Basic Physics Of Quantum Theory, The. Basil S Davis

Basic Physics Of Quantum Theory, The - Basil S Davis


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of the angular momentum vector

       11.2Quantization of angular momentum

       11.3Spin of an electron

       11.3.1Stern–Gerlach experiment

       11.4Pauli exclusion principle

       11.4.1Quantum statistics

       11.5Summary

       12.Quantum Theory and Relativity

       12.1Dirac theory

       12.1.1Negative energy states

       12.1.2Antiparticles

       12.1.3Zitterbewegung

       12.2Entangled states

       12.3Apparent conflict with relativity

       12.3.1Action at a distance

       12.3.2Action mediated by a field

       12.3.3Communication of information

       12.4Time ordering of measurements is relative

       12.5Feynman graph of entanglement and measurement

       12.6Summary

       13.Tunneling: Quantum Magic?

       13.1Extending the boundaries of the possible

       13.2Potential barriers

       13.3Tunneling

       13.4Tunneling and alpha decay

       13.5Summary

       14.The Spatial Wave Function

       14.1Probability density

       14.2Amplitude and probability

       14.3The wave function and measurements

       14.4A historical note

       14.5Summary

       15.Conclusion

       15.1Summary

       15.1.1Wave and particle

       15.1.2A statistical result

       15.1.3Uncertainty principle

       15.1.4Wave functions and operators

       15.1.5Spin and statistics

       15.1.6Zitterbewegung

       15.1.7Antiparticles

       15.1.8Entanglement

       15.1.9Tunneling

       15.2The next step

       Appendix A Answers to Exercises

       Appendix B Bibliography

       Index

      Chapter 1

      Introduction

      There have been some major upheavals in the history of science, when humans were forced to rethink their deeply entrenched ideas of reality, with the result that a prevailing worldview had to make room for a new emerging worldview. Such upheavals — or paradigm shifts — include Copernicus’ heliocentric solar system, Newton’s discovery that the laws of gravity and motion are the same on the earth as on the distant stars, Maxwell’s insight into the nature of light as an electromagnetic wave, Darwin’s theory of evolution according to which humans and animals have a shared origin, and Einstein’s Relativity that brought together space, time and gravitation. Some of these discoveries provoked great consternation, since they conflicted with dominant philosophical and religious worldviews. Others were controversial within the scientific community, but with the growing success of the scientific method — according to which theories must be tested by experiment — controversies gradually yielded to consensus.

      There is one significant discovery, not mentioned in the foregoing paragraph, which stands apart from all the others. The genesis of quantum theory represents the greatest intellectual leap that science has taken in the history of human civilization.

      By the end of the nineteenth century, science had scored a decisive victory as a means of defining a reality that could be agreed upon by everyone regardless of their spiritual, religious or metaphysical traditions. Science had established the material universe with its component objects as an absolute reality that was independent of every subjective belief and perception. Reality was out there. Our scientific observations did not create reality, but only served to confirm the reality that was in existence whether we chose to notice it or not. A tree that fell in a forest made a sound regardless of whether anyone heard it.

      A falling tree makes a sound even if no one hears it

      Observation could not create reality. Nor could observation alter reality. And reality in the study of physics included every physical property of a material object. So, for a particle in motion, reality included its mass, its velocity (both magnitude and direction) and its position at every instant of time — which we call the trajectory of the particle. While an actual physical observation


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