier, k=p/ ħ

Hence, – ħ² (∂²Ψ /∂x²) = p² Ψ

We now generalize this to the situation in which there is both a kinetic energy and a potential energy present, then according to equation (ii) we get,

EΨ = (p²/2m)Ψ + V(x) Ψ

Replacing p² Ψ by – ħ² (∂²Ψ /∂x²), we obtain:

Eqn (a)

Now this is the time independent Schrodinger equation.

We can also write that: E= ħ ω

hence, i ħ (∂Ψ /∂t) = ħ ωψ = EΨ (iv)

Therefore, from equation (ii) and (iii) we get,

i ħ (∂ψ /∂t) = (−ħ²/ 2m) (∂²ψ /∂x²) +V(x)Ψ

This is the final Schrodinger time dependent equation. Now to understand the equation in more details we carry out the energy state analysis of the equation for a hydrogen atom.

Each of these three rows is a wave function which satisfies the time-dependent Schrödinger equation for a harmonic oscillator. Left: The real part (blue) and imaginary part (red) of the wave function. Right: The probability distribution of finding the particle with this wave function at a given position. The top two rows are examples of **stationary states**, which correspond to standing waves. The bottom row is an example of a state which is *not* a stationary state. The right column illustrates why stationary states are called “stationary”.

Keeping in mind three fundamentals we can easily go around solving the equation, the three condition being,

Total energy (E)= Kinetic Energy + Potential energy.
The net centripetal force experience by the electron is balanced out by the columb force that helps keep the electron in the orbit around the nucleus.
Finally, the angular momentum of the electrons are quantized.

In equation (i) the potential energy term are in polar coordinates,

V(x)= – Ze²/4πr

the rest of the equation not being in polar coordinates thus needs to be converted. After converting and considering eqn(a) along with all the above mentioned conditions, we frame from equation that,

Energy(E)= – [e⁴m/8ε₀²r] (Z²/n²)

Therefore, E= – R (Z²/n²) (v)

Where R= [e⁴m/8ε₀²r] =13.6 eV is know as the Rydberg constant and as we are considering a Hydrogen atom hence Z=1 and n=1,2,3…

So, from equation (v) it is clear that,

E= – (13.6 * 1/n²) eV

Therefore, we observe that the energy states allowed for each electron is constrained by this equation. Energy levels are governed by the integer values of n. Thus, we can only have few specific values of energy depending on the values of the quantum number(n). We also see that the energy levels are inversely proportional to the quantum numbers thus as we go further away from the nucleus the energy levels decreases.

Quantum mechanically electrons are thus considered as waves which are satisfied by the Schrodinger’s equation. Schrodinger latter also introduced the Hamiltonian operator to represent the total energy of the system

Ĥ= – ħ² (∂²Ψ /∂x²)

thus, turning the equation in to,

The time-independent equation can be solved analytically for a number of simple systems. The time-dependent equation is of the first order in time but of the second order with respect to the co-ordinates, therefore it is not consistent with relativity. The solutions for bound systems will give three quantum numbers, corresponding to three co-ordinates, and an approximate relativistic correction can be done by including fourth spin quantum number.

Hence this is how a person who once commented on Quantum mechanics stating, “do not like it, and I am sorry I ever had anything to do with it” framed the Jazziest equation of all time!

Is everything quantum entangled?

If the Big Bang is the creation of everything – time included, and this came from a single “source”, would it not follow that all particles in the universe are entangled with each other? And perhaps, we cannot observe this entanglement because we are “inside the system”. Are we not all connected? Questions like these have haunted physicist for almost a century now, but the answer to this was always pretty clear. To understand the depth of this question first we need to understand the concept of quantum entanglement that had bothered scientists like Neils Bohr and Albert Einstein for the entirety of their careers. Einstein was so concerned by the idea that he once famously described entanglement to be a “spooky action at a distance”.

By definition Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole. In simpler words an entangled state is a state that is not fully separable, i.e. one that is not probability mixture of product states. This is just the quantum version of the notion of “independent random variables” in more ordinary probability theory.

For any compound system, almost all states are entangled, as the non-entangled ones vanish (measure zero). For example, any time you measure a particle with apparatus, after the measurement the apparatus indicates something about the measured system. Thus, the joint state of the compound “apparatus + particle” system is not separable because its parts are not independent of one another. Measurement produces a particular case of entanglement between the measuring and the measured.

As a macroscopic system interacts with its environment, information about it diffuses into the environment, producing entanglement between parts of the system and parts of its environment. Overall, this leakage of information is responsible for quantum decoherence and the second law of thermodynamics. But its chaotic nature means that for all practical purposes, that information is lost, and we can think of entropy increase as ‘missing information’.

However, if we just pick particles at random, chances that we can treat them as essentially independent—unentangled is overwhelming. Intuitively, one can think information about something becoming so mixed up in its environment at large that any particular microscopic parts of it and its environment are going to tell us next to nothing about each other. In other words, they’d be almost entirely independent from each other–unentangled.

By far the most particles in the visible universe aren’t quantum entangled. That’s obvious from observation, since if all electron spins would be entangled, all electrons would flip their spin at the same time, and we couldn’t observe varying statistics of electron spins in a sample, resulting in varying degrees of magnetism after the application of a gradually changing exterior magnetic fields. Also, all (bosonic) atoms of spin 0 would form a Bose-Einstein condensate not just near absolute zero, since they would be in the same quantum state, hence in the lowest.

If we try to consider some hypothetical state of all particles, that state is almost certainly entangled. However, that does not mean that we can’t (say) treat two particles at random as very probably independent of each other–effectively unentangled.

The “single source” isn’t a single quantum state. In the early phase of the big bang temperatures were very high, allowing for a huge amount of possible quantum states within a small volume. Without warranty we may think of the initial state of the universe as a superposition of all possible quantum states, the wave functions of which collapse relative to an observer, regarding the observer as a particular quantum state.

That way we get to the many world interpretation of quantum theory and a universal wave function. Hartle-Hawking state as a pre-Planck epoch of the universe can also be considered here.