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The crisis of classical physics: the Theory of Relativity and
Quantum Mechanics
From classical physics to modern physics
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“Between the late 19 century and early 20 century some experimental observations challenge the classical conception
of the physical world: on one hand the behaviour of light respect to the different reference frames moving relative to one
another, on the other the first insights regarding the particle structure of the energy released or absorbed in the form of
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radiation by various bodies. It is in the 20 century that these queries, and many others that derived from them, find their
answers, in either the Theory of Relativity or in Quantum Mechanics...”. These words were spoken by the Italian physicist
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Edoardo Amaldi in 1955 to summarise the extraordinary events that revolutionised scientific thought in the 20 century,
and that marked the transition from classical to modern physics.
Classical physics
Up until the year 1900, classical physics was able to explain all the phenomena on the basis of principles that were
simple but fundamental. The most important of these, on which all the theories of classical physics are based, assumes
that space and time are absolute physical quantities, in other words they are the same for all observers.
Considering time as an absolute physical quantity allows us to define a causal relation, in other words, to understand
with absolute precision how what happens initially affects what happens subsequently. Moreover, time is totally
independent of space.
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Before Galileo's formulation of mechanics in the 17 century, absolute space allowed the distinction between a stationary
object and a moving one and moreover every object had a definite velocity.
In his Dialogue Concerning the Two Chief World Systems (1632) Galileo introduced a new concept of space (Galilean
relativity or invariance) according to which it is not possible to distinguish whether an object is stationary or moving in
uniform linear motion (motion along a straight line at constant velocity). As a consequence, there is no absolute velocity,
but there are frames of reference, called inertial frames, in which the laws of mechanics are observed.
The crisis of classical physics: Einstein's Theory of Relativity
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In the 19 century, Maxwell's four equations, formulated by the Scottish physicist and mathematician James Clerk
Maxwell, contradicted Galilean relativity. The equations proved clearly how electricity, magnetism and light, which until
then had been treated as unrelated phenomena, were actually demonstrations of the same entity: the electromagnetic
field. By analysing the equations, Maxwell was able to deduce a fundamental result: light travels at a constant speed
which is represented by the letter c. The result was very important and, above all, it was not consistent with Galilean
relativity. It claimed that the speed of light is absolute.
For a long time scientists attempted to preserve the concept of Galilean relativity, trying to prove that there was a
particular inertial frame of reference for which Maxwell's equations held true. In other words, they attempted to show that
it was possible to accept both theories.
Einstein put an end to the debate with his Special Relativity Theory formulated in 1905, in which he claimed that time and
space are not absolute quantities and are intrinsically bound to form a four-dimensional space-time fabric. Einstein
replaced Galilean transformations, the equations that allowed the calculation of space, time and speed depending on the
observer, with Lorentz' transformations. Einstein postulated that the speed of light in a vacuum is the same for all
observers regardless of the fact that they are stationary or in movement respect to the light source.
GPS and Relativity
The Global Positioning System, more commonly known by the acronym GPS, is an essential tool for orientation today. Its
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great precision could not have been achieved using Galilean relativity. In fact, the GPS is based upon Einstein's Special
and General Theories of Relativity.
The GPS allows us to determine with high precision the distance between two points by means of various satellites in
orbit around the Earth that transmit signals which are detected by receivers on the surface of the Earth. The GPS
consists of a constellation of 27 satellites orbiting at an altitude of about 20,000 kilometres from the ground and four
monitor stations on Earth that check the state of the satellites and correct their clocks and orbital positions.
A representation of the GPS constellation of
satellites
http://www.gps.gov
The GPS works on a simple principle. Signals from at least 4 satellites are sent a to a receiver; they contain information
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regarding the satellites' position at the exact time of transmission (with an accuracy measured in nanoseconds, 10
seconds). The GPS receiver calculates the distance from each satellite by using triangulation and determines its own
location.
The GPS system is based upon the fundamental postulate of the Theory of Relativity, i.e. the fact that the speed of light
is constant regardless of the motion of the satellite and of the receiver. However, some relativistic corrections must be
taken into account. In fact, according to the Special Relativity Theory, since the satellites are in motion with respect to the
receiver, their clocks will tick more slowly; however, according to the General Theory of Relativity, a gravitational field
modifies both the rate at which the clocks tick and the propagation of radio signals. Taking these corrections into account,
it is possible to determine the receiver's position accurate to 10 m for a distance of 20,000,000 m; if uncorrected, errors
of the order of thousands of metres could be made, which would render the GPS system useless.
Quantum mechanics
Quantum mechanics was born around 1900 when the German physicist, Max Planck solved the problem of black body
radiation postulating that energy comes in discrete units. Electromagnetic radiation is emitted or absorbed by atoms only
in discrete amounts, called quanta. Quantum mechanics rapidly replaced the classical laws of mechanics at a
microscopic scale, introducing a viewpoint in contrast to the classical one, according to which physics is able to
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accurately predict the evolution of the Universe once the speeds and positions of all the particles contained in it have
been determined. Quantum mechanics replaces this deterministic character of classical physics with predictions
governed by the uncertainty principle.
In 1927, when he was only 26 years old, the German physicist Werner Karl Heisenberg, Nobel prize winner in Physics in
1932, formulated the well-known Uncertainty Principle according to which the position of a particle and its momentum
cannot be simultaneously known with precision. In other words, the more precisely one property is measured, the less
precisely the other can be measured.
As a result, it is always possible to formulate general statistical laws capable of predicting phenomena, but the physical
properties related to single particles present an ineradicable uncertainty. According to Heisenberg, quantum mechanics
establishes the final failure of causality; in fact, it is not possible to extrapolate what will happen in the future based on
knowledge of the present because of the simple fact that “we cannot know all determining elements of the present”.
God does not play dice
Many well-known physicists disagreed with quantum mechanics, the most important of which was Albert Einstein. In
short, Einstein asserted that quantum mechanics was an incomplete theory of the world and that there were some
“hidden variables” which, once discovered, would have enabled a deterministic description, even of phenomena at
microscopic scales.
In a letter dated 4/12/1926, addressed to the physicist Max Born, Einstein expressed his disagreement with quantum
mechanics: “Quantum mechanics is certainly imposing, but an inner voice tells me that it is not yet the real thing. The
theory says a lot, but does not really bring us any closer to the secret of the 'old one'. I, at any rate, am convinced the He
does not play dice”.
Einstein never modified his opinion, and stated that he believed in the “possibility of a model of reality - that is to say, of
a theory which represents things themselves and not merely the probability of their occurrence”. It must be said that,
though he was a staunch critic of this theory, Einstein utilised and, to a certain point, contributed to the quantum theory
proposing the correct physical explanation of the photoelectric effect.
The photoelectric effect
The photoelectric effect is a phenomenon which can be completely explained with quantum mechanics. It consists in the
ejection of electrically charged particles from an object upon exposure to electromagnetic radiation. In practice, the
energy transported by light incident on a metal surface brings about to the
ejection of electrons (called photoelectrons).
Image that depicts the ejection of an electron from a metal surface due to the
interaction with an incoming photon.
Source: http://www.matefilia.it
The discovery of the photoelectric effect had a fundamental role in the crisis of classical physics because it demonstrated
that electromagnetic radiation had both a wave-like nature and, in some experiments, also particle-like properties. This
behaviour came to be known as the wave-particle duality.
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The photoelectric effect had been noticed as far back as 1880. However, the classical wave theory predicted that the
energy of the ejected electrons would rise with an increase in the intensity of the incident light beam. In 1905 Albert
Einstein explained the photoelectric effect by postulating that light travels in packets of light-quanta, now called photons,
whose energy is directly proportional to the frequency of the radiation. When the light-quanta hit a metallic surface, they
transfer a part of their energy to the free electrons of the conductor, causing their emission. The photon behaves just like
a particle and the energy of the emitted electron depends only on the incoming photon's energy.
Photoelectric cells
The functioning of photoelectric cells that are used everywhere nowadays, from the automatic opening and closing of
gates to the sliding doors of elevators, can be explained by the photoelectric effect. The cells are a safety device that
prevents people from being crushed in doors. How do they work? When a person moves in front of the beam of light
produced by one of the cells, the beam does not reach the light-sensitive surface it was aimed on. The consequence is
an interruption of the flow of electrons emitted. Specific circuits detect this change and respond by immediately opening
the doors.
Wave or particle?
While experimental observations such as those regarding the photoelectric effect serve to clearly demonstrate the
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corpuscular nature of light, those regarding diffraction demonstrate its undulatory nature. In the 20 century this curious
behaviour of light seemed contradictory and highlighted the dual nature of electromagnetic waves. This behaviour was
defined wave-particle duality, which states that electromagnetic radiation can behave like a wave in phenomena such as
interference and diffraction, but can exhibit particle-like behaviour, though massless, exchanging energy and momentum
with other bodies which have mass.
Moreover, quantum mechanics demonstrated that this duality could also be observed in particles which have mass. Neils
Bohr summarised this behaviour in 1927 in his principle of complementarity according to which the undulatory and
corpuscular behaviour are never exhibited simultaneously in one experiment. If an experiment is carried out to highlight
one aspect, it will be impossible to observe the other. The act of observing a phenomenon perturbs the phenomenon
itself; in fact, it is impossible to talk about the behaviour of a physical object without taking into account the measuring
instrument. However, the two aspects, wave-like and particle-like, are complementary because in order to obtain a
complete descripton of a phenomenon, both are essential.
Agreement between classical and modern physics
For many centuries classical physics was able to explain nature perfectly. However, it is not to be considered totally
outdated and useless today. In fact, as long as sub-atomic particles are excluded from the field of study, classical
mechanics yields results that are in agreement with quantum mechanics, while for low speeds, it is in agreement with the
Theory of Relativity.
Edited by Simona Romaniello
Astrophysicist and science populariser, Ms Romaniello is responsible for formation and development and the installation
of museum exhibits for the Turin Planetarium.