Abstract Perhaps the most celebrated and discussed aspect of quantum mechanics is the probabilistic nature of its predictions. For example, if a ball is thrown toward a wall, its position and how fast it will be moving at a later time can be determined with arbitrary accuracy using Newton’s laws of motion. An amazing result is that such a deterministic behavior is no longer valid according to the laws of quantum mechanics. We cannot predict with absolute certainty where the ball will be and how fast it will be moving after a given time. The probabilistic nature of measurements is explained and discussed using the example of a single photon. A brief history of how the Schrödinger equation was formulated is also discussed. The probabilistic description according to the Schrödinger equation is elucidated using some simple examples.
Abstract Perhaps the most celebrated and discussed aspect of quantum mechanics is the probabilistic nature of its predictions. For example, if a ball is thrown toward a wall, its position and how fast it will be moving at a later time can be determined with arbitrary accuracy using Newton’s laws of motion. An amazing result is that such a deterministic behavior is no longer valid according to the laws of quantum mechanics. We cannot predict with absolute certainty where the ball will be and how fast it will be moving after a given time. The probabilistic nature of measurements is explained and discussed using the example of a single photon. A brief history of how the Schrödinger equation was formulated is also discussed. The probabilistic description according to the Schrödinger equation is elucidated using some simple examples.
Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to be a qubit and thus having the shape of a unit ball. Any item in the universe as well the universe itself is both infinitely many rolls and a single roll of that dice for it has infinitely many “sides”. Thus both the smooth motion of classical physics and the discrete motion introduced in addition by quantum mechanics can be described uniformly correspondingly as an infinite series converges to some limit and as a quantum jump directly into that limit. The second, imaginary dimension of God’s dice corresponds to energy, i.e. to the velocity of information change between two probabilities in both series and jump.
Abstract Quantum mechanics, like other enormously successful physical theories, accurately describes how the natural world behaves. Its explanatory powers regarding the indeterminate behavior of the smallest constituents of nature have proven to be both profound and practical. Many technological devices from lasers to computer chips are based on quantum mechanics. Not surprisingly, the universe filled with microscopic random events revealed by quantum mechanics has generated wonder and interpretive bewilderment. Reactions to the unsettling revelations of quantum unpredictability have included appeals to unknown variables to preserve classical physics, and even wholesale theoretical dismissals. Far from proof of mathematical trickery or theoretical incompletion however, the now well-established and irreducible quantum randomness suggests a physical universe that is open to a future not determined by the past, and perhaps to a God that really does play dice.
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described by the wave function is subatomic particle moving randomly. Therefore, the characteristics of quantum mechanics have a dual nature, one of them is the deterministic nature carried on from classical physics, and the other is the probabilistic nature coined by particle's random motion. Based on this model, almost all of open questions in quantum mechanics can be explained consistently, which include the particle-wave duality, the principle of quantum superposition, the interference pattern of double-slit experiments, and the boundary between the classical world and the quantum world. The current quantum mechanics is a mixture of matrix mechanics and wave mechanics, which are sharply conflicting in principle. Matrix mechanics treats quantum particles as classical particles with fixed relation between the particle's position and its momentum. The matrix mechanics, in fact, belongs to the old quantum theory. Both Born's non-commutative relation and Heisenberg uncertainty relation originate from matrix mechanics. However, in wave mechanics, there is no any fixed relation between the particle's position and its momentum, and the particle's position and its momentum belong to immeasurable physical quantities. Therefore, there is no need for non-commutative relation and uncertainty relation in wave mechanics.
Einstein initially objected to the probabilistic aspect of quantum mechanics— the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein saw as the abandonment of physical realism. We argue here that Einstein’s initial intuition was perfectly sound, and that it is precisely the fact that quantum mechanics is a fundamentally probabilistic theory which is at the root of all the controversies regarding its interpretation. Probability is an intrinsically logical concept. This means that the quantum state has an essentially logical significance. It is extremely difficult to reconcile that fact with Einstein’s belief, that it is the task of physics to give us a vision of the world apprehended sub specie aeternitatis. Quantum mechanics thus presents us with a simple choice: either to follow Einstein in looking for a theory which is not probabilistic at the fundamental level, or else to accept that physics does not in fact put us in the position of God looking down on things from above. There is a widespread fear that the latter alternative must inevitably lead to a greatly impoverished,
The procedure used to "do physics" in the macroscopic world is familiar: You take an object, start it off with a particular position and velocity, subject it to known forces (say gravity or friction, or both), and follow its trajectory. You then measure the dynamical properties (say position or energy) of that object at a later time and compare those measurements with the prediction using Isaac Newton's laws of motion. Newton's laws directly predict what those quantities should be at that later time, so the comparison is straightforward. However, the microscopic laws of physics, quantum mechanics, aren't so simple. The quantum concepts are so alien and counterintuitive that the language used to describe the mathematics and physics is often ambiguous and confusing. Therefore, for you to \emph{really} understand what is going on, some mathematics must be used. This is my attempt to explain some "weird facts" using a minimum of mathematics, yet eliminating as much ambiguity as possible.
The idea of determinism has had a powerful grip on the imagination of physicists ever since Pierre Simon Laplace evoked the idea of the clockwork universe. When Einstein uttered his famous phrase God doesn't play dice, he was expressing his unhappiness with the probabilistic nature of quantum mechanics, believing that beneath quantum theory must lie a deeper, deterministic theory of nature. But such has been the huge success of quantum theory that most physicists now believe that the ultimate physical theory will be quantum mechanical and that nature is fundamentally random.