Space diaries

CHAPTER 8 : Time: Reality We Live or Illusion We Believe?

What exactly is time? Is it just an imaginary thing or does it exists in real life? Is time just an imaginary part of the complex equation? We must have heard this thing that time is delusional maybe in you tube videos and some ancient scriptures. But it is just the conclusion made like the water surface but unexplored deep inside as light rays can't reach so deep. The light rays is just like a human way of thinking which is incapable to go beyond some depth of questioning ourselves. This chapter will not be philosophical, we will be going to discuss how the most accurate time is measured.

The atomic clock is the most accurate measurement of time in the modern times. As mentioned in the previous chapter that the protons and neutrons also contains the magnetic field but it is very small as compared to that in electrons, so in the SG apparatus that interaction between of the nucleus spin (proton + neutron spin) with the electron spin is ignored. For measuring time with atomic clock, this interaction between nucleus spin and electron spin is used. So like the silver atom was used in the SG experiment for the reasons mentioned in the previous chapter, for measuring time with atomic clock, we will use cesium - 133 atom. Again the question arises why choose only cesium-133 atom?

Cesium atom is the only atom in the universe explored till now which has only one naturally occurring isotope: Cs-133. It basically means that every cesium atom in the universe is identical in nuclear structure avoiding any confusion from multiple isotopes. This ensures consistency and universality for time measurement. What exactly is this number 133 and how does it came? The cesium atom contains: 55 protons, 78 neutrons so its total nuclear mass is 133 units ( in atomic mass units) and 133 - 78 = 55 electrons.

As discussed and proved in previous chapter, spin is the quantized state. Like silver atom in SG experiment has spin quantum number as S= +1/2 and/or -1/2, the cesium atom also has the same spin quantum number. It has nucleus spin of I = 7/2. The electron spin value came from the SG experiment and the value of nucleus spin came from other experiments of Hyperfine spectroscopy, Nuclear Magnetic Resonance (NMR). The NMR experiment will be explained in the other chapter. The hyperfine splitting (which will be explained in this chapter) is responsible for atomic clock measurement and the value of I. What is hyperfine splitting?

As there is interaction between the nucleus spin and electron spin due to magnetic interaction. There is always alignment and anti-alignment between the nucleus and electron spin. Depending on whether they are pointing mostly in the same (aligned) direction or the opposite (anti-aligned) direction, the total energy of the atom changes slightly. This small difference between the two arrangements is called hyperfine-splitting. So, in cesium-133 this hyperfine splitting creates two possible energy states in the ground level: one with total spin F=3 (anti-aligned) and one with total spin F=4 (aligned). The gap or jumping between them corresponds to the clock frequency. What exactly is this Energy and what exactly is F here and how did these values came?

F refers to the total angular momentum quantum number of the atom in its ground state (electron + orbital + nucleus). The values came from:
F = I+J & .... a)
J = L+S .... b)
here J = total angular momentum only due to electrons and orbit
L = orbital angular momentum
In the equation b) substitute L=0, as the only one valence electron present in cesium is in s orbital and also substitute S = + 1/2 and/or -1/2 in equation b and the result will be J = +1/2 and/or -1/2. Accordingly, F=3 and 4 came by taking J as -1/2 and +1/2 respectively and taking I = 7/2 in the equation a). To calculate the energy for F=4 and F=3, we use the following formula:

i) Energy convention

$E_{F} = \frac{A}{2} [F (F + 1) - I (I + 1) - J (J + 1)] .... c)$

$A$ has units of energy.
$A$ is called the magnetic dipole hyperfine structure constant.
It tells us how strongly the magnetic field from the nucleus interacts with the magnetic field from the electron’s spin and orbital motion.

ii) Frequency convention

$\nu_F = \frac{A_\nu}{2} \, \big[ F(F+1) - I(I+1) - J(J+1) \big]$

$A_\nu$ has units of Hz.
Relation to energy:
$E_{F} = h ν_{F}$

Cesium-133 hyperfine splitting

For the cesium-133 ground state, the measured splitting frequency difference between $F = 4 and F=3 is:$

$Δ ν = 9,192,631,770 Hz$

For an $S_{1/2}$ state (with $J=\tfrac{1}{2}$ and $I=\tfrac{7}{2}$ ), the two hyperfine levels are separated by:

$\Delta \nu = 4 A_\nu \quad \Rightarrow \quad A_\nu = \frac{\Delta \nu}{4}$

The exact value of $\Delta \nu$ is measured experimentally (using the Cesium Atomic Beam Clock or the Cesium Atomic Fountain Clock) which will be discussed in the later chapter.
After substituting the value of $\Delta \nu$ , we can determine $A_\nu$ , and from there calculate $\nu_F$

If you want $A$ in energy units:

$A = h A_{ν}$

and then you can compute $E_F$

Symbols

$E_F$ : energy of a given hyperfine level.
$\nu_F$ : frequency equivalent of that energy level (via $E_F = h \nu_F$ ).
$\nu$ : general frequency symbol, e.g. transition frequency or splitting.
$\Delta \nu$ : difference in frequency between two levels.

So, from equation c), it will be concluded that when the electron's spin and nucleus spin direction is same (aligned), the atom is in higher-energy state and when they point in the opposite direction (anti-aligned), the atom is in lower-energy state. Microwaves at exactly right frequency (9,192,631,770 Hz) can flip the system back and forth between these two states. So the frequency here basically is the number of flips done by atoms between these two alignments in one second i.e. 9,192,631,770 flips happens in one second. When microwaves of this frequency hit cesium atoms, the atoms switch (flips) back and forth between the two alignments.

So, from the above experiment it proves that time is just calculated based on the natural behavior of atoms. Here, is the question for the readers, as every object is made up of atoms, so what happens at the quantum level to the atom's flipping behavior when any object's life span expires?( for e.g, when human dies). Share the answer if you have, through my social media links, comments.

CHAPTER 7: The Revolutionary Stern-Gerlach Experiment

In Stern-Gerlach Experiment (we will call it SG experiment), Silver (Ag) atoms are heated in an oven. The oven contains small holes through which some of the silver atoms will escape. The fig 7.1 contains the visual representation of the SG experiment as follows:

Fig 7.1 The SG experiment

There must be questions raised why choose Silver atom not any other? But first before getting answer to that question one should know what exactly is spin. Spin in quantum mechanics is not something we physically describe things. Spin is just the two state of any electron which is in its purest state. Purest state means here that the probability of electron to be in a specific position is 100%. The atom can be influenced by various experiments to be in its purest state. The SG experiment is one of the experiment in understanding electron's spin behavior. Spin has two states as +1/2 and -1/2 regarded as up and down positions respectively. Spin states are not fixed meaning it is not already in either of the two positions but they just move to one of the states quickly after we start observing one of the electron spins. Its called quantum entanglement in which one state influences other very quickly. This superposition of electrons and quantum entanglement idea is used in supercomputer for sharing qubits (0 or 1) information very quickly through various algorithms. The spin in an atom is from its nucleus which is a sum of spins from protons and nucleus. The other spin is from electrons. This spin creates a tiny magnetic field and magnetic moment which is going to be very important in the SG experiment.

So, coming back to the first question raised of choosing silver atom. The silver atom is made up of nucleus and total 47 electrons where 46 out of 47 electrons can be visualized as forming a spherically symmetrical electron cloud as shown in the fig 7.1. According to Pauli's exclusion principle, in one orbital, two electrons cannot exist with same spin state. According to Pauli's exclusion principle and the following filling of orbital configuration of electrons in silver atom: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s¹ 4d¹⁰, here we see that the 5s orbital has one unpaired electron which is responsible for only spin-intrinsic angular momentum and not the orbital angular momentum because its zero for s-orbitals. The single 47th electron mass which is attached to the nucleus is very very small (~2*10^5) times smaller than the nucleus mass. So, according to the relation: μ (magnetic moment) ∝ (q/m)×(angular momentum), the magnetic moment is very very small from nucleus and the almost all the magnetic moment is just from the 47th single electron. There will not be any other external disturbance to influence the electron from not going to its spin states which is also called as quantized state because it is fixed and so μ (magnetic moment of the atom) ∝ S (electron spin). The effect of nucleus spin in electron spin is used in atomic clock. Here, in this experiment we just ignored the effect of nucleus spin. So, overall this is the reason for choosing silver atom here in the experiment.

The z component of force experienced by the atom is : Fz=∂(μ⋅B)/ ∂z = μz ∂Bz/∂z. In fig 7.1, μz > 0 ( Sz < 0) then atom experiences upward force, while μz < 0 ( Sz > 0) atom experiences downward force. The electrons negative changes sign inverses the direction and signs of μz and Sz. The beam is expected to split according to the values of μz. The SG experiment measures the z component of μ or z component of S up to a proportionality factor.

The atoms in the oven are randomly oriented; there is no preferred direction for the orientation of μ. If the electrons were like a classical spinning object, we would expect all values of μz to be realized between | μ | and | -μ |. This would lead us to expect a continuous bundle of beams coming out of the SG experiment as in fig 7.1 to be spread more or less evenly over the expected range. In the SG experiment, the electrons are passed through the inhomogeneous magnetic field which is essential for getting the observational result of spin. If we use homogeneous magnetic field then the electrons would just rotate and there will be no net force on electron spin due to homogeneous magnetic field and we will not be able to see the deflection in upward and downward direction of electrons due to spin. The inhomogeneous creates a varying strength magnetic field which forces the electrons to go into upward and downward direction according to its spin. The inhomogeneous magnetic field creates this net force on the electron which is essential because it converts the abstract quantum property (spin) into a spatial separation of the atom beam, which can be observed directly on the screen.

But the actual experiment showed that there are only 2 spots observed corresponding to one "up" and one "down" orientation. The SG apparatus splits the original silver beam from the oven into 2 distinct components (space quantized). The values of Sz are: Sz=±ℏ/2 where ℏ is Planck's constant = 1.0546 * 10^-27 erg-s = 6.5822 * 10^-16 eV-s.

In this experiment, we just setup one single SG apparatus which just quantizes the spin in only one specific direction ( z direction). In the next chapter, we are going to see what happens if the spin is quantized in multiple directions ( x, y, z) by setting multiple SG apparatus in parallel in multiple directions and what will be the classical expectation and experimental observation from this experiment.

CHAPTER 6: THE BELL'S INEQUALITY

As we know this year's nobel prize for physics was shared by three scientists for disproving Einstein's theory of relativity that the speed of light is the fastest in space and nothing can travel faster than light. How did they proved it practically? What mathematics did they used ?

This started in the year 1935 when the three physicists: Boris Podolsky, Nathan Rosen and Albert Einstein gave one Paradox named EPR Paradox. This paradox states that there exists some hidden variable which is responsible for the changing states between two quantum particles which are seperated at very large distance. In other words for e.g. take two balls one of black color and other of red color put them in two identical boxes and you don't know which color ball is in which box. Take away one box to another planet and keep one box to yourself and open the box as soon as you observe the color of one ball you will immediately come to know the color of the ball in another box. Here exists a local hidden variable which is the box through which we came to know the information of the balls and obviously there is no travelling of information. Also, there is a difference between local hidden variable and hidden variable, we will come across this difference later. Also, we can take another example of twins who look exactly same. They look identical. The local hidden variable here is genes which make them different. As soon as we detect genes we will come to know the names of the two twins. These examples was according to EPR Paradox in which everything is already fixed in nature and we can't change it. Einstein gave this thought experiment a paradox because in quantum mechanics information travels at a speed greater than speed of light which is not possible.

But things don't work like this in quantum mechanics. Any hidden variables doesn't exist in quantum theory. In the above the color of the box is fixed i.e. it does not change inside the box. But in quantum theory the quantum particles exists in two states in both the boxes at the same time. As soon as we observe the spin of one of the particle, the opposite spin will appear on the other particle. Initially, both the particles exists in superposition state, and after observing it one of the state appears. Einstein did not agreed with the quantum theory at all. This was like playing a dice in which we don't know which number will appear until the dice movement stops and we observe that number.

Quantum theory more clearly can be proved by the double-slit experiment. In this experiment one one can take a long rectangular shape cardboard paper, make two slits in it horizonal direction. Place one screen behind the cardboard to detect the electron particles emitted by the laser. There is no fix path of the particles some electrons will travel through slit (S1) other will go through slit (S2). The pattern of the particles will be random on the screen. But here happens one weird thing. As soon as we keep the camera or try to observe, we will see the wave pattern on the screen. This is only possible when one particle travels through both the slits at the same time! This experiment proved that electron exists both in waveform and in particle form.

There were two groups of scientists one who believed quantum theory and who supported Einstein. Then, in 1965 one scientist named John Steward Bell gave mathematical expressions related to the hidden variable which is known as the bell's inequality. The derivation of the bell's inequality is shown in the image inserted below:

In equation 3 the multiplication |ai bi| is always +1 because as mentioned in the image the value of ai and bi is either +1 or -1 and the absolute value of the multiplication is always +1. Also the modulus is removed in the right side of equation 3 because if we take the modulus the value of the equation on the right side will always be zero. Equation 4 is the bells inequality which is correct in terms of algebra. And this inequality is for the case in which the hidden variable exists because in this case we gave each fixed values (+1 or -1) at one time due to which the above equation holds good. But in quantum theory one list can have 1 and -1 at the same time due to which the left hand side equation will be greater than the right hand side. For e.g. if we take the value of b and c +1 in the right hand side and on the left side if we take b=+1 and c=-1 then right hand side will be smaller than left hand side.

Later on three scientists disproved the bell's inequality as mentioned above. They experimentally disproved the inequality and made a ground breaking research in quantum physics due to which they received the nobel prize in physics. The theoretical and mathematical explanation of their experimental result will be given the next chapter.

CHAPTER 5: RELATION BETWEEN GENERAL RELATIVISTIC GRAVITY AND QUANTUM GRAVITY

As mentioned in the last chapter, we learned a brief description about gravity in quantum level. In this chapter, we are going to see about the description of gravity given by Einstein and its relation with the quantum gravity.

Einstein mentioned gravity in such a way in his research paper in such a way that its effect on quantum level will be very much small(negligible) which follows the description of gravity in quantum level. The general relativistic gravity can be exemplified as follows: If we keep a football in the center of a paper and a tennis ball on the side the paper, it will be attracted strongly by the basketball, but on the other side if we keep the feather of a pigeon on the other side it will not be attracted much strongly towards the ball. The same effect is applied in reality. The quantum particles do not experience much gravity because of their very small size. But, is gravity depends only on mass and size?

The effect of gravity not only depends on the size and mass of particles, but also on the shape and curvature of the particles. To understand this, let's see an example: Take two papers which are not in contact with each other. In first paper keep the football and see the curvature of the paper on beneath the football. In other paper, keep one golf ball and note down its curvature on the paper beneath the ball. What will be noticed by these experiment? The curvature of the paper as seen in the case of football will be u shaped. And same in the second case. But the major difference in the two cases is the depth of u shape. In second case the depth of u shape is higher than that in the first case, i.e. in the first case the it will not be a perfect u shape, but in the second case the shape of the golf ball will be a perfect u. By these experiment it will be concluded that due to the perfect shape of u the gravitational effect shown by golf ball will be slightly greater than football.

The football mentioned above is like a black hole, Its not like that the gravity is weaker, the gravitational effect of a black hole is very much stronger, but not much that the light cannot escape it. Because if this happens, then the rest part will be science fiction as mentioned in the movie interstellar. The person who falls inside the black hole will experience things faster than any other object in the universe, because indirectly the person is travelling at a speed greater than light which violates all practical rules and laws of physics. But the universe is very much big beyond our imagination. Is it possible that the universe works exactly like our physics?

Here comes quantum mechanics which violates all the laws of physics. Any object in the universe can't travel at a speed of light. But this is not the case in quantum level. In quantum level there is an effect known as butterfly effect. According to this effect if we doing any basic action on the earth in one place, its effect will be sent to the universe greater than speed of light and will be reflected back towards us. This is what we call 'karma'. Are there any other any particles which carry photons with such a high speed? The answer is both yes and no. In practical world, the photon particles are massless and due to this the photon particles are not effected by any force in the universe because every object has mass. But in quantum world every object is connected with each other. In quantum level, photon particles are carried by some other particles or wave which give the photons the speed of light. Its like the air and the leaf on the ground. The air is the carrying wave or particle and the leaf is like a photon. The leaf travels as the air travels. And also air is everywhere in the earth which carry many objects like leaf. It is obvious that air travels at a speed greater than leaf. Same is the case with the carrier particles or wave of photons.

And also because of this, we can see the two nature of electrons in double slit experiment. We can say that the butterfly effect is produced by our eyes(like the air to leaf) to the electrons due to which it changes its form when we detect it with eyes and when we not. And so, the black hole can't violate the laws of physics as physics laws can only be violated in quantum level and not in the physical world. Because of the negligible effect of quantum gravity, the strings of quantum gravity can travel to other smaller dimensions and may be the quantum gravity is the unified force (origin force), and therefore we can't detect its effect on minute particles but according to relativity if our size reduces like photons then we can detect the effect of quantum gravity and therefore relatively quantum gravity may be the butterfly effect or 'karma'.

CHAPTER 4: UNDERSTANDING GRAVITY

What is gravity?

Do we really know what is gravity and how it practically works?

Do we understand the origin of gravity?

What are the force carrier particles of gravity?

How gravity really works in black hole?

Is Einstein's description of theory in general theory of relativity true?

These are some questions about gravity which we are going to discuss in this chapter.

To understand gravity we must understand the origin of all other three forces (i.e strong nuclear force, weak nuclear force, electromagnetic force) and how matters are produced in quantum level and how these forces work in quantum level.

Every particles in this universe are divided into two categories: 1.Fermions 2.Bosons

Fermions are responsible for the formation of every matter in this universe. Fermions also contain two types of particles 1.Quarks 2.Leptons Quarks are of six types 1.up (u) 2.down (d) 3.charm(c) 4.strange(s) 5.top(t) 6.bottom(b) Quarks are very unstable particles due to which they come together to form new particles which are known as hadrons. Hadrons are also divided into two types 1.Baryons 2.Mesons Baryons are formed by the combination of three quarks. Protons and neutrons are formed by the combination of two quarks(i.e. up and down). Protons are formed by the combination of two up and one down quarks whereas neutrons are formed by the combination of two down and one up quarks. Mesons are formed by the combination of one Quark and one Anti-Quark (kaon, pion, etc.). The combination of other four types of quarks gives rise to other different types of particles. Leptons are not formed by the quarks because they are stable particles. Leptons are also of six types: 1.electron neutrino(ve) 2.electron(e-) 3.muon neutrino(vu) 4.muon(u) 5.tau neutrino(vt) 6.tau(T). In the above classification of both quarks and Leptons numbers: 1&2-Family I, 3&4-Family II, 5&6-Family III. Like electrons, leptons also have anti particles. Here, fermions do not contribute to the working, construction and formation of forces.

Boson particles are responsible for the formation of some forces. Bosons are of four types 1.Photons 2.W/Z Boson 3.Gluons 4.Gravitons* The formation of electromagnetic force is due to photon particles. Electromagnetic force can't be generated without photons. The W/Z Boson particles are responsible for the formation of Weak nuclear force. Due to weak nuclear force, beta decay occurs and anti-neutrino is formed. This force converts protons into neutrons by releasing some amount of radiation. Gluon particles are responsible for the formation of strong nuclear force. This type of force is very much strong approximately 1000 times stronger than 2nd strongest force(i.e. weak nuclear force). This force is so much strong that this force can hold protons which are positively charged and neutrons which are neutral together in one nucleus.

Besides all this, the particle which is responsible for gravitational force is not discovered. We gave one hypothetical name for this particle (i.e. gravitons). In so called black hole formation we assumed that the range of gravitational force is infinite which is not possible because for this to happen the mass of that object should be zero which is again one impossible loop. This force is the weakest of all forces. This force is 1 trillion times weaker than weak nuclear force. The reason for so much amount of weakness can be explained with the help of string theory. According to string theory, quarks and electrons are attached to only one dimension because which the quarks and electrons strings cannot move in other dimensions and hence we can detect them. Gravitons are closed strings and they are not attached to any membrane due to which they keep on travelling from one dimension to another dimension. Due to this we can't easily detect them. But in Large Hadron Collider if we create enormous amount of energy at that point of second when the graviton strings are in our dimension we could know some practical properties of gravitational force.

By studying force from Big-Bang till now we came to know the combination different forces. When the Big-Bang occured all the forces were unified. Because the origin of gravitational force is not discovered we assume that after big-bang gravitational force was divided and after that strong nuclear force got divided. After that electroweak force was the 3rd existing force & and after certain time we discovered that the electroweak force gave birth to electromagnetic force and weak nuclear force.

How Einstein's gravitational force description can be related to the above formation of force and black hole will be explained in the next chapter...

CHAPTER 3: GENERAL RELATIVISTIC IN BLACK HOLE

The Black holes solutions are made by some huge non-physical assumptions. According to 2nd law of thermodynamics if a body is contracting some radiations have to pass through it for contracting. It not only has a contraction but also it has some resistance like viscosity, heat radiation, heat flow, etc . Stephen hawking, Roger Penrose gave solutions by assuming that the black holes only have gravitational collapse. And from that they assumed that there is a trapped surface around the black hole from which nothing can escape. For a rotating black hole the photon sphere gets converted into a ring. The image of a so called blackhole can be the shadow of any object ( for e.g. if we keep the tennis ball or any spherical object in front of sun's rays the shadow is created).

In Einstein's special theory of relativity as shown in the image (ve=v) if we put the value of v>c then mathematically the time(t^1) can't exist because there will be negative in the square root which diverges us to imaginary axis. And if we put v=c then the t^1 becomes infinite. As mentioned in the previous chapter time and space interchange their values and signs. If we take the x,y,z coordinates in a straight line in pythagoras theorem as shown in the image and if some object is travelling faster than light then that object can see the things earlier than other person and also time will be slow for that person and he can see future and in a sense the decrement in speed of time will be proportional to the future time (i.e. for example he can go 1hr in future for some small increase in v, 2 hrs for big increase and so on...). In the image ds is the space-time curvature. This is a science fiction and in that there comes many paradoxes which can't be solved.

However in quantum mechanics if we assume that value of h/4pie equal to 1 then we all can see that all effects of quantum mechanics. But the value of h/4pie is very much small approximately 10^-34 something. Therefore we can't see that things happening with our naked eyes. We can just calculate the probability of that position of that electron. For understanding the accurate position of that electron we must know the waves that are emitted by the person ( i.e. think that a person is walking in a path, we can't assume its exact path the maximum thing that we can do is calculate the probability, but that person knows where he is going. The waves are created after every millisecond in our body and environment and according to that waves it commands to our brain and we follow that exact path and that waves are also emitted in the surrounding from which the electron chooses its path and according to that waves that physical object works, but the biggest and most important difference is that we can the things that we can see and that object also works with our calculation but the electrons don't because the commander for that electrons are the waves that are generated by any object in the universe). But we can't calculate the waves that are generated by every object in the universe, so therefore if we detect the waves that are generated in a bounded we can predict the path more accurately than today's

technique, because today we calculate the probability by just using wavefunction. And therefore in quantum level all the laws get violated but not in the real world that we see like the so called blackholes.

Stephen hawking also gave theory of hawking radiation to strengthen the paradigm of black hole. And the theory got accepted because the radiation is due to relativistic quantum effects which is true for every object because every object emits radiation in quantum level. Highlight the point that the laws are only violated in quantum level and not in the real world ( reason mentioned above).

CHAPTER 2: HYPOTHETICAL BEHAVIOUR OF BLACKHOLE

Stars usually have two forces due to which they contract and expand. There are some limitations of expansion and contraction, meaning after a certain mass they cannot expand. Because after a certain mass the force of contraction becomes much larger than expansion. The force of contraction is due to gravity and the force of expansion is due to radiation pressure.

If the mass of a neutron star is more than 3 solar masses then gravitational force wins over repulsion due to radiation pressure . And also any star's radius in space cannot be smaller than Schwarzschild radius. The formula for Schwarzschild radius is 2GM/c^2 in which M is the mass of the object and c is speed of light in vacuum. It has a certain limit of expansion and contraction. The density of neutron star is very much higher than the Sun, approximately 100 trillion times more than the Sun. Therefore Schwarzschild radius for a neutron star is much higher than the Sun.

Gravitational shift of an object are the waves that are emitted by an object as it moves away from gravitational field. As it moves away, the color appears reddish and at only a few distance from which it stars moving away it appears blue. As it moves away the frequency of the wave decreases and the wavelength increases. And as the object is moving away, photon starts losing its energy due to which the reddish color appears. The value of gravitational shift is much smaller. For the Sun whose Schwarzschild Radius is approximately 3 km, the gravitational redshift is only about one millionth.

If the photon particles are emitting from a spherical star of Radius R1 and it reaches at some receiver (assume on the Earth) and the Radius at which the radiation is approaching is R2 and the escape velocity of that object is same as that of Earth. And the emitting wavelength is (lambda)1 and receiving wavelength is (lambda)2 and the gravitational redshift is z, then z is defined by change in wavelength/ initial wavelength. Assume the Schwarzschild radius to be RS. The Schwarzschild radius of black hole is 2M (by setting G=c=1). They came to be known as Schwarzschild black hole, derivation is written in image:

Factor for the time part A=(1-2M/R1) and for radial part B = -(1-2M/R1)^-1. Therefore at R1=2M time becomes 0 and radial distance becomes -infinity and for R1<2M the signatures are changed and inside the blackhole time becomes space and space becomes time. At the event horizon z=infinity and in this case light cannot escape from event horizon and it should appear black. For a black hole mimicker, R1=2M(1+e),z=1/e^1/2 which is a huge value of z but not infinite and for black hole, e=0 which is not possible. This proves that light can escape from a blackhole mimicker it just bends due to intense gravity which is valid in mathematics and also follows Einstein's theory of relativity. The event horizon is assumed to be the origin and therefore R1=0 (at event horizon). This point has infinite density and pressure and it is a gravitational singularity where space-time curvature is infinite. Therefore the blackhole paradigm doesn't follow Einstein's theory of relativity.

CHAPTER ONE: AN INTRODUCTION TO BLACK HOLE

When the image of first black hole was released (i.e. on April 10,2019) I was bit confused that how one could capture the image of that thing from which light cannot escape.

Therefore, to study about it in deep I purchased a book named, "A brief history of time" by Stephen Hawking.

In social media, everywhere there was only the same paradigm about black hole. Nobody discussed about the possibilities of the image. But I wanted to know the reality behind that image, so I decided to pursue knowledge about evolution of stars, thermodynamics, what actually is gravity and how it works through both in mathematical way and in practical way. But for that I needed good sources to study about that and then suddenly I remembered one thing... When I was in 10th grade in 2018 there was one chapter in my textbook of Stephen Hawking. That chapter became my turning point because from that day I came to know about new things that I didn't knew earlier. Therefore, after I remembering this I purchased that book which didn't matched much with my theories. According to Einstein's theory of relativity photon particles can't be blocked by any means and if an object can block, then how one can capture the image of that thing. This thing made me astonished and initiated me to study more about such mysterious object.