Academia Arena

NIELS BOHR (1885 — 1962)

Everything we call real is made of things that cannot be regarded as real.

If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.

Considering the particle nature of the electron the force which moves the electron mass m in a circular orbit around the nucleus is given by the equation: F = mv²/r, where v = orbital velocity of the electron and r = radius of the circular orbit.

Considering the wave nature of the electron the force which moves the electron wave in a circular orbit around the nucleus is given by the equation: F = hυ/λ, where h = Planck’s constant, υ and λ are the wavelength and frequency of the wave associated electron.

Considering the wave-particle duality of the electron:

mv² / r = hυ/λ

Since:

mv = p and h / λ = p (where p = momentum of the electron). Therefore:

v / r = υ

But v/r = ω (the angular velocity of the electron). Therefore:

ω = υ

But according to existing literature (which states that: in the case of circular motion, the angular velocity of the electron is same as its angular frequency), the angular velocity of the electron moving in circular orbit ω is = 2πυ.

Hence

ω is ≠ υ

Because ω is ≠ υ:

mv² / r is ≠ hυ/λ

Since the angular frequency of the electron is: ω = 2πυ. Therefore:

mv² / r must be equal to 2π hυ/λ

Which means: the force which moves the electron mass in a circular orbit around the nucleus is always > than the force which moves the electron wave in a circular orbit around the nucleus.

Does our universe exist inside a black hole of another universe? The question lingers, unanswered until now. Even though the existence of alternative histories with black holes, suggests this might be possible i.e., our universe lies inside a black hole of another universe, we cannot prove or disprove this conjecture any way. Meaning that the event horizon of a black hole is boundary at which nothing inside can escape and then how might one can cross its event boundary and testify whether or not our universe exist inside a black hole of another universe. Thus we cannot answer the central question in cosmology: Does our universe exist inside a black hole of another universe? However, the fact that we are simply an advanced breed of talking monkeys surviving on a sumptuous planet, have been reckoning at least from last hundred years − turning unproved belief into unswerving existence through the power of perception and spending our brief time in the sun working at understanding the deepest mysteries of nature by doing repeated calculations and getting some answer that seem very likely makes us feel something very special-- a bit premature to buy tickets to the nearest galaxy to visit the next goldilocks planet or hunt dinosaurs.

The physicist has been spending a month, as he or she does each year, sequestered with colleagues, such as fellow theoretical physicists, to discuss many great mysteries of the cosmos. But despite its simple approximation as a force, and its beautifully subtle description as a property of space-time which in turn can be summarized by Einstein's famous equation, which essentially states:

Matter-energy → curvature of space-time

, we’ve come to realize over the past century that we still don’t know what gravity actually is. It has been a closed book ever since the grand evolution of human understanding and all physicists hang this book up on their wall and distress about it. Unhesitatingly you would yearn to know where this book comes from: is it related to metaphysical science or perhaps to the greatest blast puzzles of physics still to be discovered, like cosmic string and magnetic monopoles? Nobody knows and for the moment, nature has not said yes in any sense. It’s one of the 10,000 bits puzzling cosmic story with a cracking title. You might say the laws of physics designed that book, and we don’t know how they designed that book. The elevated design of this book, an extract of which appears in the cosmic art gallery, sets out to the belief that it must have designed as it could not have created out of chaos. In some sense, the origin of the cosmic problem today remains what it was in the time of Newton (who not only put forward a theory of how bodies move in space and time, but he also developed the complicated mathematics needed to analyze those motions) – one of the greatest challenges of 21^st Century science certainly keep many an aficionado going. Yet, we toasting each other with champagne glasses in laboratories around the world-- have made a bold but brilliant move. In less than a hundred years, we have found a new way to wonder what gravity is. The usual approach of science of constructing a set of rules and equations cannot answer the question of why if you could turn off gravity, space and time would also vanish. In short, we don’t have an answer; we now have a whisper of the grandeur of the problem. We don’t know exactly how it is intimately related to space and time. It’s a mystery that we’re going to chip at from quantum theory (the theory developed from Planck’s quantum principle and Heisenberg’s uncertainty principle which deals with phenomena on extremely small scales, such as a millionth of a millionth of an inch). However, when we try to apply quantum theory to gravity, things become more complicated and confusing.

But no matter how clever the word, it is what I call a dippy process! Having to resort to such hocus pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent…. I suspect that renormalization is not mathematically legitimate. (Feynman, 1985)

Mankind’s deepest desire for scientific intervention introduced a new idea that of time. Most of the underlying assumptions of physics are concerned with time. Time may sound like a genre of fiction, but it is a well-defined genuine concept. Some argue that time is not yet discovered by us to be objective features of the mundane world: even without considering time an intrinsic feature of the mundane world, we can see that things in the physical world change, seasons change, people adapt to that drastic changes. The fact that the physical change is an objective feature of the physical world, and time is independent of under whatever circumstances we have named it. Others think time as we comprehend it does not endure beyond the bounds of our physical world. Beyond it, maybe one could run forward in time or just turn around and go back. This could probably mean that one could fall rapidly through their former selves. In a bewildering world, the question of whether the time never begin and has always been ticking, or whether it had a beginning at the big bang, is really a concern for physicists: either science could account for such an inquiry. If we find the answer to it, it would be the ultimate triumph of human justification for our continuing quest. And, our goal of a complete description of the universe we live in is self-justified. The understanding we have today is that time is not an illusion like what age-old philosophers had thought, but rather it is well defined mathematical function of an inevitable methodical framework for systematizing our experiences. If one believed that the time had a beginning, the obvious question was how it had started? The problem of whether or not the time had a beginning was a great concern to the German Philosopher, Immanuel Kant (who believed that every human concept is based on observations that are operated on by the mind so that we have no access to a mind-independent reality). He considered the entire human knowledge and came to the conclusion that time is not explored by humans to be objective features of the mundane world domain, but is a part of an inevitable systematic framework for coordinating our experiences. How and when did the time begin? No other scientific question is more fundamental or provokes such spirited debate among physicists. Since the early part of the 1900s, one explanation of the origin and fate of the universe, the Big Bang theory, has dominated the discussion. Although singularity theorem (a theorem showing that a singularity, a point where general relativity (a theory which predicts that time would come to an end inside a black hole – an invisible astrophysical entity that no one has seen, but scientists have observed gravitational evidence consistent with predictions about it, so most scientists believe it exists) breaks down, must exist under certain circumstances; in particular, that the universe must have started with a singularity) predicted that the time, the space, and the matter or energy itself had a beginning, they didn’t convey how they had a beginning. It would clearly be nice for singularity theorems if they had a beginning, but how can we distinguish whether they had a beginning? Inasmuch as the time had a beginning at the Big Bang it would deepen implication for the role of supreme divine creator (that much of humanity worships as the source of all reality) in the grand design of creation. But if it persists in the bounds of reason in that it has neither beginning nor end and nothing for a Creator to do. What role could ineffable benevolent creator have in creation? Life could start and new life forms could emerge on their own randomly sustaining themselves by reproducing in the environment fitted for the functional roles they perform. Personally, we’re sure that the time began with a hot Big Bang. But will it go on ticking forever? If not, when it will wind up its clockwork of ticking? We’re much less sure about that. However, we are just a willful gene centered breed of talking monkeys on a minor planet of a very average galaxy. But we have found a new way to question ourselves and we have learned to do them. That makes us something very special. Moreover, everything we think we understand about the universe would need to be reassessed. Every high school graduate knows cosmology, the very way we think of things, would be forever altered. The distance to the stars and galaxies and the age of the universe (13.7 billion years − number has now been experimentally determined to within 1% accuracy) would be thrown in doubt. Even the expanding universe theory, the Big Bang theory, and black holes would have to be re-examined. The Big Bang theory of universe assumes the present form of the universe originated from the hot fire ball called singularity and it assumes time did not exist before the Big Bang. But Erickcek deduced on the basis of NASA’s, Wilkinson Microwave Anisotropy Probe (WMAP) that the existence of time and empty space is possible before the Big Bang.

A photon generated at the center of the star makes its way to the surface. It may take up to several million years to get to the surface, and the gravitational potential energy of the photon at the surface of the star is given by: PE = − GMm/r, where G = 6.673 × 10 ⁻¹¹ Nm²/kg² is Gravitational constant, m is the photon mass, M and r denote the mass and radius of the star. If the photon wants to detach from the star surface, the force which moves the photon, mc²/λ, should be equal to the force of gravitation experienced by the photon, GMm/r² i.e.,

GMm/r² = mc²/λ

From this it follows that

r² = GMλ/c²

For a photon to escape from the surface of the sun of mass M = 2 × 10 ³⁰ kg and radius r = 6.96 × 10 ⁸ m, it should have to possess a wavelength of

λ = r² c² / GM = 32.6 × 10 ¹³ m

i.e., energy equivalent to 6.08 10 ⁻⁴⁰ joules.

(If a star collapses to a black hole, then r is = 2GM/c²

the equation r² = GMλ/c² takes the form:

λ= 4 GM/c²

i.e., photon should possess a wavelength of λ= 4 GM/c² to escape from the surface of the black hole).

If the condition GMm/r² = mc²/λ is satisfied and the photon detaches the star surface, its energy shifts from hυ to hυ₀. The change in photon energy is equivalent = gravitational potential energy of the photon i.e.,

(hυ − hυ₀) = − GMm/r

Since m = hυ/c²:

(hυ − hυ₀) /hυ = − GM/rc²

The gravitational binding energy of a star is given by U = −3GM²/5r. Therefore, the equation

(hυ − hυ₀) /hυ = − GM/rc² can be rewritten as:

(hυ − hυ₀) /hυ = 5U/3Mc²

or

z = 1.66U / Mc²

where z = gravitational redshift. Since z is always < than 1, Mc² is greater than 1.66 times the gravitational binding energy of a star i.e.,

Mc² > 1.66U

Which means: Mc² > 1.66U is a condition that must be satisfied for a star to allow the photon to escape from its surface.

The rate of loss of photon energy, − (dE/dt), is related to the photon frequency υ by the equation: − dE/dt = hυ², where E = hυ. But υ = c/λ. Therefore:

dλ= c × dt

Integrating over dλ from λ (the wavelength of the photon before detaching from the star surface) to λ₀ (the wavelength of the detached photon), and over dt from zero to t:

(λ₀− λ) = c × t

Since υ = c /λ. Therefore:

(υ − υ₀) /υυ₀ = t

h (υ − υ₀) /hυυ₀ = t

Since (hυ − hυ₀) /hυ = − GM/rc². Therefore:

t = − GM/rυ₀c²

The time it takes for the photon to detach from the star surface is given by:

t = − GMλ₀ /rc³

From above equation it follows that as λ₀ increases, numerical value of t increases. But, because of the negative sign the actual value of t decreases. That is, more the time the photon takes to detach the star surface the lesser is the wavelength of the detached photon.

But what would happen if you travel back in time and kill your grandfather before he conceives your father? Would the arrow of time reverse? Because motion makes the clock tick slower, can we travel back in time and kill our grandfather before he conceive our father? If not, why the universe avoids the paradox? Time Travel − Science Fiction? Taking the laws of physics and punching them in the stomach and throwing them down the stairs – it’s possible for you to break the universal speed limit. It is mind boggling to think about it – you’re actually travelling backwards in time. What if you went back in time and prevented big bang from happening? You would prevent yourself from ever having been born! But then if you hadn’t been born, you could not have gone back in time to prevent big bang from happening. The concept of time travel may sound something impressive and allow science fiction like possibilities for people who survived from the past, but somewhat it seems to be incredible like seeing broken tea cups gathering themselves together off the floor and jumping back on the table promoting cup manufacturers go out of business. However, travelling through time may not be the far-fetched science fiction theory. At the same time, can we open a portal to the past or find a shortcut to the future and master the time itself is still in question and forbidden by the second law of thermodynamics (which states that in any closed system like universe randomness, or entropy, never decreases with time). Of course, we have not seen anyone from the past (or have we?).

We asked how stars are powered and found the answer in the transformations of atomic nuclei. But there are still simple questions that we can ask. And one is: Is our universe merely the by-product of a cosmic accident? If the universe were merely the by-product of a grand accident, then our universe could have been a conglomeration of objects each going its own way. But everything we see in the universe obeys rules which are governed by a set of equations, without exception − which give philosophy a lot more attention than science. However, this does not mean that the universe obey rules because it exists in a plan which is created and shaped by a grinding hand. Maybe the universe is a lucky coincidence of a grand accident emerged with ingredients such as space, time, mass, and energy exist in one-to-one correspondence with the elements of reality, and hence it obeys a set of rational laws without exception. At this moment it seems as though Dr. Science will never be able to raise the curtain on the mystery of creation. Moreover, traditional philosophy is dead, that it has not kept up with modern developments in science, and there is no reason at justifying the grinding hand because the idea of God is extremely limited and goes no further than the opening sentence of the classical theology (which has always rejected the idea that God can classified or defined), and much is still in the speculative stage, and we must admit that there are yet no empirical or observational tests that can be used to test the idea of an accidental origin. No evidence. No scientific observation. Just a speculation. For those who have lived by their faith in the power of reason, the story may end like a bad dream since free will is just an illusion.

When a photon passes the star tangentially, the gravitational field of the star deflects the photon by an angle θ = tan^‒1 (F_G /F_P) where F_G = force of the gravitational field of the star experienced by the photon and F_P = force which moves the photon. Even if F_P ≥ F_G, θ will not be = 0 i.e., deflection occurs.

r² = GMλ/c²

Assuming hc / λ = k_BT_S:

r² = GMh/ k_BT_Sc

If a star collapses to a black hole, then r is = 2GM/c²

the equation r² = GMh/ k_BT_Sc takes the form:

T_S = hc³/ 4GMk_B … (1)

But according to the existing literature, the surface temperature of the black hole is given by:

T_S = (hc³/ 4GMk_B) (1/4π²) … (2)

The equation (1) differs from the equation (2) by the factor (1/4π²) but according to both surface temperature of the black hole is inversely proportional to its mass i.e., smaller black holes possess huge temperatures as if they were a hot body -- hence they lose large amount of its mass therefore of its energy (because E=mc²) and disappear faster than the large black holes.

From the Big Bang to the Bodies such as stars or black holes including basic facts such as particle masses and force strengths, the entire universe works because the laws of physics make things happen. But if Meta or hyper laws of physics were whatever produced the universe then what produced those laws. Or perhaps, the laws, or the cause that created them, existed forever, and didn't need to be created. We must admit that there is ignorance on some issues, that is, we don’t have a complete set of laws …. We are not sure exactly does the existing laws hold everywhere and at all time. Dr. Science gives us a clue, but there’s no definitive answer to provide a purely natural, non-causal explanation for the existence of laws of physics and our place in it. So let's just leave it at the hypothetical laws of physics. The question, then, is why are there laws of physics? And we could say, well, that required a biblical deity, who created these laws of physics and the spark that took us from the laws of physics to the notions of time and space. Well, if the laws of physics popped into existence 13.8 billion years ago with divine help whatsoever, like theologians say, why aren't we seeing a at least one evidence of an ineffable creator in our observable universe every now and then? The origin of the Meta or hyper laws of physics remains a mystery for now. However, recent breakthroughs in physics, made possible in part by fantastic revolutionary understanding of the true nature of the mathematical quantities and theories of physics, may suggest an answer that may seem as obvious to us as the earth orbiting the sun – or perhaps as ridiculous as earth is a perfect sphere. We don't know whatever the answer may be because the Meta or hyper laws of physics are completely beyond our experience, and beyond our imagination, or our mathematics. This fact leads us to a big mystery and awaits the next generation of high energy experiments, which hope to shed light on the far-reaching answer that might be found in the laws that govern elemental particles.

The Drake Equation

N = R* × f_p × n_e × f_l × f_i × f_c × L

Where:

R* = the rate at which stars are born in the galaxy,

f_p = the fraction of these stars that have planets,

n_e = the number of planets for each star that have the conditions for life,

f_l = the fraction of planets that actually develop life,

f_i = the fraction that develop intelligent life,

f_c = the fraction that are willing and able to communicate, and

L = the expected lifetime of a civilization.

Fermi’s Paradox

If there are so many aliens, where are they?

Who are we? We find that we intelligent apes who have only recently left the trees, live on an fragile planet of a humdrum star by a matter of sheer luck or by divine providence, lost in a galaxy tucked away in some forgotten corner of a universe in which there are far more galaxies than people. Sending the Beatles song across the Universe and pointing the telescopes in Deep Space Network towards the North Star, Polaris, we seek to find intellectual beings like us outside the sheer number of planets, vast ocean of existence, our solar system, and our own Milky Way galaxy. How awe hunting for them across the empty stretches of the universe would be to acquire a bit of confirmation that either we're alone in this universe or we are not. However, we are not the only life-form in the universe, is reasonable to expect since we have no reason to assume that ours is the only possible form of life. Some sort of life could have happened in a universe of greatly different form, but

Where’s the evidence?

The Burden of evidence is only on the people who regard themselves as reliable witnesses that sightings of UFOs are evidence that we are being visited by someone living in another galaxy who are much more advanced enough to spread through some hundred thousand million galaxies and visit the Earth. An alien, like the teapot, is a hypothesis that requires evidence.

The known forces of nature can be divided into four classes:

Gravity: This is the weakest of the four; it acts on everything in the universe as an attraction. And if not for this force, we would go zinging off into outer space and the sun would detonate like trillions upon trillions of hydrogen bombs.

Electromagnetism: This is much stronger than gravity; it acts only on particles with an electric charge, being repulsive between charges of the same sign and attractive between charges of the opposite sign. More than half the gross national product of the earth, representing the accumulated wealth of our planet, depends in some way on the electromagnetic force. It light up the cities of New York, fill the air with music from radios and stereos, entertain all the people in the world with television, reduce housework with electrical appliances, heat their food with microwaves, track their planes and space probes with radar, and electrify their power plants.

Weak nuclear force: This causes radioactivity and plays a vital role in the formation of the elements in stars. And a slightly stronger this force, all the neutrons in the early universe would have decayed, leaving about 100 percent hydrogen, with no deuterium for later use in the synthesizing elements in stars.