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CRC Press eBooks

Time in the QuantÜm World

Derek York

Published Apr 26, 2019• 0 citations
Publisher

Abstract

Isaac Newton, Pierre Laplace and the vast majority of the great scientists of the classical era regarded time as an absolute quantity flowing in some determined way like a great river guided by the solid banks of reality. Einstein shows his special theory of relativity that in fact time is not absolute; there are many rivers of time, each flowing at its own speed. Einstein described Schrodinger’s cat paradox as the ‘prettiest way’ of illustrating his belief that quantum theory, although it is a fantastically successful tool, is not a complete description of reality. The scientific stars were out to laud Schrodinger because, early in 1926, he published an extraordinary equation that codified much of the ghostly behaviour of the microworld. A key fact of quantum life was thus known, but far from understood: in some circumstances, light is best regarded as a wave, whereas in other situations light is far more usefully treated as a shower of minute particles.

DOI
10.1201/9780429187100-12

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Cambridge University Press eBooks•Apr 30, 1979•60 citations
Isaac Newton, Pierre Laplace and the vast majority of the great scientists of the classical era regarded time as an absolute quantity flowing in some determined way like a great river guided by the solid banks of reality. Einstein shows his special theory of relativity that in fact time is not absolute; there are many rivers of time, each flowing at its own speed. Einstein described Schrodinger’s cat paradox as the ‘prettiest way’ of illustrating his belief that quantum theory, although it is a fantastically successful tool, is not a complete description of reality. The scientific stars were out to laud Schrodinger because, early in 1926, he published an extraordinary equation that codified much of the ghostly behaviour of the microworld. A key fact of quantum life was thus known, but far from understood: in some circumstances, light is best regarded as a wave, whereas in other situations light is far more usefully treated as a shower of minute particles.
By the end of the nineteenth century all the important elements of classical physics were fully mature. Newton's Laws had been applied with success to everything from industrial machines to planetary orbits. Classical thermodynamics had extended energy conservation arguments into thermal processes, and scientists including J. Willard Gibbs and Ludwig Boltzmann had developed the statistical interpretation of entropy. James Clerk Maxwell had explained all electromagnetic phenomena, from AC generators/motors to light, with the four Maxwell's equations and three material-dependent constitutive relations. There was serious discussion that physics was on the verge of being “finished” – becoming a closed system of knowledge like classical geometry with only essentially routine tasks left of determining how the known laws could be applied to engineering problems. Yet by 1930 the foundations of mechanics, electromagnetics, and atomic-scale systems had been shaken to the core by the new revolutions in the Theory of Relativity, the photon picture of light, and quantum physics. We are still reaping the benefits of the application of these new scientific paradigms in our technology today, including semiconductor electronic devices, lasers, and GPS systems. But the description of reality that these theories provide is still deeply anti-intuitive and disturbing. Nevertheless, quantum physics is one of the most extensively experimentally verified theories that we know. Even when quantum theory and common sense seem to diverge, quantum theory gives the right answers when tested by experiment. In the next chapter we will develop the framework of quantum theory that has been so successful when people “shut up and calculate,” as one scientist suggested as the way through the philosophical thicket of quantum physics. But in this chapter, we will spend a brief time considering the historical development and continuing paradoxical implications of quantum theory. The photoelectric effect and photons In 1905, Albert Einstein, who was a key figure in the revolution of modern physics, was working as a clerk in the patent office in Zurich, Switzerland. Einstein had finished his studies in physics, but had not obtained a coveted position as a university professor. He was intensely interested in the latest developments in classical physics and was aware of a few of the remaining loose ends that were resisting explanation in the classical model.
I n the early 20th century, the groundbreaking theories of quantum mechanics and special relativity emerged at roughly the same time.At first, both theories appeared to be entirely incompatible with each other.While the quantum equations written out by Erwin Schrödinger and Wolfgang Pauli dealt with the behaviours of electrons, atoms, and molecules moving at speeds encountered in classical physics, the rules of special relativity first imagined by Albert Einstein described the behaviour of matter moving at close to the speed of light.Initially, this apparent clash of theories presented a crisis in physics.However, in the late 1920s, further theoretical work carried out by physicists including Paul Dirac, Oskar Klein, and Walter Gordon culminated in a new set of equations, which proved definitively that quantum mechanics and special relativity are compatible with each other after all. An educational challengeYet with this groundbreaking discovery came an entirely new problem.In adding a new layer of complexity to the equations of non-relativistic quantum mechanics, the more complete theories of relativistic
The intellectual adventure story of the "double-slit" experiment, showing how a sunbeam split into two paths first challenged our understanding of light and then the nature of reality itself--and continues to almost 200 years later.Many of the greatest scientific minds have grappled with this experiment. Thomas Young devised it in the early 1800s to show that light behaves like a wave, and in doing so opposed Isaac Newton's view that light is made of particles. But then Albert Einstein showed that light comes in quanta, or particles. Quantum mechanics was born. This led to a fierce debate between Einstein and Niels Bohr over the nature of reality--subatomic bits of matter and its interaction with light--again as revealed by the double-slit experiment. Richard Feynman held that it embodies the central mystery of the quantum world. Decade after decade, hypothesis after hypothesis, scientists have returned to this ingenious experiment to help them answer deeper and deeper questions about the fabric of the universe.How can a single particle behave both like a particle and a wave? Does a particle, or indeed reality, exist before we look at it, or does looking create reality, as the textbook "Copenhagen interpretation" of quantum mechanics seems to suggest? How can particles influence each other faster than the speed of light? Is there a place where the quantum world ends and the familiar classical world of our daily lives begins, and if so, can we find it? And if there's no such place, then does the universe split into two each time a particle goes through the double-slit?Through Two Doors at Once celebrates the elegant simplicity of an iconic experiment and its profound reach. With his extraordinarily gifted eloquence, Anil Ananthaswamy travels around the world, through history and down to the smallest scales of physical reality we have yet fathomed. It is the most fantastic voyage you can take.
Time – what it is and its nature – has from the beginning held mysteries for layman, philosopher, and physicist alike. Periodic phenomena from motions of heavenly bodies and pendulums to quantal atomic clocks provide the means to measure time intervals, and Newton’s absolute time is a background flow against which classical and non-relativistic quantum physics is played out. While internally consistent, these two fields of physics are incompatible with the requirement of treating space and time on an equal footing. Quantum field theories provide the answer, as both treated as parameters, physics residing instead in the states and operators. But even in classical physics and quantum mechanics, time-independent descriptions provide an alternative to an explicitly time-dependent one. These, including a general method of approach called invariant imbedding, are discussed as alternative representations of an underlying reality that is the concern of physics.
Translated by Irene Born Newton-John In this letter to his old friend, now at Edinburgh University, Einstein first responds to Born’s description of a local physician “who wouldn’t hurt a fly, but [states] that no sacrifice is too great [for] the realization of Marxist ideals, not even the destruction of millions of human lives.” And then it’s back to the old quarrel about quantum mechanics. (See Born’s comment below.) Princeton, 15 September 1950Dear Born,… People such as your Bolshevik doctor come by their fantastic attitude as a result of their objection to the harshness, injustice and absurdity of our own social order (escape from reality). If he happened to be living in Russia, no doubt he would be a rebel there as well, only in that case he would take care not to tell you about it. Nevertheless it seems to me that our own people here [in the US] make an even worse job of their foreign policy than the Russians. And the idiotic public can be talked into anything. And they really are very shortsighted, for technological superiority is transitory, and if it comes to an all-out conflict, the decisive factor is sheer numerical superiority.There is nothing analogous in relativity to what I call incompleteness of description in the quantum theory. Briefly it is because the ψ-function is incapable of describing certain qualities of an individual system, whose “reality” none of us doubt (such as a microscopic parameter). Take a (macroscopic) body that can rotate freely about an axis. Its state is fully determined by an angle. Let the initial conditions (angle and angular momentum) be defined as precisely as the quantum theory allows. The Schrödinger equation then gives the ψ-function for any subsequent time interval. If this is sufficiently large, all angles become (in practice) equally probable. But if an observation is made (e.g. by flashing a torch), a definite angle is found (with sufficient accuracy). This does not prove that the angle had a definite value before it was observed—but we believe this to be the case, because we are committed to the requirements of reality on the macroscopic scale. Thus, the ψ-function does not express the real state of affairs perfectly in this case. This is what I call “incomplete description.”So far, you may not object. But you will probably take the position that a complete description would be useless because there is no mathematical relationship for such a case. I do not say that I am able to disprove this view. But my instinct tells me that a complete formulation of the relationships is tied up with complete description of its factual state. I am convinced of this although, up to now, success is against it. I also believe that the current formulation is true in the same sense as e.g. thermodynamics, i.e. as far as the concepts used are inadequate. I do not expect to convince you, or anybody else. I just want you to understand the way I think.I see from … your letter that you, too, take the quantum theoretical description as incomplete (referring to an ensemble). But you are, after all, convinced that no (complete) laws exist for a complete description, according to the positivistic maxim: esse est percipi [to be is to be perceived]. Well, this is a programmatic attitude, not knowledge. This is where our attitudes really differ. For the time being, I am alone in my views—as Leibniz was with respect to the absolute space of Newton’s theory.… I have not changed my attitude to the Germans, which, by the way, dates not just from the Nazi period. All human beings are more or less the same from birth. The Germans, however, have a far more dangerous tradition than any of the other so-called civilized nations.Kind regards,Yours,A. E. Born’s 1969 comment: 1 1. M. Born, The Born–Einstein Letters 1916–1955: Friendship, Politics and Physics in Uncertain Times, Macmillan, New York (2005), p. 184 Original letter © Hebrew University of Jerusalem. This is probably the clearest presentation of Einstein’s philosophy of reality. … He calls my way of describing the physical world “incomplete.” In his eyes, that is a flaw which he hopes to see removed, while I am prepared to put up with it. I have in fact always regarded it as a step forward, because an exact description of the state of a physical system presupposes that one can make statements of infinite precision about it, and this seems absurd to me. REFERENCESection:ChooseTop of pageREFERENCE <<CITING ARTICLES1. M. Born, The Born–Einstein Letters 1916–1955: Friendship, Politics and Physics in Uncertain Times, Macmillan, New York (2005), p. 184 Original letter © Hebrew University of Jerusalem. Google Scholar© 2005 American Institute of Physics.
Those defile the purity of mathematical and philosophical truthy who confound real quantities with their relations and sensible measures. —ISAAC NEWTON, Principia Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size ), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).