2.6.2 End-of-course questions
Express the following numbers using scientific (powers of ten) notation:
(a) 2.1 million
(b) 36 000
(a) 2.1 × 106
(b) 3.6000 × 104
(c) 1 × 10−1
(d) 5 × 10−5
Each of these answers assumes a certain level of precision. For example, 2.1 million has been interpreted as 2.1 million, rather than 2.2 million, so only two digits have been retained in scientific notation; 36 000 has been interpreted as 36 000 rather than 36 001, and this greater precision is indicated by using five digits.
List the major revolutions in physics that have occurred since 1650. Describe each in one or two sentences, giving only enough detail to distinguish it from the others.
(i) Newtonian mechanics explained the motion of particles in terms of the forces acting on them. The law of gravitation illustrated how forces could be calculated, while Newton's laws of motion showed how forces influence the motion of particles.
(ii) Thermodynamics deals with processes involving energy transfers, including heat, and clarifies ideas about equilibrium and irreversibility.
(iii) Statistical mechanics interprets thermodynamics in terms of the statistical behaviour of a large number of particles.
(iv) Electromagnetism deals with electricity and magnetism. It replaced the concept of action at a distance by that of a field, and showed that electric and magnetic fields have their own dynamics, leading to the interpretation of light and radio waves as electromagnetic waves.
(v) Special relativity is based on the idea that all observers in uniform motion should agree about the laws of physics. When the laws of electromagnetism were included, this led to a revolution in our ideas of space and time, which were merged together into space-time. Different observers, in different states of uniform motion, disagree about which events are simultaneous in space-time.
(vi) General relativity grew from the desire to express physical laws in the same way for all observers, even those who were not moving uniformly. It became a theory of gravity in which the motion of bodies was determined by the curvature of space-time, caused by sources of gravitation.
(vii) Quantum mechanics describes systems of particles in the atomic domain. It asserts that the fundamental laws of physics involve probability in an intrinsic and unavoidable way, and so casts doubt on simple realism.
(viii) Quantum field theory extends the ideas of quantum mechanics and special relativity to fields. Particles are interpreted as quanta of excitation of the field and may be created or annihilated as the field becomes more or less excited.
Describe the concept of a field. Briefly outline the history of this concept from the time of Faraday to the present day.
A field is a physical quantity with a value at each point in space. A particle passing through a given point will experience forces that depend on the fields at that point. Thus the concept of a field replaces action at a distance.
Faraday introduced fields in the context of magnetism and electricity, and Maxwell established the reality of these fields by showing that wave-like disturbances of electric and magnetic fields can travel through space at the speed of light. He interpreted light as an electromagnetic wave and predicted the existence of longer wavelength electromagnetic waves (radio waves). Einstein's general theory of relativity is a field theory of gravitation in which the field describes the curvature of space-time.
A quantum theory of fields was developed which incorporates ideas from quantum mechanics and special relativity. Quantum electrodynamics is an example of a quantum field theory, in which the electromagnetic field is quantised and the quanta are photons. Quantum field theory also applies to ordinary matter - there are electron fields for example, with the quanta interpreted as the electrons. In quantum field theory, quanta may be created or destroyed as the field becomes more or less excited.
Briefly describe the opposition that exists between reductionism and emergence.
Reductionism is an attempt to interpret everything in terms of fundamental phenomena. For a physicist, this implies trying to explain everything in terms of fundamental particles and their interactions.
Emergence stresses the fact that certain phenomena arise only in complex systems, and have no direct counterpart in terms of fundamental phenomena, for example, an iron bar has a strength that is not directly related to the strength of iron atoms.
Most physicists believe that everything can be related, in principle, to fundamental phenomena. In principle, the strength of an iron bar can be explained in terms of the forces between atoms, which in turn can be explained in terms of quantum field theory. The hardline reductionist might therefore dismiss the strength of the rod as being of minor importance, since it is a consequence of more fundamental ideas. Most physicists (and even more engineers) would disagree. Advocates of emergence delight in the fact that new phenomena, such as rigidity, emerge from more basic laws. Far from dismissing ideas such as rigidity, they use them as valid concepts in their own right.
On the basis of dates of birth and death alone, which of the following pairs of physicists might have been able to meet for a discussion about their scientific discoveries?
Galileo and Newton
Newton and Laplace
Laplace and Coulomb
Coulomb and Faraday
Faraday and Maxwell
Maxwell and Einstein
Einstein and Bohr
Bohr and Heisenberg
Heisenberg and Dirac
Laplace and Coulomb, Faraday and Maxwell, Einstein and Bohr, Bohr and Heisenberg, and Heisenberg and Dirac could have met for a discussion of their scientific views. The other pairs either did not overlap, or did not overlap sufficiently for a meaningful scientific discussion to have been possible.