Two of the most important discoveries in the twentieth century in modern science must be Einstein's relativity theory and Schrödinger's quantum mechanics; one deals with very large objects and the other deals with very small particles. They are connected by means of Heisenberg's uncertainty principle and Boltzmann's entropy theory. The “fact” is that quantum mechanics is essentially “identical” to Hamiltonian mechanics. The major difference between them is that Schrodinger used a dynamic quantum energy as adapted from a quantum leap energy of Bohr's hypothesis that changes from classical mechanics to quantum “leap” mechanics or quantum mechanics. Wiener's communication strategy is that if the information is corrupted through transmission, it may be recovered at the receiving end, but with a “cost” mostly at the receiving end. While Shannon's communication strategy carries a step further by encoding the information before it is transmitted, such that information can be “reliably” transmitted, also with a “cost” mostly at the transmitting end.
Two of the most important discoveries in the twentieth century in modern science must be Einstein's relativity theory and Schrödinger's quantum mechanics; one deals with very large objects and the other deals with very small particles. They are connected by means of Heisenberg's uncertainty principle and Boltzmann's entropy theory. The “fact” is that quantum mechanics is essentially “identical” to Hamiltonian mechanics. The major difference between them is that Schrodinger used a dynamic quantum energy as adapted from a quantum leap energy of Bohr's hypothesis that changes from classical mechanics to quantum “leap” mechanics or quantum mechanics. Wiener's communication strategy is that if the information is corrupted through transmission, it may be recovered at the receiving end, but with a “cost” mostly at the receiving end. While Shannon's communication strategy carries a step further by encoding the information before it is transmitted, such that information can be “reliably” transmitted, also with a “cost” mostly at the transmitting end.
Since every substance has a price tag of information that includes all the building blocks in our universe, one cannot simply ignore information when dealing with science. We have shown that there is a profound connection between information and entropy, a quantity that has been well accepted in science. Without this connection, information would be more difficult to apply in science. Two of the most important pillars in modern physics must be Einstein’s relativity theory and Schrödinger’s quantum mechanics. However, there exists a profound connection between them, by means of Heisenberg’s uncertainty principle. Due to the uncertainty relation, we see that every bit of information takes time and energy to transfer, create, and observe. Since one cannot create something from nothing, anything to be created needs a huge amount of energy and a great deal of entropy to make it happen.
In the 20th century, two new terms were added to the scientific lexicon: relativistic mechanics and quantum mechanics. The challenge to the concept of the absoluteness of space and time started at the end of the 19th century and gave birth to Einstein's special relativity theory in 1905. This unified space and time to a single entity, space–time, and we have been introduced to many new concepts such as time dilation, space contraction, mass–energy relation, and the space–time continuum in relativity theory. We have also learned that the highest possible velocity in this universe is that of light and that nothing in the universe can move faster than light. Einstein's general theory of relativity took into consideration gravitation and established the chronogeometric concept of gravity. Quantum mechanics developed by Bohr, de Broglie, Heisenberg, Schrödinger, and others gave us knowledge in the atomic and subatomic domain and led to the wave–particle duality of de Broglie, the uncertainty principle of Heisenberg, the wave mechanics of Schrödinger, and so forth. We have learned that three distinct chords are at the heart of quantum mechanics—granularity, relational, and indeterminism. Although quantum mechanics is a weird subject, as we will discuss, the modern physics is totally based on it.
Abstract The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approximation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.
Science has developed through a variety of investigations more or less over the time scale of human existence. On this scale, quantum mechanics is an extremely young field, existing essentially for only just over a century. Even our understanding of classical mechanics has existed for a comparatively long period—roughly having been formalized with Newton's equations published in his Principia Mathematica , in April 1686 (1687). Up until the very end of the nineteenth century, mechanics in the form of Newton's laws were comfortable, being understood and accepted by all who dealt with the motion of reasonable bodies. With the turn of the new century, however, mechanics would be shaken to its roots. The change began already on December 14, 1900, when Planck (1900) presented his new theory of black-body radiation to the German Physical Society, and this change would affect mechanics in physically small structures (and lead to quantum mechanics). Mechanics of large bodies would similarly be changed in 1905 with the arrival of Albert Einstein's (1905a) relativity theory. In this book, we will deal with only the first of these two great breakthroughs.
Quantum mechanics is one of the great success stories of modern physics, making sense of the very small just as Einstein's theory of relativity made sense of the very large. But, for most students, the ideas that make quantum mechanics powerful can be confusing and counterintuitive. This volume in the Greenwood Guides to Great Ideas in Science series provides a history of quantum mechanics from the early breakthroughs of Planck and Einstein, at the beginning of the 20th century, to the present frontiers of quantum computing and quantum gravity. The approach is entirely non-technical, and is aimed at the general reader who may not have much mathematical background but who has a strong curiosity about some of the most important developments in modern science. Quantum Mechanics: A Historical Perspectivetraces the history of this powerful theory, including: ; The early discoveries by Max Planck and Albert Einstein regarding the quantization of radiation ; The early quantum theory, including Neils Bohr's theory of the atom ; The birth of modern quantum mechanics through the work of Heisenberg, Schrodinger, Born, Dirac and others ; Applications of quantum mechanics in chemistry, nuclear physics, electronics, and many other areas ; Recent work in quantum computation and quantum information theory The book emphasizes the fact that despite the great success of quantum mechanics, many exciting intellectual frontiers remain open for further researchers to explore. It includes a glossary, a timeline, and a bibliography of accessible resources for further research.
In this chapter, we show the mythical relationship between science and information. Since every substance has a price tag or price tags of information which includes all the building blocks in our universe, one cannot simply ignore information when dealing with science. We have shown that there is a profound connection between information and entropy, a quantity that has been well accepted in science. Without this connection, information would be more difficult to apply to science. Two of the most important pillars in modern physics must be the Einstein’s relativity theory and the Schrödinger’s quantum mechanics. We show that there exists a profound relationship between them, by means of the Heisenberg uncertainty principle. In due of the uncertainty relation, we show that every bit of information takes time and energy to transfer, to create, and to observe. Since one cannot create something from nothing, we show that, anything to be created needs a huge amount of energy and requires a great deal of entropy to make it happen! My question is that: Can we afford it?