Moore's account of Erwin Schrödinger's life isn't a bad read at all. For those unacquainted with the mathematical rigor of quantum mechanics, it is a...more Moore's account of Erwin Schrödinger's life isn't a bad read at all. For those unacquainted with the mathematical rigor of quantum mechanics, it is a little difficult to follow. The flow is somewhat choppy, and the mix of equations and technical descriptions might sidetrack the lay-reader. More emphasis could have been placed on simplification, but realistically, QM is a difficult concept to grasp even without the math.
For those who are curious to know what Schrödinger's work is all about, I wrote a brief explanation of the Schrödinger equation, and, with my limited knowledge in this area, attempted to describe some of its applications to the world (one might recall a certain experiment where a cat is placed in a 'quantum' box rigged with hydrocyanic acid - A purely hypothetical one of course.)
When it comes to sucessful theories which explain the behaviour of microscopic particles, quantum mechanics stands alone. It was developed in the 1920s by Erwin Schrödinger, Werner Heisenberg, Wolfgang Pauli, Paul Dirac, and many others. The practical implication of this theory is that it allows us to understand a host of phenomena involving atoms, molecules, nuclei, and solids. Technologies directly resulting from the development of quantum mechanics include scanning tunnelling microscopes, nanoscale machines, and quantum computers.
In 1926, Schrödinger developed the appropriate wave equation for particles. When mathematically explaining a quantum system, one must take the solution related to the behaviour of this system and apply certain boundary conditions to it. This tells us the allowed 'wavefunctions' and energy levels of the system. Reworking a wavefunction provides one with all the measurable characteristics of that system.
{For those familiar with the work of James Clerk Maxwell, recall that electromagnetic radiation is described by a wave equation (electromagnetic waves). Since particles such as atoms and molecules can also be expressed in terms of waves (wave-particle duality), the waves associated with particles also satisfy a wave equation.}
The Schrödinger equation provides the most complete description that can be given to a physical system. Its wavefunction (or state vector) describes possible points in space which are mapped by complex numbers called probability amplitudes. In a nutshell, these amplitudes are the values of wavefunctions. By squaring the absolute value of these complex numbers (looks like |ψ(x)|^2 ), one can determine the probability density (or probability distribution) of momentary states of particles, telling us where things are and how they are interacting. Schrödinger's wavefunctions can also be transformed into Heisenberg’s matrix mechanics.
The actual equation (or a 1-dimensional, time-independent variation of it), given a particle of mass m confined to moving along the x-axis and interacting with its environment through a potential energy function U(x), is something of the form
-(hbar^2/2m)[(d^2ψ)/dx^2:] + Uψ = Eψ
(where hbar^2 = Plank's constant squared)
Generally, time-dependent Schrödinger equations describe systems evolving with time, whereas time-independent ones are of a stationary state. These equations can take on several different forms, depending on the physical situation. Also, the equation doesn't break the principle of conservation of mechanical energy of a system. In fact, the first term in the above-mentioned Schrödinger equation reduces to the kinetic energy of the particle multiplied by the wave function, indicating that the total energy of a system is K + U = E = constant. Where total energy (E) is the sum of the kinetic energy (K) and the potential energy (U) - and the total energy is constant.
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Erwin Schrödinger had unconventional relationships with women. His American colleagues at Princeton were not impressed when the Austrian tried to secure a professorship with them, simply because he had 2 wives.
Schrödinger was an only child, and his mom was a chemistry professor. He died of tuberculosis in 1961. Upon realizing how fundamentally unintuitive quantum mechanics is, he is said to have proclaimed 'Verdammte Quantumspringerei!' (This damn quantum jumping!)(less)
This book provides an interesting foray into the deep mechanisms of particle physics. Nicknamed 'The Plumber'(due to his preference for experimentatio...moreThis book provides an interesting foray into the deep mechanisms of particle physics. Nicknamed 'The Plumber'(due to his preference for experimentation) by Murray Gell-Mann, it is clear from this book that Lederman's work in the 60s and 70s is nothing short of Nobel calibre. This book is fairly dense in terms of physics technicalities, but one can still appreciate the humorous anecdotes throughout.
As generally explained in the book, a neutrino ('little neutral one') is an elementary particle of neutral electric charge and almost 0 mass. Neutrinos are extremely difficult to detect, yet more than 50 trillion of them pass through our bodies every second (via the sun). Leptons (electrons, muons, and the tau) can also be neutrinos with corresponding antineutrinos. These are said to be the "flavours" of a neutrino. Lederman's Nobel Prize, in 1988, was awarded "for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino", and it was shared with Schwartz and Steinberger.
As an aside, direct evidence for the neutrino related to the tau was announced by Fermilab (a particle accelerator like the LHC, but in Chicago) in July 2000. Current studies indicate that neutrinos have a small but nonzero mass. Travel at light-speed is impossible for objects having mass. Since so many neutrinos are predicted to exist, their combined mass may be sufficient to cause all the matter in the Universe to eventually collapse into a single point, which might then explode and create a completely new Universe.(less)
(disclaimer- alcohol was consumed during the creation of this review, ideas may not be logically coherent).
is very well known for his hypothesis. Thi...more(disclaimer- alcohol was consumed during the creation of this review, ideas may not be logically coherent).
is very well known for his hypothesis. This book about Georg Friedrich Bernhard Riemann has taught me that the behaviour of the zeta function is pretty serious business. This is a zeta function: it
-> ζ(s) <-
where s is a complex variable. If the real part of this variable is greater than one then ζ(s) is defined as the sum of the convergent series ∑n ≥ 1 n^-s (a convergent series is converging, which is the arch-nemesis of diverging). Oh-and you have to extend ζ(s) through analytic continuation so that it may inhabit the whole complex plane (as opposed to simple plane, like a Fokker Dr.1). When you mash all this together, Riemann says that the real part of this complex number s is exactly 1.5 when it is between 0 and 1, and ζ(s) = 0. When this idea first showed up in Riemann's work, there were no clue as to how he developed it.
Riemann's conjecture that all of the zeroes of the zeta function have a real part of 1.5 showed no proof whatsoever. which could imply that Riemann was from outer space because his math was too complicated for our monkey brains to grasp. He teleported away to his advanced civilization where they watch sitcoms about earth-people and lol all day.
The most important thing I learned from this book is that no apple ever fell on Newton's head. Instead, it is written that he was 'occasioned by the f...moreThe most important thing I learned from this book is that no apple ever fell on Newton's head. Instead, it is written that he was 'occasioned by the fall of an apple, as he sat in contemplative mood.' One might say that if a pie graph mapping human achievement were created, there's a good chance that Newton would be given a pretty big slice. From a historical perspective, he is responsible for more than one paradigm shift in our understanding of the world around us, and if you haven't memorized his three laws of motion, then you fail.
In contrast to the glory of his later discoveries, Newton's early childhood was marked by rejection and hatred. Three months before he was born in 1643, his father died, and his birth was premature. Hannah Ayscough (Newton's mother) claimed that he could fit into a 1.1 L mug, and she did not expect him to live very long. Following that, his mother remarried when he was two years of age, and his stepfather refused to incorporate the child into the new family. Isaac was forced to live with his grandmother, where he developed resentment towards his stepfather. When he was 19, Newton recorded in his list of sins: "Threatening my father and mother Smith to burn them and the house over them."
During his school years he endured harsh, vindictive attacks from opponents as well as friends and family. In isolation, he would spend hours tinkering with mechanical models and making detailed drawings. His natural curiosity for such things aided in his scientific endeavours later on in life. However, during his early school years, he was considered one of the worst students. According to his teachers, this was due to his inattentiveness.
Throughout school, he was considered somewhat of a dunce, and was far from achieving academic success, and he was also bullied at times. On the plus side, when Newton was challenged to fight a schoolyard bully (who, compared to Newton, was a 'building with feet'), he actually won. Unfortunately, his capacity to remain spaced-out and idle in his studies caused him to be removed from school in October, 1659, and he was put him to work on the family farm, which he detested very much.
Newton's uncle William decided that it would be best for him to return to school, and Henry Stokes, the master at the King's School, convinced Hannah to let Newton complete his education. Here, Newton sought revenge against a bully by getting superior grades, and it was not long before he became a top-ranking student. It was here that some flicker of intellectual aptitude began to develop.
In 1661 he got accepted to Cambridge, where his Uncle William had gone. He joined the school as a subsizer, so he had to basically do janitorial work to cover his tuition. Luckily, he was granted scholar status in 1664, which freed him of financial burdens. But a year later, everything changed. He left school in August 1665 to avoid the Bubonic Plague- a virulent, flea-borne disease which killed about 100,000 people (20% of London's population at the time). Hannah, who was again widowed, allowed Newton to stay with her at this time. The next 18 months were among the most significant in Newton's life. "I was in the prime of my age for invention... and minded Mathematicks and Philosophy more than at any time since" he would say later on in life. It was here that he devoted himself gravitation, mathematics, mechanics, and optics- studies which would eventually allow him to push back nearly every boundary of scientific knowledge.
Upon returning to school, Newton's newfound interest could not be blocked. He immersed himself in the works of Aristotle, Descartes, Hobbes, Boyle, Copernicus, Galileo, Euclid, and Kepler. Since Galileo's work explained that the earth is not the center of the universe (geocentric model < heliocentric model), astronomy was a very controversial and exciting topic, and it is interesting to note that he died only 4 days after Newton was born.
And as an afterthought he invented calculus and the theory of gravitation, and wrote the Principia Mathematica. He had a huge feud with Robert Hooke, another English scientist, and refused to publish work that Hooke had helped him with until after Hooke had died. He also had a dispute with German mathematician Gottfried Leibniz with regard to the priority on the invention of calculus. Leibniz wrote to the Royal Society and explained that he had invented calculus first. Unfortunately for him, Newton was the president of the Royal Society. Strangely enough, anonymous letters mocking Leibniz began to appear in Royal Society publications, and Leibniz was left disgraced and impoverished (and in reality Newton had invented calculus first, but waited many years before publishing his work).
A few years after his prime, Newton was given a comfortable job at the Royal mint, where one of his duties was to prosecute counterfeiters. He performed his job with much enthusiasm, and sent many a counterfeiter to the gallows to be executed. Newton died in March 31, 1727.
Review of Dilemmas of an Upright man: Max Planck - draft {brief intro}
Max Plank (1858 – 1947) was an influential German physicist whose contributions t...more Review of Dilemmas of an Upright man: Max Planck - draft {brief intro}
Max Plank (1858 – 1947) was an influential German physicist whose contributions to quantum mechanics helped launch a revolution in science between 1900 and 1930.
Using Boltzmann's statistical mechanics and the concept of energy quantization, Planck was the first person to explain a phenomenon of quantum theory (black-body radiation). This discovery helped him to come up with a new system of measurement. One such measure is called the Plank time (tP), which is a unit of time expressed by the system of natural units known as Planck units. The interval of time associated with this unit is twenty-six orders of magnitude smaller than the current limit of observation, the attosecond (10^26 Plank times).
The progress of dimensional analysis in physics suggests that a working theory of quantum gravity, wherein the unification of quantum mechanics and general relativity would be made, will allow us to understand particle interactions occurring at time intervals associated with the Plank time. However, not a single person has been able to produce a Theory of Quantum Gravity whose predictions agree with experimental evidence. Up until his death in 1955, Einstein spent many years of his life working on this problem. A solution to this problem has proven to be so elusive and difficult, that it has been at the forefront of science for the past seven decades.
More speculative theories have called into existence quantum gravity "foam" where there are space-time fluctuations occurring on the Planck scale. This predicts that images of extremely distant objects, such as red-shifted galaxies and quasars, should be blurry. Although this prediction has not yet been proven by observation, which was shown by experiments conducted by the Hubble space telescope in 2003, these observations have lead to a debate about the physical implications of the Planck time as a physical minimum time interval. However, it was determined that "the cumulative effects of space-time ﬂuctuations on the phase coherence of light [in certain theories of 'foamy' space-time:] are too small to be observable."
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The main problem is that the mathematics of general relativity and quantum mechanics cease to cooperate when it comes to explaining each other’s properties. Efforts to describe gravity (what gives particles mass?) have proven particularly frustrating for both theories. For example, the gravitational and electrical force (phenomena which are magnetic in nature), differ in strength by about 39 orders of magnitude, with the latter being the stronger. This explains why the forces holding together the molecules of our bodies do not dissolve when subjected to the downward pull of earth's entire mass of approximately 5.9742 × 10^15 teragrams.
Without a Theory that unifies the concepts of general relativity and quantum mechanics, these observations cannot be explained. However, recent events suggest progress in this area. By smashing particles together at very high speeds (close to the speed of light), the 27 km, ~9 billion dollar CERN experiment (LHC) straddling the Franco-Swiss border has been actively involved in trying to unlock this mystery. The main goal of the scientists working there is to give us a more detailed description of quantum mechanics by recreating conditions that haven't been seen since the Big Bang-roughly 13.3 to 13.9 billion years ago. This would give us more clues about the origin of the universe, and might even allow us to construct real X-wing spacecraft, which has been the main goal of science all along.