By Anthony Leggett
Within the difficulties of Physics, first released in 1987, Anthony Leggett provides an summary of the frontiers of physics on the time, geared toward the final reader. CERN Courier, Vol forty seven No 6, July/August 2007 First released in 1987 this reissue continues to be topical because it makes a speciality of difficulties confronted via physicists, instead of solutions they supply. for example, statement of the Higgs boson wouldn't be the tip of the tale. Nature Physics, Vol.2 November 2006.
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Both these theories—special and general relativity, and quantum mechanics—violently challenged the whole conceptual framework in which classical physics had been formulated. I will discuss the special and general theories of relativity in Chapter 3 in the context of their cosmological applications, and here only summarize a few of the features of the special theory which are relevant to the topics to be mentioned in the next chapter. These are: that the velocity of light, c, is independent of the frame of reference in which it is measured, and is a fundamental constant of nature; that this velocity is the upper limit of velocity of propagation of any kind of physical effect, and that while bodies of zero mass (such as light itself) automatically Setting the stage 21 travel at speed c, no body of finite mass can in fact be accelerated up to this velocity; that energy, E, and mass, m, are interconvertible according to Einstein's famous relation E=mc2; that for isolated systems, the laws of conservation of energy and momentum are not two different principles, but the same principle viewed from different frames of reference, and that in any frame of reference, energy, E, and momentum, p, are related by the equation (the famous E = mc2 being the special case appropriate to a particle at rest—that is, with p = 0)', and that 'moving clocks appear to run slow', that is, that a physical phenomenon such as the decay of a particle which occurs at a given rate when the particle is at rest appears to an observer with respect to whom the particle is moving to take place at a reduced rate.
The ergodic approach proceeds by arguing, crudely speaking, that since the dynamics of a macroscopic system of particles is extremely complicated, it is plausible to say that whatever state it starts in, it will in time pass through all other states which are compatible with the conservation laws (for example, in the case of the gas in the flask, all states of the same total energy as the initial one). Since in a normal experiment on a macroscopic system we are in effect averaging the observed quantities over times which on an atomic scale are very long, it is argued that we are in effect averaging over all accessible states of the system.
But, by the above correspondence, this means thatpr=nh/2ir, and this was precisely 26 Setting the stage the condition originally postulated by Bohr for an orbit to be 'allowed'. Moreover, when the electron jumps between levels, it generally emits a single photon; by energy conservation, the photon energy, E, must be equal to the difference between the energies of the electron orbits involved, AE, and so from the relation E=hv above, we have AE-hv as postulated by Bohr. A quantitative account of the behaviour of the amplitude of the quantum-mechanical wave is given by the fundamental equation of non-relativistic quantum mechanics, Schrodinger's equation; but it should be emphasized that this amplitude has, itself, no direct physical interpretation—it is only the intensity which has a meaning, as a probability.